Kinetic Modeling of the Assembly, Dynamic Steady State, and Contraction of the FtsZ Ring in Prokaryotic Cytokinesis

Abstract

Cytokinesis in prokaryotes involves the assembly of a polymeric ring composed of FtsZ protein monomeric units. The Z ring forms at the division plane and is attached to the membrane. After assembly, it maintains a stable yet dynamic steady state. Once induced, the ring contracts and the membrane constricts. In this work, we present a computational deterministic biochemical model exhibiting this behavior. The model is based on biochemical features of FtsZ known from in vitro studies, and it quantitatively reproduces relevant in vitro data. An essential part of the model is a consideration of interfacial reactions involving the cytosol volume, where monomeric FtsZ is dispersed, and the membrane surface in the cell's mid-zone where the ring is assembled. This approach allows the same chemical model to simulate either in vitro or in vivo conditions by adjusting only two geometrical parameters. The model includes minimal reactions, components, and assumptions, yet is able to reproduce sought-after in vivo behavior, including the rapid assembly of the ring via FtsZ-polymerization, the formation of a dynamic steady state in which GTP hydrolysis leads to the exchange of monomeric subunits between cytoplasm and the ring, and finally the induced contraction of the ring. The model gives a quantitative estimate for coupling between the rate of GTP hydrolysis and of FtsZ subunit turnover between the assembled ring and the cytoplasmic pool as observed. Membrane constriction is chemically driven by the strong tendency of GTP-bound FtsZ to self-assembly. The model suggests a possible mechanism of membrane contraction without a motor protein. The portion of the free energy of GTP hydrolysis released in cyclization is indirectly used in this energetically unfavorable process. The model provides a limit to the mechanistic complexity required to mimic ring behavior, and it highlights the importance of parallel in vitro and in vivo modeling.

Biological Insights from a Simulation Model of the Critical FtsZ Accumulation Required for Prokaryotic Cell Division

“…CAM-FF takes as its point of departure the "Z-centric hypothesis" (viz., assembly of the Z-ring and the force of its constriction originate from FtsZ) and extends earlier work by Surovtsev et al 8 Key assumptions are (i) no dependence of Z-ring formation on the cyclisation of FtsZ polymers into closed rings (cf.…”

“…Surovtsev et al, 8 ), (ii) the addition of the diffusion of FtsZ into the midcell region, and (iii) the interaction of FtsZ polymers with membrane-binding proteins.…”

“…(Although GDP-bound FtsZ has been shown to polymerise, the equilibrium constant is significantly lower than for GTP 10 and was assumed to equal 0 in the original Surovtsev model. 8 8. The initiation threshold value α is 20,000; the wild-type contraction parameter value χ is sufficient to allow full division with the capacity to lose 15% of its value before division behaviour is affected.…”

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

“…Almost all of these polymers are dynamic, carrying out their functions through carefully orchestrated assembly, disassembly and redistribution of polymer subunits. It is becoming increasingly evident that quantitative models of polymerization are necessary to understand the collective dynamics of subunits and interacting molecules (Haviv et al, 2006;Kozlowski et al, 2007;Schek et al, 2007;Surovtsev et al, 2008;Loose et al, 2008). Polymerization models are also used to estimate subunit binding energy and activation rates (Lan et al, 2008).…”

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

“…Although a variety of quantitative methods have been developed to model protein polymerization dynamics (Haviv et al, 2006;Kozlowski et al, 2007;Schek et al, 2007;Surovtsev et al, 2008;Loose et al, 2008;Cytrynbaum and Marshall, 2007;Lan et al, 2008;Miraldi et al, 2008), many of the properties above have been omitted primarily because of the computational cost and complexity. In this chapter, we extend Spatiocyte to model polymerization of proteins and show that it can incorporate the above properties while still maintaining a reasonable computational time.…”