Fidel Santamaria

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.

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.

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.

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 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 (dw) 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 dw 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.

Modulatory Effects of Parallel Fiber and Molecular Layer Interneuron Synaptic Activity on Purkinje Cell Responses to Ascending Segment Input: A Modeling Study

Based on anatomical, physiological, and model-based studies, it has been proposed that synapses associated with the ascending segment of granule cell axons provide the principle excitatory drive on Purkinje cells which is then modulated by the more numerous parallel fiber synapses. In this study we have evaluated this idea using a detailed compartmental model of a cerebellar Purkinje cell by providing identical ascending segment synaptic inputs during different levels of random parallel fiber and molecular interneuron input. Results suggest that background inputs from parallel fibers and molecular layer interneurons can have a substantial effect on the response of Purkinje cells to ascending segment inputs. Interestingly, these effects are not reflected in the average firing rate of the Purkinje cell and are thus entirely dendritic in effect. These results are considered in the context of the known segregated spatial distribution of the parallel fibers and ascending segment synapses and a new hypothesis concerning the functional organization of cerebellar cortical circuitry.

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.

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

Changes in brain cholesterol homeostasis are associated with multiple diseases, such as Alzheimers and Huntingtons; 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.

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.

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.