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Complex mathematical models of biology at the nanoscale.

Mathematical modeling of nanobiosystems is an exciting and rapidly growing new field of research that offers the potential to guide and improve technological developments in both nanomedicine and nanobiomaterial science. Unlike the more traditional fields of science and engineering, however, models of nanobiosystems are notoriously complex. In this paper, we highlight some of the primary sources of complexity in nanobiosystems. In particular, we focus on complexity that arises from the inherent nonlinearity of natural systems, noise generated by low copy numbers of relevant biological constituents, heterogeneity that stems from structure in physical systems at the nanoscale, strong coupling between processes that occur at different scales, and the large dimensions necessary to represent typical biological systems. We then suggest how different mathematical modeling techniques are currently being explored and developed to deal with the complicated and computationally demanding problems that can arise when modeling nanobiosystems. Although a relatively new field, mathematical descriptions of nanobiology are becoming increasingly more common and more important for both directing and interpreting experimental studies on nanobiosystems. The goal of this review is to emphasize the challenges associated with modeling nanobiosystems to inspire renewed effort in this highly interdisciplinary, but certainly rewarding, field.