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.