In the light of directed evolution: Pathways of adaptive protein evolution

Directed evolution is a widely-used engineering strategy for improving the stabilities or biochemical functions of proteins by repeated rounds of mutation and selection. These experiments offer empirical lessons about how proteins evolve in the face of clearly-defined laboratory selection pressures. Directed evolution has revealed that single amino acid mutations can enhance properties such as catalytic activity or stability and that adaptation can often occur through pathways consisting of sequential beneficial mutations. When there are no single mutations that improve a particular protein property experiments always find a wealth of mutations that are neutral with respect to the laboratory-defined measure of fitness. These neutral mutations can open new adaptive pathways by at least 2 different mechanisms. Functionally-neutral mutations can enhance a protein's stability, thereby increasing its tolerance for subsequent functionally beneficial but destabilizing mutations. They can also lead to changes in “promiscuous” functions that are not currently under selective pressure, but can subsequently become the starting points for the adaptive evolution of new functions. These lessons about the coupling between adaptive and neutral protein evolution in the laboratory offer insight into the evolution of proteins in nature

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers