IDESS: a toolbox for identification and automated design of stochastic gene circuits.

MOTIVATION: One of the main causes hampering predictability during the model identification and automated design of gene circuits in synthetic biology is the effect of molecular noise. Stochasticity may significantly impact the dynamics and function of gene circuits, specially in bacteria and yeast due to low mRNA copy numbers. Standard stochastic simulation methods are too computationally costly in realistic scenarios to be applied to optimization-based design or parameter estimation. RESULTS: In this work, we present IDESS (Identification and automated Design of Stochastic gene circuitS), a software toolbox for optimization-based design and model identification of gene regulatory circuits in the stochastic regime. This software incorporates an efficient approximation of the Chemical Master Equation as well as a stochastic simulation algorithm-both with GPU and CPU implementations-combined with global optimization algorithms capable of solving Mixed Integer Nonlinear Programming problems. The toolbox efficiently addresses two types of problems relevant in systems and synthetic biology: the automated design of stochastic synthetic gene circuits, and the parameter estimation for model identification of stochastic gene regulatory networks. AVAILABILITY AND IMPLEMENTATION: IDESS runs under the MATLAB environment and it is available under GPLv3 license at https://doi.org/10.5281/zenodo.7788692.

Global Optimization Approach for Parameter Estimation in Stochastic Dynamic Models of Biosystems.

Mechanistic dynamic models have become an essential tool for understanding biomolecular networks and other biological systems. Biochemical stochasticity can be extremely important in some situations, e.g., at the single-cell level where there is a low copy number of the species involved. In these scenarios, deterministic models are not suitable to characterize the dynamics, so stochastic dynamic models should be considered. Here, we address the challenging problem of parameter estimation in stochastic dynamic models. Despite recent advances, this area is considerably less mature than its deterministic counterpart. We present a novel strategy based on two components: (i) global optimization via a hybrid stochastic-deterministic approach, and (ii) stochastic simulation techniques tailored to the sparsity of the available experimental data. Regarding the latter, for cases of dense population data we make use of a novel approach using a Partial Integro-Differential Equation (PIDE) model solved using a semilagrangian method. In order to further speed up the simulations, we also present efficient parallel implementations for multi-core CPUs and also for graphical processing units (GPUs). Importantly, whereas SDE and Fokker Planck approximations of the Chemical Master Equation (CME) apply when the reactant populations are sufficiently large, the PIDE approximation to the CME is valid for very low copy numbers, and therefore they enable us to tackle parameter estimation for systems with large intrinsic molecular noise, (highly stochastic regimes far from the thermodynamic limit). We test our strategy with four challenging problems: a Lotka-Volterra system, a polarization system in S. cerevisiae, a genetic toggle switch, and a genetic circadian oscillator. Our method could successfully solve these problems in very reasonable computation times (often a few minutes for the first two problems) using standard low-cost hardware, showing very significant speedups with respect to recent alternative methods. The code used to obtain the results reported here is available at https://doi.org/10.5281/zenodo.5195408.

Automated Design of Synthetic Gene Circuits in the Presence of Molecular Noise.

Microorganisms (mainly bacteria and yeast) are frequently used as hosts for genetic constructs in synthetic biology applications. Molecular noise might have a significant effect on the dynamics of gene regulation in microbial cells, mainly attributed to the low copy numbers of mRNA species involved. However, the inclusion of molecular noise in the automated design of biocircuits is not a common practice due to the computational burden linked to the chemical master equation describing the dynamics of stochastic gene regulatory circuits. Here, we address the automated design of synthetic gene circuits under the effect of molecular noise combining a mixed integer nonlinear global optimization method with a partial integro-differential equation model describing the evolution of stochastic gene regulatory systems that approximates very efficiently the chemical master equation. We demonstrate the performance of the proposed methodology through a number of examples of relevance in synthetic biology, including different bimodal stochastic gene switches, robust stochastic oscillators, and circuits capable of achieving biochemical adaptation under noise.