Modeling Signal Transduction Leading to Synaptic Plasticity: Evaluation and Comparison of Five Models

An essential phenomenon of the functional brain is synaptic plasticity which is associated with changes in the strength of synapses between neurons. These changes are affected by both extracellular and intracellular mechanisms. For example, intracellular phosphorylation-dephosphorylation cycles have been shown to possess a special role in synaptic plasticity. We, here, provide the first computational comparison of models for synaptic plasticity by evaluating five models describing postsynaptic signal transduction networks. Our simulation results show that some of the models change their behavior completely due to varying total concentrations of protein kinase and phosphatase. Furthermore, the responses of the models vary when models are compared to each other. Based on our study, we conclude that there is a need for a general setup to objectively compare the models and an urgent demand for the minimum criteria that a computational model for synaptic plasticity needs to meet.Peer reviewe

Postsynaptic Signal Transduction Models for Long-Term Potentiation and Depression

More than a hundred biochemical species, activated by neurotransmitters binding to transmembrane receptors, are important in long-term potentiation (LTP) and long-term depression (LTD). To investigate which species and interactions are critical for synaptic plasticity, many computational postsynaptic signal transduction models have been developed. The models range from simple models with a single reversible reaction to detailed models with several hundred kinetic reactions. In this study, more than a hundred models are reviewed, and their features are compared and contrasted so that similarities and differences are more readily apparent. The models are classified according to the type of synaptic plasticity that is modeled (LTP or LTD) and whether they include diffusion or electrophysiological phenomena. Other characteristics that discriminate the models include the phase of synaptic plasticity modeled (induction, expression, or maintenance) and the simulation method used (deterministic or stochastic). We find that models are becoming increasingly sophisticated, by including stochastic properties, integrating with electrophysiological properties of entire neurons, or incorporating diffusion of signaling molecules. Simpler models continue to be developed because they are computationally efficient and allow theoretical analysis. The more complex models permit investigation of mechanisms underlying specific properties and experimental verification of model predictions. Nonetheless, it is difficult to fully comprehend the evolution of these models because (1) several models are not described in detail in the publications, (2) only a few models are provided in existing model databases, and (3) comparison to previous models is lacking. We conclude that the value of these models for understanding molecular mechanisms of synaptic plasticity is increasing and will be enhanced further with more complete descriptions and sharing of the published models

Simulation of IP3 receptor function in cerebellar Purkinje cell dendritic spine: Importance of stochasticity

Background and aims: This thesis investigates calcium dynamics in cerebellar Purkinje cells. A special emphasis is put on the Purkinje cells dendritic spines where most of the synapses are formed. Transient rises in cytosolic calcium concentration in spines have a crucial role in initiating long-term depression (LTD) of synaptic activity. LTD is one form of synaptic plasticity and it has been found to be one of the mechanisms of motor learning. One of the most important factors in calcium dynamics is the inositol-1,4,5-trisphosphate receptor (IP3 receptor). This protein is a ligand binding calcium channel and it is responsible for releasing calcium from endoplasmic reticulum to cytosol. The IP3 receptor is highly expressed in Purkinje cell spines. Modeling and simulation are an effective way to study the dynamics of intracellular events. The small volume of the spine increases the stochasticity (randomness) in the biochemical processes and this aspect is not considered in traditional deterministic simulations. In this study, the importance of stochasticity in simulation of the function of IP3 receptor was examined. Stochastic simulations are assumed to produce more realistic results compared to deterministic simulations. The aim of my research was to study the effect of stochasticity in modeling by comparing stochastic and deterministic simulations of the function of IP3 receptor, located in cerebellar Purkinje cell dendritic spine. Methods: Based on a large literature review, two different mathematical models describing the function of IP3 receptor were chosen as test cases. In short, both models describe the reaction kinetics of IP3 receptor. These models were simulated both on a deterministic simulator and on a more biologically correct stochastic simulator. Two different kinds of simulations, open probability and dynamic, were performed with both simulators. Results: For both models, open probability simulations produced similar results with deterministic and stochastic simulators. In dynamic simulations the time evolution of cytosolic calcium concentration was examined. For small calcium concentrations, there was a significant difference between deterministic and stochastic simulation results. Conclusions: Results of the open-probability simulations verified that the models were implemented correctly. It can be shown based on dynamic simulation results, that there exists a threshold below which the effect of stochasticity in reaction kinetics becomes meaningful. In conclusion, the deterministic simulations do not produce biologically realistic results under all conditions. Asiasanat: IP3 receptor, modeling, stochastic simulation, Purkinje cell, LTD, cerebellu

Simulation of IP3 receptor function in cerebellar Purkinje cell dendritic spine: Importance of stochasticity

Background and aims: This thesis investigates calcium dynamics in cerebellar Purkinje cells. A special emphasis is put on the Purkinje cells dendritic spines where most of the synapses are formed. Transient rises in cytosolic calcium concentration in spines have a crucial role in initiating long-term depression (LTD) of synaptic activity. LTD is one form of synaptic plasticity and it has been found to be one of the mechanisms of motor learning. One of the most important factors in calcium dynamics is the inositol-1,4,5-trisphosphate receptor (IP3 receptor). This protein is a ligand binding calcium channel and it is responsible for releasing calcium from endoplasmic reticulum to cytosol. The IP3 receptor is highly expressed in Purkinje cell spines. Modeling and simulation are an effective way to study the dynamics of intracellular events. The small volume of the spine increases the stochasticity (randomness) in the biochemical processes and this aspect is not considered in traditional deterministic simulations. In this study, the importance of stochasticity in simulation of the function of IP3 receptor was examined. Stochastic simulations are assumed to produce more realistic results compared to deterministic simulations. The aim of my research was to study the effect of stochasticity in modeling by comparing stochastic and deterministic simulations of the function of IP3 receptor, located in cerebellar Purkinje cell dendritic spine. Methods: Based on a large literature review, two different mathematical models describing the function of IP3 receptor were chosen as test cases. In short, both models describe the reaction kinetics of IP3 receptor. These models were simulated both on a deterministic simulator and on a more biologically correct stochastic simulator. Two different kinds of simulations, open probability and dynamic, were performed with both simulators. Results: For both models, open probability simulations produced similar results with deterministic and stochastic simulators. In dynamic simulations the time evolution of cytosolic calcium concentration was examined. For small calcium concentrations, there was a significant difference between deterministic and stochastic simulation results. Conclusions: Results of the open-probability simulations verified that the models were implemented correctly. It can be shown based on dynamic simulation results, that there exists a threshold below which the effect of stochasticity in reaction kinetics becomes meaningful. In conclusion, the deterministic simulations do not produce biologically realistic results under all conditions. Asiasanat: IP3 receptor, modeling, stochastic simulation, Purkinje cell, LTD, cerebellu

Comparison of Models for IP3 Receptor Kinetics Using Stochastic Simulations

Inositol 1,4,5-trisphosphate receptor (IP3R) is a ubiquitous intracellular calcium (Ca2+) channel which has a major role in controlling (Ca2+) levels in neurons. A variety of computational models have been developed to describe the kinetic function of IP3R under different conditions. In the field of computational neuroscience, it is of great interest to apply the existing models of IP3R when modeling local Ca2+ transients in dendrites or overall Ca2+ dynamics in large neuronal models. The goal of this study was to evaluate existing IP3R models, based on electrophysiological data. This was done in order to be able to suggest suitable models for neuronal modeling. Altogether four models (Othmer and Tang, 1993; Dawson et al.,2003; Fraiman and Dawson, 2004; Doi et al., 2005) were selected for a more detailed comparison. The selection was based on the computational efficiency of the models and the type of experimental data that was used in developing the model. The kinetics of all four models were simulated by stochastic means, using the simulation software STEPS, which implements the Gillespie stochastic simulation algorithm. The results show major differences in the statistical properties of model functionality. Of the four compared models, the one by Fraiman and Dawson (2004) proved most satisfactory in producing the specific features of experimental findings reported in literature. To our knowledge, the present study is the first detailed evaluation of IP3R models using stochastic simulation methods, thus providing an important setting for constructing a new, realistic model of IP3R channel kinetics for compartmental modeling of neuronal functions. We conclude that the kinetics of IP3R with different concentrations of Ca2+ and IP3 should be more carefully addressed when new models for IP3R are developed.Peer reviewe

Open probability of IP₃R as a function of (A) cytosolic Ca²⁺ concentration (IP₃ = 10 M) and (B) cytosolic IP₃ concentration (Ca²⁺ = 0.25 M).

<p>Green: Othmer and Tang <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059618#pone.0059618-Othmer1" target="_blank">[55]</a>, Blue: Dawson <i>et al.. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059618#pone.0059618-Dawson1" target="_blank">[56]</a>, Red: Fraiman and Dawson <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059618#pone.0059618-Fraiman1" target="_blank">[57]</a>, Magenta: Doi <i>et al.. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059618#pone.0059618-Doi1" target="_blank">[35]</a>.</p

Distributions of IP₃R open and closed times for all the selected models obtained in simulation conditions Sim 3 (A–F) and Sim 4 (G–L).

<p>(A) Open time distributions of all the models in conditions Sim 3, (B) Enlarged from A, (C) Enlarged from B, (D) Closed time distributions of all the models in conditions Sim 3, (E) Enlarged from D, (F) Enlarged from E, (G) Open time distributions of all the models conditions Sim 4, (H) Enlarged from G, (I) Enlarged from H, (J) Closed time distributions of all the models conditions Sim 4, (K) Enlarged from J, (L) Enlarged from K. Experimental data is from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059618#pone.0059618-Moraru1" target="_blank">[20]</a>. In simulation conditions Sim 3 [Ca²⁺] = 0.1 M, [IP₃] = 2 M and Sim 4 [Ca²⁺]  =  0.1 M, [IP₃]  = 10 M (as shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0059618#pone-0059618-t006" target="_blank">Table 6</a>).</p