Sensitivity analysis of point neuron model simulations implemented on neuromorphic hardware.

With the ongoing growth in the field of neuro-inspired computing, newly arriving computational architectures demand extensive validation and testing against existing benchmarks to establish their competence and value. In our work, we break down the validation step into two parts-(1) establishing a methodological and numerical groundwork to establish a comparison between neuromorphic and conventional platforms and, (2) performing a sensitivity analysis on the obtained model regime to assess its robustness. We study the neuronal dynamics based on the Leaky Integrate and Fire (LIF) model, which is built upon data from the mouse visual cortex spanning a set of anatomical and physiological constraints. Intel Corp.'s first neuromorphic chip "Loihi" serves as our neuromorphic platform and results on it are validated against the classical simulations. After setting up a model that allows a seamless mapping between the Loihi and the classical simulations, we find that Loihi replicates classical simulations very efficiently with high precision. This model is then subjected to the second phase of validation, through sensitivity analysis, by assessing the impact on the cost function as values of the significant model parameters are varied. The work is done in two steps-(1) assessing the impact while changing one parameter at a time, (2) assessing the impact while changing two parameters at a time. We observe that the model is quite robust for majority of the parameters with slight change in the cost function. We also identify a subset of the model parameters changes which make the model more sensitive and thus, need to be defined more precisely.

Symmetry-Breaking Bifurcations of the Information Bottleneck and Related Problems.

In this paper, we investigate the bifurcations of solutions to a class of degenerate constrained optimization problems. This study was motivated by the Information Bottleneck and Information Distortion problems, which have been used to successfully cluster data in many different applications. In the problems we discuss in this paper, the distortion function is not a linear function of the quantizer. This leads to a challenging annealing optimization problem, which we recast as a fixed-point dynamics problem of a gradient flow of a related dynamical system. The gradient system possesses an SN symmetry due to its invariance in relabeling representative classes. Its flow hence passes through a series of bifurcations with specific symmetry breaks. Here, we show that the dynamical system related to the Information Bottleneck problem has an additional spurious symmetry that requires more-challenging analysis of the symmetry-breaking bifurcation. For the Information Bottleneck, we determine that when bifurcations occur, they are only of pitchfork type, and we give conditions that determine the stability of the bifurcating branches. We relate the existence of subcritical bifurcations to the existence of first-order phase transitions in the corresponding distortion function as a function of the annealing parameter, and provide criteria with which to detect such transitions.

Towards a dynamic clamp for neurochemical modalities.

The classic dynamic clamp technique uses a real-time electrical interface between living cells and neural simulations in order to investigate hypotheses about neural function and structure. One of the acknowledged drawbacks of that technique is the limited control of the cells' chemical microenvironment. In this manuscript, we use a novel combination of nanosensor and microfluidic technology and microfluidic and neural simulations to add sensing and control of chemical concentrations to the dynamic clamp technique. Specifically, we use a microfluidic lab-on-a-chip to generate distinct chemical concentration gradients (ions or neuromodulators), to register the concentrations with embedded nanosensors and use the processed signals as an input to simulations of a neural cell. The ultimate goal of this project is to close the loop and provide sensor signals to the microfluidic lab-on-a-chip to mimic the interaction of the simulated cell with other cells in its chemical environment.

Inhibition does not affect the timing code for vocalizations in the mouse auditory midbrain.

Many animals use a diverse repertoire of complex acoustic signals to convey different types of information to other animals. The information in each vocalization therefore must be coded by neurons in the auditory system. One way in which the auditory system may discriminate among different vocalizations is by having highly selective neurons, where only one or two different vocalizations evoke a strong response from a single neuron. Another strategy is to have specific spike timing patterns for particular vocalizations such that each neural response can be matched to a specific vocalization. Both of these strategies seem to occur in the auditory midbrain of mice. The neural mechanisms underlying rate and time coding are unclear, however, it is likely that inhibition plays a role. Here, we examined whether inhibition is involved in shaping neural selectivity to vocalizations via rate and/or time coding in the mouse inferior colliculus (IC). We examined extracellular single unit responses to vocalizations before and after iontophoretically blocking GABAA and glycine receptors in the IC of awake mice. We then applied a number of neurometrics to examine the rate and timing information of individual neurons. We initially evaluated the neuronal responses using inspection of the raster plots, spike-counting measures of response rate and stimulus preference, and a measure of maximum available stimulus-response mutual information. Subsequently, we used two different event sequence distance measures, one based on vector space embedding, and one derived from the Victor/Purpura D q metric, to direct hierarchical clustering of responses. In general, we found that the most salient feature of pharmacologically blocking inhibitory receptors in the IC was the lack of major effects on the functional properties of IC neurons. Blocking inhibition did increase response rate to vocalizations, as expected. However, it did not significantly affect spike timing, or stimulus selectivity of the studied neurons. We observed two main effects when inhibition was locally blocked: (1) Highly selective neurons maintained their selectivity and the information about the stimuli did not change, but response rate increased slightly. (2) Neurons that responded to multiple vocalizations in the control condition, also responded to the same stimuli in the test condition, with similar timing and pattern, but with a greater number of spikes. For some neurons the information rate generally increased, but the information per spike decreased. In many of these neurons, vocalizations that generated no responses in the control condition generated some response in the test condition. Overall, we found that inhibition in the IC does not play a substantial role in creating the distinguishable and reliable neuronal temporal spike patterns in response to different vocalizations.

Internodal mechanism of pathological afterdischarges in myelinated axons.

INTRODUCTION: Recent optical recordings of transmembrane potentials in the axons of pyramidal neurons have shown that the internodal action potentials (APs) predicted in our previous studies do exist. These novel processes are not well understood. In this study we aim to clarify electrical phenomena in peripheral myelinated axons (MAs). METHODS: We used a multi-cable Hodgkin-Huxley-type model to simulate MAs with potassium channels that were either normal or inhibited along a short region of the internodal membrane. A brief stimulus was applied to the first node. RESULTS: We demonstrated peculiarities in the internodal APs induced by a saltatory AP: They existed across internodal membranes, were detectable in periaxonal space but not in intracellular space, propagated continuously, collided near the mid-internodes, and produced internodal sources of afterdischarges. CONCLUSIONS: These results highlight the importance of the MA internodal regions as new therapeutic targets for avoiding afterdischarges provoked by reduced axonal fast potassium channel expression.

A possible link of oxaliplatin-induced neuropathy with potassium channel deficit.

INTRODUCTION: The neurotoxic side effects of oxaliplatin (a reference drug in the treatment of digestive tract tumors) can force suspension of treatment. The mechanisms of neuropathy are unclear. We aimed to simulate oxaliplatin-induced hyperactivity in myelinated axons (MA) based on published experimental data. METHODS: A Hodgkin-Huxley-type multi-cable MA model was used, which took into account active internodal processes and accumulation of ions in MA with 21 nodes. RESULTS: Even a very short (110-220 µm) internodal region devoid of potassium channels was sufficient to produce after-discharges in response to a saltatory action potential. An increase in the density of sodium channels, slowdown of their inactivation, and negative shifts along one node-internode region of the voltage dependence of sodium and potassium activation and of sodium inactivation induced no after-discharge. CONCLUSION: A combination of sodium channel blockers with drugs that obstruct the blockage of potassium channels or contribute to their opening could be effective in preventing oxaliplatin-induced "hyperexcitability."

Temporal encoding in a nervous system.

We examined the extent to which temporal encoding may be implemented by single neurons in the cercal sensory system of the house cricket Acheta domesticus. We found that these neurons exhibit a greater-than-expected coding capacity, due in part to an increased precision in brief patterns of action potentials. We developed linear and non-linear models for decoding the activity of these neurons. We found that the stimuli associated with short-interval patterns of spikes (ISIs of 8 ms or less) could be predicted better by second-order models as compared to linear models. Finally, we characterized the difference between these linear and second-order models in a low-dimensional subspace, and showed that modification of the linear models along only a few dimensions improved their predictive power to parity with the second order models. Together these results show that single neurons are capable of using temporal patterns of spikes as fundamental symbols in their neural code, and that they communicate specific stimulus distributions to subsequent neural structures.

Characterizing the fine structure of a neural sensory code through information distortion.

We present an application of the information distortion approach to neural coding. The approach allows the discovery of neural symbols and the corresponding stimulus space of a neuron or neural ensemble simultaneously and quantitatively, making few assumptions about the nature of either code or relevant features. The neural codebook is derived by quantitizing sensory stimuli and neural responses into small reproduction sets, and optimizing the quantization to minimize the information distortion function. The application of this approach to the analysis of coding in sensory interneurons involved a further restriction of the space of allowed quantitizers to a smaller family of parametric distributions. We show that, for some cells in this system, a significant amount of information is encoded in patterns of spikes that would not be discovered through analyses based on linear stimulus-response measures.

Evolution of teleost fish retroviruses: characterization of new retroviruses with cellular genes.

The interactions between retroviruses and their hosts can be of a beneficial or detrimental nature. Some endogenous retroviruses are involved in development, while others cause disease. The Genome Parsing Suite (GPS) is a software tool to track and trace all Retroid agents in any sequenced genome (M. A. McClure et al., Genomics 85:512-523, 2005). Using the GPS, the retroviral content was assessed in four model teleost fish. Eleven new species of fish retroviruses are identified and characterized. The reverse transcriptase protein sequences were used to reconstruct a fish retrovirus phylogeny, thereby, significantly expanding the epsilon-retrovirus family. Most of these novel retroviruses encode additional genes, some of which are homologous to cellular genes that would confer viral advantage. Although the fish divergence is much more ancient, retroviruses began infecting fish genomes approximately 4 million years ago.

Spatial and temporal jitter distort estimated functional properties of visual sensory neurons.

The functional properties of neural sensory cells or small neural ensembles are often characterized by analyzing response-conditioned stimulus ensembles. Many widely used analytical methods, like receptive fields (RF), Wiener kernels or spatio-temporal receptive fields (STRF), rely on simple statistics of those ensembles. They also tend to rely on simple noise models for the residuals of the conditional ensembles. However, in many cases the response-conditioned stimulus set has more complex structure. If not taken explicitly into account, it can bias the estimates of many simple statistics, and lead to erroneous conclusions about the functionality of a neural sensory system. In this article, we consider sensory noise in the visual system generated by small stimulus shifts in two dimensions (2 spatial or 1-space 1-time jitter). We model this noise as the action of a set of translations onto the stimulus that leave the response invariant. The analysis demonstrates that the spike-triggered average is a biased estimator of the model mean, and provides a de-biasing method. We apply this approach to observations from the stimulus/response characteristics of cells in the cat visual cortex and provide improved estimates of the structure of visual receptive fields. In several cases the new estimates differ substantially from the classic receptive fields, to a degree that may require re-evaluation of the functional description of the associated cells.

A possible mechanism of repetitive firing of myelinated axon.

A unique mechanism is proposed according to which processes within the internodal axolemma are responsible for repetitive activation of myelinated axon with deficit of internodal potassium conductance. A numerical simulation of activity in axon with 21 nodes was performed. The axon was represented by cables for axoplasmic and periaxonal spaces. Accumulation and diffusion of ions were taken into account. Fine segmentation of each internode (338 segments) allowed simulation of internodal activation in response to a normal saltatorial action potential initiated by a short stimulus. The internodal membrane without potassium conductance experienced considerable depolarization. This resulted in formation of a transition zone and significant currents that caused repetitive activation of the internode and neighbor node. Decline of periaxonal sodium concentration during the spike production or lowering of sodium channel density decreased the sodium currents. As a result, the interspike intervals increased up to cessation of the burst. The cessation was reversible.

Effects of changes in intracellular action potential on potentials recorded by single-fiber, macro, and belly-tendon electrodes.

Some myopathies are accompanied by abnormal calcium homeostasis. Electromyography (EMG) in such patients shows signs of normal or myopathic EMG when detected by a single-fiber electrode and abnormally increased values in macro EMG. As calcium accumulation might be accompanied by changes in intracellular action potential (IAP) and muscle-fiber propagation velocity, we simulated the effects of such changes on motor unit potentials (MUPs) recorded by different kinds of electrodes. We found that: (1) the requirements for what potential can be accepted as a single-fiber action potential (SFAP) are too rigorous; (2) macro MUP amplitude can increase while SFAP amplitude can decrease when there is an increase in the spatial length of IAP spike; and (3) changes in the second phase of a belly-tendon-detected MUP or M wave could be used for noninvasive detection of increased IAP depolarizing (negative) after-potential.

Changes in intracellular action potential profile affect parameters used in turns/amplitude analysis.

The influence of changes in the intracellular action potential (IAP) spatial profile on motor unit potentials (MUPs), number of turns per second (NTs), and mean turn amplitude were simulated and analyzed. We show why measurement of NTs was "the best indicator of neurogenic affection" and why the lower diagnostic yield of turns/amplitude analysis in myopathy could be due to changes in IAP shape caused by elevated free calcium concentration. The results explain the complications observed when interference electromyographic signals obtained during high levels of isometric contractions were analyzed. We show that, in contrast to earlier assumptions, the effect of increased IAP spike duration on NTs was stronger than that of a decrease in muscle fiber propagation velocity (MFPV). The decrease in the NTs could occur without a drop-out of MUs and/or a decrease in their firing rates, and without a change in MFPV and synchronous firing.

Effects of stimulus transformations on estimates of sensory neuron selectivity.

Stimulus selectivity of sensory systems is often characterized by analyzing response-conditioned stimulus ensembles. However, in many cases these response-triggered stimulus sets have structure that is more complex than assumed. If not taken into account, when present it will bias the estimates of many simple statistics, and distort the estimated stimulus selectivity of a neural sensory system. We present an approach that mitigates these problems by modeling some of the response-conditioned stimulus structure as being generated by a set of transformations acting on a simple stimulus distribution. This approach corrects the estimates of key statistics and counters biases introduced by the transformations. In cases involving temporal spike jitter or spatial jitter of images, the main observed effects of transformations are blurring of the conditional mean and introduction of artefacts in the spectral decomposition of the conditional covariance matrix. We illustrate this approach by analyzing and correcting a set of model stimuli perturbed by temporal and spatial jitter. We apply the approach to neurophysiological data from the cricket cercal sensory system to correct the effects of temporal jitter.

Dejittered spike-conditioned stimulus waveforms yield improved estimates of neuronal feature selectivity and spike-timing precision of sensory interneurons.

What is the meaning associated with a single action potential in a neural spike train? The answer depends on the way the question is formulated. One general approach toward formulating this question involves estimating the average stimulus waveform preceding spikes in a spike train. Many different algorithms have been used to obtain such estimates, ranging from spike-triggered averaging of stimuli to correlation-based extraction of "stimulus-reconstruction" kernels or spatiotemporal receptive fields. We demonstrate that all of these approaches miscalculate the stimulus feature selectivity of a neuron. Their errors arise from the manner in which the stimulus waveforms are aligned to one another during the calculations. Specifically, the waveform segments are locked to the precise time of spike occurrence, ignoring the intrinsic "jitter" in the stimulus-to-spike latency. We present an algorithm that takes this jitter into account. "Dejittered" estimates of the feature selectivity of a neuron are more accurate (i.e., provide a better estimate of the mean waveform eliciting a spike) and more precise (i.e., have smaller variance around that waveform) than estimates obtained using standard techniques. Moreover, this approach yields an explicit measure of spike-timing precision. We applied this technique to study feature selectivity and spike-timing precision in two types of sensory interneurons in the cricket cercal system. The dejittered estimates of the mean stimulus waveforms preceding spikes were up to three times larger than estimates based on the standard techniques used in previous studies and had power that extended into higher-frequency ranges. Spike timing precision was approximately 5 ms.

Internodal sodium channels ensure active processes under myelin manifesting in depolarizing afterpotentials.

The current opinion about processes in myelinated axon is that action potential saltatorially propagates between nodes of Ranvier and passively charges internodal axolemma thus causing depolarizing afterpotentials (DAP). Demyelination blocks the conduction that gives additional argument in favor of hypothesis that internode is not able to be activated by the existing internodal sodium channels. The results of our modeling study shows that, when periaxonal space is sufficiently narrow, saltatorial action potential is able to activate internodes. Low density of internodal sodium channels is sufficient to generate active internodal waves that slowly propagate from nodes towards corresponding midinternodes where they collide. The periaxonal width that stops internodal wave propagation (about 400 nm) is significantly larger than the highest value of the physiological range for this parameter (30 nm). Internodal activation is directly manifested as transmembrane internodal potential or as a full-sized action potential in periaxonal space where it can hardly be detected, and only as a small deflection in intracellular space. However, changes in the periaxonal potential cause transmyelin currents that lead to significant DAP. The shape and amplitude of DAP depends on myelin parameters and densities of internodal channels. Several technical parameters affect the results of calculations. Internodal spatial segmentation has to be sufficiently fine (at most 20 microm) for the model to be able to simulate internodal activation. We employ 338 internodal segments as compared with up to 21 used in previous models. Ionic accumulation together with related diffusive and electrical processes alter the calculated DAP amplitude. Inclusion of these processes in calculations demands such increase in the total number of segments that the numerical methods used up to now become unapplicable. To overcome the problem, an iterative implicit approach is proposed. It reduces a matrix of general type in multi-cable models to tridiagonal one and accelerates calculations considerably.

Analysis of neural coding through quantization with an information-based distortion measure.

We discuss an analytical approach through which the neural symbols and corresponding stimulus space of a neuron or neural ensemble can be discovered simultaneously and quantitatively, making few assumptions about the nature of the code or relevant features. The basis for this approach is to conceptualize a neural coding scheme as a collection of stimulus-response classes akin to a dictionary or 'codebook', with each class corresponding to a spike pattern 'codeword' and its corresponding stimulus feature in the codebook. The neural codebook is derived by quantizing the neural responses into a small reproduction set, and optimizing the quantization to minimize an information-based distortion function. We apply this approach to the analysis of coding in sensory interneurons of a simple invertebrate sensory system. For a simple sensory characteristic (tuning curve), we demonstrate a case for which the classical definition of tuning does not describe adequately the performance of the cell studied. Considering a more involved sensory operation (sensory discrimination), we also show that, for some cells in this system, a significant amount of information is encoded in patterns of spikes that would not be discovered through analyses based on linear stimulus-response measures.