Complex mathematical models of biology at the nanoscale

Abstract

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.

Nanoinformatics: a new area of research in nanomedicine

“…Bewick et al 101 have reported on the complexity arising from the inherent characteristics of natural biological systems. These include their heterogeneity, their multiscale space-time interactions, the noise generated in physical systems at the nanoscale, the strong coupling between processes that occur at different scales, and the challenging dimensionality size of data needed to represent typical biological systems.…”

“…These include their heterogeneity, their multiscale space-time interactions, the noise generated in physical systems at the nanoscale, the strong coupling between processes that occur at different scales, and the challenging dimensionality size of data needed to represent typical biological systems. 101 Jaramillo-Botoro et al 102 have suggested the typical components of a nanomedical model in terms of a five-level theoretical hierarchy: (1) quantum mechanics to determine electronic states, (2) force fields that result from averaging the electronic states and thereby obtaining atom-based forces, (3) simulations of atomic interactions based on force fields, (4) mesoscale or course-grained descriptions that average over many atoms, and (5) continuum mechanics using distributed properties for membranes, cells, tissues, and organs.…”

“…However, if too much complexity is assumed, mathematical models may prove too complex to be useful from a practical perspective. According to Bewick et al, 101 the challenges for nanobiosystem modeling are twofold. First, we must develop improved techniques for dealing with nanoscale biological complexity from a computational perspective.…”

Nanoinformatics: an emerging area of information technology at the intersection of bioinformatics, computational chemistry and nanobiotechnology

“…Computational chemistry is a powerful tool to design, model, simulate, and visualize nanomaterials (Gao, 2001) and nanoparticles, such as dendrimers (Belting and Wittrup, 2009;Diekmann and Lindhorst, 2002;Newkome and Shreiner, 2007;Selim and Lee, 2009) Computer-assisted nanomolecule design has emerged from recent advances in computational chemistry and nanotechnology and is considered well suited for assisting the experimental community in the design of new nanostructures (Bewick et al, 2009). The major advantage of computational nano-design is that it provides a relatively inexpensive and rapid way to explore many structural designs, including the study of stability and prediction of properties (Shapiro et al, 2008).…”

Tuning the Electronic Properties by Width and Length Modifications of Narrow- Diameter Carbon Nanotubes for Nanomedicine

“…Thus, the in silico modeling of NPs can assist in targeting and filling gaps in knowledge on the effects of these particular particles [6]. Computational models of the behaviour of NPs in biological systems [7] can be highly valuable in screening candidate particles for potential biomedical use in diagnostics, imaging and drug delivery. Chemically modified carbon nanotubes can act as nanoneedles easily crossing biological barriers and penetrating a variety of cell types [8,9].…”