Pattern Formation inside Bacteria: Fluctuations due to the Low Copy Number of Proteins

Abstract

We examine fluctuation effects due to the low copy number of proteins involved in pattern-forming dynamics within a bacterium. We focus on a stochastic model of the oscillating MinCDE protein system regulating accurate cell division in E. coli. We find that, for some parameter regions, the protein concentrations are low enough that fluctuations are essential for the generation of patterns. We also examine the role of fluctuations in constraining protein concentration levels.

Frequency of elemental events of intracellularCa2+dynamics

“…Such a small number of interacting molecules demands a stochastic approach, because fluctuations cannot be neglected anymore as deterministic modeling does. In the MinCDE system for example, only a few thousand molecules are expressed [4]. It exhibits oscillations where the deterministic equations decay to a stationary fixed point.…”

A Mechanism for Polar Protein Localization in Bacteria

“…43 As for the membrane diffusion constants, we have used similarly small values to those used in E. coli. 24,27 Previously this was an important component in the spontaneous reactiondiffusion instability; this is, however, not the case here: the small membrane diffusivities are now necessary to preserve the polar density concentration maxima and to prevent the concentrations from equalizing everywhere along the cell membrane. For the remaining parameters there is no experimental guidance, but we have taken care to check that our results are robust to variations in these parameters.…”

“…This is again similar to some of the models used for E. coli. 24,26,27 The relevant set of one-dimensional reaction-diffusion equations are:…”

“…Recently, several groups have employed simple reaction-diffusion mathematical models (either deterministic 24 -26 or stochastic 27 ) to try to understand the MinCDE dynamics (see also Meinhardt 28 and Hunding et al 29 for related models). The principal result of this modeling effort is that the oscillations are a spontaneous self-organized phenomena arising from an intrinsic instability of the reaction-diffusion dynamics.…”

Modeling Three-Dimensional Spatial Regulation of Bacterial Cell Division (Dissertation)

“…Even though many computational models of the MinDE system have been proposed (Howard et al, 2001;Meinhardt and de Boer, 2001;Kruse, 2002;Howard and Rutenberg, 2003;Huang et al, 2003;Drew et al, 2005;Kerr et al, 2006;Fange and Elf, 2006;Pavin et al, 2006;Tostevin and Howard, 2006;Cytrynbaum and Marshall, 2007;Loose et al, 2008;Derr et al, 2009;Borowski and Cytrynbaum, 2009), the possibility that MinE is transiently attached to the membrane to form the dense E-ring has not been investigated at single molecule resolution in three-dimensional (3D) space.…”