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I Z Steinberg

Publications and source records attributed to I Z Steinberg.

At least 19 recordsLinked to original sources
PubMed1996

On the analytic solution of electrotonic spread in branched passive dendritic trees.

From the classical work of Rall it is known that the spread of electric potential in a passive dendritic tree may be obtained by expressing the initial conditions as a linear combination of a set of trigonometric eigenfunctions, each decaying with the associated time constant. It is shown here that in order to evaluate the permissible parameters in these eigenfunctions one may formulate the boundary conditions at all the junctions and endings of the dendritic tree as a set of homogeneous linear equations in which the parameters in the eigenfunctions are the unknowns. These equations have a nontrivial solution if the relevant determinant vanishes, a condition that permits the evaluation of the various parameters, thus providing an analytic approach to the expression of the eigenfunctions as well as the decay time constants. The above approach is illustrated by application to a dendritic tree that has a parent segments and two generations of offspring segments, without any restrictions as to the relative diameters or lengths of the various segments in the tree. General properties of the tree may be readily derived, like the variation of the eigenvalues on scaling of the lengths or diameters of all the segments. A few special cases with specified dimensions of the various segments are derived from the general case. In the case of a dendritic tree that fulfills the "equivalent cylinder" conditions, all of the eigenvalues and eigenfunctions of the tree may be determined by the proposed method, including those that do not apply to the equivalent cylinder. The orthogonality properties of the eigenfunctions are discussed.

Animals↗
PubMed1994

Brownian motion of the end-to-end distance in oligopeptide molecules: numerical solution of the diffusion equations as coupled first order linear differential equations.

The Brownian motion of one end of an oligopeptide molecule relative to its other end was previously studied by the measurement of non-radiative energy transfer between chromophores attached to the molecular ends, and was found to conform to a model which describes this motion as a diffusional process in a force field (Haas et al., 1978a). The theoretical treatment of this diffusional problem is performed here by an approach which is different from the one used previously. In this approach advantage is taken of the fact that in the case under consideration the rate of change of the concentration of molecules with a given end-to-end distance is linearly dependent on the instantaneous concentration at this and neighboring end-to-end distances. One thus obtains a set of coupled first-order linear differential equations, which can be solved by standard techniques involving the diagonalization of the matrix of the rate constants in the above set of coupled equations. The concentration distribution at any instant is subsequently obtained as a linear combination of the eigenvectors weighted according to their respective exponential decay with time with rate constants which are related to their respective eigenvalues. Some of the advantages offered by this approach are as follows: one does not have to start the procedure from the beginning if new initial conditions are desired, and the concentration distribution at any given instant is obtained directly without the need of a stepwise build-up of the solution with time. The latter point is especially useful if one is interested in the asymptotic behavior of the changes in concentration at long times, since this behavior can be readily expressed as an exponential decay of the longest-lived eigenvector (or the sum of a few exponentially decaying eigenvectors which have the longest decay times). The above approach is used to treat the energy-transfer experiments performed previously by Haas et al. (1978b), as well as to simulate the dynamics of ring-opening of cyclic oligopeptides and ring closure of linear peptides.

Computer Simulation↗
PubMed1988

Computer simulations of the effect of non-inactivating sodium channels on the electric behavior of excitable cells.

Non-inactivating sodium channels have been discovered in various cell types. Additionally, normal voltage-gated sodium channels can be induced to lose their ability to inactivate by treatment with proteolytic enzymes, with certain chemical reagents, or with toxins. The presence of non-inactivating sodium channels in the outer membrane of a cell is expected to profoundly modify the electrical properties of the cell, because the electrical depolarization of the cell and the opening of these channels reciprocally reinforce each other without intrinsic control. The normal resting state may thus be destabilized and a new resting state at depolarized resting potentials may become possible. In this study, computer simulations were carried out to systematically explore the patterns of behavior of excitable cells which have non-inactivating sodium channels in their plasma membrane. The cells were assumed to be space clamped and the relevant Hodgkin and Huxley equations were assumed to describe the electrical behavior of the cells, except that some or all of the sodium channels could not inactivate. The sodium currents were thus represented by the sum of two terms: FI.gNa.m3.h.(V-ENa) + (1-FI).gNa.m3(V-ENa), where FI(0 less than or equal to FI less than or equal to 1) is the fraction of sodium channels which inactivate normally, and the other symbols have their usual significance. The behavior of non-inactivating sodium channels created by pronase treatment or reaction with chemical reagents was found to conform with that predicted by the second term in this expression. The simulations thus quantitatively apply to excitable cells thus treated, but may serve additionally to qualitatively illustrate patterns of electrical activity induced by non-inactivating sodium channels also in other cases. A variety of possible types of electrical behavior was obtained: Normal behavior, including capability of firing action potentials, requires values of FI which are not far from unity, the permissible range depending on the fully activated potassium ion conductance, gK. Bistability, at which the cell may exist in one of two stable states of different resting potential, occurs when the value of FI is lowered. Transitions from the polarized to the depolarized resting states, and vice versa, may be brought about by depolarizing and hyperpolarizing triggers, respectively. Such behavior is like that of memory storage devices. Monostability at depolarized potentials is favored by low FI values and can occur if gK is less than the Hodgkin and Huxley value.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗
PubMed1987

Relationship between statistical properties of single ionic channel recordings and the thermodynamic state of the channels.

Recordings of the electric conductivity of a single ionic channel usually exhibit two levels of conductance: a zero and a finite level. The channel may, however, be in a few states which have the same conductivity level, and the distribution of dwell time durations at this conductivity level is thus not monoexponential. It is shown that the joint probability p(tc,to) of the occurrence of a time interval tc during which the channel is not conducting, immediately followed by a time interval to during which the channel is conducting may or may not be equal to the joint probability pr(tc,to) of the occurrence of a non-conducting interval tc preceded by a conducting interval to. If the interconversions between the various states in which the channel can exist obey detailed balance, i.e., if the channel behaves like a system at thermodynamic equilibrium, then p(tc,to) = pr(tc,to). This should help to reveal whether irreversible processes, like metabolic reactions or flows of substances across the membrane, are coupled to the gating process of the ionic channels.

Electric Conductivity↗
PubMed1987

Frequencies of paired open-closed durations of ion channels. Method of evaluation from single-channel recordings.

The probability of the occurrence of consecutive closed-open or open-closed intervals of specified durations in single-channel recordings may be of enormous help in the establishment of the kinetic scheme that describes the behavior of the channel. The relevant probability functions are linear combinations of products of exponential functions of the closed durations and the open durations. A method is presented for the evaluation of the coefficients of the exponential functions using a set of auxiliary functions that are each orthogonal to all but one of the exponential functions. The coefficients in the probability functions may then be obtained from the experimental data by multiplication by the auxiliary functions and subsequent simple integration operations. Furthermore, the variance to be expected in the evaluated numerical magnitude of the parameters, due to the stochastic nature of the transitions in the channel conductance, is also readily estimated by use of the above auxiliary functions. The procedure is illustrated by analysis of synthetic data obtained from computer simulated experiments.

Computer Graphics↗
PubMed1986

On the time reversal of noise signals.

This paper addresses the question of whether, and under what conditions, a noise trace changes its statistical properties when the time axis is reversed in direction. The autocorrelation function of the noise or its power spectrum cannot be used to identify the directionality of time in a noise signal since both are always the same for the signal and for its time reverse, regardless of the characteristics of the noise. However, the autocorrelation function can be generalized to represent the average of the products of powers of the signal at pairs of time instances separated by a given interval. If the powers are not the same for the first and second time instances, the generalized autocorrelation function can detect whether the statistical properties of a noise signal change upon the reversal of the direction of the time axis. We show that noise generated by systems that obey microscopic reversibility, i.e., that are at thermodynamic equilibrium, show the same statistical properties when evaluated forward and backward in time. A noise signal that does not demonstrate such time-reversal behavior discloses that the system that generates it is not at thermodynamic equilibrium. Several model examples are presented for illustration.

Kinetics↗
PubMed1984

Intramolecular dynamics of chain molecules monitored by fluctuations in efficiency of excitation energy transfer. A theoretical study.

The fluorescence quantum yield of a polymer molecule to which an energy donor chromophore and an energy acceptor chromophore are attached depends on the distance between the donor and acceptor chromophores. If this distance fluctuates with time, the fluorescence intensity is expected to fluctuate as well, and the time course of the intensity fluctuations will be correlated with the time course of the changes in the interchromophore distance. The intensity fluctuations are experimentally measurable if the number of illuminated molecules is small. A theoretical treatment of such fluorescence intensity fluctuations is presented in terms of a parameter that describes the polymer chain dynamics. Computer simulations were performed to illustrate the dependence of the autocorrelation function of the intensity fluctuations on the polymer chain conformation, the interchromophore energy transfer properties, and the macromolecular dynamics. These simulations demonstrate that the intensity fluctuations due to nonradiative energy transfer between chromophores attached to polymer chains can be large enough to be experimentally useful in the study of intramolecular dynamics of macromolecules.

Biopolymers↗
PubMed1981

Presynaptic calcium currents in squid giant synapse.

A voltage clamp study has been performed in the presynaptic terminal of the squid stellate ganglion. After blockage of the voltage-dependent sodium and potassium conductances, an inward calcium current is demonstrated. Given a step-depolarization pulse, this voltage- and time-dependent conductance has an S-shaped onset. At the "break" of the voltage step, a rapid tail current is observed. From these results a kinetic model is generated which accounts for the experimental results and predicts for the time course and amplitude a possible calcium entry during presynaptic action potentials.

Action Potentials↗
PubMed1981

Relationship between presynaptic calcium current and postsynaptic potential in squid giant synapse.

The relationship between calcium current and transmitter release was studied in squid giant synapse. It was found that the voltage-dependent calcium current triggers the release of synaptic transmitter in direct proportion to its magnitude and duration. Transmitter release occurs with a delay of approximately 200 mus after the influx of calcium. A model is presented which describes these relations formally.

Action Potentials↗
PubMed1980

Transmission in the squid giant synapse: a model based on voltage clamp studies.

1. Voltage clamp studies were performed in squid giant synapse after blockage of the voltage-dependent sodium and potassium conductances. 2. Presynaptic depolarization under these conditions demonstrates the presence of voltage-dependent calcium conductance change for the duration of the voltage step, and a tail current at the break of the pulse. 2. This calcium current triggers a postsynaptic response which can be measured directly at the postsynaptic fiber. 4. These voltage clamp experiments have allowed the development of a mathematical model that describes the kinetics of the calcium current and the relationship between calcium current and transmitter release.

Animals↗
PubMed1978

Circular polarization of luminescence: biochemical and biophysical applications.

The circular polarization of the luminescence of a chromophore is one of the manifestations of its chirality. As such, CPL has the potential of probing molecular conformation, which has a tight relationship to molecular chirality. CPL has characteristic features that make it specifically useful as a tool for the investigation of conformational problems under the proper circumstances: it is related to the molecular conformation in the electronically excited state; it is specific to the luminescent chromophores when different kinds are present in the system studied; the number of electronic transitions involved are relatively few in number, often one per chromophore, thus simplifying the interpretation of the spectra; forbidden transitions are amenable to study by CPL; and CPL permits the study of the optical activity of oriented systems by simple means. The systems tackled by CPL range from small to giant molecules, which illustrates its wide applicability. Naturally, like any other research tool, CPL has limitations as to the questions to which it can be addressed and the systems that can benefit from its services (e.g. they should not be photosensitive; they should, of course, be luminescent; and they should yield measurable signals). However, for the proper questions and suitable systems it has been found to be of tremendous help.

Acridines↗
PubMed1977

The circular polarization of fluorescence of the ionophore lasalocid A(X-537A) and some of its metal complexes.

The conformation of the ionophore lasalocid A (X-537A) and its complexes with metal ions was probed by the circular polarization of their luminescence (CPL). The CPL of each complex in methanol was found to be different than when in n-hexane. Furthermore, the different metal ion complexes investigated had a different CPL spectrum in each solvent. These findings indicate wide variability in the conformation of the complexes depending on the metal ion and the solvent. From the spectral behaviour of the CPL it was concluded that at least some of the complexes exist in more than one form in solution. A comparison between the CPL and CD spectra indicates a change in the conformation of the ionophore in the vicinity of the salicylate chromophore upon electronic excitation.

Anti-Bacterial Agents↗