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I Segev

Publications and source records attributed to I Segev.

At least 37 records · Page 2Linked to original sources
PubMed1993

Signal delay and input synchronization in passive dendritic structures.

1. A novel approach for analyzing transients in passive structures called "the method of moments" is introduced. It provides, as a special case, an analytic method for calculating the time delay and speed of propagation of electrical signals in any passive dendritic tree without the need for numerical simulations. 2. Total dendritic delay (TD) between two points (y, x) is defined as the difference between the centroid (the center of gravity) of the transient current input, I, at point y[tI(y)] and the centroid of the transient voltage response, V, at point x [tV(x)]. The TD measured at the input points is nonzero and is called the local delay (LD). Propagation delay, PD(y, x), is then defined as TD(y, x)--LD(y) whereas the net dendritic delay, NDD(y, 0), of an input point, y, is defined as TD(y, 0) - LD(0), where 0 is the target point, typically the soma. The signal velocity at a point x0 in the tree, theta(x0), is defined as [1/(dtv(x)/dx)[x = x0. 3. With the use of these definitions, several properties of dendritic delay exist. First, the delay between any two points in a given tree is independent of the properties (shape and duration) of the transient current input. Second, the velocity of the signal at any given point (y) in a given direction from (y) does not depend on the morphology of the tree "behind" the signal, and of the input location. Third, TD(y, x) = TD(x, y), for any two points, x, y. 4. Two additional properties are useful for efficiently calculating delays in arbitrary passive trees. 1) The subtrees connected at the ends of any dendritic segment can each be functionally lumped into an equivalent isopotential R-C compartment. 2) The local delay at any given point (y) in a tree is the mean of the local delays of the separate structures (subtrees) connected at y, weighted by the relative input conductance of the corresponding subtrees. 5. Because the definitions for delays utilize difference between centroids, the local delay and the total delay can be interpreted as measures for the time window in which synaptic inputs affect the voltage response at a target/decision point. Large LD or TD is closely associated with a relatively wide time window, whereas small LD or TD imply that inputs have to be well synchronized to affect the decision point. The net dendritic delay may be interpreted as the cost (in terms of delay) of moving a synapse away from the target point.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1992

Single neurone models: oversimple, complex and reduced.

The single neurone stands in the midst of a controversy among modelers. Some believe that its details are functionally superfluous when the neurone operates in a large network, and very simple models can be used to represent the input/output characteristics of neurones. Others claim that the unique morphology and electrical properties of neurones do play an important role. Complicated models of neurones are developed to reveal how the various kinds of 'neurone-ware' (dendrites, spines, axons, membrane channels and synapses) create a computationally powerful unit. Various models are discussed, including new carefully reduced models that retain essential features of more complex models. Such intermediate models will play a central role in our efforts to understand information processing in large neuronal networks.

Dendrites↗
PubMed1992

Interpretation of time constant and electrotonic length estimates in multicylinder or branched neuronal structures.

1. We have investigated the theoretical and practical problems associated with the interpretation of time constants and the estimation of electrotonic length with equivalent cylinder formulas for neurons best represented as multiple cylinders or branched structures. Two analytic methods were used to compute the time constants and coefficients of passive voltage transients (and time constants of current transients under voltage clamp). One method, suitable for simple geometries, involves analytic solutions to boundary value problems. The other, suitable for neurons of any geometric complexity, is an algebraic approach based on compartmental models. Neither of these methods requires the simulation of transients. 2. We computed the time constants and coefficients of voltage transients for several hypothetical neurons and also for a spinal motoneuron whose morphology was characterized from serial reconstructions. These time constants and coefficients were used to generate voltage transients. Then exponential peeling, nonlinear regression, and transform methods were applied to these transients to test how well these procedures estimate the underlying time constants and coefficients. 3. For a serially reconstructed motoneuron with 732 compartments, we found that the theoretical and peeled tau 0 values were nearly equal, but the theoretical tau 1 was much larger than the peeled tau 1. The theoretical tau 1 could not be peeled because it was associated with a coefficient, C1, that had a very small value. In fact, there were 156 time constants between 1.0 and 6.0 ms, most of which had very small coefficients; none had a coefficient larger than 2% of the signal. The peeled value of tau 1 (called tau 1 peel) can be viewed as some sort of a weighted average of the time constants having the largest coefficients. 4. We studied simple hypothetical neurons to determine what interpretation could be applied to the multitude of theoretical time constants. We found that after tau 0, there was a group of time constants associated with eigenfunctions that were odd (or approximately odd) functions with respect to the soma. These time constants could be interpreted as "equalizing" time constants along particular paths between different pairs of dendritic terminals in the neuron. After this group of time constants, there was one that we call tau even because it was associated with an eigen-function that was approximately even with respect to the soma. This tau even could be interpreted as an equalizing time constant for charge equalization between proximal membrane (soma and proximal dendrites) and distal membrane (including all distal dendrites).4=

Animals↗
PubMed1991

Propagation of action potentials along complex axonal trees. Model and implementation.

Axonal trees are typically morphologically and physiologically complicated structures. Because of this complexity, axonal trees show a large repertoire of behavior: from transmission lines with delay, to frequency filtering devices in both temporal and spatial domains. Detailed theoretical exploration of the electrical behavior of realistically complex axonal trees is notably lacking, mainly because of the absence of a simple modeling tool. AXONTREE is an attempt to provide such a simulator. It is written in C for the SUN workstation and implements both a detailed compartmental modeling of Hodgkin and Huxley-like kinetics, and a more abstract, event-driven, modeling approach. The computing module of AXONTREE is introduced together with its input/output features. These features allow graphical construction of arbitrary trees directly on the computer screen, and superimposition of the results on the simulated structure. Several numerical improvements that increase the computational efficiency by a factor of 5-10 are presented; most notable is a novel method of dynamic lumping of the modeled tree into simpler representations ("equivalent cables"). AXONTREE's performance is examined using a reconstructed terminal of an axon from a Y cell in cat visual cortex. It is demonstrated that realistically complicated axonal trees can be handled efficiently. The application of AXONTREE for the study of propagation delays along axonal trees is presented in the companion paper (Manor et al., 1991).

Action Potentials↗
PubMed1991

Effect of geometrical irregularities on propagation delay in axonal trees.

Multiple successive geometrical inhomogeneities, such as extensive arborization and terminal varicosities, are usual characteristics of axons. Near such regions the velocity of the action potential (AP) changes. This study uses AXONTREE, a modeling tool developed in the companion paper for two purposes: (a) to gain insights into the consequence of these irregularities for the propagation delay along axons, and (b) to simulate the propagation of APs along a reconstructed axon from a cortical cell, taking into account information concerning the distribution of boutons (release sites) along such axons to estimate the distribution of arrival times of APs to the axons release sites. We used Hodgkin and Huxley (1952) like membrane properties at 20 degrees C. Focusing on the propagation delay which results from geometrical changes along the axon (and not from the actual diameters or length of the axon), the main results are: (a) the propagation delay at a region of a single geometrical change (a step change in axon diameter or a branch point) is in the order of a few tenths of a millisecond. This delay critically depends on the kinetics and the density of the excitable channels; (b) as a general rule, the lag imposed on the AP propagation at a region with a geometrical ratio GR greater than 1 is larger than the lead obtained at a region with a reciprocal of that GR value; (c) when the electronic distance between two successive geometrical changes (Xdis) is small, the delay is not the sum of the individual delays at each geometrical change, when isolated. When both geometrical changes are with GR greater than 1 or both with GR less than 1, this delay is supralinear (larger than the sum of individual delays). The two other combinations yield a sublinear delay; and (d) in a varicose axon, where the diameter changes frequently from thin to thick and back to thin, the propagation velocity may be slower than the velocity along a uniform axon with the thin diameter. Finally, we computed propagation delays along a morphologically characterized axon from layer V of the somatosensory cortex of the cat. This axon projects mainly to area 4 but also sends collaterals to areas 3b and 3a. The model predicts that, for this axon, areas 3a, 3b, and the proximal part of area 4 are activated approximately 2 ms before the activation of the distal part of area 4.

Action Potentials↗
PubMed1990

Voltage behavior along the irregular dendritic structure of morphologically and physiologically characterized vagal motoneurons in the guinea pig.

1. Intracellular recordings from neurons in the dorsal motor nucleus of the vagus (vagal motoneurons, VMs) obtained in the guinea pig brain stem slice preparation were used for both horseradish peroxidase (HRP) labeling of the neurons and for measurements of their input resistance (RN) and time constant (tau 0). Based on the physiological data and on the morphological reconstruction of the labeled cells, detailed steady-state and compartmental models of VM were built and utilized to estimate the range of membrane resistivity, membrane capacitance, and cytoplasm resistivity values (Rm, Cm, and Ri, respectively) and to explore the integrative properties of these cells. 2. VMs are relatively small cells with a simple dendritic structure. Each cell has an average of 5.3 smooth (nonspiny), short (251 microns) dendrites with a low order (2) of branching. The average soma-dendritic surface area of VMs is 9,876 microns 2. 3. Electrically, VMs show remarkably linear membrane properties in the hyperpolarizing direction; they have an average RN of 67 +/- 23 (SD) M omega and a tau 0 of 9.4 +/- 4.1 ms. Several unfavorable experimental conditions precluded the possibility of faithfully recovering ("peeling") the first equalizing time constant (tau 1) and, thereby, of estimating the electrotonic length (Lpeel) of VMs. 4. Reconciling VM morphology with the measured RN and tau 0 through the models, assuming an Ri of 70 omega.cm and a spatially uniform Rm, yielded an Rm estimate of 5,250 omega.cm2 and a Cm of 1.8 microF/cm2. Peeling theoretical transients produced by these models result in an Lpeel of 1.35. Because of marked differences in the length of dendrites within a single cell, this value is larger than the maximal cable length of the dendrites and is twice as long as their average cable length. 5. The morphological and physiological data could be matched indistinguishably well if a possible soma shunt (i.e., Rm, soma less than Rm, dend) was included in the model. Although there is no unique solution for the exact model Rm, a general conclusion regarding the integrative capabilities of VM could be drawn. As long as the model is consistent with the experimental data, the average input resistance at the dendritic terminals (RT) and the steady-state central (AFT----S) and peripheral (AFS----T) attenuation factors are essentially the same in the different models. With Ri = 70 omega.cm, we calculated RT, AFS----T, and AFT----S to be, on the average, 580 M omega, 1.1, and 13, respectively.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1990

Computer study of presynaptic inhibition controlling the spread of action potentials into axonal terminals.

1. The effect of presynaptic, axoaxonal inhibition, that exerts its action by producing a local conductance increase, on the behavior of action potentials at postsynaptic axon terminals is analyzed computationally. The significance of the location and strength of the presynaptic inhibition, as well as the morphology and membrane properties of the axonal terminals, are considered. 2. Keeping the specific properties of terminal membrane and axoplasm constant, the critical "silent" steady-state conductance change (gcrit) that blocks propagation is linearly scaled with the terminal diameter raised to the 3/2 power. At the midpoint of a 5 lambda long, 1 micron diameter axon that has the standard Hodgkin and Huxley (1952) kinetics at 18 degrees C (and an input conductance of 8.7 nS), gcrit is 72 nS. At 0 degrees C, gcrit = 200 nS, whereas at 30 degrees C gcrit = 30 nS. 3. The critical conductance change that blocks propagation depends steeply on the density of excitable channels (gNa) at the terminal. For a geometrically uniform terminal at 18 degrees C, the action potential can not be blocked by a local shunt when gNa greater than 600 mS/cm2. 4. An axoaxonal synapse in the proximity of the postsynaptic release site has graded control over the spike amplitude (and, therefore, over the postsynaptic output) at that site. Presynaptic inhibition located remotely from the release site has an all-or-none effect at the release site. 5. Inhibition is more effective in attenuating the spike at the terminal when it impinges onto a passive terminal rather than on an excitable one. 6. The detectability of the conductance increase as well as the change in action potential amplitude associated with the presynaptic inhibition is poor at only a short distance from the axoaxonal synapse. The presence of bottlenecks and varicosities at some axonal terminals enhances this decoupling effect even more. Thus presynaptic inhibition may reduce the potential near the output site of the affected axon significantly, without producing any noticeable conductance or voltage change at a distance of only several tens of micrometers (a few tenths of a space constant) away from it. 7. Varicosities and bottlenecks typically found along axonal terminals are the optimal loci for presynaptic inhibition to be most effective in attenuating the action potential at the terminal. Even with high density of excitable channels, propagation with such terminal geometry is insecure, and one, or few, quanta of inhibitory transmitter (a conductance change of several nanosiemens) can block propagation there.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗
PubMed1990

Computer simulation of group Ia EPSPs using morphologically realistic models of cat alpha-motoneurons.

1. Morphological and electrophysiological data on the electrotonic structure of six triceps surae alpha-motoneurons and on the number and location of 202 Group Ia synapses making contact with ankle extensor motoneurons, previously obtained in this laboratory, were used to construct computer models to examine the generation of composite monosynaptic Group Ia excitatory postsynaptic potentials (EPSPs). 2. A total of 300 active synapses, each generating conductance transients based on voltage-clamp data and having activation times temporally dispersed (range approximately 1.3 ms) according to the conduction velocity profile of Group Ia-afferents, were used to generate composite EPSPs. 3. The shape indexes (foot-to-peak rise times and half widths) of simulated EPSPs matched those of experimentally observed Ia EPSPs reasonably well, although the rise times were, on average, approximately 0.25 ms longer in the simulated EPSPs. This may indicate that the effective temporal dispersion of actual Group Ia monosynaptic EPSPs is less than that the temporal asynchrony used in the simulations. 4. The peak amplitudes of simulated composite EPSPs (6-14 mV), as well as EPSPs produced by single somatic synapses (80-300 microV), were comparable to those found in experimental data. 5. Simulated EPSPs in motoneuron models with two forms of nonuniform Rm distribution ("step" increase from low values of Rm on the soma to much higher but uniform values in the dendrites, versus gradual monotonic "sigmoidal" increases from soma to distal dendrites) were similar in shape and amplitude. This prevented choosing one or the other Rm model as more "correct." 6. Transmembrane voltages at synaptic sites in motoneuron dendrites during generation of composite Ia EPSPs had peak amplitudes less than twice those of the somatic EPSP. The amount of nonlinearity during EPSP production was assessed by making the delivery of synaptic current independent of the local transmembrane voltage. This non-linearity was modest (less than 10%) during composite EPSP generation, consistent with previous experimental evidence. 7. The local voltages produced in various parts of different dendrites during composite EPSP generation depended on the number and location of active synapses and on the electrotonic structure of the particular dendrite. The results show that dendrites that project in different directions away from the motoneuron soma could, in principle, exhibit different degrees of interaction between Ia and other synaptic inputs. 8. Although produced by the same number of active synapses, the simulated composite Ia EPSPs varied over a two-fold range of peak amplitude in relation to motor-unit type, cell input resistance, and cell size (total membrane area).(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1988

Electrotonic architecture of type-identified alpha-motoneurons in the cat spinal cord.

1. Measurements of input resistance (RN), time constant (tau 0), and electrotonic length (Lpeel) were derived from intracellular voltage changes produced by injection of current pulses in six type-identified triceps surae alpha-motoneurons. The motoneurons were labeled with horseradish peroxidase and subsequently reconstructed and measured from serial sections. These quantitative morphological and physiological data were incorporated into detailed computer models of the motoneurons. 2. Steady-state and dynamic models were used to determine values for specific membrane resistivity (Rm) that matched the experimental estimates of RN, tau 0, and Lpeel for each motoneurons. The models were based on the following assumptions 1) the membrane was electrically passive, 2) cytoplasmic resistivity (Ri) was 70 omega-cm, and 3) "sealed-end" boundary conditions were present at dendritic terminations. We also considered the nature and magnitude of possible errors introduced by using linear (passive) computer models to match responses from motoneurons with nonlinear (i.e., voltage-dependent) conductances. 3. If we assume that the experimental measurements of RN and tau 0 were correct, uniform Rm values that reproduced the experimentally measured RN required widely varying values of Cm (1.4-8.6 microF/cm2) to match the experimental tau 0. Furthermore, the electrotonic distance to dendritic terminals was generally much greater than expected from physiological estimates of Lpeel. However, if we assumed that the RN measurements could have been underestimated by as much as 30% and that Cm = 1.0 microF/cm2, it was possible to choose spatially uniform Rm that matched the observed tau 0 in three of six cases. 4. Relaxing the assumption of spatially uniform membrane resistivity permitted us to reconcile the anatomical and physiological characteristics of all six motoneurons. Two qualitatively different models of Rm nonuniformity gave equally good fits to the experimental results 1) a step-wise increase in Rm from a low value at the soma to a much higher but uniform value over the entire dendritic tree, and 2) a monotonic increase in Rm from soma to distal dendrites as a sigmoidal function of path distance along the dendrites. The step and sigmoidal models of the spatial distribution of Rm generated different electrotonic architectures in motoneuron dendritic trees, but both gave essentially identical electrical responses at the soma.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1988

Computational study of an excitable dendritic spine.

1. A compartmental model was employed to investigate the electrical behavior of a dendritic spine having excitable membrane at the spine head. Here we used the Hodgkin and Huxley equations to generate excitable membrane properties; in some cases the kinetics were modified to get a longer duration action potential. Passive membrane was assumed for both the spine stem and the dendritic shaft. Synaptic input was modeled as a transient conductance increase (alpha-function) that lies in series with a battery (that corresponds to an excitatory or inhibitory synaptic equilibrium potential). 2. Threshold conditions for an action potential at the spine head membrane were found to be sensitive to the membrane properties at the spine head and to the conductance loading provided by the spine stem and the dendritic tree. Increasing either the number or the open times of the excitable channels had the effect of lowering spike threshold voltage. Increasing the spine stem resistance (RSS) or increasing the input resistance at the spinal base (RSB) also lowered the spike threshold voltage. Because a preexisting dendritic depolarization reduced the spine stem current, this lowered the spike threshold voltage, and this threshold was also shown to be sensitive to the distribution of membrane potential along the dendrite. 3. For each set of spine and dendritic parameters, there was an optimal range of RSS values for which the excitable properties at the spine head membrane resulted in maximal amplification of the dendritic excitatory postsynaptic potential (EPSP), when compared with that produced by a corresponding passive spine. This optimal range depended (with nonlinear sensitivity) on the properties of the voltage-gated channels at the spine head membrane. The maximal amplification found (for each of several sets of parameters) ranged from two to thirteen times. 4. Near this optimal range of RSS values, there was maximal (nonlinear) sensitivity of the dendritic EPSP amplitude to small changes in RSS. A minor decrease resulted in a subthreshold response at the spine head, and this resulted in a large decrease in the EPSP amplitude at the spine base. Increasing the value of RSS above this optimal range decreased the amount of spine stem current flowing to the spine base (by Ohm's law); this decreased the EPSP amplitude at the spine base. The demonstration of this optimum agrees with earlier expectations and results. 5. Excitable dendritic spines can be seen to provide an anatomical arrangement that economizes both excitable and synaptic channels. A small number of these channels (located in spine head membrane) can produce a large dendritic depolarization.(ABSTRACT TRUNCATED AT 400 WORDS)

Action Potentials↗
PubMed1985

Modeling the electrical behavior of anatomically complex neurons using a network analysis program: passive membrane.

We describe the application of a popular and widely available electrical circuit simulation program called SPICE to modeling the electrical behavior of neurons with passive membrane properties and arbitrarily complex dendritic trees. Transient responses may be calculated at any location in the cell model following current, voltage or conductance perturbations at any point. A numbering method is described for binary trees which is helpful in transforming complex dendritic structures into a coded list of short cylindrical dendritic segments suitable for input to SPICE. Individual segments are modeled as isopotential compartments comprised of a parallel resistor and capacitor, representing the transmembrane impedance, in series with one or two core resistors. Synaptic current is modeled by a current source controlled by the local membrane potential and an "alpha-shaped" voltage, thus simulating a conductance change in series with a driving potential. Extensively branched test cell circuits were constructed which satisfied the equivalent cylinder constraints (Rall 1959). These model neurons were perturbed by independent current sources and by synaptic currents. Responses calculated by SPICE are compared with analytical results. With appropriately chosen model parameters, extremely accurate transient calculations may be obtained. Details of the SPICE circuit elements are presented, along with illustrative examples sufficient to allow implementation of passive nerve cell models on a number of common computers. Methods for modeling excitable membrane are presented in the companion paper (Bunow et al. 1985).

Animals↗
PubMed1985

Modeling the electrical behavior of anatomically complex neurons using a network analysis program: excitable membrane.

We present methods for using the general-purpose network analysis program, SPICE, to construct computer models of excitable membrane displaying Hodgkin-Huxley-like kinetics. The four non-linear partial differential equations of Hodgkin and Huxley (H-H; 1952) are implemented using electrical circuit elements. The H-H rate constants, alpha and beta, are approximated by polynomial functions rather than exponential functions, since the former are handled more efficiently by SPICE. The process of developing code to implement the H-H sodium conductance is described in detail. The Appendix contains a complete listing of the code required to simulate an H-H action potential. The behavior of models so constructed is validated by comparison with the space-clamped and propagating action potentials of Hodgkin and Huxley. SPICE models of multiply branched axons were tested and found to behave as predicted by previous numerical solutions for propagation in inhomogeneous axons. New results are presented for two cases. First, a detailed, anatomically based model is constructed of group Ia input to an alpha-motoneuron with an excitable soma, a myelinated axon and passive dendrites. Second, we simulate interactions among clusters of mixed excitable and passive dendritic spines on an idealized neuron. The methods presented in this paper and its companion (Segev et al. 1985) should permit neurobiologists to construct and explore models which simulate much more closely the real morphological and physiological characteristics of nerve cells.

Action Potentials↗
PubMed1985

Signal enhancement in distal cortical dendrites by means of interactions between active dendritic spines.

Pyramidal neurons in the cerebral cortex characteristically give rise to an apical dendrite, whose distal dendritic branches in layer I are covered with spines. These spines are known to be sites of synaptic connections, but the physiological properties of the spines and the functional significance of their responses are still largely unknown. The main function attributed thus far to these synaptic responses, situated at a great distance from the neuronal cell body, is slow background modulation of impulse output in the axon. In pursuing computer simulation analysis of electrical properties of dendrites, we have obtained results suggesting interactions between distal dendritic spines. If the heads of dendritic spines have excitable membrane properties, the spread of current from one or several spines could bring adjacent spines to their thresholds for impulse generation. This could give rise to a sequence of spine head action potentials, representing a saltatory propagation, from one or more excitable spine heads to nearby excitable spine heads, in the distal dendritic branches. Both the amplification due to several spine action potentials and the possibility of propagation into more proximal branches would increase the efficacy of distal synaptic inputs. Because of nonlinear dependence upon several modifiable parameters (such as spine stem resistance and membrane excitability) and upon the spatio-temporal pattern of synaptic input, such contingent synaptic enhancement would be particularly relevant to cortical functions underlying information processing and to plasticity underlying learning and memory.

Dendrites↗
PubMed1985

Nonlinear cable properties of the giant axon of the cockroach Periplaneta americana.

The steady state nonlinear properties of the giant axon membrane of the cockroach Periplaneta americana were studied by means of intracellular electrodes. The resistivity of this membrane markedly decreases in response to small subthreshold depolarizations. The specific slope resistance is reduced by twofold at 5 mV depolarization and by a factor of 14 at 20 mV depolarization. As a result, the spatial decay, V(X), of depolarizing potentials is enhanced when compared with the passive (exponential) decay. This enhancement is maximal at a distance of 1-1.5 mm from a point of subthreshold (0-20 mV) depolarizing perturbation. At that distance, the difference between the actual potential and the potential expected in the passive axon is approximately 30%. The effects of membrane rectification on V(X) were analyzed quantitatively with a novel derivation based on Cole's theorem, which enables one to calculate V(X) directly from the input current-voltage (I0-V) relation of a long axon. It is shown that when the experimental I0-V curve is replotted as (I0Rin)-1 against V (where Rin is the input resistance at the resting potential), the integral between any two potentials (V1 greater than V2) on this curve is the distance, in units of the resting space constant, over which V1 attenuates to V2. Excellent agreement was found between the experimental V(X) and the predicted value based solely on the input I0-V relation. The results demonstrate that the rectifying properties of the giant axon membrane must be taken into account when the electrotonic spread of even small subthreshold potentials is studied, and that, in the steady state, this behavior can be extracted from measurements at a single point. The effect of rectification on synaptic efficacy is also discussed.

Animals↗
PubMed1983

Synaptic integration mechanisms. Theoretical and experimental investigation of temporal postsynaptic interactions between excitatory and inhibitory inputs.

The effect of temporal activation of two closely adjacent synaptic inputs upon the postsynaptic output (voltage amplitude and time integral) is analyzed theoretically and experimentally. It is shown that (a) under certain conditions, maximal nonlinearity in the summation of postsynaptic potentials is obtained with asynchronous activation of the two synaptic inputs rather than with simultaneous activation; (b) the time integral of the voltage is more sensitive to the timing of the synaptic inputs than is the voltage amplitude; (c) an input, which by the classical definition is inhibitory, under defined conditions can and does increase the amplitude (and area) of an excitatory synaptic potential, and thus acts as an excitatory input.

Animals↗
PubMed1979

A mathematical model for conduction of action potentials along bifurcating axons.

1. A mathematical model based on the Hodgkin-Huxley equations is derived to describe quantitatively the propagation of action potentials in a branching axon. 2. The model treats the case of a bifurcating axon with branches of different diameters. The solution takes into account the changes in space constant in the different regions. 3. The model allows for investigating parameters leading to preferential conduction of action potentials in one daughter branch as seen experimentally. 4. Assuming that the only difference between the various daughter branches is in their diameters, conduction blocks should occur simultaneously rather than differentially into all daughter branches when the geometrical ratio is greater than 10. 5. In order to obtain differential conduction into the two branches changes in ionic concentrations due to the repetitive action potentials had to be introduced into the equations. 6. We find that conditions which allow differential buildup of K concentration around the two branches, produce differential conduction block. These conditions may be different periaxonal spaces around the branches or different time constant for recovery processes that eliminate K from the periaxonal space. 7. The effects of an inexcitable branch on conduction of action potentials in the second branch are described. 8. We find that the membrane current which is associated with the action potential is much more sensitive than the action potential itself and shows more distinct changes near regions of inhomogeneity such as a branch point, a step increase in diameter or an inexcitable branch.

Action Potentials↗
PubMedDate not supplied

Axons as computing devices: basic insights gained from models.

Detailed models of single neurons are typically focused on the dendritic tree and ignore the axonal tree, assuming that the axon is a simple transmission line. In the last 40 years, however, several theoretical and experimental studies have suggested that axons could implement information processing tasks by exploiting: 1) the time delay in action potential (AP) propagation along the axon; 2) the differential filtering of APs into the axonal subtrees; and 3) their activity-dependent excitability. Models for axonal trees have attempted to examine the feasibility of these ideas. However, because the physiological and anatomical data on axons are seriously limited, realistic models of axons have not been developed. The present paper summarizes the main insights that were gained from simplified models of axons; it also highlights the stochastic nature of axons, a topic that was largely neglected in classical models of axons. The advance of new experimental techniques makes it now possible to pay a very close experimental visit to axons. Theoretical tools and fast computers enable to go beyond the simplified models and to construct realistic models of axons. When tightly linked, experiments and theory will help to unravel how axons share the information processing tasks that single neurons implement.

Algorithms↗