Anatol M. Zhabotinsky

A Model of Synaptic Memory: A CaMKII/PP1 Switch that Potentiates Transmission by Organizing an AMPA Receptor Anchoring Assembly

Ca2+/calmodulin-dependent protein kinase II (CaMKII) is localized in the postsynaptic density (PSD) and is necessary for LTP induction. Much has been learned about the autophosphorylation of CaMKII and its dephosphorylation by PSD protein phosphatase-1 (PP1). Here, we show how the CaMKII/PP1 system could function as an energy-efficient, bistable switch that could be activated during LTP induction and remain active despite protein turnover. We also suggest how recently discovered binding interactions could provide a structural readout mechanism: the autophosphorylated state of CaMKII binds tightly to the NMDAR and forms, through CaMKII-actinin-actin-(4.1/SAP97) linkages, additional sites for anchoring AMPARs at synapses. The proposed model has substantial experimental support and elucidates principles by which a local protein complex could produce stable information storage and readout.

Autowave processes in a distributed chemical system

Abstract The autowave processes with a characteristic wavelength and oscillation period may arise under some initial conditions in a uniform active medium. The wavelength and period depend on the chemical and physical parameters of the system and are independent of the initial and boundary conditions and of the system linear size. The processes occur in a homogeneous solution in the course of an oscillating chemical reaction. Similar processes may play an important role in the phenomena of short-term memory, cardiac arrhythmia, morphogenesis and prebiological evolution. Different types of structures are discussed, and experimental data and mathematical models are presented.

The stability of a stochastic CaMKII switch: dependence on the number of enzyme molecules and protein turnover.

Molecular switches have been implicated in the storage of information in biological systems. For small structures such as synapses, these switches are composed of only a few molecules and stochastic fluctuations are therefore of importance. Such fluctuations could potentially lead to spontaneous switch reset that would limit the lifetime of information storage. We have analyzed a model of the calcium/calmodulin-dependent protein kinase II (CaMKII) switch implicated in long-term memory in the nervous system. The bistability of this switch arises from autocatalytic autophosphorylation of CaMKII, a reaction that is countered by a saturable phosphatase-1-mediated dephosphorylation. We sought to understand the factors that control switch stability and to determine the functional relationship between stability and the number of molecules involved. Using Monte Carlo simulations, we found that the lifetime of states of the switch increase exponentially with the number of CaMKII holoenzymes. Switch stability requires a balance between the kinase and phosphatase rates, and the kinase rate must remain high relative to the rate of protein turnover. Thus, a critical limit on switch stability is set by the observed turnover rate (one per 30 h on average). Our computational results show that, depending on the timescale of fluctuations in enzyme numbers, for a switch composed of about 15 CaMKII holoenzymes, the stable persistent activation can span from a few years to a human lifetime.

Bistability in the Ca2+/Calmodulin-Dependent Protein Kinase-Phosphatase System

A mathematical model is presented of autophosphorylation of Ca(2+)/calmodulin-dependent protein kinase (CaMKII) and its dephosphorylation by a phosphatase. If the total concentration of CaMKII subunits is significantly higher than the phosphatase Michaelis constant, two stable steady states of the CaMKII autophosphorylation can exist in a Ca(2+) concentration range from below the resting value of the intracellular [Ca(2+)] to the threshold concentration for induction of long-term potentiation (LTP). Bistability is a robust phenomenon, it occurs over a wide range of parameters of the model. Ca(2+) transients that switch CaMKII from the low-phosphorylated state to the high-phosphorylated one are in the same range of amplitudes and frequencies as the Ca(2+) transients that induce LTP. These results show that the CaMKII-phosphatase bistability may play an important role in long-term synaptic modifications. They also suggest a plausible explanation for the very high concentrations of CaMKII found in postsynaptic densities of cerebral neurons.

A history of chemical oscillations and waves

The history of the discovery and study of chemical oscillations and waves is presented from the very first accidental observations up to the systematic design of chemical oscillators. Special emphasis is devoted to the long-term debate over the possibility of pure chemical oscillations, i.e., concentration oscillations in homogeneous closed systems.

Pattern formation arising from interactions between Turing and wave instabilities

We study pattern formation arising from the interaction of the stationary Turing and wave (oscillatory Turing) instabilities. Interaction and competition between these symmetry-breaking modes lead to the emergence of a large variety of spatiotemporal patterns, including modulated Turing structures, modulated standing waves, and combinations of Turing structures and spiral waves. Spatial resonances are obtained near codimension-two Turing-wave bifurcations. Far from bifurcation lines, we obtain inwardly propagating spiral waves with Turing spots at their tips. We demonstrate that the coexistence of Turing spots and traveling waves is a result of interaction between Turing and oscillatory modes, while the inwardly propagating waves (antispirals) do not require this interaction; they can arise from the wave instability combined with a negative group velocity.

Role of the Neurogranin Concentrated in Spines in the Induction of Long-Term Potentiation

Synaptic plasticity in CA1 hippocampal neurons depends on Ca2+ elevation and the resulting activation of calmodulin-dependent enzymes. Induction of long-term depression (LTD) depends on calcineurin, whereas long-term potentiation (LTP) depends on Ca2+/calmodulin-dependent protein kinase II (CaMKII). The concentration of calmodulin in neurons is considerably less than the total concentration of the apocalmodulin-binding proteins neurogranin and GAP-43, resulting in a low level of free calmodulin in the resting state. Neurogranin is highly concentrated in dendritic spines. To elucidate the role of neurogranin in synaptic plasticity, we constructed a computational model with emphasis on the interaction of calmodulin with neurogranin, calcineurin, and CaMKII. The model shows how the Ca2+ transients that occur during LTD or LTP induction affect calmodulin and how the resulting activation of calcineurin and CaMKII affects AMPA receptor-mediated transmission. In the model, knockout of neurogranin strongly diminishes the LTP induced by a single 100 Hz, 1 s tetanus and slightly enhances LTD, in accord with experimental data. Our simulations show that exchange of calmodulin between a spine and its parent dendrite is limited. Therefore, inducing LTP with a short tetanus requires calmodulin stored in spines in the form of rapidly dissociating calmodulin–neurogranin complexes.

Pattern formation arising from wave instability in a simple reaction‐diffusion system

Pattern formation is studied numerically in a three‐variable reaction‐diffusion model with onset of the oscillatory instability at a finite wavelength. Traveling and standing waves, asymmetric standing‐traveling wave patterns, and target patterns are found. With increasing overcriticality or system length, basins of attraction of more symmetric patterns shrink, while less symmetric patterns become stable. Interaction of a defect with an impermeable boundary results in displacement of the defect. Fusion and splitting of defects are observed.

Turing patterns beyond hexagons and stripes.

The best known Turing patterns are composed of stripes or simple hexagonal arrangements of spots. Until recently, Turing patterns with other geometries have been observed only rarely. Here we present experimental studies and mathematical modeling of the formation and stability of hexagonal and square Turing superlattice patterns in a photosensitive reaction-diffusion system. The superlattices develop from initial conditions created by illuminating the system through a mask consisting of a simple hexagonal or square lattice with a wavelength close to a multiple of the intrinsic Turing patterns wavelength. We show that interaction of the photochemical periodic forcing with the Turing instability generates multiple spatial harmonics of the forcing patterns. The harmonics situated within the Turing instability band survive after the illumination is switched off and form superlattices. The square superlattices are the first examples of time-independent square Turing patterns. We also demonstrate that in a system where the Turing band is slightly below criticality, spatially uniform internal or external oscillations can create oscillating square patterns.

Spatio-temporal patterns in a reaction–diffusion system with wave instability

An intraocular lens implantation forceps, including first and second arms having handles and lens engagement blades; the blades extending generally longitudinally in laterally spaced relation and at opposite sides of a plane bisecting the forceps. The arms have primary and secondary arm sections extending between the handles and blades. The arms primary sections extend in cross-over relation to define a cross-over locus, when the blades are in open position; the secondary arm sections extending generally longitudinally in substantially parallel relation and positioned such that when the blades are in the closed positions one secondary arm section extends at one side of the plane and the other secondary arm section extends at the other side of the plane, and when the blades are in the open positions the one secondary arm section extends at the other side of the plane and the other secondary arm section extends at the one side of the plane.