Computational characterization of recombinase circuits for periodic behaviors

In nature, recombinases are site-specific proteins capable of rearranging DNA, and they are expanding the repertoire of gene editing tools used in synthetic biology. The on/off response of recombinases, achieved by inverting the direction of a promoter, makes them suitable for Boolean logic computation; however, recombinase-based logic gate circuits are single-use due to the irreversibility of the DNA rearrangement, and it is still unclear how a dynamical circuit, such as an oscillator, could be engineered using recombinases. Preliminary work has demonstrated that recombinase- based circuits can yield periodic behaviors in a deterministic setting. However, since a few molecules of recombinase are enough to perform the inverting function, it is crucial to assess how the inherent stochasticity at low copy number affects the periodic behavior. Here, we propose six different circuit designs for recombinase-based oscillators. We model them in a stochastic setting, leveraging the Gillespie algorithm for extensive simulations, and we show that they can yield periodic behaviors. To evaluate the incoherence of oscillations, we use a metric based on the statistical properties of auto-correlation functions. The main core of our design consists of two self-inhibitory, recombinase-based modules coupled by a common promoter. Since each recombinase inverts its own promoter, the overall circuit can give rise to switching behavior characterized by a regular period. We introduce different molecular mechanisms (transcriptional regulation, degradation, sequestration) to tighten the control of recombinase levels, which slows down the response timescale of the system and thus improves the coherence of oscillations. Our results support the experimental realization of recombinase-based oscillators and, more generally, the use of recombinases to generate dynamic behaviors in synthetic biology.

Stochastic model of lignocellulosic material saccharification

The processing of agricultural wastes towards extraction of renewable resources is recently being considered as a promising alternative to conventional biofuel production. The degradation of agricultural residues is a complex chemical process that is currently time intensive and costly. Various pre-treatment methods are being investigated to determine the subsequent modification of the material and the main obstacles in increasing the enzymatic saccharification. In this study, we present a computational model that complements the experimental approaches. We decipher how the three-dimensional structure of the substrate impacts the saccharification dynamics. We model a cell wall microfibril composed of cellulose and surrounded by hemicellulose and lignin, with various relative abundances and arrangements. This substrate is subjected to digestion by different cocktails of well characterized enzymes. The saccharification dynamics is simulated in silico using a stochastic procedure based on a Gillespie algorithm. As we additionally implement a fitting procedure that optimizes the parameters of the simulation runs, we are able to reproduce experimental saccharification time courses for corn stover. Our model highlights the synergistic action of enzymes, and confirms the linear decrease of sugar conversion when either lignin content or crystallinity of the substrate increases. Importantly, we show that considering the crystallinity of cellulose in addition to the substrate composition is essential to interpret experimental saccharification data. Finally, our findings support the hypothesis of xylan being partially crystalline.

Mathematical Model of Spread of the Epidemic Inside a Railway Compartment Coach

This article discusses an aspect of the most pressing problem of 2020, that of the spread of infectious diseases. The work considers a railway compartment coach as a particular object of spread of infectious diseases. The objective is to describe spread of the epidemic in a railway coach using a stochastic model. The model of the coach is represented as a network. The processes occurring on the network are considered to be Markov processes. In this paper, two methods of stochastic modelling are applied: modelling based on Kolmogorov equations and Gillespie algorithm. Kolmogorov equations are used to test applicability of Gillespie algorithm, which, in turn, is used to simulate the model of the coach. The obtained data were analysed, and based on that analysis it is possible to make a conclusion about applicability of the model to the case of a typical passenger train.

Geospatial Model of COVID-19 Spreading and Vaccination With Event Gillespie Algorithm

We developed a model and a software package for stochastic simulations of transmission of COVID-19 and other similar infectious diseases, that takes into account contact network structures and geographical distribution of population density, detailed up to a level of location of individuals. Our analysis framework includes a surrogate model optimization process for quick fitting of the model’s parameters to the observed epidemic curves for cases, hospitalizations and deaths. This set of instruments (the model, the simulation code, and the optimizer) is a useful tool for policymakers and epidemic response teams who can use it to forecast epidemic development scenarios in local environments (on the scale from towns to large countries) and design optimal response strategies. The simulation code also includes a geospatial visualization subsystem, presenting detailed views of epidemic scenarios directly on population density maps. We used the developed framework to draw predictions for COVID-19 spreading in the canton of Geneva, Switzerland.

Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation—including static extrinsic noise—exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis , a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.

VGsim: scalable viral genealogy simulator for global pandemic

As an effort to help contain the COVID-19 pandemic, large numbers of SARS-CoV-2 genomes have been sequenced from all continents. More than one million viral sequences are publicly available as of April 2021. Many studies estimate viral genealogies from these sequences, as these can provide valuable information about the spread of the pandemic across time and space. Additionally such data are a rich source of information about molecular evolutionary processes including natural selection, for example allowing the identification and investigating the spread of new variants conferring transmissibility and immunity evasion advantages to the virus. To validate new methods and to verify results resulting from these vast datasets, one needs an efficient simulator able to simulate the pandemic to approximate world-scale scenarios and generate viral genealogies of millions of samples. Here, we introduce a new fast simulatorVGsimwhich addresses this problem. The simulation process is split into two phases. During the forward run the algorithm generates a chain of events reflecting the dynamics of the pandemic using an hierarchical version of the Gillespie algorithm. During the backward run a coalescent-like approach generates a tree genealogy of samples conditioning on the events chain generated during the forward run. Our software can model complex population structure, epistasis and immunity escape. The code is freely available athttps://github.com/Genomics-HSE/VGsim.

Inferring epidemic containment probability from non-pharmaceutical interventions using a Gillespie-based epidemic model

The Gillespie algorithm, which is a stochastic numerical simulation of continuous-time Markovian processes, has been proposed for simulating epidemic dynamics. In the present study, using the Gillespie-based epidemic model, we focused on each single trajectory by the stochastic simulation to infer the probability of controlling an epidemic by non-pharmaceutical interventions (NPIs). The single trajectory analysis by the stochastic simulation suggested that a few infected people sometimes dissipated spontaneously without spreading of infection. The outbreak probability was affected by basic reproductive number but not by infectious duration and susceptible population size. A comparative analysis suggested that the mean trajectory by the stochastic simulation has equivalent dynamics to a conventional deterministic model in terms of epidemic forecasting. The probability of outbreak containment by NPIs was inferred by trajectories derived from 1000 Monte Carlo simulation trials using model parameters assuming COVID-19 epidemic. The model-based analysis indicated that complete containment of the disease could be achieved by short-duration NPIs if performed early after the import of infected individuals. Under the correctness of the model assumptions, analysis of each trajectory by Gillespie-based stochastic model would provide a unique and valuable output such as the probabilities of outbreak containment by NPIs.

Stochastic Modeling of Plant Virus Propagation with Biological Control

Plants are vital for man and many species. They are sources of food, medicine, fiber for clothes and materials for shelter. They are a fundamental part of a healthy environment. However, plants are subject to virus diseases. In plants most of the virus propagation is done by a vector. The traditional way of controlling the insects is to use insecticides that have a negative effect on the environment. A more environmentally friendly way to control the insects is to use predators that will prey on the vector, such as birds or bats. In this paper we modify a plant-virus propagation model with delays. The model is written using delay differential equations. However, it can also be expressed in terms of biochemical reactions, which is more realistic for small populations. Since there are always variations in the populations, errors in the measured values and uncertainties, we use two methods to introduce randomness: stochastic differential equations and the Gillespie algorithm. We present numerical simulations. The Gillespie method produces good results for plant-virus population models.

Simulating trajectories and phylogenies from population dynamics models with TiPS

We introduce TiPS, an R-based simulation software to generate time series and genealogies associated with a population dynamics model. The approach is flexible since it can capture any model defined with a set of ordinary differential equations (ODE), and allow parameter values to vary over time periods. Computational time is minimal thanks to the use of the Rcpp package to compile the ODEs into a program corresponding to an implementation of the Gillespie algorithm. This software is particularly suited for epidemiology and phylodynamics, where there is a need to generate numerous phylogenies for a variety of infections life cycles, and in population genetics as well.

Introducing and benchmarking the accuracy of cayenne: a Python package for stochastic simulations

Biological systems are intrinsically noisy and this noise may determine the qualitative outcome of the system. In the absence of analytical solutions to mathematical models incorporating noise, stochastic simulation algorithms are useful to explore the possible trajectories of these systems. Algorithms used for such stochastic simulations include the Gillespie algorithm and its approximations. In this study we introduce cayenne, an easy to use Python package containing accurate and fast implementations of the Gillespie algorithm (direct method), the tau-leaping algorithm and a tau-adaptive algorithm. We compare the accuracy of cayenne with other stochastic simulation libraries (BioSimulator.jl, GillespieSSA and Tellurium) and find that cayenne offers the best trade-off between accuracy and speed. Additionally, we highlight the importance of performing accuracy tests for stochastic simulation libraries, and hope that it becomes standard practice when developing the same.The cayenne package can be found at https://github.com/Heuro-labs/cayenne while the bench-marks can be found at https://github.com/Heuro-labs/cayenne-benchmarks