Mathematical and computational modeling of biosystems at different levels of organization

Modern biology increasingly relies on mathematical and computational modeling to describe complex hierarchically organized biological systems. This review considers models that cover the main levels of biological organization, from the molecular-genetic and cellular levels to tissue/organ, organismal, population and ecological ones. The aim of the work is to systematize the key modeling approaches at each of these levels, to analyze their capabilities and limitations, and to discuss strategies for constructing multiscale and hybrid models that consistently link processes operating at different spatial and temporal scales. We survey classical deterministic and stochastic models based on ordinary and partial differential equations, logical and graph-based models of regulatory networks, cellular automata, agent-based models, as well as flux-balance approaches. Typical examples are given for the modeling of gene regulatory and metabolic networks, chemotaxis, tissue and organ growth, population dynamics and genetic structure, and ecosystem functioning. Special attention is paid to comparing approaches with respect to the scale of description, complexity of modeled processes, data requirements, computational cost and interpretability of results. The analysis shows that hybrid and multiscale models provide an adequate framework to account for nonlinearity, stochasticity and structural heterogeneity of biosystems, but require substantial computational resources and careful data-driven calibration. Methodological and technological trends are outlined, including the development of specialized platforms and model repositories, standards for model representation and tools for reuse of model components.