"This, I submit, is the freedom of a real education, of learning how to be well-adjusted. You get to consciously decide what has meaning and what doesn't. You get to decide what to worship.
"Because here's something else that's weird but true: in the day-to-day trenches of adult life, there is actually no such thing as atheism. There is no such thing as not worshipping. Everybody worships. The only choice we get is what to worship. And the compelling reason for maybe choosing some sort of god or spiritual-type thing to worship--be it JC or Allah, be it YHWH or the Wiccan Mother Goddess, or the Four Noble Truths, or some inviolable set of ethical principles--is that pretty much anything else you worship will eat you alive. If you worship money and things, if they are where you tap real meaning in life, then you will never have enough, never feel you have enough. It's the truth. Worship your body and beauty and sexual allure and you will always feel ugly. And when time and age start showing, you will die a million deaths before they finally grieve you. On one level, we all know this stuff already. It's been codified as myths, proverbs, clichés, epigrams, parables; the skeleton of every great story. The whole trick is keeping the truth up front in daily consciousness.
"Worship power, you will end up feeling weak and afraid, and you will need ever more power over others to numb you to your own fear. Worship your intellect, being seen as smart, you will end up feeling stupid, a fraud, always on the verge of being found out. But the insidious thing about these forms of worship is not that they're evil or sinful, it's that they're unconscious. They are default settings.
"They're the kind of worship you just gradually slip into, day after day, getting more and more selective about what you see and how you measure value without ever being fully aware that that's what you're doing.
"And the so-called real world will not discourage you from operating on your default settings, because the so-called real world of men and money and power hums merrily along in a pool of fear and anger and frustration and craving and worship of self. Our own present culture has harnessed these forces in ways that have yielded extraordinary wealth and comfort and personal freedom. The freedom all to be lords of our tiny skull-sized kingdoms, alone at the centre of all creation. This kind of freedom has much to recommend it. But of course there are all different kinds of freedom, and the kind that is most precious you will not hear much talk about much in the great outside world of wanting and achieving.... The really important kind of freedom involves attention and awareness and discipline, and being able truly to care about other people and to sacrifice for them over and over in myriad petty, unsexy ways every day.
"That is real freedom. That is being educated, and understanding how to think. The alternative is unconsciousness, the default setting, the rat race, the constant gnawing sense of having had, and lost, some infinite thing."
- David Foster Wallace
Tuesday, May 19, 2009
Monday, April 20, 2009
The long way home
It was hot today! I'd forgotten how much I miss the heat. Even at 8:30 this morning it was too warm for gloves on my motorcycle, and it got up into the 80s as the day went on. It felt wonderful.
I got off work at about 8, and it was still warm and breezy. Instead of going up onto the highway, on an impulse, I drove west through the city, looking for a slow route home. I meandered through the colorful, off-beat Mission District until I happened on a hole-in-the-wall sushi place called Yo's Sushi Club. It felt authentic, with a clean, very Japanese aesthetic. The chef, Yo, stood behind the counter, a white towel wrapped tight around his bald head. There was no bento or teriyaki on the menu, just sushi, and I watched as Yo made all the sushi himself. The chirashi was delicious. I ate slowly, then rode the rest of the way down Mission until I found myself on the hilltop at Daly City. It was starting to cool off by the time I made my way to the road across the mountain, and saw the lights of San Francisco spread out north of me as I wound through the pass.
I've got to take the long way home more often. I hope the weather stays nice! If it's clear, tomorrow night I'm going with some friends out past Livermore in the east bay, and we're going to watch the meteor shower.
I got off work at about 8, and it was still warm and breezy. Instead of going up onto the highway, on an impulse, I drove west through the city, looking for a slow route home. I meandered through the colorful, off-beat Mission District until I happened on a hole-in-the-wall sushi place called Yo's Sushi Club. It felt authentic, with a clean, very Japanese aesthetic. The chef, Yo, stood behind the counter, a white towel wrapped tight around his bald head. There was no bento or teriyaki on the menu, just sushi, and I watched as Yo made all the sushi himself. The chirashi was delicious. I ate slowly, then rode the rest of the way down Mission until I found myself on the hilltop at Daly City. It was starting to cool off by the time I made my way to the road across the mountain, and saw the lights of San Francisco spread out north of me as I wound through the pass.
I've got to take the long way home more often. I hope the weather stays nice! If it's clear, tomorrow night I'm going with some friends out past Livermore in the east bay, and we're going to watch the meteor shower.
Sunday, April 19, 2009
If I had a million dollars...
I worked a half day today. I didn't have a particular reason for going in, but there were a few things I wanted to catch up on, so I fired up the bike and rode up to campus. I spent most of the day sitting at my desk, reading a mathematical physics textbook, and tinkering with a simulation I'd written earlier in the week.
A recurring theme of me-at-work, pretty much ever since I started working when I was 15, is the thought, Sigh...if only I had a few million dollars, so I could do X instead of this... Today, it struck me that, if I was independently wealthy and could do whatever I wanted, I probably would spend my time doing what I did today. I'd find somewhere quiet to sit, and learn some new physics.
On top of that, I found out a couple of weeks ago that I won a competition for a federal research fellowship, so I'll get an extra $4000 or so per year to do exactly what I'd be doing anyway, with no strings attached. (I worked out the total value of the fellowship, and was surprised at how large it is: it pays for everything for three years, which comes out to be around $150,000!) As an additional bonus, it's considered very prestigious, looks good on a CV, etc. (not that I'll be applying for jobs anytime soon...).
I hesitate to say so, but I feel honestly satisfied with the way things are going. It's the first time I've felt this way in a long time, so it's a bit alien to me, but...I'm happy. (On a related note, I also feel completely vindicated in my decision to switch research groups.)
A recurring theme of me-at-work, pretty much ever since I started working when I was 15, is the thought, Sigh...if only I had a few million dollars, so I could do X instead of this... Today, it struck me that, if I was independently wealthy and could do whatever I wanted, I probably would spend my time doing what I did today. I'd find somewhere quiet to sit, and learn some new physics.
On top of that, I found out a couple of weeks ago that I won a competition for a federal research fellowship, so I'll get an extra $4000 or so per year to do exactly what I'd be doing anyway, with no strings attached. (I worked out the total value of the fellowship, and was surprised at how large it is: it pays for everything for three years, which comes out to be around $150,000!) As an additional bonus, it's considered very prestigious, looks good on a CV, etc. (not that I'll be applying for jobs anytime soon...).
I hesitate to say so, but I feel honestly satisfied with the way things are going. It's the first time I've felt this way in a long time, so it's a bit alien to me, but...I'm happy. (On a related note, I also feel completely vindicated in my decision to switch research groups.)
Thursday, April 02, 2009
Everyone loves grad school!
I dug up a funny transcript of a conversation I had with my brother a few months back...pretty much captures how much I hated my previous lab:
2:49:47 PM Gheed: man grad school blows though
2:49:50 PM Me: lol
2:50:00 PM Me: WUT DO U MEAN IT'S AWESOME
2:50:01 PM Me: :\
2:50:51 PM Gheed: >:o
2:51:08 PM Me: >:o indeed
2:51:22 PM Gheed: u have any idea how useful a "masters of science" degree is?
2:51:29 PM Me: i wake up every morning and think to myself: >:o
2:51:47 PM Me: i do not
2:51:51 PM Me: inform me immediately
2:52:23 PM Me: btw i do a lot of >:o while i'm at work too
2:52:31 PM Me: then when i get home i'm all like >:o
2:52:45 PM Gheed: lol yeah that face sums me up pretty well too
2:52:47 PM Gheed: >:o
2:53:04 PM Me: there's a few :\ and :( thrown in there for good measure, too
2:53:12 PM Me: but for the most part it's all about the >:o
2:53:28 PM Gheed: >:o
2:53:32 PM Me: >:o
2:49:47 PM Gheed: man grad school blows though
2:49:50 PM Me: lol
2:50:00 PM Me: WUT DO U MEAN IT'S AWESOME
2:50:01 PM Me: :\
2:50:51 PM Gheed: >:o
2:51:08 PM Me: >:o indeed
2:51:22 PM Gheed: u have any idea how useful a "masters of science" degree is?
2:51:29 PM Me: i wake up every morning and think to myself: >:o
2:51:47 PM Me: i do not
2:51:51 PM Me: inform me immediately
2:52:23 PM Me: btw i do a lot of >:o while i'm at work too
2:52:31 PM Me: then when i get home i'm all like >:o
2:52:45 PM Gheed: lol yeah that face sums me up pretty well too
2:52:47 PM Gheed: >:o
2:53:04 PM Me: there's a few :\ and :( thrown in there for good measure, too
2:53:12 PM Me: but for the most part it's all about the >:o
2:53:28 PM Gheed: >:o
2:53:32 PM Me: >:o
Thursday, March 26, 2009
Counting things
I've got a cup that has a little glass wall dividing it in half. It's half full of salt water, and half full of fresh water. If the glass wall is suddenly removed, then the salt water mixes with the fresh water, until the salt ions are evenly distributed in the cup. This is diffusion: the tendency of particles to move from regions of high concentration to regions of low concentration.
A simple way of thinking about diffusion is to imagine the cup is composed of a large set of very small blocks, big enough to hold a salt ion. Each block may be filled or empty. (This is called a lattice model.) If there is no bias built in to the particles, the probability of each system arrangement should be equal. An even distribution of particles is the most probable system configuration because it contains the highest number of total possible arrangements.
To see this, imagine there are four salt particles in a very small cup, and we partition the cup into four little boxes in the left half, and four more in the right. How many ways are there to have all four particles on the left side, and none on the right? Assuming the particles are indistinguishable (that is, we don't care what order they're in), since there are only four boxes, there is only 1 system configuration that has all four particles on the left side. On the other hand, there are 6 different ways to arrange the particles to have 2 on the left side and 2 on the right. If each individual arrangement is equally likely, the most probable state in which to find the system is with 2 particles on the left, and 2 on the right. To be precise, this would be six times more likely than having all the salt on one side! (Mathematically, these are just binomial coefficients, so if you're lazy like me and don't like doing a bunch of counting, you can get the number of arrangements by reading across the fifth row of Pascal's triangle, 1 4 6 4 1.)
The idea of maximizing the number of states is central to statistical mechanics. The number of states (or, more specifically, its natural logarithm) is a measure of the amount of disorder, or entropy, in a system. One of most important conclusions of thermodynamics is that in a system with a conserved amount of total energy (and number of particles, taking the classical view that these are distinct items), its entropy will always increase. (This has a number of interesting, and disquieting, implications for, for example, the future of our universe, if it is an isolated system.) This counting approach is a microscopic model for systems at equilibrium, but in a real system -- e.g., a real-life cup of water -- of course we don't sit there and count the number of salt ions in the cup. In one gram of table salt, there's around 3.6x1025 pairs of sodium and chloride ions. This is a ridiculously huge number: it's 36 followed by 24 zeros, or 36 trillion trillion ions in a single gram. If you consider the number of arrangements of 36 trillion trillion ions where all the ions are on one side of the cup (total: 1), versus the number of arrangements where they are approximately equally distributed (total: a stupidly big number), it's clear that in this simple lattice model, generally all the salt is not going to be on one side of the cup!
Instead of counting trillions of ions, instead what we measure are macroscopic quantities -- for example, the average concentration of ions on each side of the cup. If we take this measurement, and discover that there's actually a higher concentration on the right side than the left on average, then that tells us something about our system: it gives us a constraint that we can use to weight the entropy calculation we did before. As mentioned before, if our system contains 36 trillion trillion particles, we're probably only going to be interested in average quantities, since the stupidly big number-of-states will make shifts away from the average very improbable: the probability distribution, in this case, will be approximately Gaussian (a bell curve), with a tiny standard deviation. But, what about our oversimplified tiny cup with only four particles of salt in it? In that case, there's a 1 in 6 chance of finding all the salt on one side of the cup! Given this non-negligibly small probability, for very small systems, the microscopic fluctuations can be important. That is to say, we're interested in how the system evolves with time -- we care about its dynamics.
Let's go back to our tiny cup, and start with 2 particles on the left side, and 2 on the right. Assume there's no bias built in to the system, and that every particle is independent of the others, so that each particle has some fixed probability of jumping to the other side. The sequence of jumps and stays that a particle follows over a period of time is called its trajectory. If there are no constraints on the system, we'd predict that every trajectory is equally likely, and if we tabulate the number of trajectories that result in 0, 1, or 2 particles jumping, 6 out of 16 trajectories result in 2 particles on the left, and 2 on the right (the same result as before). However, the table also says that there is a 1 in 16 chance for 2 particles to jump from left to right, and 0 to jump from right to left, putting all the salt on one side of the cup! For a given starting distribution of particles, this quantifies how the system's fluctuations are likely to alter the overall state of the system with time, and also how the fluctuations themselves are likely to change over time. A system's trajectory multiplicity is called its caliber.
We think that the idea of maximum caliber will be a useful way to analyze systems far from equilibrium, very small systems, as well as highly correlated systems. All three are true of many biological systems, and one system I'm particularly interested in applying maximum caliber to is long term potentiation, the way we form memories. My short-term project is a little farther afield: I'd like to apply caliber to correlated stock prices, and see if the predicted fluctuations in the stock market correspond to what's actually been observed. Because stock prices can be highly correlated, the independent-particle assumption does not work, which is why random-walk statistics do not accurately describe the probability of large fluctuations in the market. Instead, markets approximately follow an inverse quartic power law, but as far as I'm aware, no one's provided a quantitative, microscopic explanation for this. It will be interesting to see if a power law distribution follows naturally from thinking about the caliber of the market.
A simple way of thinking about diffusion is to imagine the cup is composed of a large set of very small blocks, big enough to hold a salt ion. Each block may be filled or empty. (This is called a lattice model.) If there is no bias built in to the particles, the probability of each system arrangement should be equal. An even distribution of particles is the most probable system configuration because it contains the highest number of total possible arrangements.
To see this, imagine there are four salt particles in a very small cup, and we partition the cup into four little boxes in the left half, and four more in the right. How many ways are there to have all four particles on the left side, and none on the right? Assuming the particles are indistinguishable (that is, we don't care what order they're in), since there are only four boxes, there is only 1 system configuration that has all four particles on the left side. On the other hand, there are 6 different ways to arrange the particles to have 2 on the left side and 2 on the right. If each individual arrangement is equally likely, the most probable state in which to find the system is with 2 particles on the left, and 2 on the right. To be precise, this would be six times more likely than having all the salt on one side! (Mathematically, these are just binomial coefficients, so if you're lazy like me and don't like doing a bunch of counting, you can get the number of arrangements by reading across the fifth row of Pascal's triangle, 1 4 6 4 1.)
The idea of maximizing the number of states is central to statistical mechanics. The number of states (or, more specifically, its natural logarithm) is a measure of the amount of disorder, or entropy, in a system. One of most important conclusions of thermodynamics is that in a system with a conserved amount of total energy (and number of particles, taking the classical view that these are distinct items), its entropy will always increase. (This has a number of interesting, and disquieting, implications for, for example, the future of our universe, if it is an isolated system.) This counting approach is a microscopic model for systems at equilibrium, but in a real system -- e.g., a real-life cup of water -- of course we don't sit there and count the number of salt ions in the cup. In one gram of table salt, there's around 3.6x1025 pairs of sodium and chloride ions. This is a ridiculously huge number: it's 36 followed by 24 zeros, or 36 trillion trillion ions in a single gram. If you consider the number of arrangements of 36 trillion trillion ions where all the ions are on one side of the cup (total: 1), versus the number of arrangements where they are approximately equally distributed (total: a stupidly big number), it's clear that in this simple lattice model, generally all the salt is not going to be on one side of the cup!
Instead of counting trillions of ions, instead what we measure are macroscopic quantities -- for example, the average concentration of ions on each side of the cup. If we take this measurement, and discover that there's actually a higher concentration on the right side than the left on average, then that tells us something about our system: it gives us a constraint that we can use to weight the entropy calculation we did before. As mentioned before, if our system contains 36 trillion trillion particles, we're probably only going to be interested in average quantities, since the stupidly big number-of-states will make shifts away from the average very improbable: the probability distribution, in this case, will be approximately Gaussian (a bell curve), with a tiny standard deviation. But, what about our oversimplified tiny cup with only four particles of salt in it? In that case, there's a 1 in 6 chance of finding all the salt on one side of the cup! Given this non-negligibly small probability, for very small systems, the microscopic fluctuations can be important. That is to say, we're interested in how the system evolves with time -- we care about its dynamics.
Let's go back to our tiny cup, and start with 2 particles on the left side, and 2 on the right. Assume there's no bias built in to the system, and that every particle is independent of the others, so that each particle has some fixed probability of jumping to the other side. The sequence of jumps and stays that a particle follows over a period of time is called its trajectory. If there are no constraints on the system, we'd predict that every trajectory is equally likely, and if we tabulate the number of trajectories that result in 0, 1, or 2 particles jumping, 6 out of 16 trajectories result in 2 particles on the left, and 2 on the right (the same result as before). However, the table also says that there is a 1 in 16 chance for 2 particles to jump from left to right, and 0 to jump from right to left, putting all the salt on one side of the cup! For a given starting distribution of particles, this quantifies how the system's fluctuations are likely to alter the overall state of the system with time, and also how the fluctuations themselves are likely to change over time. A system's trajectory multiplicity is called its caliber.
We think that the idea of maximum caliber will be a useful way to analyze systems far from equilibrium, very small systems, as well as highly correlated systems. All three are true of many biological systems, and one system I'm particularly interested in applying maximum caliber to is long term potentiation, the way we form memories. My short-term project is a little farther afield: I'd like to apply caliber to correlated stock prices, and see if the predicted fluctuations in the stock market correspond to what's actually been observed. Because stock prices can be highly correlated, the independent-particle assumption does not work, which is why random-walk statistics do not accurately describe the probability of large fluctuations in the market. Instead, markets approximately follow an inverse quartic power law, but as far as I'm aware, no one's provided a quantitative, microscopic explanation for this. It will be interesting to see if a power law distribution follows naturally from thinking about the caliber of the market.
Monday, March 23, 2009
An anecdote
"I'd like to spend a week or two doing some reading," I said to my new research advisor, vaguely apprehensive. "I want to get a better feel for what's been done and how master equations work, and to review some math and physics I don't remember as well as I'd like."
He grinned at me. "That's fine. Work at your own pace."
I returned the grin. Suddenly, the future looks very bright.
He grinned at me. "That's fine. Work at your own pace."
I returned the grin. Suddenly, the future looks very bright.
Tuesday, February 24, 2009
It's winter, and I'm discontented
Science for its own sake can be really cool, if you're studying the right things. Aging interests me. Cancer interests me, although to a lesser extent. I love physics for its own sake, and of course I am interested in anything space-related. I am also interested in the medical applications of science. The medical applications are really the only applications of science that interest me.
I joined my current lab with the expectation of working on medically relevant problems, or, failing that, at least to be able to do interesting theoretical, physics-based work. My current research does not fall into this category. I write scripts to assist with genetic circuit design. There's little to no actual physics involved. It's not basic science. It's applied science (engineering, really), with essentially no medical relevance. It's not even novel work, really; I'm applying some neat work that's already been completed and integrating it for larger-scale design work. It bores me to tears.
I'm frustrated. I joined this lab with a fairly specific project in mind, and was encouraged by my future boss that I would be allowed to design and work on this project. After joining, I was curtly denied this opportunity. I don't doubt that his reasons for this denial are good but I suspect he knew of these reasons prior to my agreeing to work with him. I have requested more than once to switch off of my current project, which I find to be both conceptually uninteresting and dull in its implementation, and I have been denied not only the chance to switch projects, but indeed to have any real creative input even into the implementation of this current project. My boss pays lip service to the idea that I should have my own interests and area of expertise, but in practice, what he wants is not independent thought, but a diligent servant to carry out exactly what he wants done.
Also, my boss is an asshole. There's no polite way to put this, really. He's charming enough when he cares to be, and he's a sharp guy, no question, but when it comes down to it, he's a fucking jerk. He also has invested essentially nothing in me, so far. I'm funded by my program until the end of May (I think it's May), so he's really got no basis for complaint if I left.
I am seriously considering leaving the lab. I'm meeting up with my boss this week, and am going to lay this out in so many words, as politely and firmly as I can. I have a few ideas for projects that I'd be willing to work on, that are somewhat related to work currently taking place in his lab, but I have the sinking feeling that he is just going to point-blank refuse again. And then...well, it's not an idle threat. I'll threaten to leave if he won't work to accomodate me, and I'll follow through on the spot if he doesn't.
I joined my current lab with the expectation of working on medically relevant problems, or, failing that, at least to be able to do interesting theoretical, physics-based work. My current research does not fall into this category. I write scripts to assist with genetic circuit design. There's little to no actual physics involved. It's not basic science. It's applied science (engineering, really), with essentially no medical relevance. It's not even novel work, really; I'm applying some neat work that's already been completed and integrating it for larger-scale design work. It bores me to tears.
I'm frustrated. I joined this lab with a fairly specific project in mind, and was encouraged by my future boss that I would be allowed to design and work on this project. After joining, I was curtly denied this opportunity. I don't doubt that his reasons for this denial are good but I suspect he knew of these reasons prior to my agreeing to work with him. I have requested more than once to switch off of my current project, which I find to be both conceptually uninteresting and dull in its implementation, and I have been denied not only the chance to switch projects, but indeed to have any real creative input even into the implementation of this current project. My boss pays lip service to the idea that I should have my own interests and area of expertise, but in practice, what he wants is not independent thought, but a diligent servant to carry out exactly what he wants done.
Also, my boss is an asshole. There's no polite way to put this, really. He's charming enough when he cares to be, and he's a sharp guy, no question, but when it comes down to it, he's a fucking jerk. He also has invested essentially nothing in me, so far. I'm funded by my program until the end of May (I think it's May), so he's really got no basis for complaint if I left.
I am seriously considering leaving the lab. I'm meeting up with my boss this week, and am going to lay this out in so many words, as politely and firmly as I can. I have a few ideas for projects that I'd be willing to work on, that are somewhat related to work currently taking place in his lab, but I have the sinking feeling that he is just going to point-blank refuse again. And then...well, it's not an idle threat. I'll threaten to leave if he won't work to accomodate me, and I'll follow through on the spot if he doesn't.
Sunday, November 23, 2008
It's all about science!
The phrase 'global warming' brings a slight froth to both far-leftists (who I will affectionately call by their not-at-all preferred name, moonbats) and far-rightists (who will likewise be referred to by that timeless endearment, wingnuts). Moonbats, who recently received instructions from their hive mind to start using the phrase 'climate change' instead and will take great exception to any attempt to use the older term, get a bit religiously frothy about it -- there is no god but Al Gore, and I am his Prophet! Raise the specter of doubt to these rabid fans of (certain kinds of politically correct) science and like as not you'll be faced with a self-appointed Clarence Darrow thundering righteously against a frightening amalgamation of George W. Bush, Adolf Hitler, Ned Ludd, and William Jennings Bryan (also known as 'you'). Wingnuts, on the other hand, will egg you on into their pre-prepared verbal mine-field, citing misleading popular sources and asking probing but utterly loaded questions. The worst of these folks are ace debaters who wouldn't know science from scientology if Tom Cruise picked them up and strangled them with it.
But who cares, right? Someone recently enthusiastically recommended I read an anti-global warming tract written by some guy. I forget his name, but I looked it up at the time. He wasn't a climatologist, or even a scientist. He was a lawyer with a conservative advocacy group. I pointed out to my mine laying interlocutor that it seemed a bit odd to try and refute the significant library of peer-reviewed scientific literature on global warming with a non-technical, non-scientific policy tract written by a conservative lawyer. He responded, and I quote:
"This is not about science." (emphasis his)
It is, though. You've absolutely got to design policy from a knowledgeable standpoint of the underlying issue. What should our policies be with regard to climate change? Yes, it's a cost/benefit analysis -- but those costs and benefits can only be determined if you understand the process under consideration.
So, what does the science say? Here's my take:
There's three distinct issues here: first, do we observe warming, second, can we draw a reasonable conclusion that warming is anthropogenic, and third, how much can we trust the general circulation models? So, let me state that I don't trust the GCMs. A lot of my own research involves dynamical simulations, so I'm wary of trying to make forward predictions for such a complex system. With a GCM, you can't build-a-little-test-a-little with controlled experiments, so you're stuck saying, Well, this matched previous data pretty well. But that can just be curve fitting: you bounced around parameter space until you found a set that fit pretty well, but that doesn't guarantee your parameters are physically meaningful. If they're not, will that model work for making forward predictions? Probably not. In particular, I think there's so many external factors that are not taken into consideration in the GCMs, as well as parametrizations for factors that are included but that we know we're not able to model accurately (the effects of cloud cover, surface albedo, etc.), that quantitative in silico predictions about climate change shouldn't be taken too seriously. It's important to differentiate between doubts about GCM accuracy, which can be well-founded, and saying The observed global temperature data is wrong!, which isn't.
That said, back to the empirical question: have we observed statistically significant warming? Yes, and perhaps more importantly, the observed warming is nonlinear: recent years have seen it accelerate, and the per-continent surface temperature average increases are consistent with increased sulfate aerosols and greenhouse gases. Furthermore, although ocean temperature has been increasing at a slower rate (about half) of the land surface warming, it absolutely is increasing, and this observation isn't limited to the ocean surface -- temperature increases are observed down to depths of several thousand feet. The issue of the lack of a warming trend in Antarctica illustrates two important points -- that global and local temperature trends are often conflated, by people who should know better, and also that Antarctica (and parts of the tropics) has substantial gaps in its historical temperature data set. This data has been 'filled in' with data interpolation and averaging techniques, but in any consideration of Antarctic temperature trends, it's important to keep this caveat in mind.
Second, is this observed warming trend anthropogenic? This is tricky, because you need to de-couple it from natural climate forcings -- for example, obviously the Medieval Warm Period wasn't caused by man-made aerosols. So, you're trying to draw a statistical correlation between anthropogenic forcings (GHGs, aerosols) and temperature, and you've got GCMs to make this link -- and as I mentioned before, I'm leery of the predictive power of these models.
But who cares, right? Someone recently enthusiastically recommended I read an anti-global warming tract written by some guy. I forget his name, but I looked it up at the time. He wasn't a climatologist, or even a scientist. He was a lawyer with a conservative advocacy group. I pointed out to my mine laying interlocutor that it seemed a bit odd to try and refute the significant library of peer-reviewed scientific literature on global warming with a non-technical, non-scientific policy tract written by a conservative lawyer. He responded, and I quote:
"This is not about science." (emphasis his)
It is, though. You've absolutely got to design policy from a knowledgeable standpoint of the underlying issue. What should our policies be with regard to climate change? Yes, it's a cost/benefit analysis -- but those costs and benefits can only be determined if you understand the process under consideration.
So, what does the science say? Here's my take:
There's three distinct issues here: first, do we observe warming, second, can we draw a reasonable conclusion that warming is anthropogenic, and third, how much can we trust the general circulation models? So, let me state that I don't trust the GCMs. A lot of my own research involves dynamical simulations, so I'm wary of trying to make forward predictions for such a complex system. With a GCM, you can't build-a-little-test-a-little with controlled experiments, so you're stuck saying, Well, this matched previous data pretty well. But that can just be curve fitting: you bounced around parameter space until you found a set that fit pretty well, but that doesn't guarantee your parameters are physically meaningful. If they're not, will that model work for making forward predictions? Probably not. In particular, I think there's so many external factors that are not taken into consideration in the GCMs, as well as parametrizations for factors that are included but that we know we're not able to model accurately (the effects of cloud cover, surface albedo, etc.), that quantitative in silico predictions about climate change shouldn't be taken too seriously. It's important to differentiate between doubts about GCM accuracy, which can be well-founded, and saying The observed global temperature data is wrong!, which isn't.
That said, back to the empirical question: have we observed statistically significant warming? Yes, and perhaps more importantly, the observed warming is nonlinear: recent years have seen it accelerate, and the per-continent surface temperature average increases are consistent with increased sulfate aerosols and greenhouse gases. Furthermore, although ocean temperature has been increasing at a slower rate (about half) of the land surface warming, it absolutely is increasing, and this observation isn't limited to the ocean surface -- temperature increases are observed down to depths of several thousand feet. The issue of the lack of a warming trend in Antarctica illustrates two important points -- that global and local temperature trends are often conflated, by people who should know better, and also that Antarctica (and parts of the tropics) has substantial gaps in its historical temperature data set. This data has been 'filled in' with data interpolation and averaging techniques, but in any consideration of Antarctic temperature trends, it's important to keep this caveat in mind.
Second, is this observed warming trend anthropogenic? This is tricky, because you need to de-couple it from natural climate forcings -- for example, obviously the Medieval Warm Period wasn't caused by man-made aerosols. So, you're trying to draw a statistical correlation between anthropogenic forcings (GHGs, aerosols) and temperature, and you've got GCMs to make this link -- and as I mentioned before, I'm leery of the predictive power of these models.
Tuesday, November 11, 2008
Using Statistical Mechanics to Link the Sequence and Dynamics of a Genetic Circuit
Bacteria can be reprogrammed with new genetic commands encoded in synthetic DNA. These programs require a signal processing circuit to analyze sensory input and control the cell's response. Genetic circuits have been developed that function as toggle switches, oscillators, pulse generators, and band-pass filters. This circuitry is needed to write the complex instructions necessary for applications such as nanoscale manufacturing, metabolic engineering, programmed therapeutics, and embedded intelligence in materials.
Genetic circuit assembly is challenging because genes are specific to their native systems. There is currently no method to predict the spatiotemporal dynamics of a genetic circuit directly from its DNA sequence, and coupling components from different systems requires the tedious trial-and-error adjustment of the components' kinetic characteristics. My objective is to apply biophysical models of gene regulation to predict the DNA sequence of genetic circuits in silico for a desired dynamical behavior.
Natural components of biological systems have widely varying gene expression levels. To effectively design large or complex genetic programs, we will need a detailed biophysical link between DNA sequence and gene expression dynamics. Gene expression is controlled by the transcription of DNA to produce mRNA, and the translation of mRNA to produce proteins. The rates of these processes are controlled by the DNA sequence around the expressed gene, so it is possible to tune the dynamical expression of the gene by adjusting these sequences. The promoter and ribosome binding site (RBS) sequences can be used to modify the transcription and translation rates, respectively.
Quantitative biophysical models of bacterial transcription and translation initiation have recently been developed, and their predictions are consistent with experimental data.1,2 These models present a starting point to connect the dynamics of a genetic circuit directly to its DNA sequence. Genetic circuits can utilize a variety of sensory input signals, including chemicals, light, and temperature; here I will consider a single transcription factor input processed by a genetic inverter circuit in Escherichia coli3, shown schematically in Fig. 1. The inverter's dynamics are well-characterized for many promoter and RBS sequences, making it an ideal test circuit.
Aim 1: Predict the dynamics of a genetic inverter circuit from its DNA sequence.
Using the models referenced above, I will calculate transcription and translation rates from the DNA sequence. The equilibrium thermodynamic model of translation predicts the free energy change of ribosome binding to the mRNA, which is proportional to the translation initiation rate.
The rate-limiting step in transcription initiation is open complex formation. Prediction of transcription rate from the promoter sequence is done by computing the rate of open complex formation. However, the initiation rate is adjusted by the equilibrium binding probability of RNA polymerase to the promoter DNA. This permits the use of a statistical thermodynamic approach to model how transcription factor concentrations affect the circuit: calculating the system's partition function provides a way of adjusting the predicted transcription rates according to the population of each discrete system configuration.4
These predicted rates will be incorporated into a dynamical mathematical framework: a system of differential equations describing the rates of change of the inverter’s internal concentrations. This system of equations will be solved numerically to update the concentrations of the inverter's components. The result of this model will be a transfer function (Fig. 2) showing the predicted dependence of the inverter’s output, a fluorescent protein, on the concentration of its input signal, a transcription factor. Comparison of the in silico transfer functions with previous experimental data will provide a convenient way to assess and modify the model described here.
Aim 2: Forward engineer the sequence of an inverter circuit for a specified dynamical behavior.
I will wrap this model with an optimization routine to search parameter space for optimal transcription and translation rates for a given transfer function. The unknown shape of the parameter space makes a Monte Carlo simulation well-suited for this problem. The dynamical mathematical model described in aim 1 quantitatively links these parameters to the promoter and RBS DNA sequences. This link provides a systematic way to search for optimal DNA sequences, given a known parameter list.
I will generate in silico transfer functions by mutating each nucleotide in the promoter and RBS sequences, followed by experimental construction of these sequences using site-directed mutagenesis. Analysis of the in silico transfer functions should provide guidelines for efficient mutagenesis, by identifying nucleotides predicted to significantly alter the transfer function.
Verification and stress testing will be done by generating in silico promoter and RBS sequences for diverse transfer functions, then comparing the requested transfer function shape to an empirical transfer function measured using flow cytometry. These tests will focus on quantitative adjustment of the transfer function's shape, in particular, the curve's steepness (how well it approximates a digital output signal) and its gain (the range between its on and off states).
Impact: This modeling strategy is useful because it can be generalized to more complex genetic systems. Applications of this method include automated tuning of existing genetic components as well as guiding the assembly of new, more complex genetic circuits: synthetic constructs to perform arithmetic and other logical operations, such as conditionals and control logic. Automated in silico control of the dynamical behavior of synthetic genetic circuits will help synthetic biology mature into a practical and useful engineering discipline.
References:
1. Salis H, Mirsky E, Voigt C. “Designing synthetic ribosome binding sites.” Submitted 11/2008.
2. Djordjevic M, Bundschuh R. 2008. Biophys J 94.
3. Yokobayashi Y, Weiss R, Arnold FH. 2002. Proc Natl Acad Sci USA 99.
4. Bintu L et al. 2005. Curr Opin Genes Dev 15.
Genetic circuit assembly is challenging because genes are specific to their native systems. There is currently no method to predict the spatiotemporal dynamics of a genetic circuit directly from its DNA sequence, and coupling components from different systems requires the tedious trial-and-error adjustment of the components' kinetic characteristics. My objective is to apply biophysical models of gene regulation to predict the DNA sequence of genetic circuits in silico for a desired dynamical behavior.
Natural components of biological systems have widely varying gene expression levels. To effectively design large or complex genetic programs, we will need a detailed biophysical link between DNA sequence and gene expression dynamics. Gene expression is controlled by the transcription of DNA to produce mRNA, and the translation of mRNA to produce proteins. The rates of these processes are controlled by the DNA sequence around the expressed gene, so it is possible to tune the dynamical expression of the gene by adjusting these sequences. The promoter and ribosome binding site (RBS) sequences can be used to modify the transcription and translation rates, respectively.Quantitative biophysical models of bacterial transcription and translation initiation have recently been developed, and their predictions are consistent with experimental data.1,2 These models present a starting point to connect the dynamics of a genetic circuit directly to its DNA sequence. Genetic circuits can utilize a variety of sensory input signals, including chemicals, light, and temperature; here I will consider a single transcription factor input processed by a genetic inverter circuit in Escherichia coli3, shown schematically in Fig. 1. The inverter's dynamics are well-characterized for many promoter and RBS sequences, making it an ideal test circuit.
Aim 1: Predict the dynamics of a genetic inverter circuit from its DNA sequence.
Using the models referenced above, I will calculate transcription and translation rates from the DNA sequence. The equilibrium thermodynamic model of translation predicts the free energy change of ribosome binding to the mRNA, which is proportional to the translation initiation rate.
The rate-limiting step in transcription initiation is open complex formation. Prediction of transcription rate from the promoter sequence is done by computing the rate of open complex formation. However, the initiation rate is adjusted by the equilibrium binding probability of RNA polymerase to the promoter DNA. This permits the use of a statistical thermodynamic approach to model how transcription factor concentrations affect the circuit: calculating the system's partition function provides a way of adjusting the predicted transcription rates according to the population of each discrete system configuration.4
These predicted rates will be incorporated into a dynamical mathematical framework: a system of differential equations describing the rates of change of the inverter’s internal concentrations. This system of equations will be solved numerically to update the concentrations of the inverter's components. The result of this model will be a transfer function (Fig. 2) showing the predicted dependence of the inverter’s output, a fluorescent protein, on the concentration of its input signal, a transcription factor. Comparison of the in silico transfer functions with previous experimental data will provide a convenient way to assess and modify the model described here.
Aim 2: Forward engineer the sequence of an inverter circuit for a specified dynamical behavior.
I will wrap this model with an optimization routine to search parameter space for optimal transcription and translation rates for a given transfer function. The unknown shape of the parameter space makes a Monte Carlo simulation well-suited for this problem. The dynamical mathematical model described in aim 1 quantitatively links these parameters to the promoter and RBS DNA sequences. This link provides a systematic way to search for optimal DNA sequences, given a known parameter list.I will generate in silico transfer functions by mutating each nucleotide in the promoter and RBS sequences, followed by experimental construction of these sequences using site-directed mutagenesis. Analysis of the in silico transfer functions should provide guidelines for efficient mutagenesis, by identifying nucleotides predicted to significantly alter the transfer function.
Verification and stress testing will be done by generating in silico promoter and RBS sequences for diverse transfer functions, then comparing the requested transfer function shape to an empirical transfer function measured using flow cytometry. These tests will focus on quantitative adjustment of the transfer function's shape, in particular, the curve's steepness (how well it approximates a digital output signal) and its gain (the range between its on and off states).
Impact: This modeling strategy is useful because it can be generalized to more complex genetic systems. Applications of this method include automated tuning of existing genetic components as well as guiding the assembly of new, more complex genetic circuits: synthetic constructs to perform arithmetic and other logical operations, such as conditionals and control logic. Automated in silico control of the dynamical behavior of synthetic genetic circuits will help synthetic biology mature into a practical and useful engineering discipline.
References:
1. Salis H, Mirsky E, Voigt C. “Designing synthetic ribosome binding sites.” Submitted 11/2008.
2. Djordjevic M, Bundschuh R. 2008. Biophys J 94.
3. Yokobayashi Y, Weiss R, Arnold FH. 2002. Proc Natl Acad Sci USA 99.
4. Bintu L et al. 2005. Curr Opin Genes Dev 15.
Wednesday, November 05, 2008
Snake oil
Sirtris has developed a new wonder drug, it's an all-in-one caloric restriction mimetic and no-effort-required weight loss program! It's like resveratrol but 1000 times better!!!
...
Wait, is there any actual evidence of resveratrol extending lifespan in metazoans? Even the yeast and C. elegans evidence is unconvincing; to my knowledge, no one outside his lab has ever been able to duplicate Sinclair's results. Since the lifespan assay is so prone to experimenter-introduced bias, Linda Partridge went through and did a more thorough analysis of the putative lifespan extension, and didn't find anything. (Being a veteran kool-aid drinker, I actually ran an experiment myself using wild type C. elegans and some other worms treated with dsRNA to give them an unusual germ-cell 'cancerous' phenotype...didn't help with aging, or the cancer, for that matter.)
I'd be pretty leery about using large amounts of resveratrol (which is effectively what this new compound is) as a supplement. People have picked up all kinds of low-affinity (~micromolar) targets for it, with a variety of mechanisms, which isn't surprising, given its structure. In particular, it seems to hit the adrenergic receptors and affect Wnt signaling, which is ok in small amounts but you wouldn't want to deluge your system with this stuff.
...
Wait, is there any actual evidence of resveratrol extending lifespan in metazoans? Even the yeast and C. elegans evidence is unconvincing; to my knowledge, no one outside his lab has ever been able to duplicate Sinclair's results. Since the lifespan assay is so prone to experimenter-introduced bias, Linda Partridge went through and did a more thorough analysis of the putative lifespan extension, and didn't find anything. (Being a veteran kool-aid drinker, I actually ran an experiment myself using wild type C. elegans and some other worms treated with dsRNA to give them an unusual germ-cell 'cancerous' phenotype...didn't help with aging, or the cancer, for that matter.)
I'd be pretty leery about using large amounts of resveratrol (which is effectively what this new compound is) as a supplement. People have picked up all kinds of low-affinity (~micromolar) targets for it, with a variety of mechanisms, which isn't surprising, given its structure. In particular, it seems to hit the adrenergic receptors and affect Wnt signaling, which is ok in small amounts but you wouldn't want to deluge your system with this stuff.
Tuesday, November 04, 2008
Obamania!
I hovered over the Barr/Root checkbox for a long moment, but I ended up voting for Barack Obama. I have many reservations about him, but ultimately, for me at least, the combination of McCain's temperament, age, and astonishing bad judgment in choosing Sarah Palin as his running mate did it for me. And, let's face it, Bob Barr just plain sucks.
Here's hoping he governs well...
Here's hoping he governs well...
Thursday, October 16, 2008
I'd better just change the subject
I should qualify this by saying that my field is physics, not economics, but I think there's a strong argument you can make about the financial crisis that is not at all an indictment of the free market. My understanding of the financial crisis is that there's three primary culprits: 1) a systematic underestimation of credit risk, 2) excessive subprime lending, 3) mortgage derivatives linked to the excessive subprime lending (credit default swaps, CDOs that apparently no one knew how to quantify).
(1) seems to me the underlying factor. One interpretation of this is that bankers just used the wrong probability distribution to estimate risk (a normal instead of a Lorentz distribution, and a gaussian decays much faster than a Lorentz function, which follows a power law). Alright, but why? One answer, I guess, is that bankers (to paraphrase the unlamented Rumsfeld) didn't know what they didn't know. If you're modeling a chaotic system containing lots of recursive feedback loops, and things seem to be following a roughly bell-shaped curve, to start with, shouldn't you examine the function's asymptotic behavior carefully to make sure it's actually a bell curve, and not, for example, a Lorentz function, which has a completely different scaling form? Another, possibly more convincing answer, is that bankers just assumed that even though their mathematical model was incorrect, it wouldn't matter, because they could just use (in my opinion, absurdly complicated) derivatives to push the risk off onto the big investment banks, by way of Fannie Mae and Freddie Mac. Which are, of course, government-sponsored enterprises, which had, as I understand it, fairly explicit instructions from Congress to encourage subprime lending. At least some of the complex credit derivatives, and the special legal classifications built around them, were created by Fannie and Freddie, as well.
So, as a political football (and it's nothing if not that), there's plenty of blame to go around. From what I've read, there was plenty of bona fide stupidity involved. (Anecdotally, the guys I knew in college who went into banking didn't seem like the brightest folks around, but they were geniuses compared to the people who wanted to go into politics.) My understanding is that both John McCain and Barack Obama were complicit, although they're both dissembling ferociously and scrambling for the moral high ground. Not having Rick Davis blathering on his behalf has probably helped Obama in this regard. Congressional Democrats have firmly exonerated themselves, which makes no sense, but the Republicans see the whole economic mess as such electoral poison (economic issues tend to favor the Democrats, etc.) that they're not making an issue of it. This is reasonable short-term (read: electoral) but disastrous long-term politics, to say nothing of policy. The worst part is that the argument is so simple: the Republicans could really drive home the point that 1) the housing and financial markets were actually heavily regulated, 2) these regulations were a big part of the problem, so 3) in reality it wasn't anything like a free market, so this isn't an indictment of free market economics.
This doesn't mean the bailout is good or bad, and I really have no idea what ought to be done at this point. But I think the near-universal consensus that this was caused by an unregulated market run amok is wrong, and while I do think the bailout itself has to be very carefully regulated, I don't think a blind charge into more regulations on this or other markets is necessarily going to help. Obama's been quite vocal about McCain's history of deregulation, but unfortunately, McCain's response to this has been to recklessly invent schemes to out-regulate the Democrats. But hey, who needs principles when you can change the subject?
Sigh.
Further thoughts: I guess I should append to this that the actual unregulated markets were the secondary markets (credit default swaps and collateralized debt obligations), and it's the fact that each default had a huge number of derivatives attached to it that allowed the subprime crisis to amplify to the point where it could sink these huge investment banks. This is, of course, what everyone's focusing on, and why the Republicans are so leery about confronting the issue: the deregulation of the secondary markets was, I think, pushed through by Republicans. But the key point that often gets missed is that this only became an issue because of the heavily (but poorly) regulated mortgage market. To draw the analogy out a bit, everyone's up in arms trying to figure out how the signal got amplified (which is important), and completely ignoring the faulty wiring that produced the signal in the first place.
(1) seems to me the underlying factor. One interpretation of this is that bankers just used the wrong probability distribution to estimate risk (a normal instead of a Lorentz distribution, and a gaussian decays much faster than a Lorentz function, which follows a power law). Alright, but why? One answer, I guess, is that bankers (to paraphrase the unlamented Rumsfeld) didn't know what they didn't know. If you're modeling a chaotic system containing lots of recursive feedback loops, and things seem to be following a roughly bell-shaped curve, to start with, shouldn't you examine the function's asymptotic behavior carefully to make sure it's actually a bell curve, and not, for example, a Lorentz function, which has a completely different scaling form? Another, possibly more convincing answer, is that bankers just assumed that even though their mathematical model was incorrect, it wouldn't matter, because they could just use (in my opinion, absurdly complicated) derivatives to push the risk off onto the big investment banks, by way of Fannie Mae and Freddie Mac. Which are, of course, government-sponsored enterprises, which had, as I understand it, fairly explicit instructions from Congress to encourage subprime lending. At least some of the complex credit derivatives, and the special legal classifications built around them, were created by Fannie and Freddie, as well.
So, as a political football (and it's nothing if not that), there's plenty of blame to go around. From what I've read, there was plenty of bona fide stupidity involved. (Anecdotally, the guys I knew in college who went into banking didn't seem like the brightest folks around, but they were geniuses compared to the people who wanted to go into politics.) My understanding is that both John McCain and Barack Obama were complicit, although they're both dissembling ferociously and scrambling for the moral high ground. Not having Rick Davis blathering on his behalf has probably helped Obama in this regard. Congressional Democrats have firmly exonerated themselves, which makes no sense, but the Republicans see the whole economic mess as such electoral poison (economic issues tend to favor the Democrats, etc.) that they're not making an issue of it. This is reasonable short-term (read: electoral) but disastrous long-term politics, to say nothing of policy. The worst part is that the argument is so simple: the Republicans could really drive home the point that 1) the housing and financial markets were actually heavily regulated, 2) these regulations were a big part of the problem, so 3) in reality it wasn't anything like a free market, so this isn't an indictment of free market economics.
This doesn't mean the bailout is good or bad, and I really have no idea what ought to be done at this point. But I think the near-universal consensus that this was caused by an unregulated market run amok is wrong, and while I do think the bailout itself has to be very carefully regulated, I don't think a blind charge into more regulations on this or other markets is necessarily going to help. Obama's been quite vocal about McCain's history of deregulation, but unfortunately, McCain's response to this has been to recklessly invent schemes to out-regulate the Democrats. But hey, who needs principles when you can change the subject?
Sigh.
Further thoughts: I guess I should append to this that the actual unregulated markets were the secondary markets (credit default swaps and collateralized debt obligations), and it's the fact that each default had a huge number of derivatives attached to it that allowed the subprime crisis to amplify to the point where it could sink these huge investment banks. This is, of course, what everyone's focusing on, and why the Republicans are so leery about confronting the issue: the deregulation of the secondary markets was, I think, pushed through by Republicans. But the key point that often gets missed is that this only became an issue because of the heavily (but poorly) regulated mortgage market. To draw the analogy out a bit, everyone's up in arms trying to figure out how the signal got amplified (which is important), and completely ignoring the faulty wiring that produced the signal in the first place.
Tuesday, October 14, 2008
A cure for cancer
I thought of a way to cure cancer, using gold, light, and a genetic circuit. I'll update this later; I'm going to flesh this out for a fellowship proposal!
Monday, October 13, 2008
Thought of the day
Is the life of a graduate student much different from that of a monk? I guess I don't know that much about how monks live, but I spend most of my waking hours isolated, thinking. It's possible for me to go entire days in total silence. It's sometimes jarring for me to return to normal conversation, since the thought patterns accompanying it are so different. I tend to eat sparingly and simply because I can't really afford anything better. I haven't been in a real relationship for...I don't even want to think how long. A year and a half now, I guess.
Not sure how I ought to feel about this...
Not sure how I ought to feel about this...
Saturday, October 04, 2008
What happens when you poke a red blood cell?
First of all, I've got to ask...why call it an erythrocyte? Red blood cell is so much better, just rolls off the tongue. Almost seems like something you'd want to know more about, just based on how great the name is! Almost. But! If you couple that great name with its simplicity - and the fact that they're damn important, and red blood cell structural deficiencies are implicated in a whole host of diseases, the most famous of which is probably sickle-cell anemia - then you've got something worth looking at, I'd say.
You can use an experimental technique called optical trapping to analyze the mechanical properties of red blood cells, and this can get you force-displacement data all the way down to the piconewton level. (For reference, the force exerted by the Earth's gravity on the typical person is between 600 and 700 newtons. A piconewton is 10-12 newtons, or 1 trillionth of a newton. Impressively precise information, in other words!) Optical trapping works on the principle that when a laser is passed through a high-refractive index dielectric (in this case, a tiny silica bead), its photons lose momentum, which causes the bead to move towards the laser's focal point. Attaching these microbeads onto red blood cells can be used to extract information about how much force is required to stretch the cell a certain amount (the resulting plot of this information is called a force-displacement or force-extension curve). The question is, can you use this information to build a model that accurately describes red blood cell deformation?
Well, you can try, and it turns out some pretty sharp folks have been trying for a while, since red blood cells are unusually tractable for eukaryotic cells because they're so simple. There's no nucleus. No mitochondria, no insulin receptors, no organelles at all. They're just small, not-quite-donut shaped bags of hemoglobin. This is nice, because it lets you focus just on that bag, and ask, What's its structure?
That simple question turns out to be fairly complicated, though. The RBC cell wall (composed of a phospholipid bilayer, membrane proteins, and cholesterol molecules), sits atop a flexible grid of a structural protein called spectrin, which looks like a ropy mesh joined together in a network of interlinked triangles, with a complex of other structural proteins at each vertex. Think of a fat man lying on a hammock, and you've got the right basic idea (fat and cholesterol sitting on top, and a concave grid beneath...it's a better analogy than I realized, actually!). Each of these spectrin links is like a rope, composed of two long, flexible rods (called polypeptides), very similar to one another, which are twisted together, running antiparallel between the junction vertices.
So it turns out materials scientists have already done the hard work of developing mathematical frameworks for different sorts of polymers, including the aptly-named worm-like-chain (WLC) model. This is pretty much what it sounds like: it's just a way of modeling a polymer that is a continuously flexible rod, and has been used to model things as disparate as strands of DNA and strands of cooked spaghetti. By using this model to describe the force-displacement behavior of the individual spectrin molecules, we can extract three key pieces of information about it: its length at equilibrium, the maximum extension length of the link, and its persistence length. Considering the polymer as a parametric curve described by a single path variable, the persistence length is defined as the value of this variable at which there's no longer a correlation between the unit vector tangent to the curve at 0 and that at the current value. Less formally, the persistence length tells you how stiff your polymer is: if you poke one end of a piece of uncooked spaghetti, that affects the whole strand, but if you do the same thing to a piece of cooked spaghetti, only the end and a little length near it will move. It turns out this 'little length' is about 10 centimeters; that's the persistence length value. In contrast, a DNA double-helix has a persistence length of around 50 nanometers: it's about 2 million times floppier!
What the WLC model gives you, mathematically, is the force exerted on each spectrin chain as a function of the chain's length. This is useful because you can integrate over the chain's length to derive the Helmholtz free energy (which is a thermodynamic state function that tells you, basically, how much work you can get out of an isochoric, isothermal process) contribution from each spectrin chain. Do this for every chain in your system, and add them up, and add that whole sum to the total hydrostatic elastic energy stored in the membrane and assorted proteins, and you've got an expression for the free energy in the entire plane defined by your spectrin network. This in-plane free energy can, in turn, be summed together with the bending free energy, as well as the surface area and volume free energy constraints on the system. The upshot of all this is that you've now got a way to mathematically describe how a red blood cell responds to mechanical stress, by calculating how the total free energy of the system changes.
This model is very high-resolution: it gives you a description of the network all the way down to the individual junction complexes. However, the computational cost of these simulations is steep: since each junction complex is a degree of freedom in this model, this results in about 30,000 degrees of freedom! A useful adjunct to this model, then, would be a way of systematically coarse-graining this model in order to reduce these degrees of freedom and the corresponding computational cost. Coupling this with a coarse-grained flow model, it would be possible to model large numbers of RBCs in the bloodstream.
And, that's the punchline, of course...there was a nifty paper, published last month in Physical Review Letters, that outlined how you'd go about doing this.
So, how can you coarse-grain this model? Basically, you just need to decrease the number of vertices you're considering, but how do you do this without losing accuracy, since the original model was set up so that the number of vertices approximated the number of junction complexes in an actual red blood cell? One simple way is to consider coarse-grained versions of the parameters in the finer-grained model: that is, estimating the effective parameters (equilibrium length, persistence length, hydrostatic elastic energy, and spontaneous angle) based on geometric arguments. The effective equilibrium length (and maximum length, which is taken to be around triple the equilibrium length) can then be estimated as the actual equilibrium length in the finer-grained model multiplied by the square root of the ratio of the number of particles in the finer to the coarser model. A similar argument can be made for the spontaneous angle between adjacent triangles: the effective angle is the original angle multiplied by the ratio of the coarse to the finer equilibrium length.
Coarse-graining the parameters in the in-plane energy equation is more complicated. One way to accomplish this is using a mean-field argument, which is a way of estimating the properties of the network by ignoring the correlations between vertices. That is, estimate the physics of the whole network from that of a single vertex! Using this approach, you can derive expressions for the shear modulus (the ratio of shear stress to shear strain) and the bulk modulus (the resistance of the membrane to compression). This method provides a handy way to coarse-grain the persistence length, as well, since in this mean-field argument the shear and bulk moduli are unchanged from their fine-grained values if the ratio of the equilibrium to the maximum length is fixed. The persistence length can then be systematically adjusted as the product of the original persistence length with the ratio of the fine to the coarse grained equilibrium lengths.
Taken together, this gives us a framework for extracting a complete set of parameters for the model at any level of coarse-graining. Of course, although you can extract effective parameters for an arbitrary level of coarseness, this approach won't be useful if you pick a vertex number of, say, 3. So how far can you take this approach, exactly, before you lose the ability to describe the cell deformation meaningfully? The most straightforward way to answer this, as well as to assess how useful this procedure is in general, is to just brute-force the question (AKA heave a big pile of simulations at your hapless cluster and spend a week drunk and high with a giddy pack of scantily-clad valley girl strippers in Vegas as your data collects itself, not that I would ever do that of course). So, cheap suits and bowls of cocaine at the ready, the authors run a bunch of simulations and discover...the lower limit is about 100 vertices. Below that, the simulated deviations in the cell's axial and transverse diameters become more pronounced. Here's a snapshot of their data:
The plot shows both axial and transverse force-displacement curves. The black diamonds are experimental data points, whereas the solid colored lines represent simulation results at different levels of coarseness (blue line: 23867 points, red: 5000, green: 500, magenta: 100). Except for the magenta axial (lower) curve, the simulated curves are in relatively good agreement with the experimental results. The inset gives an idea of how sensitive their model is to the way they adjusted the persistence length. All the curves except the magenta curve use the adjustment procedure described by the authors; the magenta curve retains the fine-grained value for the persistence length, and as you can see, the results are nothing like the desired linear relation!
So, this is interesting because it shows that their coarse-graining procedure produces results that are comparable to the much more computationally intensive fine-grained model, and fast is always good, of course, because faster = more time to tweak = less power used = less money used, etc. But the real value here is in using the coarse-grained model to do flow simulations of RBCs in circulation. They do this using the dissipative particle dynamics (DPD) method, which is a way of describing clusters of molecules moving together in a flow. The RBC and surrounding fluid are both modeled as DPD particles, and their interactions are modeled using soft quadratic potentials. The flow domain (the simulated capillary) is a tube 10 microns in diameter. The RBC starts out immersed in the fluid, at rest, in the middle of the tube, and then they watch the flow simulation develop. The deformation sequence for 500 vertices is shown below:
The 'parachute' shape observed in (c) is consistent with experimental observations, as well as is the ultimate restoration of the RBC's biconcave shape. They also simulated the behavior of the RBC in a shear flow, and confirmed that their simulations seemed to match experimental evidence.
Pretty neat, all in all. I still need to look into how DPD works (I have only the most general sense of the technique), as well as exactly how you do an optical tweezers experiment, since that data is kind of at the heart of all this!
You can use an experimental technique called optical trapping to analyze the mechanical properties of red blood cells, and this can get you force-displacement data all the way down to the piconewton level. (For reference, the force exerted by the Earth's gravity on the typical person is between 600 and 700 newtons. A piconewton is 10-12 newtons, or 1 trillionth of a newton. Impressively precise information, in other words!) Optical trapping works on the principle that when a laser is passed through a high-refractive index dielectric (in this case, a tiny silica bead), its photons lose momentum, which causes the bead to move towards the laser's focal point. Attaching these microbeads onto red blood cells can be used to extract information about how much force is required to stretch the cell a certain amount (the resulting plot of this information is called a force-displacement or force-extension curve). The question is, can you use this information to build a model that accurately describes red blood cell deformation?
Well, you can try, and it turns out some pretty sharp folks have been trying for a while, since red blood cells are unusually tractable for eukaryotic cells because they're so simple. There's no nucleus. No mitochondria, no insulin receptors, no organelles at all. They're just small, not-quite-donut shaped bags of hemoglobin. This is nice, because it lets you focus just on that bag, and ask, What's its structure?
That simple question turns out to be fairly complicated, though. The RBC cell wall (composed of a phospholipid bilayer, membrane proteins, and cholesterol molecules), sits atop a flexible grid of a structural protein called spectrin, which looks like a ropy mesh joined together in a network of interlinked triangles, with a complex of other structural proteins at each vertex. Think of a fat man lying on a hammock, and you've got the right basic idea (fat and cholesterol sitting on top, and a concave grid beneath...it's a better analogy than I realized, actually!). Each of these spectrin links is like a rope, composed of two long, flexible rods (called polypeptides), very similar to one another, which are twisted together, running antiparallel between the junction vertices.
So it turns out materials scientists have already done the hard work of developing mathematical frameworks for different sorts of polymers, including the aptly-named worm-like-chain (WLC) model. This is pretty much what it sounds like: it's just a way of modeling a polymer that is a continuously flexible rod, and has been used to model things as disparate as strands of DNA and strands of cooked spaghetti. By using this model to describe the force-displacement behavior of the individual spectrin molecules, we can extract three key pieces of information about it: its length at equilibrium, the maximum extension length of the link, and its persistence length. Considering the polymer as a parametric curve described by a single path variable, the persistence length is defined as the value of this variable at which there's no longer a correlation between the unit vector tangent to the curve at 0 and that at the current value. Less formally, the persistence length tells you how stiff your polymer is: if you poke one end of a piece of uncooked spaghetti, that affects the whole strand, but if you do the same thing to a piece of cooked spaghetti, only the end and a little length near it will move. It turns out this 'little length' is about 10 centimeters; that's the persistence length value. In contrast, a DNA double-helix has a persistence length of around 50 nanometers: it's about 2 million times floppier!
What the WLC model gives you, mathematically, is the force exerted on each spectrin chain as a function of the chain's length. This is useful because you can integrate over the chain's length to derive the Helmholtz free energy (which is a thermodynamic state function that tells you, basically, how much work you can get out of an isochoric, isothermal process) contribution from each spectrin chain. Do this for every chain in your system, and add them up, and add that whole sum to the total hydrostatic elastic energy stored in the membrane and assorted proteins, and you've got an expression for the free energy in the entire plane defined by your spectrin network. This in-plane free energy can, in turn, be summed together with the bending free energy, as well as the surface area and volume free energy constraints on the system. The upshot of all this is that you've now got a way to mathematically describe how a red blood cell responds to mechanical stress, by calculating how the total free energy of the system changes.
This model is very high-resolution: it gives you a description of the network all the way down to the individual junction complexes. However, the computational cost of these simulations is steep: since each junction complex is a degree of freedom in this model, this results in about 30,000 degrees of freedom! A useful adjunct to this model, then, would be a way of systematically coarse-graining this model in order to reduce these degrees of freedom and the corresponding computational cost. Coupling this with a coarse-grained flow model, it would be possible to model large numbers of RBCs in the bloodstream.
And, that's the punchline, of course...there was a nifty paper, published last month in Physical Review Letters, that outlined how you'd go about doing this.
So, how can you coarse-grain this model? Basically, you just need to decrease the number of vertices you're considering, but how do you do this without losing accuracy, since the original model was set up so that the number of vertices approximated the number of junction complexes in an actual red blood cell? One simple way is to consider coarse-grained versions of the parameters in the finer-grained model: that is, estimating the effective parameters (equilibrium length, persistence length, hydrostatic elastic energy, and spontaneous angle) based on geometric arguments. The effective equilibrium length (and maximum length, which is taken to be around triple the equilibrium length) can then be estimated as the actual equilibrium length in the finer-grained model multiplied by the square root of the ratio of the number of particles in the finer to the coarser model. A similar argument can be made for the spontaneous angle between adjacent triangles: the effective angle is the original angle multiplied by the ratio of the coarse to the finer equilibrium length.
Coarse-graining the parameters in the in-plane energy equation is more complicated. One way to accomplish this is using a mean-field argument, which is a way of estimating the properties of the network by ignoring the correlations between vertices. That is, estimate the physics of the whole network from that of a single vertex! Using this approach, you can derive expressions for the shear modulus (the ratio of shear stress to shear strain) and the bulk modulus (the resistance of the membrane to compression). This method provides a handy way to coarse-grain the persistence length, as well, since in this mean-field argument the shear and bulk moduli are unchanged from their fine-grained values if the ratio of the equilibrium to the maximum length is fixed. The persistence length can then be systematically adjusted as the product of the original persistence length with the ratio of the fine to the coarse grained equilibrium lengths.
Taken together, this gives us a framework for extracting a complete set of parameters for the model at any level of coarse-graining. Of course, although you can extract effective parameters for an arbitrary level of coarseness, this approach won't be useful if you pick a vertex number of, say, 3. So how far can you take this approach, exactly, before you lose the ability to describe the cell deformation meaningfully? The most straightforward way to answer this, as well as to assess how useful this procedure is in general, is to just brute-force the question (AKA heave a big pile of simulations at your hapless cluster and spend a week drunk and high with a giddy pack of scantily-clad valley girl strippers in Vegas as your data collects itself, not that I would ever do that of course). So, cheap suits and bowls of cocaine at the ready, the authors run a bunch of simulations and discover...the lower limit is about 100 vertices. Below that, the simulated deviations in the cell's axial and transverse diameters become more pronounced. Here's a snapshot of their data:
The plot shows both axial and transverse force-displacement curves. The black diamonds are experimental data points, whereas the solid colored lines represent simulation results at different levels of coarseness (blue line: 23867 points, red: 5000, green: 500, magenta: 100). Except for the magenta axial (lower) curve, the simulated curves are in relatively good agreement with the experimental results. The inset gives an idea of how sensitive their model is to the way they adjusted the persistence length. All the curves except the magenta curve use the adjustment procedure described by the authors; the magenta curve retains the fine-grained value for the persistence length, and as you can see, the results are nothing like the desired linear relation!
So, this is interesting because it shows that their coarse-graining procedure produces results that are comparable to the much more computationally intensive fine-grained model, and fast is always good, of course, because faster = more time to tweak = less power used = less money used, etc. But the real value here is in using the coarse-grained model to do flow simulations of RBCs in circulation. They do this using the dissipative particle dynamics (DPD) method, which is a way of describing clusters of molecules moving together in a flow. The RBC and surrounding fluid are both modeled as DPD particles, and their interactions are modeled using soft quadratic potentials. The flow domain (the simulated capillary) is a tube 10 microns in diameter. The RBC starts out immersed in the fluid, at rest, in the middle of the tube, and then they watch the flow simulation develop. The deformation sequence for 500 vertices is shown below:
The 'parachute' shape observed in (c) is consistent with experimental observations, as well as is the ultimate restoration of the RBC's biconcave shape. They also simulated the behavior of the RBC in a shear flow, and confirmed that their simulations seemed to match experimental evidence.
Pretty neat, all in all. I still need to look into how DPD works (I have only the most general sense of the technique), as well as exactly how you do an optical tweezers experiment, since that data is kind of at the heart of all this!
Thursday, September 25, 2008
Thursday, September 18, 2008
Tuesday, September 16, 2008
Friday, September 12, 2008
Politics ad nauseam
There's one thing to be said for this year's election circus: it's a much more interesting spectacle than any I've seen before. What's also interesting about it is that the candidates are not reaching for the middle: Obama and Biden are both pretty far left, both economically and socially, and McCain's pretty much the personification of national greatness conservatism. The media's made a lot of hay out of McCain's policy shifts (and correctly so, in my view), but his real core's always been about America's awesome, our military is ridiculously powerful and we should use it like a battering ram whenever possible, and also have you heard that I was a prisoner of war because it's not like I mention it six times a day prior to shaving. I'm still trying to figure out exactly what Palin's all about. She certainly seems to lie a lot. You'd think if you were going to introduce yourself to the nation by telling lies, they'd be about things that were not easily verifiable.
GOV. SARAH PALIN: [repeat forcefully 25x] I hate earmarks, America! I told the federal government Thanks but no thanks on the Bridge to Nowhere!
CHARLIE GIBSON: That's actually not true. In fact here's a picture of you literally wearing a T-shirt saying you support it.
GOV. SARAH PALIN: Uh, well, I-
SEN. JOHN MCCAIN: [raging] BARACK OBAMA WANTS TO SHOW YOUR KINDERGARTENER PICTURES OF HIS BLACK COCK, I SWEAR TO GOD! LOOK HOW CREEPY AND BLACK HE LOOKS IN THIS PICTURE AS HE HOVERS OVER VARIOUS YOUNG WHITE CHILDREN! DID I MENTION I WAS A PRISONER OF WAR BY THE WAY BECAUSE I THOUGHT YOU MIGHT NOT HAVE HEARD SINCE YOU'VE BEEN LIVING IN A CAVE, VERY SIMILAR TO THE PRISON WHERE I WAS ONCE BRUTALLY TORTURED BY THE VIET CONG!
...which is more or less what the past week has seemed like to me. Entertaining, in sort of an idiotic, surreal way, and kind of depressing for the same reason. This is our politics, huh. How about debating policy, guys? Anyone? Mention a policy? Joe Biden had some policy tidbits, too bad he fell down an open manhole cover and died, which is what must have happened because why haven't we heard from him in like a week?
That said, what's interesting about the race is that it makes you review your political leanings, since it isn't permeated with the odd feeling that all the candidates are actually the same guy (the guy being the bastard love child of Ronald Reagan and John F. Kennedy, actually a robot controlled by Karl Rove, who is actually a robot owned by Halliburton). When people ask, I tell them I'm 'basically a libertarian.' Kinda. I like the idea of small government, anyway. Or, more precisely:
Economically, I'm in favor of free markets. They're efficient, they're responsive, they're Adam Smith's cold dead invisible hands crushing our lives into meaningless dust. Just kidding. But in general, I think if a job can be reasonably done by private industry, it should be done that way and the government should leave them alone to do it. There are areas that are not handled adequately by private industry, in which case I'm fine with the government doing it. Environmental protection is one really obvious example of this, and one where I differ sharply from orthodox libertarianism. Yes, you can imagine hypothetical scenarios where a private company would want to protect the environment. But there are enough cases where profit and conservation part ways that the free market, left to its own devices, will give the environment a nice firm rogering. The solution isn't to nationalize these industries, as some of the more fringe leftists would suggest, but to regulate them. This is already being done. Tweaking the level at which this is done is fine and probably a good idea, proposing to either massively deregulate everything or nationalize everything is not fine.
Socially, I'm about as liberal as you can get. While I've got a relatively boring personal life, I fully support your right to use all manner of wild and crazy drugs, have sex with and marry whoever suits your fancy, believe in whatever the hell you want to believe in, and so on. I've got mixed feelings about abortion, but I certainly don't think it's the federal government's business to say you can't have one.
Pet hot button issues of mine: science (more funding for all the natural sciences, please, both basic and applied), space (more space development and exploration, not just lip service, and support commercial space initiatives, please), free speech (book banning, censoring, and excessive political correctness are all pretty horrible things, and yes 'speech' on the internet and in video games still qualifies as speech), guns (don't own one myself, but it's really not ok to say that people shouldn't be able to defend themselves, and yes the second amendment really does guarantee that right, so stop pissing on it).
Where does this odd melange of ideas leave me with regard to this year's elections? If you just look at policy details, it's actually kind of a toss-up. The elephant in the room (pun intended) is that John McCain is older than the big bang and has a temper hotter than dirt (OOPS, DID I FLUB THAT LINE? MAYBE IT'S BECAUSE I'M 72 YEARS OLD AND SENILE AND HAVE NO BUSINESS RUNNING FOR PRESIDENT BECAUSE I HAVE ONE FOOT IN THE GRAVE AND THE OTHER IN MY MOUTH BECAUSE I'M SENILE AS HELL), and regardless of his particular policy stances, really isn't temperamentally suited to be President. Frankly, I'm not sure Sarah Palin is, either, although in her case I'm willing to chalk it up to ignorance. Not that that's much better. Perhaps we should go to war with Russia? Not even the most diehard supporters of the Bush doctrine think that. Not that Mrs. Palin would know.
So, damning him with faint praise, I'm supporting Obama. I do like his idea of changing the tone of politics in Washington. Too bad the McCain camp ruined that by burying him and his change of tone underneath a giant stinking mound of political feces. Thanks for nothing, assholes.
GOV. SARAH PALIN: [repeat forcefully 25x] I hate earmarks, America! I told the federal government Thanks but no thanks on the Bridge to Nowhere!
CHARLIE GIBSON: That's actually not true. In fact here's a picture of you literally wearing a T-shirt saying you support it.
GOV. SARAH PALIN: Uh, well, I-
SEN. JOHN MCCAIN: [raging] BARACK OBAMA WANTS TO SHOW YOUR KINDERGARTENER PICTURES OF HIS BLACK COCK, I SWEAR TO GOD! LOOK HOW CREEPY AND BLACK HE LOOKS IN THIS PICTURE AS HE HOVERS OVER VARIOUS YOUNG WHITE CHILDREN! DID I MENTION I WAS A PRISONER OF WAR BY THE WAY BECAUSE I THOUGHT YOU MIGHT NOT HAVE HEARD SINCE YOU'VE BEEN LIVING IN A CAVE, VERY SIMILAR TO THE PRISON WHERE I WAS ONCE BRUTALLY TORTURED BY THE VIET CONG!
...which is more or less what the past week has seemed like to me. Entertaining, in sort of an idiotic, surreal way, and kind of depressing for the same reason. This is our politics, huh. How about debating policy, guys? Anyone? Mention a policy? Joe Biden had some policy tidbits, too bad he fell down an open manhole cover and died, which is what must have happened because why haven't we heard from him in like a week?
That said, what's interesting about the race is that it makes you review your political leanings, since it isn't permeated with the odd feeling that all the candidates are actually the same guy (the guy being the bastard love child of Ronald Reagan and John F. Kennedy, actually a robot controlled by Karl Rove, who is actually a robot owned by Halliburton). When people ask, I tell them I'm 'basically a libertarian.' Kinda. I like the idea of small government, anyway. Or, more precisely:
Economically, I'm in favor of free markets. They're efficient, they're responsive, they're Adam Smith's cold dead invisible hands crushing our lives into meaningless dust. Just kidding. But in general, I think if a job can be reasonably done by private industry, it should be done that way and the government should leave them alone to do it. There are areas that are not handled adequately by private industry, in which case I'm fine with the government doing it. Environmental protection is one really obvious example of this, and one where I differ sharply from orthodox libertarianism. Yes, you can imagine hypothetical scenarios where a private company would want to protect the environment. But there are enough cases where profit and conservation part ways that the free market, left to its own devices, will give the environment a nice firm rogering. The solution isn't to nationalize these industries, as some of the more fringe leftists would suggest, but to regulate them. This is already being done. Tweaking the level at which this is done is fine and probably a good idea, proposing to either massively deregulate everything or nationalize everything is not fine.
Socially, I'm about as liberal as you can get. While I've got a relatively boring personal life, I fully support your right to use all manner of wild and crazy drugs, have sex with and marry whoever suits your fancy, believe in whatever the hell you want to believe in, and so on. I've got mixed feelings about abortion, but I certainly don't think it's the federal government's business to say you can't have one.
Pet hot button issues of mine: science (more funding for all the natural sciences, please, both basic and applied), space (more space development and exploration, not just lip service, and support commercial space initiatives, please), free speech (book banning, censoring, and excessive political correctness are all pretty horrible things, and yes 'speech' on the internet and in video games still qualifies as speech), guns (don't own one myself, but it's really not ok to say that people shouldn't be able to defend themselves, and yes the second amendment really does guarantee that right, so stop pissing on it).
Where does this odd melange of ideas leave me with regard to this year's elections? If you just look at policy details, it's actually kind of a toss-up. The elephant in the room (pun intended) is that John McCain is older than the big bang and has a temper hotter than dirt (OOPS, DID I FLUB THAT LINE? MAYBE IT'S BECAUSE I'M 72 YEARS OLD AND SENILE AND HAVE NO BUSINESS RUNNING FOR PRESIDENT BECAUSE I HAVE ONE FOOT IN THE GRAVE AND THE OTHER IN MY MOUTH BECAUSE I'M SENILE AS HELL), and regardless of his particular policy stances, really isn't temperamentally suited to be President. Frankly, I'm not sure Sarah Palin is, either, although in her case I'm willing to chalk it up to ignorance. Not that that's much better. Perhaps we should go to war with Russia? Not even the most diehard supporters of the Bush doctrine think that. Not that Mrs. Palin would know.
So, damning him with faint praise, I'm supporting Obama. I do like his idea of changing the tone of politics in Washington. Too bad the McCain camp ruined that by burying him and his change of tone underneath a giant stinking mound of political feces. Thanks for nothing, assholes.
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