Motoneuron membrane potentials follow a time inhomogeneous jump diffusion process

Stochastic leaky integrate-and-fire models are popular due to their simplicity and statistical tractability. They have been widely applied to gain understanding of the underlying mechanisms for spike timing in neurons, and have served as building blocks for more elaborate models. Especially the Ornstein–Uhlenbeck process is popular to describe the stochastic fluctuations in the membrane potential of a neuron, but also other models like the square-root model or models with a non-linear drift are sometimes applied. Data that can be described by such models have to be stationary and thus, the simple models can only be applied over short time windows. However, experimental data show varying time constants, state dependent noise, a graded firing threshold and time-inhomogeneous input. In the present study we build a jump diffusion model that incorporates these features, and introduce a firing mechanism with a state dependent intensity. In addition, we suggest statistical methods to estimate all unknown quantities and apply these to analyze turtle motoneuron membrane potentials. Finally, simulated and real data are compared and discussed. We find that a square-root diffusion describes the data much better than an Ornstein–Uhlenbeck process with constant diffusion coefficient. Further, the membrane time constant decreases with increasing depolarization, as expected from the increase in synaptic conductance. The network activity, which the neuron is exposed to, can be reasonably estimated to be a threshold version of the nerve output from the network. Moreover, the spiking characteristics are well described by a Poisson spike train with an intensity depending exponentially on the membrane potential.     

Central and peripheral neurosecretory pathways to an insect flight motor nerve

Ultrastructural examination of the IIN1b nerve to the dorsal longitudinal flight muscle of Manduca sexta L. verified the presence of neurosecretory processes. Subspherical and irregular vesicles were found where the nerve enters the muscle, while spherical vesicles were found in the proximal region only. A dorsal unpaired median (DUM) cell, the median nervous system, and two or more peripheral cells are the sources of these neurosecretory inclusions. Light the electron microscopy CoCl2 backfills of the transverse nerve produced intensification of a peripheral neuron (#1) and processes in nerves IIN1a and IIN1b. Similar backfills of nerve IIN1b produced intensification of a DUM cell, a second peripheral neuron (#2), and processes in the transverse nerve and nerve IIN1a. Neuron #1 contained large spherical electron-dense vesicles while neuron #2 contained smaller subspherical vesicles. These cells were situated upon the link and/or transverse nerves. Based on these results, we suspect central and peripheral neurosecretory processes reach nerve IIN1b as follows: the link nerve projects prothoracic median nervous system and neuron #2 processes, nerve IIN1a projects neuron #1 processes, and nerve IIN1 projects mesothoracic DUM cell processes, although this latter pathway was less clear.     

And the noise played on: stochastic gene expression and HIV-1 infection

Stochastic gene expression has been implicated in a variety of cellular processes, including cell differentiation and disease. In this issue of Cell, take an integrated computational-experimental approach to study the Tat transactivation feedback loop of HIV-1. They show that fluctuations in a key regulator, Tat, in an isogenic population of infected cells result in two distinct expression states corresponding to latent and productive HIV-1 infection. These findings demonstrate the importance of stochastic gene expression in molecular "decision-making."     

Stochastic fluctuations in frequency-dependent selection: a one-locus, two-allele and two-phenotype model

Stochastic fluctuations in a simple frequency-dependent selection model with one-locus, two-alleles and two-phenotypes are investigated. The steady-state statistics of allele frequencies for an interior stable phenotypic equilibrium are shown to be similar to the stochastic fluctuations in standard evolutionary game dynamics [Tao, Y., Cressman, R., 2007. Stochastic fluctuations through intrinsic noise in evolutionary game dynamics. Bull. Math. Biol. 69, 1377-1399]. On the other hand, for an interior stable phenotypic or genotypic equilibrium, our main results show that the deterministic model cannot be used to predict the expectation of phenotypic frequency. The variance of phenotypic frequency for an interior stable genotypic equilibrium is more sensitive to the expected population size than for an interior stable phenotypic equilibrium. Furthermore, the stochastic fluctuations of allele frequency and phenotypic frequency can be considered approximately independent of each other for these genotypic equilibria, but not for phenotypic.     

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.     

双层Hodgkin-Huxley神经元网络中的随机共振

随机共振是一种非零噪声优化系统响应的现象。运用信噪比的评价方式,研究单个Hodgkin-Huxley神经元及其所构建的双层神经元网络中的随机共振,来模拟生物感觉系统中检测微弱信号的随机共振现象。结果表明,单个神经元在阈值下存在噪声优化系统检测性能的随机共振现象,但是最优的噪声强度却随外部信号性质的改变而变化;双层神经元网络不但可以在固定的噪声强度上对一定幅度范围内的阈下信号进行优化检测,而且噪声的存在并没有降低网络对阈上信号的检测能力。     

Cytoplasmic syncytial interneuronal connection in molluscs

The absolute criteria developed by the authors have been presented; they allow revealing cytoplasmic syncytial connections between processes of nerve cells in vivo and in vitro at the light microscopy level by using classical methods and time lapse videoshooting in the phase contrast. With aid of electron microscopy, metastable membrane contacts and their perforations, cytoplasmic syncytial interneuronal pores, and fusion of nerve processes are demonstrated. In the culture of isolated molluscan neurons, the process of formation of syncytial connections between processes of the same neuron or of different neurons is reproduced. Processes of one neuron, which have syncytial connection with another neuron, are shown to remain viable after death of its neuronal soma. The cytoplasmic varicosities formed on processes of one neuron are able to overcome the place of syncytial contact with processes of another neuron and to move to the body of the latter. A hypothesis is put forward that the cytoplasmic syncytial connection between nerve processes is formed under the conditions of the absence of their glial sheaths.     

Signal detection theory,detectability and stochastic resonance effects

 Stochastic resonance is a phenomenon in which the performance of certain non-linear detectors can be enhanced by the addition of appropriate levels of random noise. Signal detection theory offers a powerful tool for analysing this type of system, through an ability to separate detection processes into reception and classification, with the former generally being linear and the latter always non-linear. Through appropriate measures of signal detectability it is possible to decide whether a local improvement in detection via stochastic resonance occurs due to the non-linear effects of the classification process. In this case, improvement of detection through the addition of noise can never improve detection beyond that of a corresponding adaptive system. Signal detection and stochastic resonance is investigated in several integrate-and-fire neuron models. It is demonstrated that the stochastic resonance observed in spiking models is caused by non-linear properties of the spike-generation process itself. The true detectability of the signal, as seen by the receiver part of the spiking neuron (the integrator part), decreases monotonically with input noise level for all signal and noise intensities. Received: 3 April 2001 / Accepted in revised form: 8 March 2002     

Modern Concepts of Cholinergic Neurotransmission at the Motor Synapse

Cholinergic synaptic contact between motor neuron and skeletal muscle fiber is perhaps one of the core objects for investigations of molecular mechanisms underlying the communication between neurons and innervated cells. In the studies conducted on this object in the past few decades, a large amount of experimental data was obtained that substantially complemented a traditional view on synaptic transmission. In particular, it was established that (i) acetylcholine is released from the nerve ending in both quantal and nonquantal ways; (ii) molecular mechanisms of the processes of the quantal acetylcholine release—spontaneous and evoked by electrical stimuli—have unique features and can be regulated independently; (iii) acetylcholine release from the nerve ending is accompanied by a release of a number of synaptically active molecules modulating the processes of secretion or reception of the main mediator; (iv) signal molecules affecting the process of cholinergic neurotransmission can be released not only from the nerve ending but also from glial cells and muscle fiber; (v) molecular mechanisms of the regulation of synaptic transmission are highly diverse and go beyond the alteration of the number of the released acetylcholine quanta. Thus, the neuromuscular junction shall be deemed currently as complicated and adaptive synapse characterized by a wide range of multiloop intercellular signaling pathways between presynaptic motor neuron ending, muscle fiber, and glial cells ensuring a high safety factor of synaptic transmission and the possibility of its fine tuning.     

Bistable MAP kinase activity: a plausible mechanism contributing to maintenance of late long-term potentiation

Bistability of MAP kinase (MAPK) activity has been suggested to contribute to several cellular processes, including differentiation and long-term synaptic potentiation. A recent model (Markevich NI, Hoek JB, Kholodenko BN. J Cell Biol 164: 353–359, 2004) predicts bistability due to interactions of the kinases and phosphatases in the MAPK pathway, without feedback from MAPK to earlier reactions. Using this model and enzyme concentrations appropriate for neurons, we simulated bistable MAPK activity, but bistability was present only within a relatively narrow range of activity of Raf, the first pathway kinase. Stochastic fluctuations in molecule numbers eliminated bistability for small molecule numbers, such as are expected in the volume of a dendritic spine. However, positive-feedback loops have been posited from MAPK up to Raf activation. One proposed loop in which MAPK directly activates Raf was incorporated into the model. We found that such feedback greatly enhanced the robustness of both stable states of MAPK activity to stochastic fluctuations and to parameter variations. Bistability was robust for molecule numbers plausible for a dendritic spine volume. The upper state of MAPK activity was resistant to inhibition of MEK activation for >1 h, which suggests that inhibitor experiments have not sufficed to rule out a role for persistent MAPK activity in the maintenance of long-term potentiation (LTP). These simulations suggest that persistent MAPK activity and consequent upregulation of translation may contribute to LTP maintenance and to long-term memory. Experiments using a fluorescent MAPK substrate may further test this hypothesis. feedback; bistability; memory; model; stochastic     

Emergence of resonances in neural systems: the interplay between adaptive threshold and short-term synaptic plasticity

In this work we study the detection of weak stimuli by spiking (integrate-and-fire) neurons in the presence of certain level of noisy background neural activity. Our study has focused in the realistic assumption that the synapses in the network present activity-dependent processes, such as short-term synaptic depression and facilitation. Employing mean-field techniques as well as numerical simulations, we found that there are two possible noise levels which optimize signal transmission. This new finding is in contrast with the classical theory of stochastic resonance which is able to predict only one optimal level of noise. We found that the complex interplay between adaptive neuron threshold and activity-dependent synaptic mechanisms is responsible for this new phenomenology. Our main results are confirmed by employing a more realistic FitzHugh-Nagumo neuron model, which displays threshold variability, as well as by considering more realistic stochastic synaptic models and realistic signals such as poissonian spike trains.     

A quantitative analysis of single protein-ligand complex separation with the atomic force microscope

Force measurements on and within single macromolecular complexes utilizing techniques such as atomic force microscopy, optical trapping, flexible glass fibers, and magnetic beads provide a rich source of quantitative data on biomolecular processes. Stochastic thermal fluctuations, an undesirable source of noise in macroscopic biochemical experiments, are an essential element of these sensitive and novel experiments. With the proper analysis, a great deal of information can be gleaned from measurements of these fluctuations. A quantitative framework for analyzing such measurements, based on Kramers' theory of molecular dissociation, is developed. The analysis reveals the kinetic origin and stochastic nature of the measurements. This framework is presented in the context of protein-ligand separation with the atomic force microscope.     

Stochastic Ion Channel Gating in Dendritic Neurons: Morphology Dependence and Probabilistic Synaptic Activation of Dendritic Spikes

Neuronal activity is mediated through changes in the probability of stochastic transitions between open and closed states of ion channels. While differences in morphology define neuronal cell types and may underlie neurological disorders, very little is known about influences of stochastic ion channel gating in neurons with complex morphology. We introduce and validate new computational tools that enable efficient generation and simulation of models containing stochastic ion channels distributed across dendritic and axonal membranes. Comparison of five morphologically distinct neuronal cell types reveals that when all simulated neurons contain identical densities of stochastic ion channels, the amplitude of stochastic membrane potential fluctuations differs between cell types and depends on sub-cellular location. For typical neurons, the amplitude of membrane potential fluctuations depends on channel kinetics as well as open probability. Using a detailed model of a hippocampal CA1 pyramidal neuron, we show that when intrinsic ion channels gate stochastically, the probability of initiation of dendritic or somatic spikes by dendritic synaptic input varies continuously between zero and one, whereas when ion channels gate deterministically, the probability is either zero or one. At physiological firing rates, stochastic gating of dendritic ion channels almost completely accounts for probabilistic somatic and dendritic spikes generated by the fully stochastic model. These results suggest that the consequences of stochastic ion channel gating differ globally between neuronal cell-types and locally between neuronal compartments. Whereas dendritic neurons are often assumed to behave deterministically, our simulations suggest that a direct consequence of stochastic gating of intrinsic ion channels is that spike output may instead be a probabilistic function of patterns of synaptic input to dendrites.     

Influence of temporal correlation of synaptic input on the rate and variability of firing in neurons

The spike trains that transmit information between neurons are stochastic. We used the theory of random point processes and simulation methods to investigate the influence of temporal correlation of synaptic input current on firing statistics. The theory accounts for two sources for temporal correlation: synchrony between spikes in presynaptic input trains and the unitary synaptic current time course. Simulations show that slow temporal correlation of synaptic input leads to high variability in firing. In a leaky integrate-and-fire neuron model with spike afterhyperpolarization the theory accurately predicts the firing rate when the spike threshold is higher than two standard deviations of the membrane potential fluctuations. For lower thresholds the spike afterhyperpolarization reduces the firing rate below the theory's predicted level when the synaptic correlation decays rapidly. If the synaptic correlation decays slower than the spike afterhyperpolarization, spike bursts can occur during single broad peaks of input fluctuations, increasing the firing rate over the prediction. Spike bursts lead to a coefficient of variation for the interspike intervals that can exceed one, suggesting an explanation of high coefficient of variation for interspike intervals observed in vivo.     

Acceleratory nervous regulation of juvenile myogenic hearts in the isopod crustacean Ligia exotica

We examined regulation of the myogenic heart by two identified cardioacceleratory neurons (CA1, CA2) in early juveniles of the isopod Ligia exotica. Repetitive stimulation of either the CA1 or CA2 axon increased the frequency and plateau amplitude of the action potential and decreased the maximum hyperpolarization of the cardiac muscle. These effects were larger with increasing stimulus frequency. The rate of increase in the frequency caused by CA1 stimulation was significantly larger than that by CA2. No impulse activity of the cardiac ganglion was induced by acceleratory nerve stimulation. The frequency of the muscle activity was decreased by injection of a hyperpolarizing current into the muscle during stimulation of the acceleratory nerve. In a quiescent heart, acceleratory nerve stimulation caused an overall depolarization in the muscle membrane and the amplitude of the depolarization induced by CA1 stimulation was significantly larger than that by CA2. These results suggest that CA1 and CA2 neurons regulate the myogenic heart affecting directly the cardiac muscle; the CA1 neuron produces more potent effects than does the CA2 neuron.     

Scanning electron microscopy of nerve-muscle contacts in embryonic cell culture.

Scanning electron microscopy (SEM) of cell cultures of dissociated nerve and muscle from chick embryos has shown that developing muscle fibers can be contacted at many sites by one or more than one neuron, and that a single nerve can send branches to several myofibers. At these contact regions of nerve with muscle, the neurons send out terminal or lateral sprouts with fine tips which initially lack terminal swellings, but later acquire small “bouton”-like structures in contact with the sarcolemma, which resemble embryonic synapses. At these points, the sarcolemma does not appear to differ in ultrastructure from other surface regions of the myofiber. Transmission electron microscopy (TEM) has revealed the presence of both electron lucent and dense-cored vesicles at some nerve terminals. However, fluorescence histochemistry (Falck-Hillarp technique) failed to detect the presence of catecholamines in these cultures. The SEM pictures at substantially higher resolutions than the light microscope, and the enhanced three dimensional perspective of this technique, provide additional information about the developmental morphology of the nerve-muscle cell culture system. The results are correlated with previous findings by light microscopy, TEM and electrophysiology, and discussed in relationship to proposed innervation processes of skeletal muscle fibers in vivo.     

On the linear birth and death processes of biology as Markoff chains

Stochastic Markoff models for the linear birth and death population growth processes of biology are constructed using the Q-matrix method of Doob. The relationship of the stochastic theory to the classical deterministic foundations of these processes is stressed by showing in detail how the classical postulates are mathematically transformed via the Q-matrix elements into the basis for a stationary Markoff process with continuous time parameter and denumerably many “populations states.” It is shown that the resulting stochastic models predict that the population size will fluctuate about the deterministic time curve, the extent of fluctuation being measured by the variance functions. General formulas covering all possible transitions from one population size to another are derived.     

Presymptomatic biochemical changes in hindlimb muscle of G93A human Cu/Zn superoxide dismutase 1 transgenic mouse model of amyotrophic lateral sclerosis

Amyotrophic lateral sclerosis (ALS) is primarily a motor neuron disorder. Intriguingly, early muscle denervation preceding motor neuron loss is observed in mouse models of ALS. Enhanced muscle vulnerability to denervation process has been suggested by accelerated muscle deterioration following peripheral nerve injury in an ALS mouse model. Here we provide evidence of biochemical changes in the hindlimb muscle of young, presymptomatic G93A hSOD1 transgenic mice. In this report, we demonstrate that cdk5 activity is reduced in hindlimb muscle of 27-day-old G93A hSOD1 transgenic mice. In vitro analysis revealed mutant hSOD1-mediated suppression of cdk5 activity. Furthermore, the decrease in muscle cdk5 activity was accompanied by a significant reduction in MyoD and cyclin D1 levels. These early muscle changes raise the possibility that the progressive deterioration of muscle function is potentiated by altered muscle biochemistry in these mice at a very young, presymptomatic age.     

Stochastic effects and bistability in T cell receptor signaling

The stochastic dynamics of T cell receptor (TCR) signaling are studied using a mathematical model intended to capture kinetic proofreading (sensitivity to ligand-receptor binding kinetics) and negative and positive feedback regulation mediated, respectively, by the phosphatase SHP1 and the MAP kinase ERK. The model incorporates protein-protein interactions involved in initiating TCR-mediated cellular responses and reproduces several experimental observations about the behavior of TCR signaling, including robust responses to as few as a handful of ligands (agonist peptide-MHC complexes on an antigen-presenting cell), distinct responses to ligands that bind TCR with different lifetimes, and antagonism. Analysis of the model indicates that TCR signaling dynamics are marked by significant stochastic fluctuations and bistability, which is caused by the competition between the positive and negative feedbacks. Stochastic fluctuations are such that single-cell trajectories differ qualitatively from the trajectory predicted in the deterministic approximation of the dynamics. Because of bistability, the average of single-cell trajectories differs markedly from the deterministic trajectory. Bistability combined with stochastic fluctuations allows for switch-like responses to signals, which may aid T cells in making committed cell-fate decisions.