A differentiable Gillespie algorithm for simulating chemical kinetics, parameter estimation, and designing synthetic biological circuits
- Department of Physics, Boston University, United States
Figures
Figure 1
Comparison between the exact Gillespie algorithm and the differentiable Gillespie algorithm (DGA) for simulating chemical kinetics.
(a) Example of kinetics with reactions with rates . (b) Illustration of the DGA’s approximations: replacing the non-differentiable Heaviside and Kronecker delta functions with smooth sigmoid …
Figure 2
Flow chart of the parameter optimization process using the differentiable Gillespie algorithm (DGA).
The process begins by initializing the parameters . Simulations are then run using the DGA to obtain statistics like moments. These statistics are used to compute the loss , and the gradient …
Figure 3
Two-state gene regulation architecture.
(a) Schematic of gene regulatory circuit for transcriptional repression. RNA polymerase (RNAP) binds to the promoter region to initiate transcription at a rate , leading to the synthesis of mRNA …
Figure 4
Accuracy of the differentiable Gillespie algorithm (DGA) in simulating the two-state promoter architecture in Figure 3a.
Comparison between the DGA and exact simulations for (a) steady-state mRNA distribution, (b) moments of the steady-state mRNA distribution, and (d) the probability for the promoter to be in the ‘ON’ …
Figure 5
Gradient-based learning via differentiable Gillespie algorithm (DGA) is applied to the synthetic data for the gene expression model in Figure 3a.
Parameters are fixed at 1, with and for a simulation time of 10. (a) Scatter plot of true versus inferred parameters ( and ) with constant. Error bars are 95% confidence intervals …
Figure 6
Gradient-based learning via differentiable Gillespie algorithm (DGA) is applied to the synthetic data for the gene expression model in Figure 3a.
Parameters are fixed at 1, with and for a simulation time of 10. (a) Scatter plot of true versus inferred parameters (, , and ). Error bars are 95% confidence intervals (CIs). Panel (b…
Figure 7
Fitting of experimental data from Jones et al., 2014 using the differentiable Gillespie algorithm (DGA).
(a) Comparison between theoretical predictions from the DGA (solid curves) and experimental values of mean and the Fano factor for the steady-state mRNA levels are represented by square markers, …
Figure 8
Design of the four-state promoter architecture using the differentiable Gillespie algorithm (DGA).
(a) Schematic of four-state promoter model. (b) Target input–output relationships (solid curves) and learned input–output relationships (blue dots) between activator concentration and average …
Appendix 1—figure 1
In panels (a) and (b), we plot the ratio of the Jensen–Shannon divergence between the differentiable Gillespie PDF and the exact steady-state PDF , and the Shannon entropy of the exact steady-state PDF, as a function of the two sharpness parameters and .
In panel (a), ; in panel (b), . The simulation time is set to 10. In panels (c) and (d), for these same values, we show the gradient of the loss function with respect to the parameter …
Appendix 3—figure 1
