Reaction‐Diffusion Systems in Intracellular Molecular Transport and Control

Abstract

Chemical reactions make cells work only if the participating chemicals are delivered to desired locations in a timely and precise fashion. While most research to date has focused on the so-called active-transport mechanisms, “passive” diffusion is often equally rapid and is always energetically less costly. Capitalizing on these advantages, cells have developed sophisticated reaction-diffusion (RD) systems that control a wide range of cellular functions – from chemotaxis and cell division, through signaling cascades and oscillations, to cell motility. Despite their apparent diversity, these systems share many common features and are “wired” according to “generic” motifs involving non-linear kinetics, autocatalysis, and feedback loops. Understanding the operation of these complex (bio)chemical systems requires the analysis of pertinent transport-kinetic equations or, at least on a qualitative level, of the characteristic times describing constituent sub-processes. Therefore, in reviewing the manifestations of cellular RD, we also attempt to familiarize the reader with the basic theory of these processes.

Spatiotemporal control of microtubule nucleation and assembly using magnetic nanoparticles

“…Remarkable studies have enabled the discovery of intracellular gradients of RanGTP, stimulated by RCC1 and emanating from chromosomes, which can be described as a reaction-diffusion process that supports the spindle machinery in cell division 27,29,[35][36][37] . Interestingly, by manipulating RanQ69L-GTP and RCC1 signalling grafted to magnetic nanoparticles, we have demonstrated experimentally how cascading reaction-diffusion signals may directly influence the position of asymmetric microtubule arrays.…”

Microscopic agents programmed by DNA circuits

“…We analytically solved the steady-state concentration profile generated by shell-like selfactivating particles in the presence of a global sink (Supplementary Note 2). Above a critical size, or grafting density, a stable concentration profile is generated, the precise mathematical expression of which will depend on the dimensionality of the problem 23 , but whose length parameter is always controlled by (where D is the diffusion rate and k the first-order degradation rate for the signaling compound). Under our conditions, these parameters are D = 18 × 10 3 μm 2 min −1 and k = 0.07 min −1 (Supplementary Note 3), suggesting that active particles generate a steady-state diffusion 'cone' with a length scale of ∼500 μm.…”

Physical‐Organic Chemistry: A Swiss Army Knife

“…(Whether these synthetic methods apply in the peribiotic environment is another question.) There is, however, still no compelling understanding of how these reactions and molecules began to self-assemble-to put themselves together-to form the first cells, in the chaotic, heterogeneous, peribiotic world [106][107][108] .…”