A Spiking Neuron Model for Binocular Rivalry

We present a biologically plausible model of binocular rivalry consisting of a network of Hodgkin-Huxley type neurons. Our model accounts for the experimentally and psychophysically observed phenomena: (1) it reproduces the distribution of dominance durations seen in both humans and primates, (2) it exhibits a lack of correlation between lengths of successive dominance durations, (3) variation of stimulus strength to one eye influences only the mean dominance duration of the contralateral eye, not the mean dominance duration of the ipsilateral eye, (4) increasing both stimuli strengths in parallel decreases the mean dominance durations. We have also derived a reduced population rate model from our spiking model from which explicit expressions for the dependence of the dominance durations on input strengths are analytically calculated. We also use this reduced model to derive an expression for the distribution of dominance durations seen within an individual.     

Strain-specific virulence phenotypes of Streptococcus pneumoniae assessed using the Chinchilla laniger model of otitis media

Background

Streptococcus pneumoniae [Sp] infection is associated with local and systemic disease. Our current understanding of the differential contributions of genetic strain variation, serotype, and host response to disease phenotype is incomplete. Using the chinchilla model of otitis media [OM] we investigated the disease phenotype generated by the laboratory strain TIGR4 and each of thirteen clinical strains (BS68-75, BS290, BS291, BS293, BS436 and BS437); eleven of the thirteen strains have been genomically sequenced.

Methodology/Principal Findings

For each strain 100 colony forming units were injected bilaterally into the tympanic bullae of 6 young adult chinchillas under general anesthesia. All animals were examined daily for local and systemic disease by a blinded observer. Pneumatic otoscopy was used to evaluate local disease, and behavioral assessments served as the measure of systemic disease. Virulence scoring was performed using a 4-point scale to assess four clinical parameters [severity and rapidity of local disease onset; and severity and rapidity of systemic disease onset] during a 10-day evaluation period. Highly significant variation was observed among the strains in their ability to cause disease and moribundity.

Conclusions/Significance

As expected, there was a significant correlation between the rapidity of systemic disease onset and severity of systemic disease; however, there was little correlation between the severity of otoscopic changes and severity of systemic disease. Importantly, it was observed that different strains of the same serotype produced as broad an array of disease phenotypes as did strains of different serotypes. We attribute these phenotypic differences among the strains to the high degree of genomic plasticity that we have previously documented.     

Reliability of signal transmission in stochastic nerve axon equations

We introduce a method for computing probabilities for spontaneous activity and propagation failure of the action potential in spatially extended, conductance-based neuronal models subject to noise, based on statistical properties of the membrane potential. We compare different estimators with respect to the quality of detection, computational costs and robustness and propose the integral of the membrane potential along the axon as an appropriate estimator to detect both spontaneous activity and propagation failure. Performing a model reduction we achieve a simplified analytical expression based on the linearization at the resting potential (resp. the traveling action potential). This allows to approximate the probabilities for spontaneous activity and propagation failure in terms of (classical) hitting probabilities of one-dimensional linear stochastic differential equations. The quality of the approximation with respect to the noise amplitude is discussed and illustrated with numerical results for the spatially extended Hodgkin-Huxley equations. Python simulation code is supplied on GitHub under the link https://github.com/deristnochda/Hodgkin-Huxley-SPDE.     

A Statistical Model for In Vivo Neuronal Dynamics

Single neuron models have a long tradition in computational neuroscience. Detailed biophysical models such as the Hodgkin-Huxley model as well as simplified neuron models such as the class of integrate-and-fire models relate the input current to the membrane potential of the neuron. Those types of models have been extensively fitted to in vitro data where the input current is controlled. Those models are however of little use when it comes to characterize intracellular in vivo recordings since the input to the neuron is not known. Here we propose a novel single neuron model that characterizes the statistical properties of in vivo recordings. More specifically, we propose a stochastic process where the subthreshold membrane potential follows a Gaussian process and the spike emission intensity depends nonlinearly on the membrane potential as well as the spiking history. We first show that the model has a rich dynamical repertoire since it can capture arbitrary subthreshold autocovariance functions, firing-rate adaptations as well as arbitrary shapes of the action potential. We then show that this model can be efficiently fitted to data without overfitting. We finally show that this model can be used to characterize and therefore precisely compare various intracellular in vivo recordings from different animals and experimental conditions.     

A Hodgkin-Huxley model exhibiting bursting oscillations

We investigate bursting behaviour generated in an electrophysiological model of pituitary corticotrophs. The active and silent phases of this mode of bursting are generated by moving between two stable oscillatory solutions. The bursting is indirectly driven by slow modulation of the endoplasmic reticulum Ca²⁺ concentration. The model exhibits different modes of bursting, and we investigate mode transitions and similar modes of bursting in other Hodgkin-Huxley models. Bifurcation analysis and the use of null-surfaces facilitate a geometric interpretation of the model bursting modes and action potential generation, respectively.     

The ionic requirements for the initiation of action potentials in insect muscle fibers

Electrical properties of locust leg muscle fibers were studied by means of intracellular electrodes. In most fibers, a depolarizing current pulse initiated a local response. A delayed decrease in membrane resistance appeared with more than about 10 mv depolarization. In some fibers a regenerative response also was found. Membrane constants were measured, applying the short cable model. The value of the space constant λ was 1.6 mm and the calculated value of R_m was about 1750 ohm cm². Action potentials could be elicited when the bathing fluid contained more than 2–5 mM Ba or Sr. Similar responses were seen with 2 mM Ca in the presence of tetraethylammonium (TEA). The overshoot of these action potentials increased with increasing [Ca⁺⁺]_o, [Sr⁺⁺]_o, or [Ba⁺⁺]_o, the increment for a 10-fold increase being about 29 mv for Ca and Sr and between 40 and 50 mv for Ba. These action potentials were inhibited by Mn ions but were not affected by tetrodotoxin or procaine. In solutions containing Ba or Sr, action potentials generated were suppressed by addition of Ca. The removal of Na ions did not change the configuration of the action potential. The results suggest that an increase in permeability to Ca, Ba, or Sr ions makes a major contribution to the initiation of action potentials in this tissue.     

Biophysical mechanism of spike threshold dependence on the rate of rise of the membrane potential by sodium channel inactivation or subthreshold axonal potassium current

Spike threshold filters incoming inputs and thus gates activity flow through neuronal networks. Threshold is variable, and in many types of neurons there is a relationship between the threshold voltage and the rate of rise of the membrane potential (dVm/dt) leading to the spike. In primary sensory cortex this relationship enhances the sensitivity of neurons to a particular stimulus feature. While Na⁺ channel inactivation may contribute to this relationship, recent evidence indicates that K⁺ currents located in the spike initiation zone are crucial. Here we used a simple Hodgkin-Huxley biophysical model to systematically investigate the role of K⁺ and Na⁺ current parameters (activation voltages and kinetics) in regulating spike threshold as a function of dVm/dt. Threshold was determined empirically and not estimated from the shape of the Vm prior to a spike. This allowed us to investigate intrinsic currents and values of gating variables at the precise voltage threshold. We found that Na⁺ inactivation is sufficient to produce the relationship provided it occurs at hyperpolarized voltages combined with slow kinetics. Alternatively, hyperpolarization of the K⁺ current activation voltage, even in the absence of Na⁺ inactivation, is also sufficient to produce the relationship. This hyperpolarized shift of K⁺ activation allows an outward current prior to spike initiation to antagonize the Na⁺ inward current such that it becomes self-sustaining at a more depolarized voltage. Our simulations demonstrate parameter constraints on Na⁺ inactivation and the biophysical mechanism by which an outward current regulates spike threshold as a function of dVm/dt.     

Application of the Hodgkin-Huxley equations to an electric field model for interaction between excitable cells

We previously described a model for the electrical transfer of excitation from one cell to the next which utilized the electric potential generated in the junctional cleft between the cells. Low-resistance connections between the cells were not used in the model, and it was assumed that the junctional membranes were excitable. This model was analyzed for the static case without capacitances and for the dynamic case in which capacitances were part of the circuit elements. For simplicity, the Na⁺ resistance (R_Na), after a threshold potential was exceeded, was allowed to decrease exponentially (to 1% of its initial value) within 0·25–1·0 ms, and possible changes in the K⁺ resistance were ignored. In this paper, we have incorporated the Hodgkin-Huxley equations into the operation of the lumped membrane units for the electrical equivalent circuit of the cell membrane. The parameters varied are the membrane capacitances, resistances, maximum Na⁺ conductance ($\text{g}{}_{\mathrm{<mtext>Na</mtext>}}$), and the radial cleft resistance (R_jc). We demonstrated that our model worked very well, i.e. the successful transfer of action potentials was achieved, with the membrane units following Hodgkin-Huxley dynamics for changes in g_Na and g_K. The calculations indicate that transmission is facilitated when the junctional units have a higher $\text{g}{}_{\mathrm{<mtext>Na</mtext>}}$ and a lower capacitance and when R_jc is elevated. Lowering the resistance of the junctional membrane units several fold, relative to the surface membrane units, also facilitated transmission; however, the absolute resistance of the junctional membrane was still well above the maximum value that would allow sufficient local-circuit current to flow to effect transmission. Thus, the electric field model provides an alternative means of cell-to-cell propagation between myocardial cells which is electrical in nature but does not require the presence of low-resistance connections between cells.     

A fully coupled transient excited state model for the sodium channel

Summary The axon membrane is simulated by standard Hodgkin-Huxley leakage and potassium channels plus a coupled transient excited state kinetic scheme for the sodium channel. This scheme for the sodium channel is as proposed previously by the author. Simultations are presented showing the form of the action potential, threshold behavior, accommodation, and repetitive firing. It is seen that the form of the individual action potential, its all-or-none nature, and its refractory period are well simulated by this model, as they are by the standard Hodgkin-Huxley model. However, the model differs markedly from the Hodgkin-Huxley model with respect to repetitive firing and accommodation to stimulating currents of slowly rising intensity, in ways that are anomn to be related to those features of the sodium inactivation which are anomalous to the H-H model. The tendency for repetitive firing is highly dependent on that parameter which primarily determintes the existence of the inactivation shift in voltage clamp experiments, in such a way that the more pronounced the inactivation shift, the less the tendency for repetitive firing,. The tendency for accommodation is highly dependent on that parameter which primarily determines the “τ_c − τ_h” separation, in such a way that the greater the separation the greater the tendency for the membrane to accommodate without firing action potentials to a slowly rising current.     

A unified model for two modes of bursting in GnRH neurons

Gonadotropin-releasing hormone (GnRH) neurons exhibit at least two intrinsic modes of action potential burst firing, referred to as parabolic and irregular bursting. Parabolic bursting is characterized by a slow wave in membrane potential that can underlie periodic clusters of action potentials with increased interspike interval at the beginning and at the end of each cluster. Irregular bursting is characterized by clusters of action potentials that are separated by varying durations of interburst intervals and a relatively stable baseline potential. Based on recent studies of isolated ionic currents, a stochastic Hodgkin-Huxley (HH)-like model for the GnRH neuron is developed to reproduce each mode of burst firing with an appropriate set of conductances. Model outcomes for bursting are in agreement with the experimental recordings in terms of interburst interval, interspike interval, active phase duration, and other quantitative properties specific to each mode of bursting. The model also shows similar outcomes in membrane potential to those seen experimentally when tetrodotoxin (TTX) is used to block action potentials during bursting, and when estradiol transitions cells exhibiting slow oscillations to irregular bursting mode in vitro. Based on the parameter values used to reproduce each mode of bursting, the model suggests that GnRH neurons can switch between the two through changes in the maximum conductance of certain ionic currents, notably the slow inward Ca²⁺ current I _s, and the Ca²⁺ -activated K⁺ current I _KCa. Bifurcation analysis of the model shows that both modes of bursting are similar from a dynamical systems perspective despite differences in burst characteristics.     

How noisy adaptation of neurons shapes interspike interval histograms and correlations

Channel noise is the dominant intrinsic noise source of neurons causing variability in the timing of action potentials and interspike intervals (ISI). Slow adaptation currents are observed in many cells and strongly shape response properties of neurons. These currents are mediated by finite populations of ionic channels and may thus carry a substantial noise component. Here we study the effect of such adaptation noise on the ISI statistics of an integrate-and-fire model neuron by means of analytical techniques and extensive numerical simulations. We contrast this stochastic adaptation with the commonly studied case of a fast fluctuating current noise and a deterministic adaptation current (corresponding to an infinite population of adaptation channels). We derive analytical approximations for the ISI density and ISI serial correlation coefficient for both cases. For fast fluctuations and deterministic adaptation, the ISI density is well approximated by an inverse Gaussian (IG) and the ISI correlations are negative. In marked contrast, for stochastic adaptation, the density is more peaked and has a heavier tail than an IG density and the serial correlations are positive. A numerical study of the mixed case where both fast fluctuations and adaptation channel noise are present reveals a smooth transition between the analytically tractable limiting cases. Our conclusions are furthermore supported by numerical simulations of a biophysically more realistic Hodgkin-Huxley type model. Our results could be used to infer the dominant source of noise in neurons from their ISI statistics.     

Vulnerable window for conduction block in a one-dimensional cable of cardiac cells, 1: single extrasystoles

Spatial dispersion of refractoriness, which is amplified by genetic diseases, drugs, and electrical and structural remodeling during heart disease, is recognized as a major factor increasing the risk of lethal arrhythmias and sudden cardiac death. Dispersion forms the substrate for unidirectional conduction block, which is required for the initiation of reentry by extrasystoles or rapid pacing. In this study, we examine theoretically and numerically how preexisting gradients in refractoriness control the vulnerable window for unidirectional conduction block by a single premature extrasystole. Using a kinematic model to represent wavefront-waveback interactions, we first analytically derived the relationship (under simplified conditions) between the vulnerable window and various electrophysiological parameters such as action potential duration gradients, refractoriness barriers, conduction velocity restitution, etc. We then compared these findings to numerical simulations using the kinematic model or the Luo-Rudy action potential model in a one-dimensional cable of cardiac cells. The results from all three methods agreed well. We show that a critical gradient in action potential duration for conduction block can be analytically derived, and once this critical gradient is exceeded, the vulnerable window increases proportionately with the refractory barrier and is modulated by conduction velocity restitution and gap junctional conductance. Moreover, the critical gradient for conduction block is higher for an extrasystole traveling in the opposite direction from the sinus beat than for one traveling in the same direction (e.g., an epicardial extrasystole versus an endocardial extrasystole).     

A two-variable model of somatic-dendritic interactions in a bursting neuron

We present a two-variable delay-differential-equation model of a pyramidal cell from the electrosensory lateral line lobe of a weakly electric fish that is capable of burst discharge. It is a simplification of a six-dimensional ordinary differential equation model for such a cell whose bifurcation structure has been analyzed (Doiron et al., J. Comput. Neurosci., 12, 2002). We have modeled the effects of back-propagating action potentials by a delay, and use an integrate-and-fire mechanism for action potential generation. The simplicity of the model presented here allows one to explicitly derive a two-dimensional map for successive interspike intervals, and to analytically investigate the effects of time-dependent forcing on such a model neuron. Some of the effects discussed include ‘burst excitability’, the creation of resonance tongues under periodic forcing, and stochastic resonance. We also investigate the effects of changing the parameters of the model.     

Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure

A system of partial differential equations is derived as a model for the dynamics of a honey bee colony with a continuous age distribution, and the system is then extended to include the effects of a simplified infectious disease. In the disease-free case, we analytically derive the equilibrium age distribution within the colony and propose a novel approach for determining the global asymptotic stability of a reduced model. Furthermore, we present a method for determining the basic reproduction number \(R_0\) of the infection; the method can be applied to other age-structured disease models with interacting susceptible classes. The results of asymptotic stability indicate that a honey bee colony suffering losses will recover naturally so long as the cause of the losses is removed before the colony collapses. Our expression for \(R_0\) has potential uses in the tracking and control of an infectious disease within a bee colony.     

Initiation of an Inflammatory Response in Resident Intestinal Lamina Propria Cells -Use of a Human Organ Culture Model

Resident human lamina propria immune cells serve as powerful effectors in host defense. Molecular events associated with the initiation of an intestinal inflammatory response in these cells are largely unknown. Here, we aimed to characterize phenotypic and functional changes induced in these cells at the onset of intestinal inflammation using a human intestinal organ culture model. In this model, healthy human colonic mucosa was depleted of epithelial cells by EDTA treatment. Following loss of the epithelial layer, expression of the inflammatory mediators IL1B, IL6, IL8, IL23A, TNFA, CXCL2, and the surface receptors CD14, TLR2, CD86, CD54 was rapidly induced in resident lamina propria cells in situ as determined by qRT-PCR and immunohistology. Gene microarray analysis of lamina propria cells obtained by laser-capture microdissection provided an overview of global changes in gene expression occurring during the initiation of an intestinal inflammatory response in these cells. Bioinformatic analysis gave insight into signalling pathways mediating this inflammatory response. Furthermore, comparison with published microarray datasets of inflamed mucosa in vivo (ulcerative colitis) revealed a significant overlap of differentially regulated genes underlining the in vivo relevance of the organ culture model. Furthermore, genes never been previously associated with intestinal inflammation were identified using this model. The organ culture model characterized may be useful to study molecular mechanisms underlying the initiation of an intestinal inflammatory response in normal mucosa as well as potential alterations of this response in inflammatory bowel disease.     

Threshold dynamics of an infective disease model with a fixed latent period and non-local infections

In this paper, we derive and analyze an infectious disease model containing a fixed latency and non-local infection caused by the mobility of the latent individuals in a continuous bounded domain. The model is given by a spatially non-local reaction–diffusion system carrying a discrete delay associated with the zero-flux condition on the boundary. By applying some existing abstract results in dynamical systems theory, we prove the existence of a global attractor for the model system. By appealing to the theory of monotone dynamical systems and uniform persistence, we show that the model has the global threshold dynamics which can be described either by the principal eigenvalue of a linear non-local scalar reaction diffusion equation or equivalently by the basic reproduction number ${\mathcal{R}_0}$ for the model. Such threshold dynamics predicts whether the disease will die out or persist. We identify the next generation operator, the spectral radius of which defines basic reproduction number. When all model parameters are constants, we are able to find explicitly the principal eigenvalue and ${\mathcal{R}_0}$ . In addition to computing the spectral radius of the next generation operator, we also discuss an alternative way to compute ${\mathcal{R}_0}$ .