Eric Y. Hu

Integrated Multiscale Modeling of the Nervous System: Predicting Changes in Hippocampal Network Activity by a Positive AMPA Receptor Modulator

One of the fundamental characteristics of the brain is its hierarchical organization. Scales in both space and time that must be considered when integrating across hierarchies of the nervous system are sufficiently great as to have impeded the development of routine multilevel modeling methodologies. Complex molecular interactions at the level of receptors and channels regulate activity at the level of neurons; interactions between multiple populations of neurons ultimately give rise to complex neural systems function and behavior. This spatial complexity takes place in the context of a composite temporal integration of multiple, different events unfolding at the millisecond, second, minute, hour, and longer time scales. In this study, we present a multiscale modeling methodology that integrates synaptic models into single neuron, and multineuron, network models. We have applied this approach to the specific problem of how changes at the level of kinetic parameters of a receptor-channel model are translated into changes in the temporal firing pattern of a single neuron, and ultimately, changes in the spatiotemporal activity of a network of neurons. These results demonstrate how this powerful methodology can be applied to understand the effects of a given local process within multiple hierarchical levels of the nervous system.

Synaptic Efficacy as a Function of Ionotropic Receptor Distribution: A Computational Study.

Glutamatergic synapses are the most prevalent functional elements of information processing in the brain. Changes in pre-synaptic activity and in the function of various post-synaptic elements contribute to generate a large variety of synaptic responses. Previous studies have explored postsynaptic factors responsible for regulating synaptic strength variations, but have given far less importance to synaptic geometry, and more specifically to the subcellular distribution of ionotropic receptors. We analyzed the functional effects resulting from changing the subsynaptic localization of ionotropic receptors by using a hippocampal synaptic computational framework. The present study was performed using the EONS (Elementary Objects of the Nervous System) synaptic modeling platform, which was specifically developed to explore the roles of subsynaptic elements as well as their interactions, and that of synaptic geometry. More specifically, we determined the effects of changing the localization of ionotropic receptors relative to the presynaptic glutamate release site, on synaptic efficacy and its variations following single pulse and paired-pulse stimulation protocols. The results indicate that changes in synaptic geometry do have consequences on synaptic efficacy and its dynamics.

Paired-pulse stimulation at glutamatergic synapses - pre- and postsynaptic components

Paired-pulse stimulation is a standard protocol that has been used for decades to characterize dynamic systems: the differences in responses to two sequential identical stimuli as a function of inter-stimulus interval provide quantitative information on the dynamics of the system. In neuroscience, the paired-pulse protocol is also widely used at multiple levels of analysis, from behavioral conditioning to synaptic plasticity, and in particular to define the biomolecular mechanism of learning and memory. In a system as small and complex as synapses, it is extremely challenging - if not impossible - to experimentally gain access to the multitude of possible readouts. In the present study, we first introduce a computational synaptic modeling platform that we developed and calibrated based on experimental data from both our laboratories and a variety of publications. We then show how this platform allows not only to replicate experimental data, but also to go beyond technological boundaries and investigate the main parameters responsible for regulation of synaptic transmission and plasticity. The results provide critical information regarding the respective role of various subsynaptic processes and of their interactions. Additionally, this approach can strengthen our understanding of potential dysfunctions (pathologies) and suggest potential approaches to re-establish normal function.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Maximizing predictability of a bottom-up complex multi-scale model through systematic validation and multi-objective multi-level optimization

Computational models are mathematical representations meant to replicate the biological system they represent, as well as provide insights and predict the systems dynamics in response to changing conditions. In a bottom-up modeling approach, a multitude of models may be compounded to represent more complex higher level biological systems. However, guaranteeing the validity and predictability of the compounded ensemble may become increasingly challenging as more components are integrated. We herein present a sequential and iterative method to maximize predictability of a complex multiscale model. We have successfully developed a multiscale modeling platform comprised of mechanisms ranging from the biomolecular level to multi-cellular networks. To maintain a high level of predictability of the global platform, we introduce a systematic approach to not only validate all models independently, but also verify the validity of compounded models as additional information becomes available at higher levels of complexity. Iterative and systematic application of these validation steps at increasing levels of complexity is intended to maximize the predictive power of the platform, making it a powerful tool to study the impacts of low-levels modifications (pathologies, drugs, etc.) on higher functional levels. The work presented lays down the rationale of the approach, the open design implementation and results.

Modeling of the nervous system: From modulation of glutamatergic and gabaergic molecular dynamics to neuron spiking activity

One of the fundamental characteristics of the brain is its hierarchical and temporal organization: scales in both space and time must be considered to fully grasp the systems underlying mechanisms and their impact on brain function. Complex interactions taking place at the molecular level regulate neuronal activity that further modifies the function of millions of neurons connected by trillions of synapses, ultimately giving rise to complex function and behavior at the system level. Likewise, the spatial complexity is accompanied by a complex temporal integration of events taking place at the microsecond scale leading to slower changes occurring at the second, minute and hour scales. These integrations across hierarchies of the nervous system are sufficiently complex to have impeded the development of routine multi-level modeling methodologies. The present study describes an example of our multiscale efforts to rise from the biomolecular level to the neuron level. We more specifically describe how we integrate biomolecular mechanisms taking place at glutamatergic and gabaergic synapses and integrate them to study the impact of these modifications on spiking activity of a CA1 pyramidal cell in the hippocampus.

Influence of ionotropic receptor location on their dynamics at glutamatergic synapses

In this paper we study the effects of the location of ionotropic receptors, especially AMPA and NMDA receptors, on their function at excitatory glutamatergic synapses. As few computational models only allow to evaluate the influence of receptor location on state transition and receptor dynamics, we present an elaborate computational model of a glutamatergic synapse that takes into account detailed parametric models of ionotropic receptors along with glutamate diffusion within the synaptic cleft. Our simulation results underscore the importance of the wide spread distribution of AMPA receptors which is required to avoid massive desensitization of these receptors following a single glutamate release event while NMDA receptor location is potentially optimal relative to the glutamate release site thus, emphasizing the contribution of location dependent effects of the two major ionotropic receptors to synaptic efficacy.

Modeling of the nervous system: From molecular dynamics and synaptic modulation to neuron spiking activity

The brain is a perfect example of an integrated multi-scale system, as the complex interactions taking place at the molecular level regulate neuronal activity that further modifies the function of millions of neurons connected by trillions of synapses, ultimately giving rise to complex function and behavior at the system level. Likewise, the spatial complexity is accompanied by a complex temporal integration of events taking place at the microsecond scale leading to slower changes occurring at the second, minute and hour scales. In the present study we illustrate our approach to model and simulate the spatio-temporal complexity of the nervous system by developing a multi-scale model integrating synaptic models into the neuronal and ultimately network levels. We apply this approach to a concrete example and demonstrate how changes at the level of kinetic parameters of a receptor model are translated into significant changes in the firing of a pyramidal neuron. These results illustrate the abilities of our modeling approach and support its direct application to the evaluation of the effects of drugs, from functional target to integrated system.

Development of a detailed model of calcium dynamics at the postsynaptic spine of an excitatory synapse

Postsynaptic calcium dynamics play a critical role in synaptic plasticity, but are often difficult to measure in experimental protocols due to their relatively fast rise and decay times, and the small spine dimensions. To circumvent these limitations, we propose to develop a computational model of calcium dynamics in the postsynaptic spine. This model integrates the main elements that participate in calcium concentration influx, efflux, diffusion and buffering. These consist of (i) spine geometry; (ii) calcium influx through NMDA receptors and voltage-dependent calcium channels (VDCC); (iii) calcium efflux with plasma membrane calcium pumps (PMCA) and sodium-calcium exchangers (NCX); (iv) intracellular calcium stores; and (v) calcium buffers. We herein present computational results we obtained and compare them with experimentally measured data, thereby validating the proposed model. Overall the development of such postsynaptic calcium model may help us better understand the intricacies of interplay between the different elements that shape calcium dynamics and impact synaptic plasticity in normal functions and pathologies. This model also constitutes a first step in the development of a nonlinear input-output calcium dynamics model for multi-scale, large scale neuronal simulations.Postsynaptic calcium dynamics play a critical role in synaptic plasticity, but are often difficult to measure in experimental protocols due to their relatively fast rise and decay times, and the small spine dimensions. To circumvent these limitations, we propose to develop a computational model of calcium dynamics in the postsynaptic spine. This model integrates the main elements that participate in calcium concentration influx, efflux, diffusion and buffering. These consist of (i) spine geometry; (ii) calcium influx through NMDA receptors and voltage-dependent calcium channels (VDCC); (iii) calcium efflux with plasma membrane calcium pumps (PMCA) and sodium-calcium exchangers (NCX); (iv) intracellular calcium stores; and (v) calcium buffers. We herein present computational results we obtained and compare them with experimentally measured data, thereby validating the proposed model. Overall the development of such postsynaptic calcium model may help us better understand the intricacies of interplay between the different elements that shape calcium dynamics and impact synaptic plasticity in normal functions and pathologies. This model also constitutes a first step in the development of a nonlinear input-output calcium dynamics model for multi-scale, large scale neuronal simulations.

Insights on synaptic paired-pulse response using parametric and non-parametric models

Paired-pulse protocol is a well-established stimulation pattern used to characterize short-term changes in synaptic potency. Due to the experimental difficulty in accessing and measuring responses and interactions between subsynaptic elements, understanding the mechanisms that shape synaptic response is extremely challenging. We already proposed to address this issue and gain insights on the matter using a complex integrated modeling platform called EONS (Elementary Objects of the Nervous System). The use of this parametric platform provided us with insightful information on the subsynaptic components and how their interactions shape synaptic dynamics. We herein propose to add and combine a non-parametric model to (i) simplify the modeling framework, the number of underlying parameters and the overall computational complexity while faithfully maintaining the desirable synaptic behavior and (ii) provide a clear and concise framework to characterize AMPA and NMDA contributions to the observed paired-pulse responses.