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Multi-level modelling via stochastic multi-level multiset rewriting

机译:通过随机多级多集重写进行多级建模

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We present a simple stochastic rule-based approach to multi-level modelling for computational systems biology. Populations are modelled using multi-level multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such multisets, but they may now also include variables (as well as species and agents), together with an associated stochastic rate. We give two illustrative examples. The first is an extracellular model of virus infection, coupled with an intracellular model of viral reproduction; this model can demonstrate successive waves of infection. The second is a model of cell division in which a repressor protein is diluted in successive generations, so eventually repression no longer occurs. The multi-level multiset approach can also be seen in terms of stochastic term rewriting for the theory of a commutative monoid equipped with extra constants (for the species) and unary operations (for the agents). We further discuss the relationship of this approach with two others: Krivine et al.'s stochastic bigraphs, restricted to Milner's place graphs, and Coppo et al.'s Stochastic Calculus of Wrapped Compartments. These various relationships provide evidence for the fundamental nature of the approach.
机译:我们为计算系统生物学提供了一种基于随机规则的简单多级建模方法。人口使用多级多集建模;它们既包含物种又包含试剂,而后者可能包含其他此类多集。规则是这种多集的对,但现在它们可能还包括变量(以及物种和主体)以及相关的随机率。我们给出两个说明性的例子。首先是病毒感染的细胞外模型,再加上病毒繁殖的细胞内模型。该模型可以证明感染的连续波。第二个是细胞分裂模型,其中阻遏蛋白在连续的世代中被稀释,因此最终不再发生阻遏。多级多集方法还可以从随机术语重写的角度来看,该术语具有交换常数的半定式理论,该常数具有额外的常数(对于物种)和一元运算(对于代理)。我们进一步讨论了这种方法与其他两个方法之间的关系:Krivine等人的随机二元图(仅限于米尔纳的位置图)和Coppo等人的随机包裹式微积分。这些各种关系为该方法的基本性质提供了证据。

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