On the evaluation of firing densities for periodically driven neuron models

The leaky integrate-and-fire model for neuronal spiking events driven by a periodic stimulus is studied by using the Fokker-Planck formulation. To this purpose, an essential use is made of the asymptotic behavior of the first-passage-time probability density function of a time homogeneous diffusion process through an asymptotically periodic threshold. Numerical comparisons with some recently published results derived by a different approach are performed. Use of a new asymptotic approximation is then made in order to design a numerical algorithm of predictor-corrector type to solve the integral equation in the unknown first-passage-time probability density function. Such algorithm, characterized by a reduced (linear) computation time, is seen to provide a high computation accuracy. Finally, it is shown that such an approach yields excellent approximations to the firing probability density function for a wide range of parameters, including the case of high stimulus frequencies.     

Properties of synaptic noise in tonically active human motoneurons

The objective of these experiments was to determine the amount of synaptic noise on the cell membrane at various intervals after an action potential in a motoneuron firing at a specified frequency. Sources of noise such as variations in the level of voluntary drive were minimized by selecting only segments of the spike train in which the unit was running within prescribed frequency limits. The level of the membrane potential of the motoneuron during these intervals was determined using two test “pulses” (compound Ia excitatory postsynaptic potentials) of known amplitude. This enabled the probability of the membrane potential falling within a voltage “window” of known size at known times after the preceding spike to be determined. The probability density histograms showed that the fluctuations of membrane potential about a target interspike trajectory (i.e., the membrane noise) increased with time after the preceding spike. These fluctuations in the membrane potential can be accounted for by a one-dimensional “random walk” model of membrane noise. This model explains the salient features of the interval histograms, such as positive skewness at low target frequencies. A quantitative test of the model demonstrated its applicability to the motor pools of tibialis and masseter.     

Computing numerically the access resistance of a pore

The access resistance (AR) of a channel is an important component of the conductance of ion channels, particularly in wide and short channels, where it accounts for a substantial fraction of the total resistance to the movement of ions. The AR is usually calculated by using a classical and simple expression derived by Hall from electrostatics (J.E. Hall 1975 J. Gen. Phys. 66:531-532), though other expressions, both analytical and numerical, have been proposed. Here we report some numerical results for the AR of a channel obtained by solving the Poisson-Nernst-Planck equations at the entrance of a circular pore. Agreement is found between numerical calculations and analytical results from Hall's equation for uncharged pores in neutral membranes. However, for channels embedded in charged membranes, Hall's expression overestimates the AR, which is much lower and can even be neglected in some cases. The weak dependence of AR on the pore radius for charged membranes at low salt concentration can be exploited to separate the channel and the access contributions to the measured conductance.     

Depolarization-induced release of l-glutamic acid from isolated-resealed synaptic membrane vesicles

l-Glutamic acid actively loaded into resealed brain synaptic membrane vesicles was rapidly released into the incubation medium following the introduction of KCl and CaCl₂, or nigericin, or veratridine into the external medium. The KCl-induced release was enhanced by the presence of low (0.1 mM), extravesicular [Ca²⁺]. Neither the KCl-induced nor the veratridine-stimulated l-glutamate efflux were carrier-mediated processes. Finally, the KCl-stimulated l-glutamate efflux was dependent on the ratio of intra- to extravesicular [K⁺]. The observations described in this study were indicative of depolarization-induced l-glutamate release from isolated synaptic plasma membrane vesicles.     

Excitability changes in the crustacean motor axon following activity

It has been shown experimentally that the crustacean motor axon is supernormally excitable following a train of action potentials (Zucker 1974). Such a phenomenon can lead to recruitment of terminals which are unexcited at low rates of stimulation. Although currents underlying the crustacean motor axon have been characterized (Connor et al. 1977), it is not known whether this membrane model accounts for a supernormal period, what might cause superexcitablity in this model, or how excitability might change during repetitive stimulation. In present study, it is demonstrated that the crustacean motor axon model does predict a supernormal period, that the supernormal period results from slow recovery from inactivation of the transient potassium, or A, current, and that supernormal excitability is enhanced by repetitive stimulation.     

Proper synaptic vesicle formation and neuronal network activity critically rely on syndapin I

Synaptic transmission relies on effective and accurate compensatory endocytosis. F-BAR proteins may serve as membrane curvature sensors and/or inducers and thereby support membrane remodelling processes; yet, their in vivo functions urgently await disclosure. We demonstrate that the F-BAR protein syndapin I is crucial for proper brain function. Syndapin I knockout (KO) mice suffer from seizures, a phenotype consistent with excessive hippocampal network activity. Loss of syndapin I causes defects in presynaptic membrane trafficking processes, which are especially evident under high-capacity retrieval conditions, accumulation of endocytic intermediates, loss of synaptic vesicle (SV) size control, impaired activity-dependent SV retrieval and defective synaptic activity. Detailed molecular analyses demonstrate that syndapin I plays an important role in the recruitment of all dynamin isoforms, central players in vesicle fission reactions, to the membrane. Consistently, syndapin I KO mice share phenotypes with dynamin I KO mice, whereas their seizure phenotype is very reminiscent of fitful mice expressing a mutant dynamin. Thus, syndapin I acts as pivotal membrane anchoring factor for dynamins during regeneration of SVs.     

Synthesis, characteristics and biological activity of pentacoordinated spirophosphoranes derived from amino acids

Summary. The reactions of phosphorus trichloride with various amino acids afford the pentacoordinated spirophosphoranes. The reaction procedures were traced by ³¹P NMR spectra techniques. A new crystal structure of alanine derivative was characterized, which is a slightly distorted TBP structure. Besides, this kind of spirophosphoranes are potent inhibitors to tyrosinase.     

Variability v.s. synchronicity of neuronal activity in local cortical network models with different wiring topologies

Dynamical behavior of a biological neuronal network depends significantly on the spatial pattern of synaptic connections among neurons. While neuronal network dynamics has extensively been studied with simple wiring patterns, such as all-to-all or random synaptic connections, not much is known about the activity of networks with more complicated wiring topologies. Here, we examined how different wiring topologies may influence the response properties of neuronal networks, paying attention to irregular spike firing, which is known as a characteristic of in vivo cortical neurons, and spike synchronicity. We constructed a recurrent network model of realistic neurons and systematically rewired the recurrent synapses to change the network topology, from a localized regular and a “small-world” network topology to a distributed random network topology. Regular and small-world wiring patterns greatly increased the irregularity or the coefficient of variation (Cv) of output spike trains, whereas such an increase was small in random connectivity patterns. For given strength of recurrent synapses, the firing irregularity exhibited monotonous decreases from the regular to the random network topology. By contrast, the spike coherence between an arbitrary neuron pair exhibited a non-monotonous dependence on the topological wiring pattern. More precisely, the wiring pattern to maximize the spike coherence varied with the strength of recurrent synapses. In a certain range of the synaptic strength, the spike coherence was maximal in the small-world network topology, and the long-range connections introduced in this wiring changed the dependence of spike synchrony on the synaptic strength moderately. However, the effects of this network topology were not really special in other properties of network activity. Action Editor: Xiao-Jing Wang     

Inferring patterns of influenza transmission in swine from multiple streams of surveillance data

Swine populations are known to be an important source of new human strains of influenza A, including those responsible for global pandemics. Yet our knowledge of the epidemiology of influenza in swine is dismayingly poor, as highlighted by the emergence of the 2009 pandemic strain and the paucity of data describing its origins. Here, we analyse a unique dataset arising from surveillance of swine influenza at a Hong Kong abattoir from 1998 to 2010. We introduce a state–space model that estimates disease exposure histories by joint inference from multiple modes of surveillance, integrating both virological and serological data. We find that an observed decrease in virus isolation rates is not due to a reduction in the regional prevalence of influenza. Instead, a more likely explanation is increased infection of swine in production farms, creating greater immunity to disease early in life. Consistent with this, we find that the weekly risk of exposure on farms equals or exceeds the exposure risk during transport to slaughter. We discuss potential causes for these patterns, including competition between influenza strains and shifts in the Chinese pork industry, and suggest opportunities to improve knowledge and reduce prevalence of influenza in the region.     

Voltage dependence of sodium-calcium exchange: Predictions from kinetic models

Summary Voltage effects on the Na–Ca exchange system are analyzed on the basis of two kinetic models, a consecutive and a simultaneous reaction scheme. The voltage dependence of a given rate constant is directly related to the amount of charge which is translocated in the corresponding reaction step. Charge translocation may result from movement of an ion along the transport pathway, from displacement of charged ligand groups of the ion-binding site, or from reorientation of polar residues of the protein in the course of a conformational transition. The voltage dependence of ion fluxes is described by a set of coefficients reflecting the dielectric distances over which charge is translocated in the individual reaction steps. Depending on the charge of the ligand system and on the values of the dielectric coefficients, the flux-voltage curve can assume a variety of different shapes. When part of the transmembrane voltage drops between aqueous solution and binding site, the equilibrium constant of ion binding becomes a function of membrane potential. By studying the voltage dependence of ion fluxes in a wide range of sodium and calcium concentrations, detailed information on the microscopic properties of the transport system may be obtained.     

Transporters – The View from Industry

The involvement of transport proteins in the disposition of drugs is receiving much attention of the scientific community. Recently, researchers from academia have surmised that drug transport rather than passive diffusion is the regular mechanism for molecules to cross cell membranes. On bare face value, however, sound evidence of the impact of transport proteins on clinical pharmacokinetics has been a trickle rather than a stream of convincing studies during the last decade, in stark contrast to the number of in vitro studies published. Progress in this area may have been impeded by a number of factors. Only a limited number of small‐molecule drugs fall within the physicochemical property space (i.e., high hydrophilicity and low passive permeability) that makes them predestined as transport protein substrates without other pharmacokinetic processes (e.g., passive diffusion, metabolism, nonspecific binding to tissue proteins) blurring the picture. The vast majority of drug molecules are lipophilic enough to be amenable to passive diffusion across cell membranes and to undergo metabolism to some extent. In these cases, clinical evidence relies heavily on the observation of pharmacokinetic drug–drug interactions not readily explained by the interference with drug metabolizing enzymes. Given the circumstances outlined above, it is not surprising that, based upon clinical observations, the final assessment as to the overall relevance of drug transport for clinical pharmacokinetics is still pending.     

Tracking peptide-membrane interactions: insights from in situ coupled confocal-atomic force microscopy imaging of NAP-22 peptide insertion and assembly

Elucidating the role that charged membrane proteins play in determining cell membrane structure and dynamics is an area of active study. We have applied in situ correlated atomic force and confocal microscopies to characterize the interaction of the NAP-22 peptide with model membranes prepared as supported planar bilayers containing both liquid-ordered and liquid-disordered domains. Our results demonstrated that the NAP-22 peptide interacts with membranes in a concentration-dependent manner, preferentially inserting into DOPC (ld) domains. While at low peptide concentrations, the NAP-22 peptide formed aggregate-like structures within the ld domains, at high peptide concentrations, it appeared to sequester cholesterol into the ld domains and recruited phosphatidyl-myo-inositol 4,5-bisphosphate by inducing a blending effect that homogenizes the phase-segregated domains into one liquid-ordered domain. This study describes a possible mechanism by which the NAP-22 peptide can affect neuronal morphology.     

Superorganisms or loose collections of species? A unifying theory of community patterns along environmental gradients

The question whether communities should be viewed as superorganisms or loose collections of individual species has been the subject of a long‐standing debate in ecology. Each view implies different spatiotemporal community patterns. Along spatial environmental gradients, the organismic view predicts that species turnover is discontinuous, with sharp boundaries between communities, while the individualistic view predicts gradual changes in species composition. Using a spatially explicit multispecies competition model, we show that organismic and individualistic forms of community organisation are two limiting cases along a continuum of outcomes. A high variance of competition strength leads to the emergence of organism‐like communities due to the presence of alternative stable states, while weak and uniform interactions induce gradual changes in species composition. Dispersal can play a confounding role in these patterns. Our work highlights the critical importance of considering species interactions to understand and predict the responses of species and communities to environmental changes.     

Identifying Predator–Prey Processes from Time-Series

The functional response is a key element in predator–prey models as well as in food chains and food webs. Classical models consider it as a function of prey abundance only. However, many mechanisms can lead to predator dependence, and there is increasing evidence for the importance of this dependence. Identification of the mathematical form of the functional response from real data is therefore a challenging task. In this paper we apply model-fitting to test if typical ecological predator–prey time series data, which contain both observation error and process error, can give some information about the form of the functional response. Working with artificial data (for which the functional response is known) we will show that with moderate noise levels, identification of the model that generated the data is possible. However, the noise levels prevailing in real ecological time-series can give rise to wrong identifications. We will also discuss the quality of parameter estimation by fitting differential equations to such time-series.     

A kinetic analysis of the electrogenic pump ofChara corallina: III. Pump activity during action potential

Summary The current-voltage curve (I–V curve) of theChara membrane was obtained by applying a slow ramp hyper- and depolarization by use of voltage clamp. By inhibiting the electrogenic pump with 50m DCCD (dicyclohexylcarbodiimide), theI–V curve approached a steadyI–V curve within two hours, which gave thei _d -V curve of the passive diffusion channel. Thei _p -V curve of the electrogenic pump channel was obtained by subtracting the latter from the former. The sigmoidali _p -V curve could be simulated satisfactorily with a simple reaction kinetic model which assumes a stoichiometric ratio of 2. The emf of the pump (E _p ) is given as the voltage at which the pump current changes its sign. The conductance of the pump (g _p ) can be calculated as the chord conductance from thei _p -V curve, which is highly voltage dependent having a peak at a definite voltage. The changes of emf and conductance during excitation were determined by use of the current clamp (I=0). Since theE _p andg _p (V) are known, the changes, during excitation, of emf (E _d ) and conductance (g _d ) of the passive diffusion channel can be calculated. The marked increase of the membrane conductance and the large depolarization during the action potential are caused by the marked increase of the conductance of the passive diffusion channel and the large depolarization of its emf. The conductance of the electrogenic pump decreases to about half at the peak of action potential, while the pump current increases almost to a saturated level.     

Zinc inhibition of chloride efflux from skeletal muscle ofRana pipiens and its modification by external pH and chloride activity

Summary Efflux of³⁶Cl^– from frog sartorius muscles equilibrated in depolarizing solutions was measured. Cl^– efflux consists of a component present at low pH and a pH-dependent component which increases as external pH increases. In depolarized muscles fromRana pipiens, the pH-dependent Cl^– efflux has an apparent pK _a near 6.4.The reduction of Cl^– efflux by external Zn²⁺ was determined at different external pHs and chloride activities. The effect of external chloride activity on the pH-dependent Cl^– efflux was also examined.At pH 6.5 and a membrane potential of –22 mV, increasing external Cl^– activity from 0.108 to 0.28m decreased inhibition of the pH-dependent Cl^– efflux at all activities of Zn²⁺. The Zn²⁺ activity needed to reduce Cl^– efflux by half increased from 0.39×10^–3 to 2.09×10^–3 m. By contrast, external Cl^– activity had no measurable effect on the apparent pK _a of the pH-dependent efflux.At constant Cl^– activity less than 0.21m, increasing external pH from 6.5 to 7.5 decreased inhibition by low Zn²⁺ activities with either a slight increase or no change in the Zn²⁺ activity producing half-inhibition. In other words, for relatively low Cl^– activities, protection against inhibition of Cl^– efflux by low Zn²⁺ activities was obtained by raising, not lowering, external pH; this is not what is expected if H⁺ and Zn²⁺ ions compete at the same site to produce inhibition of Cl^– efflux. We conclude that Zn²⁺ and low pH inhibit Cl^– efflux by separate and distinct mechanisms.By contrast, the protection against Zn²⁺ inhibition produced by high external Cl^– activity (0.28m) was partially reversed by raising external pH from 6.5 to 7.5 at all Zn²⁺ activities. The half-inhibition Zn²⁺ activity decreased from 2.09×10^–3 to 0.68×10^–3 m.The results can be simulated quantitatively by a model in which single Cl^– channel elements are in equilibrium with sextets of associated single-channel elements, each sextet having a conductance six times that of a single-channel element. The association into sextets is promoted by OH^– or Cl^– binding to a control site on the single-channel elements. Both the single Cl^– channel element and the sextet of Cl^– channel elements are closed when this same control site instead binds ZnOH⁺. The sextet has a much higher affinity for ZnOH⁺ than does the single Cl^– channel element.