PREFACE Neuronal function arises from the complex interplay among synaptic inputs, ionic channels, and the modulatory signaling pathways that are activated by G-protein-coupled receptors or calcium influx. Not only do these interactions span multiple time scales, but elongated dendrites with tiny dendritic spines introduce multiple spatial scales of interactions. Experiments using cutting-edge imaging and other novel techniques, rather than adding clarity, have instead added to the complexity. The nonlinear temporal and spatial interactions among diverse ionic channels and signaling pathways produce unexpected neuron behavior and hinder a deep understanding of how enzyme or ion channel mutations bring about abnormal behavior and disease. Mathematical and computational modeling offers a powerful approach for examining the interaction between molecular pathways and ionic channels in producing neuron electrical activity. Modeling is an approach to integrate myriad data sources into a cohesive and quantitative formulation in order to evaluate hypotheses about neuron function. In particular, a validated model developed using in vitro data allows simulations of the response to in vivo-like spatiotemporal patterns of synaptic input. Such models can be utilized to perform in silico experiments, the results of which can guide experiments into more productive domains. Models further allow inspection of all molecular species and ion channels simultaneously at all spatial locations and time points, providing additional insight into mechanisms. Incorporating molecular signaling pathways and morphology into an electrical model allows a greater range of models to be developed, ones that can predict the response to pharmaceutical treatments, many of which target neuromodulator pathways. In this volume, we bring together different aspects of and approaches to molecular and multiscale modeling, with consequences for a diverse range of neurological diseases. The book opens with the topic of ion channel modeling. Chapter 1 by Lampert and Korngreen describes an approach to combine electrophysiology and Markov kinetic modeling to understand how single channel mutations contribute to epilepsy and pain perception. The role of ion channels in pain is further explored in Chapter 2 by Franse´n, which explains the interaction among diverse ion channels and synaptic channels in mediating peripheral pain. Due to complex interactions between channel activity, they xv



demonstrate that novel and unexpected ion channel changes could explain neuron activity changes connected to pain sensitivity. Chapter 3 by Yu et al. continues the exposition on ionic channel interactions, by illuminating the ionic mechanisms controlling activity of dopamine neurons, which are the targets for antipsychotic and schizophrenia drugs. The next section of the book presents models of calcium and other subcellular components of neurons. Chapter 4 by Ullah et al. shows how dynamics of calcium wave propagation are controlled by spatial distribution of calcium release channels on the endoplasmic reticulum. Though simulated in oocytes, similar principles likely operate in neurons. Chapter 5 by Jafri and Kumar investigates energy metabolism in mitochondria and shows how calcium and reactive oxygen species can modify energy metabolism, which can produce neuronal dysfunction. The next two chapters focus on two aspects of cell morphology. Chapter 6 by Naoki and Ishii demonstrates how transport of growth factors interacts with a bistable switch of biochemical reactions to allow selection of a single neurite as an axon during neuronal polarization. Chapter 7 by Rangamani et al. introduces a novel type of multiscale modeling of the interaction between the biochemical reaction networks governing the actin cytoskeleton and the biophysics of the membrane controlling the change in membrane geometry. The next two chapters move outside of single neurons to discuss issues crucial for large-scale neuronal network and tissue modeling. Chapter 8 by Marinov and Santamaria explains the complexities of diffusion not only intracellularly, where spines can produce anomalous diffusion, but also extracellularly, where the tortuosity of the extracellular space creates a larger than expected path distance for diffusing molecules. Chapter 9 by Linne and Jalonen reviews models and the role of astrocytes in various diseases, which include astrocyte calcium dynamics and the interaction of astrocytes with neurons, especially at the tripartite synapse. The last section of the book presents additional types of multiscale models. Chapter 10 by Hille et al. describes a remarkable integration of FRET imaging and electrophysiology with model development to produce a highly constrained and validated model of the control of a potassium channel by a GPCR signaling pathway. Chapter 11 by Taxin et al. brings together numerous concepts from previous chapters including astrocytes, mitochondria, calcium dynamics, and large-scale networks of biochemical reaction pathways to explore the consequences of neuronal ischemia. Chapter 12 by Nair et al. addresses issues crucial to all model development, namely, integration of data from diverse experimental sources, general issues of



constraining parameters, and evaluating sensitivity to parameters. This chapter gives examples of large-scale models of signaling pathways in the basal ganglia, with the aim to understanding mechanisms of Parkinson’s disease. Chapter 13 by Rothman and Silver presents a step-by-step approach for modeling synaptic responses, beginning with the standard equations for postsynaptic currents and adding in equations describing vesicle release controlled by depletion and facilitation resulting from vesicle cycling. The book closes with Chapter 14 on the issues facing an expansion of multiscale modeling to multiphysics modeling, including the issues of “synchronizing” the different spatial and temporal scales that are required for integrating biochemical activity with electrical activity and even changes to morphology. A large diversity of software tools is represented here, including VCell, Neuron, Moose, XPPAUT, as well as the custom software required when embarking on new approaches. Similarly, a variety of numerical methods is presented, including Boolean networks, ordinary and partial differential equations and solvers, as well as stochastic methods such as Monte Carlo methods, some of which use the Gillespie method for exact stochastic stimulation. Several chapters discuss the selection of numerical techniques, in particular the question of stochastic versus deterministic simulation. Stochastic simulations are needed in small volumes where the number of interacting molecules is small and the approximation of concentration is not valid. The role of noise produced by stochasticity is also discussed. I would like to express my gratitude to the contributing authors and coauthors of this book for their expertise, time, and contribution to making this volume a truly educational and informative work. I would also like to acknowledge the generous funding of my research through the NSF NIH CRCNS program (R01AA016022 & R01AA18066) and by ONR (MURI N00014-10-1-0198). KIM “AVRAMA” BLACKWELL

Preface. Computational neuroscience.

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