Abstract
Natural systems are, almost by definition, heterogeneous: this can be either a boon or an obstacle to be overcome, depending on the situation. Traditionally, when constructing mathematical models of these systems, heterogeneity has typically been ignored, despite its critical role. However, in recent years, stochastic computational methods have become commonplace in science. They are able to appropriately account for heterogeneity; indeed, they are based around the premise that systems inherently contain at least one source of heterogeneity (namely, intrinsic heterogeneity).In this mini-review, we give a brief introduction to theoretical modelling and simulation in systems biology and discuss the three different sources of heterogeneity in natural systems. Our main topic is an overview of stochastic simulation methods in systems biology.There are many different types of stochastic methods. We focus on one group that has become especially popular in systems biology, biochemistry, chemistry and physics. These discrete-state stochastic methods do not follow individuals over time; rather they track only total populations. They also assume that the volume of interest is spatially homogeneous. We give an overview of these methods, with a discussion of the advantages and disadvantages of each, and suggest when each is more appropriate to use. We also include references to software implementations of them, so that beginners can quickly start using stochastic methods for practical problems of interest.
Highlights
A well-known example might be a flight training simulator for pilots that simulates flying an aeroplane. This is based on a complicated mathematical model that is composed of equations for flight dynamics and for how the aeroplane should react to the controls, as well as other factors such as weather
A model is a vehicle for gaining understanding [6], and we would not gain any new understanding from a model that was as complicated as the real system
In this mini-review, our aim has been to give an introduction to the background and an overview of discrete-state stochastic modelling and simulation methods that are commonly used in systems biology today to take account of stochasticity
Summary
Heterogeneity is a key property of biological systems at all scales: from the molecular level all the way up to the population level [24,25,26]. It is possible to separate the contributions of intrinsic and extrinsic noise in a gene expression network inside a single cell: this is the classic experiment of Elowitz et al [44] They incorporated two fluorescent proteins (cyan and yellow, they are usually represented as red and green for conceptual purposes) into the genome of an isogenic population of Escherichia coli bacterial cells at equidistant points from the origin of replication. Some biological systems have evolved to make use of it: a good example is the case of persister-type bacteria, which form a subset of some bacterial populations and can withstand antibiotic treatments even though they do not have genetic mutations for resistance [47,48] This is an example of cellular decision making, the ability of cells to randomly transition between different stable, heritable states [49]. A powerful example of the interplay of all three types of heterogeneity is evolution, one of the most fundamental processes in nature: evolution acts on phenotypes, which have a genetic basis but are affected by both extrinsic and intrinsic noise [40]
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