Using single-cell models to predict the functionality of synthetic circuits at the population scale

Mathematical modeling has become a major tool to guide the characterization and synthetic construction of cellular processes. However, models typically lose their capacity to explain or predict experimental outcomes as soon as any, even minor, modification of the studied system or its operating conditions is implemented. This limits our capacity to fully comprehend the functioning of natural biological processes and is a major roadblock for the de novo design of complex synthetic circuits. Here, using a specifically constructed yeast optogenetic differentiation system as an example, we show that a simple deterministic model can explain system dynamics in given conditions but loses validity when modifications to the system are made. On the other hand, deploying theory from stochastic chemical kinetics and developing models of the system's components that simultaneously track single-cell and population processes allows us to quantitatively predict emerging dynamics of the system without any adjustment of model parameters. We conclude that carefully characterizing the dynamics of cell-to-cell variability using appropriate modeling theory may allow one to unravel the complex interplay of stochastic single-cell and population processes and to predict the functionality of composed synthetic circuits in growing populations before the circuit is constructed.

Beyond the chemical master equation: Stochastic chemical kinetics coupled with auxiliary processes

The chemical master equation and its continuum approximations are indispensable tools in the modeling of chemical reaction networks. These are routinely used to capture complex nonlinear phenomena such as multimodality as well as transient events such as first-passage times, that accurately characterise a plethora of biological and chemical processes. However, some mechanisms, such as heterogeneous cellular growth or phenotypic selection at the population level, cannot be represented by the master equation and thus have been tackled separately. In this work, we propose a unifying framework that augments the chemical master equation to capture such auxiliary dynamics, and we develop and analyse a numerical solver that accurately simulates the system dynamics. We showcase these contributions by casting a diverse array of examples from the literature within this framework and applying the solver to both match and extend previous studies. Analytical calculations performed for each example validate our numerical results and benchmark the solver implementation.

RSSALib: a library for stochastic simulation of complex biochemical reactions

Motivation Stochastic chemical kinetics is an essential mathematical framework for investigating the dynamics of biological processes, especially when stochasticity plays a vital role in their development. Simulation is often the only option for the analysis of many practical models due to their analytical intractability. Results We present in this article, the simulation library RSSALib, implementing our recently developed rejection-based stochastic simulation algorithm (RSSA) and a wide range of its improvements, to accelerate the simulation and analysis of biochemical reactions. RSSALib supports reactions with complex kinetics and time delays, necessary to model complexities of reaction mechanisms. Our library provides both an application program interface and a graphic user interface to ease the set-up and visualization of the simulation results. Availability and implementation RSSALib is freely available at: https://github.com/vo-hong-thanh/rssalib. Supplementary information Supplementary data are available at Bioinformatics online.

Some mechanistic requirements for major transitions

Major transitions in nature and human society are accompanied by a substantial change towards higher complexity in the core of the evolving system. New features are established, novel hierarchies emerge, new regulatory mechanisms are required and so on. An obvious way to achieve higher complexity is integration of autonomous elements into new organized systems whereby the previously independent units give up their autonomy at least in part. In this contribution, we reconsider the more than 40 years old hypercycle model and analyse it by the tools of stochastic chemical kinetics. An open system is implemented in the form of a flow reactor. The formation of new dynamically organized units through integration of competitors is identified with transcritical bifurcations. In the stochastic model, the fully organized state is quasi-stationary whereas the unorganized state corresponds to a population with natural selection. The stability of the organized state depends strongly on the number of individual subspecies, n , that have to be integrated: two and three classes of individuals, and , readily form quasi-stationary states. The four-membered deterministic dynamical system, , is stable but in the stochastic approach self-enhancing fluctuations drive it into extinction. In systems with five and more classes of individuals, , the state of cooperation is unstable and the solutions of the deterministic ODEs exhibit large amplitude oscillations. In the stochastic system self-enhancing fluctuations lead to extinction as observed with . Interestingly, cooperative systems in nature are commonly two-membered as shown by numerous examples of binary symbiosis. A few cases of symbiosis of three partners, called three-way symbiosis , have been found and were analysed within the past decade. Four-way symbiosis is rather rare but was reported to occur in fungus-growing ants. The model reported here can be used to illustrate the interplay between competition and cooperation whereby we obtain a hint on the role that resources play in major transitions. Abundance of resources seems to be an indispensable prerequisite of radical innovation that apparently needs substantial investments. Economists often claim that scarcity is driving innovation. Our model sheds some light on this apparent contradiction. In a nutshell, the answer is: scarcity drives optimization and increase in efficiency but abundance is required for radical novelty and the development of new features. This article is part of the themed issue ‘The major synthetic evolutionary transitions’.