Biomedical subjects

I R Epstein

Publications and source records attributed to I R Epstein.

At least 19 recordsLinked to original sources

PubMed2001

Spatial periodic forcing of Turing structures.

Spontaneously evolving Turing structures in the chlorine dioxide-iodine-malonic acid reaction-diffusion system typically exhibit many defects that break the symmetry of the pattern. Periodic spatial forcing interacts with the Turing structures and modifies the pattern symmetry and wavelength. We investigate the role of the amplitude and wavelength of spatial periodic forcing on the hexagonal pattern of Turing structures. Experimental results and numerical simulations reveal that forcing at wavelengths slightly larger than the natural wavelength of the pattern is most effective in removing defects and producing ordered symmetric hexagonal patterns.

Journal Article↗

PubMed2001

Pattern formation in a tunable medium: the Belousov-Zhabotinsky reaction in an aerosol OT microemulsion.

Turing structures, standing waves, oscillatory clusters, and accelerating waves have been found in the spatially extended Belousov-Zhabotinsky system dispersed in water droplets of a reverse AOT microemulsion. The variety of patterns is determined by the tunable microstructure of the medium, i.e., by the concentration and size of water droplets. We propose a simple model to describe this system.

Aerosols↗

PubMed2001

Inwardly rotating spiral waves in a reaction-diffusion system.

Almost 30 years have passed since the discovery of concentric (target) and spiral waves in the spatially extended Belousov-Zhabotinsky (BZ) reaction. Since then, rotating spirals and target waves have been observed in a variety of physical, chemical, and biological reaction-diffusion systems. All of these waves propagate out from the spiral center or pacemaker. We report observations of inwardly rotating spirals found in the BZ system dispersed in water droplets of a water-in-oil microemulsion. These "antispirals" were also generated in computer simulations.

Journal Article↗

PubMed2001

Dynamics of kinks in one- and two-dimensional hyperbolic models with quasidiscrete nonlinearities.

We study the evolution of fronts in the Klein-Gordon equation when the nonlinear term is inhomogeneous. Extending previous works on homogeneous nonlinear terms, we describe the derivation of an equation governing the front motion, which is strongly nonlinear, and, for the two-dimensional case, generalizes the damped Born-Infeld equation. We study the motion of one- and two-dimensional fronts finding a much richer dynamics than in the homogeneous system case, leading, in most cases, to the stabilization of one phase inside the other. For a one-dimensional front, the function describing the inhomogeneity of the nonlinear term acts as a "potential function" for the motion of the front, i.e., a front initially placed between two of its local maxima asymptotically approaches the intervening minimum. Two-dimensional fronts, with radial symmetry and without dissipation can either shrink to a point in finite time, grow unboundedly, or their radius can oscillate, depending on the initial conditions. When dissipation effects are present, the oscillations either decay spirally or not depending on the value of the damping dissipation parameter. For fronts with a more general shape, we present numerical simulations showing the same behavior.

Journal Article↗

PubMed2001

Turing pattern formation induced by spatially correlated noise.

The effect of spatially correlated noise on Turing structures is analyzed both experimentally and numerically. Using the photosensitive character of the chlorine dioxide-iodine-malonic acid reaction-diffusion system, spatial randomness is introduced in the system. In the presence of noise, Turing patterns appear and are stable at levels of average illumination that would be more than sufficient to suppress pattern formation in the case of homogeneous illumination.

Journal Article↗

PubMed2001

Oscillatory clusters in the periodically illuminated, spatially extended Belousov-Zhabotinsky reaction.

Cluster-cluster transitions in the periodically illuminated photosensitive Belousov-Zhabotinsky (BZ) reaction-diffusion system exhibit the same scenario as in the autonomous BZ system with negative global feedback: two-phase clusters <--> three-phase clusters <--> irregular clusters <--> localized clusters. Transitions induced by changing the dark ( TD) or light ( TL) phases of the periodic external square wave illumination are dependent not only on the frequency of illumination at constant TD/TL, but also on the ratio TD/TL at constant frequency (when TD+TL = const).

Journal Article↗

PubMed2001

Resonant suppression of Turing patterns by periodic illumination.

We study the resonant behavior of Turing pattern suppression in a model of the chlorine dioxide-iodine-malonic acid reaction with periodic illumination. The results of simulations based on integration of partial differential equations display resonance at the frequency of autonomous oscillations in the corresponding well stirred system. The resonance in Turing pattern suppression is sharper at lower complexing agent concentration and is affected by the waveform of the periodic driving force. Square wave (on-off) periodic forcing is more effective in suppressing Turing patterns than sinusoidal forcing. We compare the dynamics of periodically forced Turing patterns with the dynamics of periodically forced nonhomogeneous states in a system of two identical coupled cells. Bifurcation analysis based on numerical continuation of the latter system gives good predictions for the boundaries of the major resonance regions of the periodically forced patterns.

Journal Article↗

PubMed2001

A new chemical system for studying pattern formation: bromate-hypophosphite-acetone-dual catalyst.

A modified version of the short-lived BrO3(-)-H2PO2(-)-Mn(II)-N2 oscillator, the BrO3(-)-H2PO2(-)-acetone-dual catalyst system, where the catalyst pair can be Mn(II)-Ru(bpy)3SO4, or Mn(II)-ferroin, or Mn(II)-diphenylamine, shows long-lasting batch oscillations in the potential of a Pt electrode and in colour, accompanying periodic transitions between the oxidised and reduced forms of the catalysts. Experimental conditions for the oscillations are established. The origin of the batch oscillations and the role of the catalyst pair in the oscillatory behaviour are discussed. The new system is ideally suited to the study of waves and patterns in reaction-diffusion systems, since in addition to the longevity of its spatial behaviour in batch, it produces no gaseous or solid products and exhibits significant photosensitivity.

Journal Article↗

PubMed1997

Calcium waves in a model with a random spatially discrete distribution of Ca2+ release sites.

We study the propagation of intracellular calcium waves in a model that features Ca2+ release from discrete sites in the endoplasmic reticulum membrane and random spatial distribution of these sites. The results of our simulations qualitatively reproduce the experimentally observed behavior of the waves. When the level of the channel activator inositol trisphosphate is low, the wave undergoes fragmentation and eventually vanishes at a finite distance from the region of initiation, a phenomenon we refer to as an abortive wave. With increasing activator concentration, the mean distance of propagation increases. Above a critical level of activator, the wave becomes stable. We show that the heterogeneous distribution of Ca2+ channels is the cause of this phenomenon.

Animals↗

PubMed1995

The consequences of imperfect mixing in autocatalytic chemical and biological systems.

When chemical reactions whose rate increases with the concentration of a product species are carried out in imperfectly mixed systems, a variety of complex behaviours can occur. These phenomena, which have relevance for biological processes as well, include chaotic and stochastic behaviour and selection of one final state over an equally probable alternative.

Catalysis↗

PubMed1994

Glycolytic pH oscillations in a flow reactor.

A new type of flow reactor (UCSTR) has been developed that uses anisotropic ultrafiltration membranes in a continuous flow stirred tank reactor (CSTR) to facilitate the study of nonlinear enzyme catalyzed reactions. The design allows the study of enzymes with subunit molecular weights > or = 9000 dalton and protein concentrations up to at least 2 mg/ml under flow conditions with a residence time of 3 min or more, in a reactor of volume 1.67 ml. The UCSTR allows continuous potentiometric or spectrophotometric measurement without design change. Calibration of reactor performance was carried out by reproducing pH oscillations in the ferrocyanide-hydrogen peroxide reaction. Experimental verification of oscillatory glycolysis in the UCSTR was carried out with extract of rat skeletal muscle. Input feeds were fructose-6-phosphate and ATP with low concentrations of phosphate as buffer. Oscillations in pH, sustained for over eight hours, were observed. A six-step mechanism, including product activation and substrate inhibition, seven concentration variables, and four enzymes sufficed simulate the pH oscillations observed in the UCSTR.

Animals↗

PubMed1992

A chemical approach to designing Turing patterns in reaction-diffusion systems.

A systematic approach is suggested to design chemical systems capable of displaying stationary, symmetry-breaking reaction diffusion patterns (Turing structures). The technique utilizes the fact that reversible complexation of an activator species to form an unreactive, immobile complex reduces the effective diffusion constant of the activator, thereby facilitating the development of Turing patterns. The chlorine dioxide/iodine/malonic acid reaction is examined as an example, and it is suggested that a similar phenomenon may occur in some biological pattern formation processes.

Journal Article↗

PubMed1992

Mathematical model of an identified stomatogastric ganglion neuron.

1. The ionic currents in the lateral pyloric (LP) cell of the stomatogastric ganglion (STG) described in the preceding paper of the rock crab Cancer borealis were fit with a set of differential equations that describe their voltage, time, and Ca2+ dependence. The voltage-dependent currents modeled are a delayed rectifier-like current, id; a Ca(2+)-activated outward current, io(Ca); a transient A-like current, iA; a Ca2+ current, iCa; an inwardly rectifying current, ih; and a fast tetrodotoxin (TTX)-sensitive Na+ current, iNa. 2. A single-compartment, isopotential model of the LP cell was constructed from the six voltage-dependent currents, a voltage-independent leak current il, a Ca2+ buffering system, and the membrane capacitance. 3. The behavior of the model LP neuron was compared with that of the biological neuron by simulating physiological experiments carried out in both voltage-clamp and current-clamp modes. The model and biological neurons show similar action-potential shapes, durations, steady-state current-voltage (I-V) curves, and respond to injected current in a comparable way.

Action Potentials↗

PubMed1992

Contribution of individual ionic currents to activity of a model stomatogastric ganglion neuron.

1. The behavior of the mathematical model for the lateral pyloric (LP) neuron of the crustacean stomatogastric ganglion (STG) developed in the previous paper was further studied. 2. The action of proctolin, a neuromodulatory peptide that acts directly on the LP neuron, was modeled. The effect of the proctolin-activated current (iproc) on the model neuron mimics the effects of proctolin on the isolated biological LP neuron. The depolarization and increased frequency of firing seen when iproc is activated are associated with changes in the relative contributions of the delayed rectifier (id) and the Ca(2+)-activated outward current (io(Ca] to the repolarization phase of the action potential. 3. The effects of turning off the A-current (iA) in the model were compared with those obtained by pharmacologically blocking iA in the biological neuron. iA appears to regulate action-potential frequency as well as postinhibitory rebound activity. 4. The role of iA on the rhythmic activity of the cell was studied by modifying several of its parameters while periodically activating a simulated synaptically activated conductance, isyn. 5. The effects of manipulations of the maximal conductances (g) for id and io(Ca) were studied. id strongly influences action-potential frequency, whereas io(Ca) strongly influences action-potential duration. 6. Modifications of the maximal conductance of the inward Ca2+ current (iCa) were compared with the effects of blocking iCa in the real cell. 7. The role of the hyperpolarization-activated inward current (ih) during ongoing rhythmic activity was assessed by periodically activating isyn while modifying ih.

Action Potentials↗

PubMed1991

Geometric phase shifts in chemical oscillators.

One of the most remarkable developments in quantum mechanics in recent years has been the discovery that when a system is moved adiabatically around a closed loop in parameter space there occurs, besides the familiar dynamical phase shift, an additional phase shift (sometimes referred to as 'Berry's phase') that is purely geometric in nature. The dynamical phase shift, which results from the variation of the period of the oscillatory system with the change in parameters, is relatively easily understood and is proportional to the time over which the parameter change occurs. The geometric phase shift, on the other hand, is less intuitive and depends on the curvature of the surface in parameter space bounded by the closed path, but is independent of the time taken to traverse the circuit. Here we present evidence for time-independent geometric phase shifts in numerical solutions for a model of an oscillating chemical reaction. The conditions for the occurrence of such shifts seem to be sufficiently general that geometric phase effects should be experimentally observable in essentially all chemical oscillators as well as in biological networks such as the brain and the central nervous system, where phase control is of vital importance.

Brain↗

PubMed1990

Multiple modes of a conditional neural oscillator.

We present a model for a conditional bursting neuron consisting of five conductances: Hodgkin-Huxley type time- and voltage-dependent Na+ and K+ conductances, a calcium activated voltage-dependent K+ conductance, a calcium-inhibited time- and voltage-dependent Ca++ conductance, and a leakage Cl- conductance. With an initial set of parameters (version S), the model shows a hyperpolarized steady-state membrane potential at which the neuron is silent. Increasing gNa and decreasing gCl, where gi is the maximal conductance for species i, produces bursts of action potentials (Burster N). Alternatively, an increase in gCa produces a different bursting state (Burster C). The two bursting states differ in the periods and amplitudes of their bursting pacemaker potentials. They show different steady-state I-V curves under simulated voltage-clamp conditions; in simulations that mimic a steady-state I-V curve taken under experimental conditions only Burster N shows a negative slope resistance region. Model C continues to burst in the presence of TTX, while bursting in Model N is suppressed in TTX. Hybrid models show a smooth transition between the two states.

Action Potentials↗

PubMed1989

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution.

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.

Kinetics↗

PubMed1988

Kinetics of actin-myosin binding. Myosin cooperativity and mixed single-headed and two-headed binding.

A model is proposed for the kinetics of actin-myosin interaction that allows for the presence of both one- and two-headed myosin fragments, cooperativity between myosin sites, and the molecular weight distribution of actin filaments. The approach employed makes use of the notion of effectivity factors. In the most general case, the system is described by six coupled first-order differential equations. When only single-headed myosin (S1) is present, the model reduces to simpler versions introduced previously.

Actins↗