Simulated Diffusion of Phosphorylated CheY through the Cytoplasm of Escherichia coli

Abstract

Many aspects of the biochemistry and physiology of living cells have in the past been simulated by networks of reactions as though they were electronic circuits. In such studies, components such as receptors, enzymes, or metabolites are portrayed as being wired together in a spatially defined manner through enzymatic and other reactions. But it is clear that living circuitry is not like this; it has unique features such as a highly malleable internal architecture and the existence of a multitude of molecular states that differ in fundamental respects from those of silicon devices. Moreover, the wiring of the cell depends on the diffusive movement of myriad different molecules large and small through the watery interstices of the cytoplasm. In order to understand such systems, we need experimental techniques that can identify individual molecules and track their locations and movements within the cell. Moreover, once data of this kind are obtained we will need advanced computational methods by which spatial locations and diffusive movements of individual molecules can be represented.We recently developed a computer program for the study of intracellular reactions that allows us to take into account both the spatial location of proteins and protein complexes and their diffusive movements (1). This program uses an approach known as Brownian dynamics, in which molecules are treated as individuals rather than as concentrations and space is treated continuously instead of being subdivided into finite elements (10). Our program is called Smoldyn, for Smoluchowski dynamics, because it is based on a theory for the diffusive encounter of molecules in solution developed by the Polish physicist Marjan Smoluchowski (27). Since molecules are treated as individuals, this program can accurately capture stochastic behavior and also simulate diffusive gradients naturally and accurately. We were also inspired in our work by the MCell program, which has been developed to account for ionic and molecular events occurring within neuromuscular synapses (32). However, Smoldyn has certain advantages over MCell for our purposes since it allows reactions to occur between diffusing molecules in solution (in the current version of MCell, reactions occur only at membrane surfaces). Moreover, the code of Smoldyn, unlike that of MCell, is publicly available (http://sahara.lbl.gov/ϳsandrews/software.html).In this paper, we describe the application of Smoldyn to the well-characterized phenomenon of bacterial chemotaxis in Escherichia coli. We first predict the activity of the cluster of chemotactic receptors at one end of the cell in response to different stimulus conditions by using previously described software. We then use the temporal activity profile created in this way as an input to Smoldyn to calculate the locations of the diffusing molecules CheY, CheYp, and CheZ within the cell. As a first demonstration of the capabilities of this program, we report a series of simulations in which the diffusion of the signaling protein CheYp is followe...

Spatiotemporal modelling of CheY complexes in Escherichia coli chemotaxis

“…Previous studies have concluded that the localization of the phosphatase, CheZ, to the polar cluster, minimizes the formation of spatial gradients of CheY P along the length of the cell (Vaknin and Berg, 2004;Lipkow et al, 2005). In line with these studies, our model predicts that outside the polar regions there is a uniform concentration of free CheY P along the length of the cell.…”

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

“…Although these simulation results are coherent and in agreement with 2D simulations [36][37][38][39][40][41][44][45][46][47] , there are experimental 3D studies 31,35 that show a reverse result for the limiting diffusion coefficient and the anomalous diffusion exponent values.…”

“…Lipkow and his coworkers 46 have developed a computational program, Smoldyn, for studying cellular molecular processes taking into account both the spatial location of proteins (and their complexes) and their diffusive motion. This program has shown results in good agreement with experimental data for diffusion of signaling protein CheYp through the cell.…”

Regulation of kinase activity by diffusion and feedback

“…In a simple system in which kinase molecules are phosphorylated at the cell membrane and dephosphorylated by a phosphatase molecules located homogeneously in the cell cytosol (analyzed by Brown and Kholodenko 1999) small diffusion implies high gradient and low kinase activity in the cell center. The problem of receptor-kinase interaction has been also studied in the context of diffusion with obstacles in the stochastic numerical simulations of bacterial chemotaxis (Lipkow et al 2005). One of the conclusions of Lipkow et al 2005 is that crowding results in a fall of the apparent diffusion coefficient and at the anterior end, where CheY is phosphorylated, the local concentration of CheYp increases and therefore accelerates the response of the anterior close motor.…”

“…The problem of receptor-kinase interaction has been also studied in the context of diffusion with obstacles in the stochastic numerical simulations of bacterial chemotaxis (Lipkow et al 2005). One of the conclusions of Lipkow et al 2005 is that crowding results in a fall of the apparent diffusion coefficient and at the anterior end, where CheY is phosphorylated, the local concentration of CheYp increases and therefore accelerates the response of the anterior close motor. At the other, posterior, end of the cell, the local CheYp concentration is reduced by the need to diffuse through the obstacles and the responses of motors in this region is consequently delayed.…”