In silico modeling of biochemical pathways

We present in silico modeling methods for the investigation of dynamical properties of biochemical pathways, that are chemical reaction networks underlying cell functioning. Since pathways are (complex) dynamical systems, in-silico models are often studied by applying numerical integration techniques for Ordinary Differential Equations (ODEs), or stochastic simulation algorithms. However, these techniques require a rather accurate knowledge of the kinetic parameters of the modeled chemical reactions. Moreover, in the case of very complex reaction networks, in silico analysis can become unfeasible from the computational viewpoint. Consequently, in the last few years several approaches have been proposed that focus on estimating or predicting dynamical properties from the analysis of the structure of the biochemical pathway. This means that the analysis focuses more on the interaction patterns than on the kinetic parameters, and this usually makes it possible to deduce the role of each molecule and how each molecule qualitatively influences each other, by abstracting away from quantitative details about concentrations and reaction rates.

Stochastic simulation algorithms for Interacting Particle Systems

Interacting Particle Systems (IPSs) are used to model spatio-temporal stochastic systems in many disparate areas of science. We design an algorithmic framework that reduces IPS simulation to simulation of well-mixed Chemical Reaction Networks (CRNs). This framework minimizes the number of associated reaction channels and decouples the computational cost of the simulations from the size of the lattice. Decoupling allows our software to make use of a wide class of techniques typically reserved for well-mixed CRNs. We implement the direct stochastic simulation algorithm in the open source programming language Julia. We also apply our algorithms to several complex spatial stochastic phenomena. including a rock-paper-scissors game, cancer growth in response to immunotherapy, and lipid oxidation dynamics. Our approach aids in standardizing mathematical models and in generating hypotheses based on concrete mechanistic behavior across a wide range of observed spatial phenomena.

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

sismonr: simulation of in silico multi-omic networks with adjustable ploidy and post-transcriptional regulation in R

Summary We present sismonr, an R package for an integral generation and simulation of in silico biological systems. The package generates gene regulatory networks, which include protein-coding and non-coding genes along with different transcriptional and post-transcriptional regulations. The effect of genetic mutations on the system behaviour is accounted for via the simulation of genetically different in silico individuals. The ploidy of the system is not restricted to the usual haploid or diploid situations but can be defined by the user to higher ploidies. A choice of stochastic simulation algorithms allows us to simulate the expression profiles of the genes in the in silico system. We illustrate the use of sismonr by simulating the anthocyanin biosynthesis regulation pathway for three genetically distinct in silico plants. Availability and implementation The sismonr package is implemented in R and Julia and is publicly available on the CRAN repository (https://CRAN.R-project.org/package=sismonr). A detailed tutorial is available from GitHub at https://oliviaab.github.io/sismonr/. Supplementary information Supplementary data are available at Bioinformatics online.

A Tensor Decomposition Algorithm for Large ODEs with Conservation Laws

We propose an algorithm for solution of high-dimensional evolutionary equations (ODEs and discretized time-dependent PDEs) in the Tensor Train (TT) decomposition, assuming that the solution and the right-hand side of the ODE admit such a decomposition with a low storage. A linear ODE, discretized via one-step or Chebyshev differentiation schemes, turns into a large linear system. The tensor decomposition allows to solve this system for several time points simultaneously using an extension of the Alternating Least Squares algorithm. This method computes a reduced TT model of the solution, but in contrast to traditional offline-online reduction schemes, solving the original large problem is never required. Instead, the method solves a sequence of reduced Galerkin problems, which can be set up efficiently due to the TT decomposition of the right-hand side. The reduced system allows a fast estimation of the time discretization error, and hence adaptation of the time steps. Besides, conservation laws can be preserved exactly in the reduced model by expanding the approximation subspace with the generating vectors of the linear invariants and correction of the Euclidean norm. In numerical experiments with the transport and the chemical master equations, we demonstrate that the new method is faster than traditional time stepping and stochastic simulation algorithms, whereas the invariants are preserved up to the machine precision irrespectively of the TT approximation accuracy.

On Oscillations and Noise in Multicomponent Adsorption: The Nature of Multiple Stationary States

Starting from the fact that monocomponent adsorption, whether modeled by Lagergren or nonlinear Riccati equation, does not sustain oscillations, we speculate about the nature of multiple steady state states in multicomponent adsorption with second-order kinetics and about the possibility that multicomponent adsorption might exhibit oscillating behavior, in order to provide a tool for better discerning possible oscillations from inevitable fluctuations in experimental results or a tool for a better control of adsorption process far from equilibrium. We perform an analysis of stability of binary adsorption with second-order kinetics in multiple ways. We address perturbations around the steady state analytically, first in a classical way, then by introducing Langevin forces and analyzing the reaction flux and cross-correlations, then by applying the stochastic chemical master equation approach, and finally, numerically, by using stochastic simulation algorithms. Our results show that stationary states in this model are stable nodes. Hence, experimental results with purported oscillations in response should be addressed from the point of view of fluctuations and noise analysis.