Atamas Sergei P, Bell Jonathan
Department of Medicine and Department of Microbiology and Immunology, University of Maryland School of Medicine, MSTF 834, Baltimore, MD 21201, USA.
Bull Math Biol. 2009 Aug;71(6):1349-65. doi: 10.1007/s11538-009-9404-z. Epub 2009 Apr 1.
Numerous biological interactions, such as interactions between T cell receptors or antibodies with antigens, interactions between enzymes and substrates, or interactions between predators and prey are often not strictly specific. In such less specific, or "sloppy," systems, referred to here as degenerate systems, a given unit of a diverse resource (antigens, enzymatic substrates, prey) is at risk of being recognized and consumed by multiple consumers (lymphocytes, enzymes, predators). In this study, we model generalized degenerate consumer-resource systems of Lotka-Volterra and Verhulst types. In the degenerate systems of Lotka-Volterra, there is a continuum of types of consumer and resource based on variation of a single trait (characteristic, or preference). The consumers experience competition for a continuum of resource types. This non-local interaction system is modeled with partial differential-integral equations and shows spontaneous self-structuring of the consumer population that depends on the degree of interaction degeneracy between resource and consumer, but does not mirror the distribution of resource. We also show that the classical Verhulst (i.e. logistic) single population model can be generalized to a degenerate model, which shows qualitative behavior similar to that in the degenerate Lotka-Volterra model. These results provide better insight into the dynamics of selective systems in biology, suggesting that adaptation of degenerate repertoires is not a simple "mirroring" of the environment by the "fittest" elements of population.
许多生物相互作用，例如T细胞受体或抗体与抗原之间的相互作用、酶与底物之间的相互作用，或者捕食者与猎物之间的相互作用，往往并非严格特异性的。在这种特异性较低或“不精确”的系统中，这里称为简并系统，一种多样资源（抗原、酶底物、猎物）的给定单元有被多种消费者（淋巴细胞、酶、捕食者）识别和消耗的风险。在本研究中，我们对洛特卡 - 沃尔泰拉（Lotka-Volterra）型和韦尔胡斯特（Verhulst）型的广义简并消费者 - 资源系统进行建模。在洛特卡 - 沃尔泰拉简并系统中，基于单一性状（特征或偏好）的变化存在消费者和资源类型的连续统。消费者对连续统的资源类型存在竞争。这个非局部相互作用系统用偏微分 - 积分方程建模，并显示出消费者群体的自发自组织，这取决于资源与消费者之间相互作用的简并程度，但并不反映资源的分布。我们还表明，经典的韦尔胡斯特（即逻辑斯谛）单种群模型可以推广为简并模型，其定性行为与简并洛特卡 - 沃尔泰拉模型相似。这些结果为生物学中选择性系统的动态提供了更好的见解，表明简并库的适应性并非种群中“最适应”元素对环境的简单“映射”。
