Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources

We investigated how selected electromorphological parameters of myelinated axons influence the preservation of interspike intervals when the propagation of action potentials is corrupted by axonal intrinsic noise. Hereby we tried to determine how the intrinsic axonal noise influences the performance of axons serving as carriers for temporal coding. The strategy of this coding supposes that interspike intervals presented to higher order neurons would minimally be deprived of information included in interspike intervals at the axonal initial segment. Our experiments were conducted using a computer model of the myelinated axon constructed in a software environment GENESIS (GEneral NEural SImulation System). We varied the axonal diameter, myelin sheath thickness, axonal length, stimulation current and channel distribution to determine how these parameters influence the role of noise in spike propagation and hence in preserving the interspike intervals. Our results, expressed as the standard deviation of spike travel times, showed that by stimulating the axons with regular rectangular pulses the interspike intervals were preserved with a microsecond accuracy. Stimulating the axons with pulses imitating postsynaptic currents, greater changes of interspike intervals were found, but the influence of implemented noise on the jitter of interspike intervals was approximately the same.     

Model of spike propagation reliability along the myelinated axon corrupted by axonal intrinsic noise sources

We investigated how selected electromorphological parameters of myelinated axons influence the preservation of interspike intervals when the propagation of action potentials is corrupted by axonal intrinsic noise. Hereby we tried to determine how the intrinsic axonal noise influences the performance of axons serving as carriers for temporal coding. The strategy of this coding supposes that interspike intervals presented to higher order neurons would minimally be deprived of information included in interspike intervals at the axonal initial segment. Our experiments were conducted using a computer model of the myelinated axon constructed in a software environment GENESIS (GEneral NEural SImulation System). We varied the axonal diameter, myelin sheath thickness, axonal length, stimulation current and channel distribution to determine how these parameters influence the role of noise in spike propagation and hence in preserving the interspike intervals. Our results, expressed as the standard deviation of spike travel times, showed that by stimulating the axons with regular rectangular pulses the interspike intervals were preserved with a microsecond accuracy. Stimulation with pulses imitating postsynaptic currents, greater changes of interspike intervals were found, but the influence of implemented noise on the jitter of interspike intervals was approximately the same.     

Threshold fatigue and information transfer

Neurons in vivo must process sensory information in the presence of significant noise. It is thus plausible to assume that neural systems have developed mechanisms to reduce this noise. Theoretical studies have shown that threshold fatigue (i.e. cumulative increases in the threshold during repetitive firing) could lead to noise reduction at certain frequencies bands and thus improved signal transmission as well as noise increases and decreased signal transmission at other frequencies: a phenomenon called noise shaping. There is, however, no experimental evidence that threshold fatigue actually occurs and, if so, that it will actually lead to noise shaping. We analyzed action potential threshold variability in intracellular recordings in vivo from pyramidal neurons in weakly electric fish and found experimental evidence for threshold fatigue: an increase in instantaneous firing rate was on average accompanied by an increase in action potential threshold. We show that, with a minor modification, the standard Hodgkin–Huxley model can reproduce this phenomenon. We next compared the performance of models with and without threshold fatigue. Our results show that threshold fatigue will lead to a more regular spike train as well as robustness to intrinsic noise via noise shaping. We finally show that the increased/reduced noise levels due to threshold fatigue correspond to decreased/increased information transmission at different frequencies. Action Editor: David Golomb     

Intrinsic Noise of microRNA-Regulated Genes and the ceRNA Hypothesis

MicroRNAs are small noncoding RNAs that regulate genes post-transciptionally by binding and degrading target eukaryotic mRNAs. We use a quantitative model to study gene regulation by inhibitory microRNAs and compare it to gene regulation by prokaryotic small non-coding RNAs (sRNAs). Our model uses a combination of analytic techniques as well as computational simulations to calculate the mean-expression and noise profiles of genes regulated by both microRNAs and sRNAs. We find that despite very different molecular machinery and modes of action (catalytic vs stoichiometric), the mean expression levels and noise profiles of microRNA-regulated genes are almost identical to genes regulated by prokaryotic sRNAs. This behavior is extremely robust and persists across a wide range of biologically relevant parameters. We extend our model to study crosstalk between multiple mRNAs that are regulated by a single microRNA and show that noise is a sensitive measure of microRNA-mediated interaction between mRNAs. We conclude by discussing possible experimental strategies for uncovering the microRNA-mRNA interactions and testing the competing endogenous RNA (ceRNA) hypothesis.     

Effect of channel block on the spiking activity of excitable membranes in a stochastic Hodgkin-Huxley model

The influence of intrinsic channel noise on the spontaneous spiking activity of poisoned excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels is known to affect the collective properties of the whole ion channel cluster. For example, there exists an optimal size of the membrane patch for which the internal noise alone causes a regular spontaneous generation of action potentials. In addition to varying the size of ion channel clusters, living organisms may adapt the densities of ion channels in order to optimally regulate the spontaneous spiking activity. The influence of a channel block on the excitability of a membrane patch of a certain size is twofold: first, a variation of ion channel densities primarily yields a change of the conductance level; second, a down-regulation of working ion channels always increases the channel noise. While the former effect dominates in the case of sodium channel block resulting in a reduced spiking activity, the latter enhances the generation of spontaneous action potentials in the case of a tailored potassium channel blocking. Moreover, by blocking some portion of either potassium or sodium ion channels, it is possible to either increase or decrease the regularity of the spike train.     

On the Firing Rate Dependency of the Phase Response Curve of Rat Purkinje Neurons In Vitro

Synchronous spiking during cerebellar tasks has been observed across Purkinje cells: however, little is known about the intrinsic cellular mechanisms responsible for its initiation, cessation and stability. The Phase Response Curve (PRC), a simple input-output characterization of single cells, can provide insights into individual and collective properties of neurons and networks, by quantifying the impact of an infinitesimal depolarizing current pulse on the time of occurrence of subsequent action potentials, while a neuron is firing tonically. Recently, the PRC theory applied to cerebellar Purkinje cells revealed that these behave as phase-independent integrators at low firing rates, and switch to a phase-dependent mode at high rates. Given the implications for computation and information processing in the cerebellum and the possible role of synchrony in the communication with its post-synaptic targets, we further explored the firing rate dependency of the PRC in Purkinje cells. We isolated key factors for the experimental estimation of the PRC and developed a closed-loop approach to reliably compute the PRC across diverse firing rates in the same cell. Our results show unambiguously that the PRC of individual Purkinje cells is firing rate dependent and that it smoothly transitions from phase independent integrator to a phase dependent mode. Using computational models we show that neither channel noise nor a realistic cell morphology are responsible for the rate dependent shift in the phase response curve.     

A fiber-based ratiometric optical cardiac mapping channel using a diffraction grating and split detector

Optical fiber-based mapping systems are used to record the cardiac action potential (AP) throughout the myocardium. The optical AP contains a contraction-induced motion artifact (MA), which makes it difficult to accurately measure the action potential duration (APD). MA is removed by preventing contraction with electrical-mechanical uncoupling drugs, such as 2,3-butanedione monoxime (BDM). We designed a novel fiber-based ratiometric optical channel using a blue light emitting diode, a diffraction grating, and a split photodetector that can accurately measure the cardiac AP without the need for BDM. The channel was designed based on simulations using the optical design software ZEMAX. The channel has an electrical bandwidth of 150 Hz and an root mean-square dark noise of 742 muV. The channel successfully recorded the cardiac AP from the wall of five rabbit heart preparations without the use of BDM. After 20-point median filtering, the mean signal/noise ratio was 25.3 V/V. The APD measured from the base of a rabbit heart was 134 +/- 8.4 ms, compared to 137.6 +/- 3.3 ms from simultaneous microelectrode recordings. This difference was not statistically significant (p-value = 0.3). The quantity of MA removed was also measured using the motion ratio. The reduction in MA was significant (p-value = 0.0001). This fiber-based system is the first of its kind to enable optical APD measurements in the beating heart wall without the use of BDM.     

Thermal properties of rhodopsin: insight into the molecular mechanism of dim-light vision

Rhodopsin has developed mechanisms to optimize its sensitivity to light by suppressing dark noise and enhancing quantum yield. We propose that an intramolecular hydrogen-bonding network formed by ～20 water molecules, the hydrophilic residues, and peptide backbones in the transmembrane region is essential to restrain thermal isomerization, the source of dark noise. We studied the thermal stability of rhodopsin at 55 °C with single point mutations (E181Q and S186A) that perturb the hydrogen-bonding network at the active site. We found that the rate of thermal isomerization increased by 1-2 orders of magnitude in the mutants. Our results illustrate the importance of the intact hydrogen-bonding network for dim-light detection, revealing the functional roles of water molecules in rhodopsin. We also show that thermal isomerization of 11-cis-retinal in solution can be catalyzed by wild-type opsin and that this catalytic property is not affected by the mutations. We characterize the catalytic effect and propose that it is due to steric interactions in the retinal-binding site and increases quantum yield by predetermining the trajectory of photoisomerization. Thus, our studies reveal a balancing act between dark noise and quantum yield, which have opposite effects on the thermal isomerization rate. The acquisition of the hydrogen-bonding network and the tuning of the steric interactions at the retinal-binding site are two important factors in the development of dim-light vision.     

Intrinsic coherence resonance in excitable membrane patches

The influence of intrinsic channel noise on the spiking activity of excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels does affect the electric properties of the cell-membrane patches. There exists an optimal size of the membrane patch for which the internal noise alone can cause a nearly regular spontaneous generation of action potentials. We consider the influence of intrinsic channel noise in presence of a constant and an oscillatory current driving for both, the mean interspike interval and the phenomenon of coherence resonance for neuronal spiking. Given small membrane patches, implying that channel noise dominates the excitable dynamics, we find the phenomenon of intrinsic coherence resonance. In this case, the relatively regular spiking behavior becomes essentially independent of an applied stimulus. We observed, however, the occurrence of a skipping of supra-threshold input events due to channel noise for intermediate patch sizes. This effect consequently reduces the overall coherence of the spiking.     

Interior-Point Methods for Estimating Seasonal Parameters in Discrete-Time Infectious Disease Models

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.     

Can quantum-bumps in photoreceptors be reconstructed from noise-data?

The method of reconstructing quantum bumps in photoreceptor cells from noise data by making use of shot noise theory is critically reviewed. The application of this method produces results irrespective of whether the conditions for reconstructing bumps by the method are satisfied or not and even irrespective of whether at high stimulus intensities quantum bumps exist or not. We argue that at high intensities the concept of quantum bumps indeed becomes physically meaningless and degenerates to a purely mathematical concept. In order to investigate the meaning of the results of the reconstruction method, we submit it to a test model for which bumps and single channel opening events can be evaluated analytically. By comparing the analytical results of the test model with that of the reconstruction method applied to the test model we find: (1) even at low intensities, the reconstructed bump values deviate from the analytical results by up to an order of magnitude due to the variability of the bumps, (2) at high intensities, the reconstruction method produces single chennel opening events rather than anything like a quantum bump. We also find, however, that there is no continuous transition from a bump at low intensities to a single channel event at high intensities.     

Axonal Noise as a Source of Synaptic Variability

Post-synaptic potential (PSP) variability is typically attributed to mechanisms inside synapses, yet recent advances in experimental methods and biophysical understanding have led us to reconsider the role of axons as highly reliable transmission channels. We show that in many thin axons of our brain, the action potential (AP) waveform and thus the Ca⁺⁺ signal controlling vesicle release at synapses will be significantly affected by the inherent variability of ion channel gating. We investigate how and to what extent fluctuations in the AP waveform explain observed PSP variability. Using both biophysical theory and stochastic simulations of central and peripheral nervous system axons from vertebrates and invertebrates, we show that channel noise in thin axons (<1 µm diameter) causes random fluctuations in AP waveforms. AP height and width, both experimentally characterised parameters of post-synaptic response amplitude, vary e.g. by up to 20 mV and 0.5 ms while a single AP propagates in C-fibre axons. We show how AP height and width variabilities increase with a ¾ power-law as diameter decreases and translate these fluctuations into post-synaptic response variability using biophysical data and models of synaptic transmission. We find for example that for mammalian unmyelinated axons with 0.2 µm diameter (matching cerebellar parallel fibres) axonal noise alone can explain half of the PSP variability in cerebellar synapses. We conclude that axonal variability may have considerable impact on synaptic response variability. Thus, in many experimental frameworks investigating synaptic transmission through paired-cell recordings or extracellular stimulation of presynaptic neurons, causes of variability may have been confounded. We thereby show how bottom-up aggregation of molecular noise sources contributes to our understanding of variability observed at higher levels of biological organisation.     

Quantum transport in the FMO photosynthetic light-harvesting complex

The very high light-harvesting efficiency of natural photosynthetic systems in conjunction with recent experiments, which showed quantum-coherent energy transfer in photosynthetic complexes, raised questions regarding the presence of non-trivial quantum effects in photosynthesis. Grover quantum search, quantum walks, and entanglement have been investigated as possible effects that lead to this efficiency. Here we explain the near-unit photosynthetic efficiency without invoking non-trivial quantum effects. Instead, we use non-equilibrium Green’s functions, a mesoscopic method used to study transport in nano-conductors to compute the transmission function of the Fenna–Matthews–Olson (FMO) complex using an experimentally derived exciton Hamiltonian. The chlorosome antenna and the reaction center play the role of input and output contacts, connected to the FMO complex. We show that there are two channels for which the transmission is almost unity. Our analysis also revealed a dephasing-driven regulation mechanism that maintains the efficiency in the presence of varying dephasing potentials.     

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.     

Dark Energy from Discrete Spacetime

Dark energy accounts for most of the matter-energy content of our universe, yet current theories of its origin rely on radical physical assumptions such as the holographic principle or controversial anthropic arguments. We give a better motivated explanation for dark energy, claiming that it arises from a small negative scalar-curvature present even in empty spacetime. The vacuum has this curvature because spacetime is fundamentally discrete and there are more ways for a discrete geometry to have negative curvature than positive. We explicitly compute this effect using a variant of the well known dynamical-triangulations (DT) model for quantum gravity. Our model predicts a time-varying non-zero cosmological constant with a current value, in natural units, in agreement with observation. This calculation is made possible by a novel characterization of the possible DT action values combined with numerical evidence concerning their degeneracies.     

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane, but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential, the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley-like modeling takes into account both the channel noise-i.e. the fluctuations of the number of open ion channels-and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of a variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.     

Ion-channel noise places limits on the miniaturization of the brain's wiring

The action potential (AP) is transmitted by the concerted action of voltage-gated ion channels. Thermodynamic fluctuations in channel proteins produce probabilistic gating behavior, causing channel noise. Miniaturizing signaling systems increases susceptibility to noise, and with many cortical, cerebellar, and peripheral axons <0.5 mum diameter [1, 2 and 3], channel noise could be significant [4 and 5]. Using biophysical theory and stochastic simulations, we investigated channel-noise limits in unmyelinated axons. Axons of diameter below 0.1 microm become inoperable because single, spontaneously opening Na channels generate spontaneous AP at rates that disrupt communication. This limiting diameter is relatively insensitive to variations in biophysical parameters (e.g., channel properties and density, membrane conductance and leak) and will apply to most spiking axons. We demonstrate that the essential molecular machinery can, in theory, fit into 0.06 microm diameter axons. However, a comprehensive survey of anatomical data shows a lower limit for AP-conducting axons of 0.08-0.1 microm diameter. Thus, molecular fluctuations constrain the wiring density of brains. Fluctuations have implications for epilepsy and neuropathic pain because changes in channel kinetics or axonal properties can change the rate at which channel noise generates spontaneous activity.     

Field-dependent effect of crown ether (18-crown-6) on ionic conductance of alpha-hemolysin channels

Closing linear poly(ethylene glycol) (PEG) into a circular "crown" dramatically changes its dynamics in the alpha-hemolysin channel. In the electrically neutral crown ether (C2H4O)6, six ethylene oxide monomers are linked into a circle that gives the molecule ion-complexing capacity and increases its rigidity. As with linear PEG, addition of the crown to the membrane-bathing solution decreases the ionic conductance of the channel and generates additional conductance noise. However, in contrast to linear PEG, both the conductance reduction (reporting on crown partitioning into the channel pore) and the noise (reporting on crown dynamics in the pore) now depend on voltage strongly and nonmonotonically. Within the whole frequency range accessible in channel reconstitution experiments, the noise power spectrum is "white", showing that crown exchange between the channel and the bulk solution is fast. Analyzing these data in the framework of a Markovian two-state model, we are able to characterize the process quantitatively. We show that the lifetime of the crown in the channel reaches its maximum (a few microseconds) at about the same voltage (approximately 100 mV, negative from the side of protein addition) where the crown's reduction of the channel conductance is most pronounced. Our interpretation is that, because of its rigidity, the crown feels an effective steric barrier in the narrowest part of the channel pore. This barrier together with crown-ion complexing and resultant interaction with the applied field leads to behavior usually associated with voltage-dependent binding in the channel pore.