Modeling in the Neurosciences

From Ionic Channels to Neural Networks

R.R. Poznanski

• Editore: Routledge
• Anno: 2019
• ISBN:
  9781351430968
• Edizione: 1
• Argomento: Informatik
• Categoria: Neuronale Netzwerke

With contributions from more than 40 renowned experts, Modeling in the Neurosciences: From Ionic Channels to Neural Networks is essential for those interested in neuronal modeling and quantitative neiroscience. Focusing on new mathematical and computer models, techniques and methods, this monograph represents a cohesive and comprehensive treatment

CHAPTER 1

INTRODUCTION TO MODELING IN THE NEUROSCIENCES

Roman R. Poznanski

Evolution through millions of years of variation and selection has produced an immensely complex structure- the human brain, believed to contain about 100 billion neurons interconnected with a high degree of specificity totaling about 1000 trillion connections. The ability of the brain to process information which ultimately leads to behavior stems from this high degree of complexity. These functional connections between neurons as well as their morphological structure and electrical characteristics is the result of repeated cycles of variation and selection which are both genetic in origin and driven by physiological plasticity. Thus the brain is a Darwinian neural network, and a processor of information governed by Darwinian evolutionary selectionist mechanisms (Edelman, 1987; Sporns and Tonomi, 1994). The mystery of how the brain works must clearly be dependent on the interaction between the circuitry and properties of its constituent elements, the neurons. In this respect, models of single neurons are essential to the gradual development of higher brain function. These models must span from the level of individual synaptic connections to synaptic integration and dendritic function, and to eventually the exploration of high level multineuronal realistic network functioning.

This book does not deal with molecular models of permeability changes in nerve membranes or relationship between ion channels structure and function on the molecular level, nor does it deal with selectionist models, connectionist models or pyschophysical models found in cognitive neurosciences. There already exists good introductory texts in such fields (see Kandel, 1976; Levine, 1991; Smith, 1996). Neither will this book attempt to provide an explanation of behavior in terms of single neurons, i.e. the neurophysiology of the mind (see Horridge, 1977) or to provide a blueprint for building ‘artificial’ brains or assume that the brain ‘computes’. These notions have their origins in cybernetics (see Wiener, 1961) and more recently in computational neuroscience (see Durbin et al., 1989; McKenna et al., 1992; Koch, 1998), and so a clear differentiation between computation is expected from readers, since modeling in the neurosciences represents a movement away from the computational doctrines towards a noncomputational neuroscience (see e.g. Globus, 1992). This movement is necessary if we want to embrace neural Darwinism (Edelman, 1987; 1993) and challenge the metaphor of the brain being entirely mechanical (Barlow, 1990). The metaphor that the brain is a computer whose sole function is to transform incoming neuroelectric signals into neuronal output is gratuitously weak as it requires a ‘mind’ controlling the ‘thinking machine’ (see Bennett, 1997 for a modern viewpoint). A more closer definition befitting this metaphor should be a Darwinian ‘machine’ as advocated by Calvin (1987).

Another weakness in the metaphor is that the brain does not turn on and off like some sort of computational machine. The activity of the brain is interwoven with the spontaneous activity generated when the brain is not evoked by any external incoming stimuli. Chapters 2, 3, and 4 deal with such spontaneous activity, for three different sources of variability: (i) ionic channel current fluctuations, (ii) synaptic release of neurotransmitter, and (iii) dendritic morphogenesis. By these modeling studies it is possible to identify levels of biological organization at which structures and dynamics can be described in terms of random events. It is then plausible to assume that at such a level the phenomena are not governed by a well-defined underlying organizing plan but are the result of many contributing underlying processes. These findings are relevant in issues of the organizational plan of the brain, the involvement of genes, and aspects of self-organization. By understanding the mechanisms governing cognition are firmly based upon the processes of natural selection and variability among others, the computational or metaphysical approach can be abandoned. This will be a pinnacle achievement for modeling in the neurosciences.

In the past decade great advances have been achieved in the study of ion channels (see Hille, 1992); electrophysiologists are discovering new ideas and concepts that had been impossible to determine only a decade ago. For example, patch clamp recording allows pico-amp ionic currents through a membrane channel to be directly recorded (see Sakmann and Neher, 1995). In Chapter 2 by Mino fluctuations of current caused by the gating mechanisms of ionic channels observed at all neuronal membranes with the patch clamp method are analyzed by applying methods of statistical inference for the analysis of the data. Two situations are considered: 1) stationary ionic channel current fluctuations (ICFs) observed during a constant application of chemical transmitter, and 2) non-stationary ICFs observed during repetitive stimulation. A Markov process represents the ion channel gating mechanism of a finite number of channels (see Tuckwell, 1989). Important parameters of the stochastic gating mechanism of single ionic channels are found from the statistical analysis of the ionic channel current fluctuation data. In particular, the number of ionic channels activated, current amplitude of single ionic channels, and state transition rates of the gating mechanism. Electrophysiological measurements usually create an additional source of noise that is Gaussian. In this noisy situation third order statistics are insensitive to the additive Gaussian noise component, and can provide information on the parameters of single ionic channels from the stationary ICFs data. The method for non-stationary ICFs is based on the second-order regression model including not only the ICF components but also the Gaussian noise component.

The activation of a multiple number of synaptic sites that are spatially distributed along the dendrites of a neuron contributes to the overall physiological response. The physiological efficacy of responses at each synaptic site can be defined by the following critical parameters: 1) different amounts of neurotransmitter released both between junctional sites and over time, 2) the probability of realease, 3) postsynaptic site response amplitude (‘quantal’ amplitude), 4) the degree of fluctuation around that characteristic amplitude (‘quantal’ variance) distributed both over time and between sites, 5) the efficacy of electrotonic conduction between the synaptic site of origin and the output or summation site, and 6) variable postsynaptic ligand binding with a ligand receptor mismatch. These parameters all vary as a highly dynamic process, fluctuating with the history of use at each synapse over short and long time periods, and between adjacent synaptic sites on dendritic trees. Such heterogeneity between synaptic responses can lead to summated synaptic responses which are difficult to interpret in terms of the behavior of each individual synaptic site. Statistical models for analysis of synaptic function, i.e. the physiological behavior of individual synaptic sites (consisting of a single postsynaptic density and presynaptic release region) have become increasingly sophisticated to account quantitatively for the diverse sources of variability. Chapter 3 by Turner, Chen, West and Wheal presents various statistical modeling approaches to synaptic data analysis, including binomial, Poisson and more complex (less restrictive) methods, to infer on the characteristics of synaptic release under appropriate physiological conditions. These approaches use several algorithms or statistical methods to gain insight into the data, including maximum likelihood and a novel Bayesian approach to investigate many of these sources of variability. Both constrained physiological preparations and statistical models have defined the presence of heterogeneity between synaptic sites and Hebbian mechanisms which may contribute to synaptic plasticity in the CNS.

The variation in dendritic morphology emerges during neurite outgrowth from the dynamic behavior of growth cones in the process of branching and lengthening of dendritic segments. In Chapter 4 by van Pelt and Uylings the question of how dendritic morphology emerges from the basic actions of growth cones is addressed and whether randomness in growth cone behavior is a sufficient condition for generating the typical variability in dendritic shapes, found in neurons of different types and in different species. This question is very difficult or even impossible to answer experimentally. By modeling growth cone actions, and simulating the growth process, one gets an understanding how these actions lead to the emergence of morphological characteristics and the morphological variation. Furthermore, based on these findings one can analyze quantitatively experimentally reconstructed dendritic trees and can make predictions of the time course of the branching and migration process of the growth cones during development of these dendrites. The dendritic growth cone models provide a way of producing random dendritic geometries with realistic morphological variations. These random trees can be used in studies of functional consequences of dendritic geometries and the construction of realistic morphoelectrical models of neurons. There is a great need for such tools in computational studies of neural structure-function relationships, since in recent years computer software developers have created a rise in the application of compartmental modeling originally developed in the 1960s, aiming at modeling neurons with increasing structural realism (see Bower, 1992; Bower and Beeman, 1994). An important aspect of dendritic geometry is its embedding in 3D space. Branch angles between individual segments are in this respect important parameters, but compartmental models of single neurons are lacking this structural realism, leaving a 1D caricature of the cells. The only description of compartmental models with branch angles appears fragmented in Macgregor’s books (see Macgregor, 1987; 1993). The critical aspect of including branch angles is to explore the relationship of single neurons to extracellular space and other volume elements in the neuropil, including processes and glia. The realistic complication of a finite extracellular space is rarely treated in single neuron models because of the difficulties in portraying the neuron in three dimensions and surpassing the infinite media assumption so commonly used. However, critical physiological questions regarding both electrical function and chemical changes require that specific neuronal geometry embedded in a three dimensional neuropil be explicitly considered. Thus, model neurons generated randomly are an excellent supplement to realistic neurons obtained from three dimensional reconstruction allowing for future modeling based on 3D characterization of neurons and networks to be included in new and more realistic future compartmental models of neurons (see for example Chapter 18 for a unique approach in this direction).

Another point concerning the interdependence between neuronal structure and function is that the relationship may not be made out to be perfect. For example, if one function of dendrites is to maximize the surface area for synaptic contact then why are not all the dendritic surface area covered with synaptic knobs? Furthermore, there is no experimental evidence to suggest that all neurons in the brain have dendrites with generic functions. In fact, selectionist theories see the variability within population of neurons as an important key in the development of brain function (see Sporns and Tononi, 1994). It is most likely that dendritic trees of some specific neuronal types are influenced by the intrinsic membrane voltage-dependent conductances on dendritic branches and the topology of the tree, while other neuron types simply convey synaptic inputs to the cell body providing dendrites with two different modes of integration (cf. Yuste and Tank, 1996). Indeed, it may turn out that the variability hidden behind the morphologies of dendritic trees is influenced by the dynamic behavior of growth cones (i.e. migration and branching) governed by undirected random mechanisms during development, such as exploratory interactions of filopodia with their local environment, receptor mediated transmembrane signaling to cytoplasmic regulatory systems, the dynamically instable depolymerization of cytoskeletal elements, and activity-dependent processes. A hypothetical neuron possessing no dendritic tree, only a large spherical soma that accommodates all the synaptic input would make a highly unrealistic target for such random connections to emerge. Thus it may be that structure alone cannot guide us to function!

Models are indispensable, because (i) they can provide a means to formulate a hypothesis in a quantitative manner, (ii) they allow the study of the consequences of a hypothesis in many or all its aspects, (iii) they allow statistical testing of a hypothesis and its consequences, and (iv) they may lead to new experiments that would not otherwise have been considered. The use of models to help elucidate neural behavior has grown exponentially over the last decade (see Koch and Segev, 1998), but worthwhile models that can predict experimental behavior are not so common, and more often are built on the successes of earlier models that were able to satisfactorily predict experimental phenomena albeit in less detail. Some examples are the Hodgkin-Huxley (1952) model for initiation and conduction of action potentials in axons built on the membrane theories of Bernstein, and the Rall (1962) model for the distribution of synaptic potentials in the dendritic tree of a neuron built on the core-conductor theories of Weber. Thus, modeling can predict all sorts of wonderful new theories and clarify functions of neuronal activity, but must be based on a firm experimental platform, otherwise the outcome remains in the realm of neurocomputing or computational neuroscience.

Chapters 5, 6, 7, 8, 9, 10 deal with reduced models of single neurons, and the role of information processing in neural function and the latest methods to measure parameters (i.e. inverse problems). Finding a simple but equivalent representation for complex dendritic trees arises from the common observation that neurons, the basic anatomical building blocks of the nervous system, come in a bewildering variety of shapes and sizes (as discussed in Chapter 3). Although the importance of appropriate analytical tools for investigating the functional consequences of neuron geometry in signal processing in the nervous system is recognized (cf. Major et al., 1993), incorporating reduced models based on analytical methods in biologically realistic neural networks is not available. One approach in understanding neuron geometry entails replacing the given dendritic tree with a multiple branched or even unbranched equivalent structure. Such models might be used as the basis for inferring the position of activated synaptic inputs on dendritic trees, given the geometry of the tree and a somatically recorded voltage transient, and to explore how neuron geometry contributes to synaptic integration. For example, what is the likely efficacy of synaptic inputs on different parts of the dendritic tree. Consequently, the spread of current in cable structures is a major theme in neuroscience and represents the largest component of the book.

In Chapter 5 by Evans an overview is given of the multiple equivalent cylinder model used to describe the passive electrical behavior of neurons. The lumping of all branches of a dendrite into an equivalent cable is assumed. Such lumping does not affect the interesting function that may occur in individual branches and can still capture the essential synaptic integration that may occur in the dendritic tree. Separate models have been specifically developed to investigate the role of dendritic branching, dendritic tapering, nonuniform electrical parameters and dendritic spines on the voltage spread within passive neurons. A mathematical analysis of such a multiple cable model is given and standard techniques are used such as Green’s functions and Fourier methods to obtain exact and approximate analytical solutions to the multi-cylinder somatic shunt cable model. The approach presented is generally well suited to the study of such linear models and extends to passive cable models that involve branching and tapering of dendrites as shown in the next chapter.

A complementary approach presented in Chapter 6 by Glenn and Knisley to obtain the time-dependent membrane potential distribution in dendritic trees of arbitrary geometry with continuously tapering dendrites with arbitrary diameter, membrane time constants, lengths, and rates of tapering. The analytical solution is expressed as a Fourier cosine series, and is shown to be more compact than solutions based on error functions; numerical calculations using compartmental models are used to approximate the solution. Application of this model to spinal motoneurons shows the average electrotonic length to be between 0.4 and 0.8 length constants. The multiple equivalent cable model can be regarded as a model of intermediate complexity because it is not as simple as the tapering equivalent cable model, but less complex than the arbitrary branching models, preserving the size differences between dendritic trees. Therefore, cable modeling of dendritic neurons can provide quantitative analysi...

Indice dei contenuti

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Contributors
• Chapter 1 Introduction to Modeling in the Neurosciences
• Chapter 2 Statistical Analysis of Ionic Channel Current Fluctuations
• Chapter 3 Physiological and Statistical Approaches to Modeling of Synaptic Responses
• Chapter 4 Natural Variability in the Geometry of Dendritic Branching Patterns
• Chapter 5 The Multiple Equivalent Cylinder Model
• Chapter 6 Voltage Transients in Multipolar Neurons with Tapering Dendrites
• Chapter 7 The Lanczos Procedure for Generating Equivalent Cables
• Chapter 8 Parameter Estimation Algorithms for the Shunt Cable Model
• Chapter 9 Determination of Cable Parameters for Neurons with Gap Junctions
• Chapter 10 Syncytial Integration in the Outer Retina
• Chapter 11 Ionic Current Model of the Outer Retinal Cells
• Chapter 12 Ephaptic Interactions Between Neurons. The Example of the Hippocampus
• Chapter 13 Numerical Modeling of Neocortical Pyramidal Cells
• Chapter 14 Some Problems Arising in Models of Conduction in Excitable Dendrites
• Chapter 15 Semi-Quantitative Theory of Bistable Dendrites with Wind-Up
• Chapter 16 Bifurcation Analysis of Neuronal Excitability and Oscillations
• Chapter 17 Dynamics of Associative Memory Networks
• Chapter 18 Analysis and Synthesis of Morphologically Realistic Neural Networks
• Index
• Color Plates