The delicate bistability of CaMKII.

Calcium/calmodulin-dependent protein kinase II (CaMKII) is a synaptic, autophosphorylating kinase that is essential for learning and memory. Previous models have suggested that CaMKII functions as a bistable switch that could be the molecular correlate of long-term memory, but experiments have failed to validate these predictions. These models involved significant approximations to overcome the combinatorial complexity inherent in a multisubunit, multistate system. Here, we develop a stochastic particle-based model of CaMKII activation and dynamics that overcomes combinatorial complexity without significant approximations. We report four major findings. First, the CaMKII model system is never bistable at resting calcium concentrations, which suggests that CaMKII activity does not function as the biochemical switch underlying long-term memory. Second, the steady-state activation curves are either laserlike or steplike. Both are characterized by a well-defined threshold for activation, which suggests that thresholding is a robust feature of this system. Third, transiently activated CaMKII can maintain its activity over the time course of many experiments, and such slow deactivation may account for the few reports of bistability in the literature. And fourth, under in vivo conditions, increases in phosphatase activity can increase CaMKII activity. This is a surprising and counterintuitive effect, as dephosphorylation is generally associated with CaMKII deactivation.

CaMKII activation and dynamics are independent of the holoenzyme structure: an infinite subunit holoenzyme approximation.

The combinatorial explosion produced by the multi-state, multi-subunit character of CaMKII has made analysis and modeling of this key signaling protein a significant challenge. Using rule-based and particle-based approaches, we construct exact models of CaMKII holoenzyme dynamics and study these models as a function of the number of subunits per holoenzyme, N. Without phosphatases the dynamics of activation are independent of the holoenzyme structure unless phosphorylation significantly alters the kinase activity of a subunit. With phosphatases the model is independent of holoenzyme size for N > 6. We introduce an infinite subunit holoenzyme approximation (ISHA), which simplifies the modeling by eliminating the combinatorial complexities encountered in any finite holoenzyme model. The ISHA is an excellent approximation to the full system over a broad range of physiologically relevant parameters. Finally, we demonstrate that the ISHA reproduces the behavior of exact models during synaptic plasticity protocols, which justifies its use as a module in large models of synaptic plasticity.

A model actin comet tail disassembling by severing.

We use a numerical simulation to model an actin comet tail as it grows from the surface of a small object (a bead) and disassembles by severing. We explore the dependence of macroscopic properties such as the local tail radius and tail length on several controllable properties, namely the bead diameter, the bead velocity, the severing rate per unit length, and the actin gel mesh size. The model predicts an F-actin density with an initial exponential decay followed by an abrupt decay at the edge of the tail, and predicts that the comet tail diameter is constant along the length of the tail. The simulation results are used to fit a formula relating the comet tail length to the control parameters, and it is proposed that this formula offers a means to extract quantitative information on the actin gel mesh size and severing kinetics from simple macroscopic measurements.

The effects of filament aging and annealing on a model lamellipodium undergoing disassembly by severing.

We use numerical simulations to study the properties of a model lamellipodium as it disassembles by filament severing. The growing lamellipodium is modeled as a 2D or 3D periodic lattice of crosslinked actin filaments. At each time step a new layer of actin filaments is added at the membrane, existing filaments are severed stochastically and disconnected sections of the network are removed. Filament aging is modeled by including several different filament chemical states. Filament annealing is included by allowing existing filaments to grow new filaments. The properties of the model are studied as functions of the number of states and the severing and annealing rates. The network width is proportional to the sum of the average lifetimes of the states, and is well modeled by a simple kinetic theory. The length of the network scales linearly with actin concentration and has a finite width even at high severing protein concentrations. The edge of the growing network becomes sharper as either the number of states or the dimensionality is increased. Annealing increases the average length of the network, and the network length diverges at a critical annealing rate.

Continuum theory for nanotube piezoelectricity.

We develop and solve a continuum theory for the piezoelectric response of one-dimensional nanotubes and nanowires, and apply the theory to study electromechanical effects in boron-nitride nanotubes. We find that the polarization of a nanotube depends on its aspect ratio, and a dimensionless constant specifying the ratio of the strengths of the elastic and electrostatic interactions. The solutions of the model as these two parameters are varied are discussed. The theory is applied to estimate the electric potential induced along the length of a boron-nitride nanotube in response to a uniaxial stress.