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.

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.

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.

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.

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.

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.

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.

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.

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.

Ca2+ requirements for cerebellar long-term synaptic depression: role for a postsynaptic leaky integrator.

Photolysis of a caged Ca(2+) compound was used to characterize the dependence of cerebellar long-term synaptic depression (LTD) on postsynaptic Ca(2+) concentration ([Ca(2+)](i)). Elevating [Ca(2+)](i) was sufficient to induce LTD without requiring any of the other signals produced by synaptic activity. A sigmoidal relationship between [Ca(2+)](i) and LTD indicated a highly cooperative triggering of LTD by Ca(2+). The duration of the rise in [Ca(2+)](i) influenced the apparent Ca(2+) affinity of LTD, and this time-dependent behavior could be described by a leaky integrator process with a time constant of 0.6 s. A computational model, based on a positive-feedback cycle that includes protein kinase C and MAP kinase, was capable of simulating these properties of Ca(2+)-triggered LTD. Disrupting this cycle experimentally also produced the predicted changes in the Ca(2+) dependence of LTD. We conclude that LTD arises from a mechanism that integrates postsynaptic Ca(2+) signals and that this integration may be produced by the positive-feedback cycle.

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.

Quantifying the effects of elastic collisions and non-covalent binding on glutamate receptor trafficking in the post-synaptic density.

One mechanism of information storage in neurons is believed to be determined by the strength of synaptic contacts. The strength of an excitatory synapse is partially due to the concentration of a particular type of ionotropic glutamate receptor (AMPAR) in the post-synaptic density (PSD). AMPAR concentration in the PSD has to be plastic, to allow the storage of new memories; but it also has to be stable to preserve important information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which AMPAR can enter, leave and remain in the synapse are unclear. We used Monte Carlo simulations to determine the influence of PSD structure and activity in maintaining homeostatic concentrations of AMPARs in the synapse. We found that, the high concentration and excluded volume caused by PSD molecules result in molecular crowding. Diffusion of AMPAR in the PSD under such conditions is anomalous. Anomalous diffusion of AMPAR results in retention of these receptors inside the PSD for periods ranging from minutes to several hours in the absence of strong binding of receptors to PSD molecules. Trapping of receptors in the PSD by crowding effects was very sensitive to the concentration of PSD molecules, showing a switch-like behavior for retention of receptors. Non-covalent binding of AMPAR to anchored PSD molecules allowed the synapse to become well-mixed, resulting in normal diffusion of AMPAR. Binding also allowed the exchange of receptors in and out of the PSD. We propose that molecular crowding is an important biophysical mechanism to maintain homeostatic synaptic concentrations of AMPARs in the PSD without the need of energetically expensive biochemical reactions. In this context, binding of AMPAR with PSD molecules could collaborate with crowding to maintain synaptic homeostasis but could also allow synaptic plasticity by increasing the exchange of these receptors with the surrounding extra-synaptic membrane.

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.

Anomalous diffusion in Purkinje cell dendrites caused by spines.

We combined local photolysis of caged compounds with fluorescence imaging to visualize molecular diffusion within dendrites of cerebellar Purkinje cells. Diffusion of a volume marker, fluorescein dextran, within spiny dendrites was remarkably slow in comparison to its diffusion in smooth dendrites. Computer simulations indicate that this retardation is due to a transient trapping of molecules within dendritic spines, yielding anomalous diffusion. We considered the influence of spine trapping on the diffusion of calcium ions (Ca(2+)) and inositol-1,4,5-triphospate (IP(3)), two synaptic second messengers. Diffusion of IP(3) was strongly influenced by the presence of dendritic spines, while Ca(2+) was removed so rapidly that it could not diffuse far enough to be trapped. We conclude that an important function of dendritic spines may be to trap chemical signals and thereby create slowed anomalous diffusion within dendrites.

Cholesterol homeostasis markers are localized to mouse hippocampal pyramidal and granule layers.

Changes in brain cholesterol homeostasis are associated with multiple diseases, such as Alzheimer's and Huntington's; however, controversy persists as to whether adult neurons produce their own cholesterol, or if it is outsourced to astrocytes. To address this issue, we analyzed 25 genes most immediately involved in cholesterol homeostasis from in situ data provided by the Allen Brain Mouse Atlas. We compared the relative mRNA expression in the pyramidal and granule layers, populated with neurons, with the rest of the hippocampus which is populated with neuronal processes and glia. Comparing the expression of the individual genes to markers for neurons and astrocytes, we found that cholesterol homeostasis genes are preferentially targeted to neuronal layers. Therefore, changes in gene expression levels might affect neuronal populations directly.

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.

Local calcium signaling in neurons.

Transient rises in the cytoplasmic concentration of calcium ions serve as second messenger signals that control many neuronal functions. Selective triggering of these functions is achieved through spatial localization of calcium signals. Several qualitatively different forms of local calcium signaling can be distinguished by the location of open calcium channels as well as by the distance between these channels and the calcium binding proteins that serve as the molecular targets of calcium action. Local calcium signaling is especially prominent at presynaptic active zones and postsynaptic densities, structures that are distinguished by highly organized macromolecular arrays that yield precise spatial arrangements of calcium signaling proteins. Similar forms of local calcium signaling may be employed throughout the nervous system, though much remains to be learned about the molecular underpinnings of these events.

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.

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.