J. J. Morgan

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

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 cells 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.

A Mathematical Model of the Spread of Feline Leukemia Virus (FeLV) Through a Highly Heterogeneous Spatial Domain

We are concerned with a system of partial differential equations modeling the spread of feline leukemia virus (FeLV) through highly heterogeneous habitats or spatial domains. Our differential equations may feature discontinuities in the coefficients of divergence from differential operators and discontinuities in the coupling terms. Global well posedness, long term behavior, approximation, and homogenization results are provided.

Stability and Lyapunov functions for reaction-diffusion systems

It is shown for a large class of reaction-diffusion systems with Neumann boundary conditions that in the presence of a separable Lyapunov structure, the existence of an a priori

Mathematical Model of a Cell Size Checkpoint

L^r

Interior estimates for a class of reaction-diffusion systems from L1 a priori estimates

estimate, uniform in time, for some

The existence of periodic solutions to reaction-diffusion systems with periodic data

r>0

Mathematical model for positioning the FtsZ contractile ring in Escherichia coli

, implies the

Modeling the Circulation of a Disease Between Two Host Populations on non Coincident Spatial Domains

L^\infty

Eventually uniform bounds for a class of quasipositive reaction diffusion systems

-uniform stability of steady states. The results are applied to a general class of Lotka--Volterra systems and are seen to provide a partial answer to the global existence question for a large class of balanced systems with nonlinearities that are not bounded by any polynomial.

An outbreak vector-host epidemic model with spatial structure: the 2015–2016 Zika outbreak in Rio De Janeiro

How cells regulate their size from one generation to the next has remained an enigma for decades. Recently, a molecular mechanism that links cell size and cell cycle was proposed in fission yeast. This mechanism involves changes in the spatial cellular distribution of two proteins, Pom1 and Cdr2, as the cell grows. Pom1 inhibits Cdr2 while Cdr2 promotes the G2 → M transition. Cdr2 is localized in the middle cell region (midcell) whereas the concentration of Pom1 is highest at the cell tips and declines towards the midcell. In short cells, Pom1 efficiently inhibits Cdr2. However, as cells grow, the Pom1 concentration at midcell decreases such that Cdr2 becomes activated at some critical size. In this study, the chemistry of Pom1 and Cdr2 was modeled using a deterministic reaction-diffusion-convection system interacting with a deterministic model describing microtubule dynamics. Simulations mimicked experimental data from wild-type (WT) fission yeast growing at normal and reduced rates; they also mimicked the behavior of a Pom1 overexpression mutant and WT yeast exposed to a microtubule depolymerizing drug. A mechanism linking cell size and cell cycle, involving the downstream action of Cdr2 on Wee1 phosphorylation, is proposed.