Abstract
BackgroundPrecise description of the dynamics of biological processes would enable the mathematical analysis and computational simulation of complex biological phenomena. Languages such as Chemical Reaction Networks and Process Algebras cater for the detailed description of interactions among individuals and for the simulation and analysis of ensuing behaviors of populations. However, often knowledge of such interactions is lacking or not available. Yet complete oblivion to the environment would make the description of any biological process vacuous. Here we present a language for describing population dynamics that abstracts away detailed interaction among individuals, yet captures in broad terms the effect of the changing environment, based on environment-dependent Stochastic Tree Grammars (eSTG). It is comprised of a set of stochastic tree grammar transition rules, which are context-free and as such abstract away specific interactions among individuals. Transition rule probabilities and rates, however, can depend on global parameters such as population size, generation count, and elapsed time.ResultsWe show that eSTGs conveniently describe population dynamics at multiple levels including cellular dynamics, tissue development and niches of organisms. Notably, we show the utilization of eSTG for cases in which the dynamics is regulated by environmental factors, which affect the fate and rate of decisions of the different species. eSTGs are lineage grammars, in the sense that execution of an eSTG program generates the corresponding lineage trees, which can be used to analyze the evolutionary and developmental history of the biological system under investigation. These lineage trees contain a representation of the entire events history of the system, including the dynamics that led to the existing as well as to the extinct individuals.ConclusionsWe conclude that our suggested formalism can be used to easily specify, simulate and analyze complex biological systems, and supports modular description of local biological dynamics that can be later used as “black boxes” in a larger scope, thus enabling a gradual and hierarchical definition and simulation of complex biological systems. The simple, yet robust formalism enables to target a broad class of stochastic dynamic behaviors, especially those that can be modeled using global environmental feedback regulation rather than direct interaction between individuals.
Highlights
Precise description of the dynamics of biological processes would enable the mathematical analysis and computational simulation of complex biological phenomena
Throughout the paper, we demonstrate the usability of the language by presenting a wide range of examples that can be modeled and simulated using this approach
In addition to single executions, environment-dependent Stochastic Tree Grammars (eSTG) can be used for obtaining overall population statistics, for example, to calculate the average population size over time (Figure 1D) and the distribution of clone sizes (Figure 1E)
Summary
Precise description of the dynamics of biological processes would enable the mathematical analysis and computational simulation of complex biological phenomena. We present a language for describing population dynamics that abstracts away detailed interaction among individuals, yet captures in broad terms the effect of the changing environment, based on environment-dependent Stochastic Tree Grammars (eSTG). Many processes can be described using CRNs, for example, Predator-Prey models [8], Cellular cascade pathways [9], Cancer progression [10], Epidemics dynamics [11], and many others [1] Each of these processes consists of a continuous interaction between individual species (the reactants) that occurs at a certain rate and produces a group of other individuals (the products, which may be empty) that can be of the same (autocatalytic) or of different type. When using a CRN abstraction such molecules cannot retain identity while changing state
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