Signaling in Small Subcellular Volumes. I. Stochastic and Diffusion Effects on Individual Pathways

Abstract

Many cellular signaling events occur in small subcellular volumes and involve low-abundance molecular species. This context introduces two major differences from mass-action analyses of nondiffusive signaling. First, reactions involving small numbers of molecules occur in a probabilistic manner which introduces scatter in chemical activities. Second, the timescale of diffusion of molecules between subcellular compartments and the rest of the cell is comparable to the timescale of many chemical reactions, altering the dynamics and outcomes of signaling reactions. This study examines both these effects on information flow through four protein kinase regulatory pathways. The analysis uses Monte Carlo simulations in a subcellular volume diffusively coupled to a bulk cellular volume. Diffusion constants and the volume of the subcellular compartment are systematically varied to account for a range of cellular conditions. Each pathway is characterized in terms of the probabilistic scatter in active kinase levels as a measure of "noise" on the pathway output. Under the conditions reported here, most signaling outcomes in a volume below one femtoliter are severely degraded. Diffusion and subcellular compartmentalization influence the signaling chemistry to give a diversity of signaling outcomes. These outcomes may include washout of the signal, reinforcement of signals, and conversion of steady responses to transients.

Dynamic Single-Cell Analysis for Quantitative Biology

“…Underlying the links between inputs and outputs are systems of interconnected molecular interactions, also known as signaling pathways. Cross talk between pathways, localization of reactions, and the small number of molecules involved in signaling lead to stochastic behavior in these systems (14,16,19,20). Because of their ubiquity and importance in cellular function, signaling pathways and the molecules involved have received the most attention from those researchers interested in the complex behaviors of cells and how they may be controlled or fixed when they have gone awry (20).…”

Stochastic hybrid modeling of intracellular calcium dynamics

“…51 However, in the present work, the need to use deterministic equations arises when one or more of the fluxes involved in the corresponding ODEs cannot be modeled as reactions. This does not depend on the number of molecules.…”

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

“…Noise has profound implications especially when the number of molecules is small, as in the case of transcription factors (Rao et al, 2002). Moreover, noise is further amplified in finite subvolumes such as the one used by the Virtual Cell because molecule numbers in each subvolume will be smaller than when they are taken as a whole (Bhalla, 2004). Therefore, stochastic based simulation approaches should be considered in such conditions.…”

“…Intracellular spatial features that can influence polymer assembly and function include the 3D position of subunits and polymer nucleation sites (Lutkenhaus, 2007), volume exclusion by polymer filaments (Haviv et al, 2006), molecular crowding (Popp et al, 2007;Wieczorek and Zielenkiewicz, 2008), intercompartmental interaction and subcellular localization of reacting molecules (Lutkenhaus, 2007), and diffusion-influenced reactions of molecules that are either small numbered or heterogeneously distributed (Shih et al, 2002;Lutkenhaus, 2007). Diffusion and small numbers of reacting molecules may also induce stochasticity (Rao et al, 2002;Bhalla, 2004;Wilkinson, 2009) in polymer assembly (VanBuren et al, 2002).…”

“…The phosphorylation state of target molecules with spatially separated membrane protein kinases and cytosolic phosphatases also depends heavily on diffusion (Kholodenko et al, 2000). In addition, subcompartments diffusively formed by localized proteins can significantly alter the effects of noise on signaling (Bhalla, 2004), implying the important coupling of noise and diffusion.…”