A Glutamatergic Spine Model to Enable Multi-Scale Modeling of Nonlinear Calcium Dynamics

Biophysical Modeling of Synaptic Plasticity

Dendritic spines are small, bulbous compartments that function as postsynaptic sites and undergo intense biochemical and biophysical activity. The role of the myriad signaling pathways that are implicated in synaptic plasticity is well studied. A recent abundance of quantitative experimental data has made the events associated with synaptic plasticity amenable to quantitative biophysical modeling. Spines are also fascinating biophysical computational units because spine geometry, signal transduction, and mechanics work in a complex feedback loop to tune synaptic plasticity. In this sense, ideas from modeling cell motility can inspire us to develop multiscale approaches for predictive modeling of synaptic plasticity. In this article, we review the key steps in postsynaptic plasticity with a specific focus on the impact of spine geometry on signaling, cytoskeleton rearrangement, and membrane mechanics. We summarize the main experimental observations and highlight how theory and computation can aid our understanding of these complex processes.

Computational modeling of AMPK and mTOR crosstalk in glutamatergic synapse calcium signaling

Neuronal energy consumption is vital for information processing and memory formation in synapses. The brain consists of just 2% of the human body's mass, but consumes almost 20% of the body's energy budget. Most of this energy is attributed to active transport in ion signaling, with calcium being the canonical second messenger of synaptic transmission. Here, we develop a computational model of synaptic signaling resulting in the activation of two protein kinases critical in metabolic regulation and cell fate, AMP-Activated protein kinase (AMPK) and mammalian target of rapamycin (mTOR) and investigate the effect of glutamate stimulus frequency on their dynamics. Our model predicts that frequencies of glutamate stimulus over 10 Hz perturb AMPK and mTOR oscillations at higher magnitudes by up to 36% and change the area under curve (AUC) by 5%. This dynamic difference in AMPK and mTOR activation trajectories potentially differentiates high frequency stimulus bursts from basal neuronal signaling leading to a downstream change in synaptic plasticity. Further, we also investigate the crosstalk between insulin receptor and calcium signaling on AMPK and mTOR activation and predict that the pathways demonstrate multistability dependent on strength of insulin signaling and metabolic consumption rate. Our predictions have implications for improving our understanding of neuronal metabolism, synaptic pruning, and synaptic plasticity.

Dendritic spine morphology regulates calcium-dependent synaptic weight change

Dendritic spines act as biochemical computational units and must adapt their responses according to their activation history. Calcium influx acts as the first signaling step during postsynaptic activation and is a determinant of synaptic weight change. Dendritic spines also come in a variety of sizes and shapes. To probe the relationship between calcium dynamics and spine morphology, we used a stochastic reaction-diffusion model of calcium dynamics in idealized and realistic geometries. We show that despite the stochastic nature of the various calcium channels, receptors, and pumps, spine size and shape can modulate calcium dynamics and subsequently synaptic weight updates in a deterministic manner. Through a series of exhaustive simulations and analyses, we found that the calcium dynamics and synaptic weight change depend on the volume-to-surface area of the spine. The relationships between calcium dynamics and spine morphology identified in idealized geometries also hold in realistic geometries, suggesting that there are geometrically determined deterministic relationships that may modulate synaptic weight change.

The glutamatergic synapse: a complex machinery for information processing

Being the most abundant synaptic type, the glutamatergic synapse is responsible for the larger part of the brain's information processing. Despite the conceptual simplicity of the basic mechanism of synaptic transmission, the glutamatergic synapse shows a large variation in the response to the presynaptic release of the neurotransmitter. This variability is observed not only among different synapses but also in the same single synapse. The synaptic response variability is due to several mechanisms of control of the information transferred among the neurons and suggests that the glutamatergic synapse is not a simple bridge for the transfer of information but plays an important role in its elaboration and management. The control of the synaptic information is operated at pre, post, and extrasynaptic sites in a sort of cooperation between the pre and postsynaptic neurons which also involves the activity of other neurons. The interaction between the different mechanisms of control is extremely complicated and its complete functionality is far from being fully understood. The present review, although not exhaustively, is intended to outline the most important of these mechanisms and their complexity, the understanding of which will be among the most intriguing challenges of future neuroscience.

A Mechanistic Model of NMDA and AMPA Receptor-Mediated Synaptic Transmission in Individual Hippocampal CA3-CA1 Synapses: A Computational Multiscale Approach

Inside hippocampal circuits, neuroplasticity events that individual cells may undergo during synaptic transmissions occur in the form of Long-Term Potentiation (LTP) and Long-Term Depression (LTD). The high density of NMDA receptors expressed on the surface of the dendritic CA1 spines confers to hippocampal CA3-CA1 synapses the ability to easily undergo NMDA-mediated LTP and LTD, which is essential for some forms of explicit learning in mammals. Providing a comprehensive kinetic model that can be used for running computer simulations of the synaptic transmission process is currently a major challenge. Here, we propose a compartmentalized kinetic model for CA3-CA1 synaptic transmission. Our major goal was to tune our model in order to predict the functional impact caused by disease associated variants of NMDA receptors related to severe cognitive impairment. Indeed, for variants Glu413Gly and Cys461Phe, our model predicts negative shifts in the glutamate affinity and changes in the kinetic behavior, consistent with experimental data. These results point to the predictive power of this multiscale viewpoint, which aims to integrate the quantitative kinetic description of large interaction networks typical of system biology approaches with a focus on the quality of a few, key, molecular interactions typical of structural biology ones.

A Computational Model of the Cholinergic Modulation of CA1 Pyramidal Cell Activity

Dysfunction in cholinergic modulation has been linked to a variety of cognitive disorders including Alzheimer's disease. The important role of this neurotransmitter has been explored in a variety of experiments, yet many questions remain unanswered about the contribution of cholinergic modulation to healthy hippocampal function. To address this question, we have developed a model of CA1 pyramidal neuron that takes into consideration muscarinic receptor activation in response to changes in extracellular concentration of acetylcholine and its effects on cellular excitability and downstream intracellular calcium dynamics. This model incorporates a variety of molecular agents to accurately simulate several processes heretofore ignored in computational modeling of CA1 pyramidal neurons. These processes include the inhibition of ionic channels by phospholipid depletion along with the release of calcium from intracellular stores (i.e., the endoplasmic reticulum). This paper describes the model and the methods used to calibrate its behavior to match experimental results. The result of this work is a compartmental model with calibrated mechanisms for simulating the intracellular calcium dynamics of CA1 pyramidal cells with a focus on those related to release from calcium stores in the endoplasmic reticulum. From this model we also make various predictions for how the inhibitory and excitatory responses to cholinergic modulation vary with agonist concentration. This model expands the capabilities of CA1 pyramidal cell models through the explicit modeling of molecular interactions involved in healthy cognitive function and disease. Through this expanded model we come closer to simulating these diseases and gaining the knowledge required to develop novel treatments.

Multicoding in neural information transfer suggested by mathematical analysis of the frequency-dependent synaptic plasticity in vivo

Two elements of neural information processing have primarily been proposed: firing rate and spike timing of neurons. In the case of synaptic plasticity, although spike-timing-dependent plasticity (STDP) depending on presynaptic and postsynaptic spike times had been considered the most common rule, recent studies have shown the inhibitory nature of the brain in vivo for precise spike timing, which is key to the STDP. Thus, the importance of the firing frequency in synaptic plasticity in vivo has been recognized again. However, little is understood about how the frequency-dependent synaptic plasticity (FDP) is regulated in vivo. Here, we focused on the presynaptic input pattern, the intracellular calcium decay time constants, and the background synaptic activity, which vary depending on neuron types and the anatomical and physiological environment in the brain. By analyzing a calcium-based model, we found that the synaptic weight differs depending on these factors characteristic in vivo, even if neurons receive the same input rate. This finding suggests the involvement of multifaceted factors other than input frequency in FDP and even neural coding in vivo.

Coincidence Detection within the Excitable Rat Olfactory Bulb Granule Cell Spines

In the mammalian olfactory bulb, the inhibitory axonless granule cells (GCs) feature reciprocal synapses that interconnect them with the principal neurons of the bulb, mitral, and tufted cells. These synapses are located within large excitable spines that can generate local action potentials (APs) upon synaptic input ("spine spike"). Moreover, GCs can fire global APs that propagate throughout the dendrite. Strikingly, local postsynaptic Ca²⁺ entry summates mostly linearly with Ca²⁺ entry due to coincident global APs generated by glomerular stimulation, although some underlying conductances should be inactivated. We investigated this phenomenon by constructing a compartmental GC model to simulate the pairing of local and global signals as a function of their temporal separation Δt. These simulations yield strongly sublinear summation of spine Ca²⁺ entry for the case of perfect coincidence Δt = 0 ms. Summation efficiency (SE) sharply rises for both positive and negative Δt. The SE reduction for coincident signals depends on the presence of voltage-gated Na⁺ channels in the spine head, while NMDARs are not essential. We experimentally validated the simulated SE in slices of juvenile rat brain (both sexes) by pairing two-photon uncaging of glutamate at spines and APs evoked by somatic current injection at various intervals Δt while imaging spine Ca²⁺ signals. Finally, the latencies of synaptically evoked global APs and EPSPs were found to correspond to Δt ≈ 10 ms, explaining the observed approximately linear summation of synaptic local and global signals. Our results provide additional evidence for the existence of the GC spine spike.SIGNIFICANCE STATEMENT Here we investigate the interaction of local synaptic inputs and global activation of a neuron by a backpropagating action potential within a dendritic spine with respect to local Ca²⁺ signaling. Our system of interest, the reciprocal spine of the olfactory bulb granule cell, is known to feature a special processing mode, namely, a synaptically triggered action potential that is restricted to the spine head. Therefore, coincidence detection of local and global signals follows different rules than in more conventional synapses. We unravel these rules using both simulations and experiments and find that signals coincident within ≈±7 ms around 0 ms result in sublinear summation of Ca²⁺ entry because of synaptic activation of voltage-gated Na⁺ channels within the spine.

Dendritic spine geometry and spine apparatus organization govern the spatiotemporal dynamics of calcium

Dendritic spines are small subcompartments that protrude from the dendrites of neurons and are important for signaling activity and synaptic communication. These subcompartments have been characterized to have different shapes. While it is known that these shapes are associated with spine function, the specific nature of these shape-function relationships is not well understood. In this work, we systematically investigated the relationship between the shape and size of both the spine head and spine apparatus, a specialized endoplasmic reticulum compartment within the spine head, in modulating rapid calcium dynamics using mathematical modeling. We developed a spatial multicompartment reaction-diffusion model of calcium dynamics in three dimensions with various flux sources, including N-methyl-D-aspartate receptors (NMDARs), voltage-sensitive calcium channels (VSCCs), and different ion pumps on the plasma membrane. Using this model, we make several important predictions. First, the volume to surface area ratio of the spine regulates calcium dynamics. Second, membrane fluxes impact calcium dynamics temporally and spatially in a nonlinear fashion. Finally, the spine apparatus can act as a physical buffer for calcium by acting as a sink and rescaling the calcium concentration. These predictions set the stage for future experimental investigations of calcium dynamics in dendritic spines.