Fractional order memcapacitive neuromorphic elements reproduce and predict neuronal function.

There is an increasing need to implement neuromorphic systems that are both energetically and computationally efficient. There is also great interest in using electric elements with memory, memelements, that can implement complex neuronal functions intrinsically. A feature not widely incorporated in neuromorphic systems is history-dependent action potential time adaptation which is widely seen in real cells. Previous theoretical work shows that power-law history dependent spike time adaptation, seen in several brain areas and species, can be modeled with fractional order differential equations. Here, we show that fractional order spiking neurons can be implemented using super-capacitors. The super-capacitors have fractional order derivative and memcapacitive properties. We implemented two circuits, a leaky integrate and fire and a Hodgkin-Huxley. Both circuits show power-law spiking time adaptation and optimal coding properties. The spiking dynamics reproduced previously published computer simulations. However, the fractional order Hodgkin-Huxley circuit showed novel dynamics consistent with criticality. We compared the responses of this circuit to recordings from neurons in the weakly-electric fish that have previously been shown to perform fractional order differentiation of their sensory input. The criticality seen in the circuit was confirmed in spontaneous recordings in the live fish. Furthermore, the circuit also predicted long-lasting stimulation that was also corroborated experimentally. Our work shows that fractional order memcapacitors provide intrinsic memory dependence that could allow implementation of computationally efficient neuromorphic devices. Memcapacitors are static elements that consume less energy than the most widely studied memristors, thus allowing the realization of energetically efficient neuromorphic devices.

On the Role of Theory and Modeling in Neuroscience.

In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and modeling approaches used in the field. This issue is particularly complex in neuroscience because the field studies phenomena that cross a wide range of scales and often require consideration at varying degrees of abstraction, from precise biophysical interactions to the computations they implement. We argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative models and theories each play a distinct role in defining and bridging levels of abstraction, will facilitate neuroscientific practice. This analysis leads to methodological suggestions, including selecting a level of abstraction that is appropriate for a given problem, identifying transfer functions to connect models and data, and the use of models themselves as a form of experiment.

Macromolecular rate theory explains the temperature dependence of membrane conductance kinetics.

The factor Q10 is used in neuroscience to adjust reaction rates of voltage-activated membrane conductances to different temperatures and is widely assumed to be constant. By performing an analysis of published data of the reaction rates of sodium, potassium, and calcium membrane conductances, we demonstrate that 1) Q10 is temperature dependent, 2) this relationship is similar across conductances, and 3) there is a strong effect at low temperatures (<15°C). We show that macromolecular rate theory (MMRT) explains this temperature dependency. MMRT predicts the existence of optimal temperatures at which reaction rates decrease as temperature increases, a phenomenon that we also found in the published data sets. We tested the consequences of using MMRT-adjusted reaction rates in the Hodgkin-Huxley model of the squid's giant axon. The MMRT-adjusted model reproduces the temperature dependence of the rising and falling times of the action potential. Furthermore, the model also reproduces these properties for different squid species that live in different climates. In a second example, we compare spiking patterns of biophysical models based on human pyramidal neurons from the Allen Cell Types database at room and physiological temperatures. The original models, calibrated at 34°C, failed to generate realistic spikes at room temperature in more than half of the tested models, while the MMRT produces realistic spiking in all conditions. In another example, we show that using the MMRT correction in hippocampal pyramidal cell models results in 100% differences in voltage responses. Finally, we show that the shape of the Q10 function results in systematic errors in predicting reaction rates. We propose that the optimal temperature could be a thermodynamical barrier to avoid over excitation in neurons. While this study is centered on membrane conductances, our results have important consequences for all biochemical reactions involved in cell signaling.

Effects of environmental enrichment and sexual dimorphism on the expression of cerebellar receptors in C57BL/6 and BTBR + Itpr3tf/J mice.

OBJECTIVE: Environmental enrichment is used to treat social, communication, and behavioral deficits and is known to modify the expression of synaptic receptors. We compared the effects of environmental enrichment in the expression of glutamate and endocannabinoid receptors, which are widely expressed in the cerebellar cortex. These two receptors interact to regulate neuronal function and their dysregulation is associated with behavioral changes. We used BTBR + Itpr3tf/J mice, a strain that models behavioral disorders, and C57BL/6 mice for comparison. We studied the effects of genetic background, sex, environmental conditions, and layer of the cerebellar cortex on the expression of each receptor. RESULTS: The influence of genetic background and environmental enrichment had the same pattern on glutamate and endocannabinoid receptors in males. In contrast, in females, the effect of environmental enrichment and genetic background were different than the ones obtained for males and were also different between the glutamate and endocannabinoid receptors. Furthermore, an analysis of both receptors from tissue obtained from the same animals show that their expression is correlated in males, but not in females. Our results suggest that environmental enrichment has a receptor dependent and sexual dimorphic effect on the molecular expression of different receptors in the cerebellar cortex.

The allometric propagation of COVID-19 is explained by human travel.

We analyzed the number of cumulative positive cases of COVID-19 as a function of time in countries around the World. We tracked the increase in cases from the onset of the pandemic in each region for up to 150 days. We found that in 81 out of 146 regions the trajectory was described with a power-law function for up to 30 days. We also detected scale-free properties in the majority of sub-regions in Australia, Canada, China, and the United States (US). We developed an allometric model that was capable of fitting the initial phase of the pandemic and was the best predictor for the propagation of the illness for up to 100 days. We then determined that the power-law COVID-19 exponent correlated with measurements of human mobility. The COVID-19 exponent correlated with the magnitude of air passengers per country. This correlation persisted when we analyzed the number of air passengers per US states, and even per US metropolitan areas. Furthermore, the COVID-19 exponent correlated with the number of vehicle miles traveled in the US. Together, air and vehicular travel explained 70% of the variability of the COVID-19 exponent. Taken together, our results suggest that the scale-free propagation of the virus is present at multiple geographical scales and is correlated with human mobility. We conclude that models of disease transmission should integrate scale-free dynamics as part of the modeling strategy and not only as an emergent phenomenological property.

The allometric propagation of COVID-19 is explained by human travel.

We analyzed the number of cumulative positive cases of COVID-19 as a function of time in countries around the World. We tracked the increase in cases from the onset of the pandemic in each region for up to 150 days. We found that in 81 out of 146 regions the trajectory was described with a power-law function for up to 30 days. We also detected scale-free properties in the majority of sub-regions in Australia, Canada, China, and the United States (US). We developed an allometric model that was capable of fitting the initial phase of the pandemic and was the best predictor for the propagation of the illness for up to 100 days. We then determined that the power-law COVID-19 exponent correlated with measurements of human mobility. The COVID-19 exponent correlated with the magnitude of air passengers per country. This correlation persisted when we analyzed the number of air passengers per US states, and even per US metropolitan areas. Furthermore, the COVID-19 exponent correlated with the number of vehicle miles travelled in the US. Together, air and vehicular travel explained 70 % of the variability of the COVID-19 exponent. Taken together, our results suggest that the scale-free propagation of the virus is present at multiple geographical scales and is correlated with human mobility. We conclude that models of disease transmission should integrate scale-free dynamics as part of the modeling strategy and not only as an emergent phenomenological property.

Fractional Lotka-Volterra-Type Cooperation Models: Impulsive Control on Their Stability Behavior.

We present a biological fractional n-species delayed cooperation model of Lotka-Volterra type. The considered fractional derivatives are in the Caputo sense. Impulsive control strategies are applied for several stability properties of the states, namely Mittag-Leffler stability, practical stability and stability with respect to sets. The proposed results extend the existing stability results for integer-order n-species delayed Lotka-Volterra cooperation models to the fractional-order case under impulsive control.

Impact of Auditory Experience on the Structural Plasticity of the AIS in the Mouse Brainstem Throughout the Lifespan.

Sound input critically influences the development and maintenance of neuronal circuits in the mammalian brain throughout life. We investigate the structural and functional plasticity of auditory neurons in response to various auditory experiences during development, adulthood, and aging. Using electrophysiology, computer simulation, and immunohistochemistry, we study the structural plasticity of the axon initial segment (AIS) in the medial nucleus of the trapezoid body (MNTB) from the auditory brainstem of the mice (either sex), in different ages and auditory environments. The structure and spatial location of the AIS of MNTB neurons depend on their functional topographic location along the tonotopic axis, aligning high- to low-frequency sound-responding neurons (HF or LF neurons). HF neurons dramatically undergo structural remodeling of the AIS throughout life. The AIS progressively shortens during development, is stabilized in adulthood, and becomes longer in aging. Sound inputs are critically associated with setting and maintaining AIS plasticity and tonotopy at various ages. Sound stimulation increases the excitability of auditory neurons. Computer simulation shows that modification of the AIS length, location, and diameter can affect firing properties of MNTB neurons in the developing brainstem. The adaptive capability of axonal structure in response to various auditory experiences at different ages suggests that sound input is important for the development and maintenance of the structural and functional properties of the auditory brain throughout life.

Integrating the Allen Brain Institute Cell Types Database into Automated Neuroscience Workflow.

We developed software tools to download, extract features, and organize the Cell Types Database from the Allen Brain Institute (ABI) in order to integrate its whole cell patch clamp characterization data into the automated modeling/data analysis cycle. To expand the potential user base we employed both Python and MATLAB. The basic set of tools downloads selected raw data and extracts cell, sweep, and spike features, using ABI's feature extraction code. To facilitate data manipulation we added a tool to build a local specialized database of raw data plus extracted features. Finally, to maximize automation, we extended our NeuroManager workflow automation suite to include these tools plus a separate investigation database. The extended suite allows the user to integrate ABI experimental and modeling data into an automated workflow deployed on heterogeneous computer infrastructures, from local servers, to high performance computing environments, to the cloud. Since our approach is focused on workflow procedures our tools can be modified to interact with the increasing number of neuroscience databases being developed to cover all scales and properties of the nervous system.

Automating NEURON Simulation Deployment in Cloud Resources.

Simulations in neuroscience are performed on local servers or High Performance Computing (HPC) facilities. Recently, cloud computing has emerged as a potential computational platform for neuroscience simulation. In this paper we compare and contrast HPC and cloud resources for scientific computation, then report how we deployed NEURON, a widely used simulator of neuronal activity, in three clouds: Chameleon Cloud, a hybrid private academic cloud for cloud technology research based on the OpenStack software; Rackspace, a public commercial cloud, also based on OpenStack; and Amazon Elastic Cloud Computing, based on Amazon's proprietary software. We describe the manual procedures and how to automate cloud operations. We describe extending our simulation automation software called NeuroManager (Stockton and Santamaria, Frontiers in Neuroinformatics, 2015), so that the user is capable of recruiting private cloud, public cloud, HPC, and local servers simultaneously with a simple common interface. We conclude by performing several studies in which we examine speedup, efficiency, total session time, and cost for sets of simulations of a published NEURON model.

Purkinje cell intrinsic excitability increases after synaptic long term depression.

Coding in cerebellar Purkinje cells not only depends on synaptic plasticity but also on their intrinsic membrane excitability. We performed whole cell patch-clamp recordings of Purkinje cells in sagittal cerebellar slices in mice. We found that inducing long-term depression (LTD) in the parallel fiber to Purkinje cell synapses results in an increase in the gain of the firing rate response. This increase in excitability is accompanied by an increase in the input resistance and a decrease in the amplitude of the hyperpolarization-activated cyclic nucleotide-gated (HCN) channel-mediated voltage sag. Application of a HCN channel blocker prevents the increase in input resistance and excitability without blocking the expression of synaptic LTD. We conclude that the induction of parallel fiber-Purkinje cell LTD is accompanied by an increase in excitability of Purkinje cells through downregulation of the HCN-mediated h current. We suggest that HCN downregulation is linked to the biochemical pathway that sustains synaptic LTD. Given the diversity of information carried by the parallel fiber system, we suggest that changes in intrinsic excitability enhance the coding capacity of the Purkinje cell to specific input sources.

Spines slow down dendritic chloride diffusion and affect short-term ionic plasticity of GABAergic inhibition.

Cl(-) plays a crucial role in neuronal function and synaptic inhibition. However, the impact of neuronal morphology on the diffusion and redistribution of intracellular Cl(-) is not well understood. The role of spines in Cl(-) diffusion along dendritic trees has not been addressed so far. Because measuring fast and spatially restricted Cl(-) changes within dendrites is not yet technically possible, we used computational approaches to predict the effects of spines on Cl(-) dynamics in morphologically complex dendrites. In all morphologies tested, including dendrites imaged by super-resolution STED microscopy in live brain tissue, spines slowed down longitudinal Cl(-) diffusion along dendrites. This effect was robust and could be observed in both deterministic as well as stochastic simulations. Cl(-) extrusion altered Cl(-) diffusion to a much lesser extent than the presence of spines. The spine-dependent slowing of Cl(-) diffusion affected the amount and spatial spread of changes in the GABA reversal potential thereby altering homosynaptic as well as heterosynaptic short-term ionic plasticity at GABAergic synapses in dendrites. Altogether, our results suggest a fundamental role of dendritic spines in shaping Cl(-) diffusion, which could be of relevance in the context of pathological conditions where spine densities and neural excitability are perturbed.

Power-Law Dynamics of Membrane Conductances Increase Spiking Diversity in a Hodgkin-Huxley Model.

We studied the effects of non-Markovian power-law voltage dependent conductances on the generation of action potentials and spiking patterns in a Hodgkin-Huxley model. To implement slow-adapting power-law dynamics of the gating variables of the potassium, n, and sodium, m and h, conductances we used fractional derivatives of order η≤1. The fractional derivatives were used to solve the kinetic equations of each gate. We systematically classified the properties of each gate as a function of η. We then tested if the full model could generate action potentials with the different power-law behaving gates. Finally, we studied the patterns of action potential that emerged in each case. Our results show the model produces a wide range of action potential shapes and spiking patterns in response to constant current stimulation as a function of η. In comparison with the classical model, the action potential shapes for power-law behaving potassium conductance (n gate) showed a longer peak and shallow hyperpolarization; for power-law activation of the sodium conductance (m gate), the action potentials had a sharp rise time; and for power-law inactivation of the sodium conductance (h gate) the spikes had wider peak that for low values of η replicated pituitary- and cardiac-type action potentials. With all physiological parameters fixed a wide range of spiking patterns emerged as a function of the value of the constant input current and η, such as square wave bursting, mixed mode oscillations, and pseudo-plateau potentials. Our analyses show that the intrinsic memory trace of the fractional derivative provides a negative feedback mechanism between the voltage trace and the activity of the power-law behaving gate variable. As a consequence, power-law behaving conductances result in an increase in the number of spiking patterns a neuron can generate and, we propose, expand the computational capacity of the neuron.

NeuroManager: a workflow analysis based simulation management engine for computational neuroscience.

We developed NeuroManager, an object-oriented simulation management software engine for computational neuroscience. NeuroManager automates the workflow of simulation job submissions when using heterogeneous computational resources, simulators, and simulation tasks. The object-oriented approach (1) provides flexibility to adapt to a variety of neuroscience simulators, (2) simplifies the use of heterogeneous computational resources, from desktops to super computer clusters, and (3) improves tracking of simulator/simulation evolution. We implemented NeuroManager in MATLAB, a widely used engineering and scientific language, for its signal and image processing tools, prevalence in electrophysiology analysis, and increasing use in college Biology education. To design and develop NeuroManager we analyzed the workflow of simulation submission for a variety of simulators, operating systems, and computational resources, including the handling of input parameters, data, models, results, and analyses. This resulted in 22 stages of simulation submission workflow. The software incorporates progress notification, automatic organization, labeling, and time-stamping of data and results, and integrated access to MATLAB's analysis and visualization tools. NeuroManager provides users with the tools to automate daily tasks, and assists principal investigators in tracking and recreating the evolution of research projects performed by multiple people. Overall, NeuroManager provides the infrastructure needed to improve workflow, manage multiple simultaneous simulations, and maintain provenance of the potentially large amounts of data produced during the course of a research project.

Transient extracellular application of gold nanostars increases hippocampal neuronal activity.

BACKGROUND: With the increased use of nanoparticles in biomedical applications there is a growing need to understand the effects that nanoparticles may have on cell function. Identifying these effects and understanding the mechanism through which nanoparticles interfere with the normal functioning of a cell is necessary for any therapeutic or diagnostic application. The aim of this study is to evaluate if gold nanoparticles can affect the normal function of neurons, namely their activity and coding properties. RESULTS: We synthesized star shaped gold nanoparticles of 180 nm average size. We applied the nanoparticles to acute mouse hippocampal slices while recording the action potentials from single neurons in the CA3 region. Our results show that CA3 hippocampal neurons increase their firing rate by 17% after the application of gold nanostars. The increase in excitability lasted for as much as 50 minutes after a transient 5 min application of the nanoparticles. Further analyses of the action potential shape and computational modeling suggest that nanoparticles block potassium channels responsible for the repolarization of the action potentials, thus allowing the cell to increase its firing rate. CONCLUSIONS: Our results show that gold nanoparticles can affect the coding properties of neurons by modifying their excitability.

Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model.

The voltage trace of neuronal activities can follow multiple timescale dynamics that arise from correlated membrane conductances. Such processes can result in power-law behavior in which the membrane voltage cannot be characterized with a single time constant. The emergent effect of these membrane correlations is a non-Markovian process that can be modeled with a fractional derivative. A fractional derivative is a non-local process in which the value of the variable is determined by integrating a temporal weighted voltage trace, also called the memory trace. Here we developed and analyzed a fractional leaky integrate-and-fire model in which the exponent of the fractional derivative can vary from 0 to 1, with 1 representing the normal derivative. As the exponent of the fractional derivative decreases, the weights of the voltage trace increase. Thus, the value of the voltage is increasingly correlated with the trajectory of the voltage in the past. By varying only the fractional exponent, our model can reproduce upward and downward spike adaptations found experimentally in neocortical pyramidal cells and tectal neurons in vitro. The model also produces spikes with longer first-spike latency and high inter-spike variability with power-law distribution. We further analyze spike adaptation and the responses to noisy and oscillatory input. The fractional model generates reliable spike patterns in response to noisy input. Overall, the spiking activity of the fractional leaky integrate-and-fire model deviates from the spiking activity of the Markovian model and reflects the temporal accumulated intrinsic membrane dynamics that affect the response of the neuron to external stimulation.

Computational modeling of diffusion in the cerebellum.

Diffusion is a major transport mechanism in living organisms. In the cerebellum, diffusion is responsible for the propagation of molecular signaling involved in synaptic plasticity and metabolism, both intracellularly and extracellularly. In this chapter, we present an overview of the cerebellar structure and function. We then discuss the types of diffusion processes present in the cerebellum and their biological importance. We particularly emphasize the differences between extracellular and intracellular diffusion and the presence of tortuosity and anomalous diffusion in different parts of the cerebellar cortex. We provide a mathematical introduction to diffusion and a conceptual overview of various computational modeling techniques. We discuss their scope and their limit of application. Although our focus is the cerebellum, we have aimed at presenting the biological and mathematical foundations as general as possible to be applicable to any other area in biology in which diffusion is of importance.

FRACTIONAL INTEGRATION TOOLBOX.

The problems formulated in the fractional calculus framework often require numerical fractional integration/differentiation of large data sets. Several existing fractional control toolboxes are capable of performing fractional calculus operations, however, none of them can efficiently perform numerical integration on multiple large data sequences. We developed a Fractional Integration Toolbox (FIT), which efficiently performs fractional numerical integration/differentiation of the Riemann-Liouville type on large data sequences. The toolbox allows parallelization and is designed to be deployed on both CPU and GPU platforms.

Gold nanostar synthesis with a silver seed mediated growth method.

The physical, chemical and optical properties of nano-scale colloids depend on their material composition, size and shape. There is a great interest in using nano-colloids for photo-thermal ablation, drug delivery and many other biomedical applications. Gold is particularly used because of its low toxicity. A property of metal nano-colloids is that they can have a strong surface plasmon resonance. The peak of the surface plasmon resonance mode depends on the structure and composition of the metal nano-colloids. Since the surface plasmon resonance mode is stimulated with light there is a need to have the peak absorbance in the near infrared where biological tissue transmissivity is maximal. We present a method to synthesize star shaped colloidal gold, also known as star shaped nanoparticles or nanostars. This method is based on a solution containing silver seeds that are used as the nucleating agent for anisotropic growth of gold colloids. Scanning electron microscopy (SEM) analysis of the resulting gold colloid showed that 70 % of the nanostructures were nanostars. The other 30 % of the particles were amorphous clusters of decahedra and rhomboids. The absorbance peak of the nanostars was detected to be in the near infrared (840 nm). Thus, our method produces gold nanostars suitable for biomedical applications, particularly for photo-thermal ablation.

The diffusional properties of dendrites depend on the density of dendritic spines.

We combined computational modeling and experimental measurements to determine the influence of dendritic structure on the diffusion of intracellular chemical signals in mouse cerebellar Purkinje cells and hippocamal CA1 pyramidal cells. Modeling predicts that molecular trapping by dendritic spines causes diffusion along spiny dendrites to be anomalous and that the value of the anomalous exponent (d(w) ) is proportional to spine density in both cell types. To test these predictions we combined the local photorelease of an inert dye, rhodamine dextran, with two-photon fluorescence imaging to track diffusion along dendrites. Our results show that anomalous diffusion is present in spiny dendrites of both cell types. Further, the anomalous exponent is linearly related to the density of spines in pyramidal cells and d(w) in Purkinje cells is consistent with such a relationship. We conclude that anomalous diffusion occurs in the dendrites of multiple types of neurons. Because spine density is dynamic and depends on neuronal activity, the degree of anomalous diffusion induced by spines can dynamically regulate the movement of molecules along dendrites.