Multiscale Analysis and Nonlinear Dynamics

From Genes to the Brain

Misha Meyer Pesenson, Heinz Georg Schuster

• Publisher: Wiley-VCH
• Year: 2013
• Print ISBN:
  9783527411986
• eBook ISBN:
  9783527671656
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mathematical & Computational Physics

Since modeling multiscale phenomena in systems biology and neuroscience is a highly interdisciplinary
task, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience,
computer science, and applied mathematics, to provide their perspectives.

Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fields. While multiscale
analysis is the major integrating theme of the book, its subtitle does not call for bridging the
scales from genes to behavior, but rather stresses the unifying perspective offered by the concepts
referred to in the title.

It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fields.

1

Introduction: Multiscale Analysis – Modeling, Data, Networks, and Nonlinear Dynamics

Misha (Meyer) Z. Pesenson

“...the twin difficulties of scale and complexity.”

P. Anderson [1]

“...I spelled out a moral for the general structure of scientific knowledge: that scale changes in a wide variety of instances can lead to qualitative change in the nature of phenomenon.”

P. Anderson [2]

“...to find a really appropriate name for that stratification or layering of the structures involved which we are all tempted to describe as ‘hierarchies’. ...We need a conception of tiers of networks with the highest tier as complex as the lower ones.”

F. Hayek [3]

The human brain is the archetype of a natural complex adaptive system. It is composed of impenetrable “jungles” of neurons, which interact both within and across multiple spatial and temporal scales (see, for example, recent books: [4–13]). In Systems Biology the situation is similarly complicated and biological systems, besides being characterized by a large number of components and their interactions, demonstrate a very complex organization at multiple spatial scales [14,15]. As a result, the fields of Systems Neuroscience and Systems Biology deal with phenomena of intricate complexity that are governed by various mechanisms integrated across many levels of detail. In addition, high-throughput experimental technologies and powerful simulation/analysis tools generate new types of heterogeneous data with a density and depth previously unimaginable. All this creates a critical need for modeling sophisticated, natural/artificial systems and analyzing modern high-dimensional data from multiple levels ranging from molecules → synapses → neurons → networks (and ideally, all the way to behavior). The attempts to model/analyze such complex phenomena/data are hindered by the fact that traditional mathematical approaches are often limited because of the multiscale nature of the problems.

This book concentrates on the investigation of multiscale problems in Systems Biology and Systems Neuroscience, and on mathematical approaches to multiresolution analysis (MRA). Systems Biology analyzes how hierarchical, multiscale molecular structures control the dynamic linkages between different genes and their products and give rise to the emergent properties and functions of a unified organism [14,15]. Similarly, the goal of Systems Neuroscience is to unravel how neurons and the intricate structure of neural networks shape information flow, perceptual grouping, multiscale processing, the emergent functions of neural circuits, and ultimately – cognition and behavior [13]. Despite these obvious parallels between Systems Biology and Systems Neuroscience, there is, surprisingly little interaction among the corresponding research communities [16]. It is unfortunate, since these two fields can learn quite a bit from each other regarding the use of physical, mathematical/computational modeling, data processing, and so on. In addition, identifying methods common to both, Systems Biology and Systems Neuroscience, may, in turn, drive the development of systematic mathematical approaches to modeling complex phenomena/data. To promote stronger interaction between these fields and to aid their “coming together,” as Kandel¹ phrased it, the editor of this book invited contributions from experts representing a highly interdisciplinary group of scientists in computer science, applied mathematics, bioengineering, chemistry, cardiology, and neuroscience. The chapters in this book may broadly be categorized as belonging to mathematical methods, Systems Biology, and Systems Neuroscience. One of the goals of this book is to attract the attention of scientists working in these supposedly distinct fields, by demonstrating that some of the seemingly unrelated problems in Systems Biology and Systems Neuroscience may be modeled using virtually identical powerful methods from the inclusive paradigms articulated here. There are three main paradigms, which are the unifying threads of this book – multiscale analysis, networks, and nonlinear dynamics. Multiscale analysis is the major integrating theme of the book, as indicated by its title. The subtitle does not call for bridging the scales all the way from genes to behavior, but rather stresses the unifying perspective provided by the concepts referred to in the title, and especially by multiscaling. Multiscaling, in essence the consideration of problems on many spatial and temporal scales, is one of the major recent developments in solid-state physics, fluid mechanics, and applied mathematics (some examples are briefly discussed later in this introduction). This book emphasizes the importance of taking into account the interplay between multiscale structure and multiscale dynamics. It is network theory that provides a general framework for the integration of multiscaling and collective dynamics.

In neuroscience, multiscale network interactions may account for much of the brain's complex behavior. The importance of multiple time/space scales and their interaction was emphasized by Hebb, Hayek, and Luria [18–20], and has been stressed by a number of authors over the past few years [5–12,21–25]. Nunez focuses on the importance of nested modular hierarchy in brain tissue and quotes V. Mountcastle: “the brain is a complex of widely and reciprocally interconnected systems and the dynamic interplay of neural activity within and between these systems is the very essence of brain function.” [8]. Mountcastle also explicitly referred to the emergent behavior of the brain: “The properties of microcircuit operations are emergent, for they cannot be predicted from what is known of the action of single neurons.” [26]. The hierarchy of neural networks figures in the global neuronal workspace model of consciousness that is based on dynamic links between specialized processing modules (dynamically formed networks) [27–31]. This model includes long-range cortico-cortical axons (densely distributed in prefrontal, parieto-temporal, and cingulate cortices) that integrate sub networks into a single large system, and suggests that highly distributed synchronized activity provides neural correlates of conscious states of the brain. Another model of memory and consciousness, the multiregional retroactivation framework, also rejects a single anatomical site for the integration of memory and motor processes, and involves time-locked neuronal ensembles located in multiple and separate regions [32,33]. Based on simultaneous electrophysiological and fMRI measurements in non-human primates, Logothetis [34] states that “the concurrent study of components and networks” is needed and “simultaneous studies of microcircuits, of local and long-range interconnectivity between small assemblies, and of the synergistic activity of larger neuronal populations are essential.” Another experimental illustration of the significance of dynamics and multiple scales comes from a work of Salazar et al. [35], who, by using simultaneous recordings of neural activity from various areas, demonstrated that short-term memories are represented by patterns of synchronization, widely distributed throughout the frontoparietal network (I'd like to thank Lester Ingber for bringing this work to my attention). Overall, there is mounting experimental evidence that sensory neurons change their responses, as well as the structure of neuronal correlations, adaptively. In Systems Biology it is also being increasingly recognized that various bionetworks are interrelated and influence each other dynamically. To sum up, modeling in Systems Neuroscience and Systems/Synthetic Biology must take into account a large number of components, their nonlinear dynamic interactions, and multiscale, dynamically changing hierarchical interconnections.

These factors may lead to an emergent, self-organized (in contrast to centrally controlled), adaptive behavior that is often encountered in Systems Neuroscience and Systems Biology. Indeed, in the context of neural networks, it was shown some 30 years ago that new properties may emerge as a result of the collective dynamic interaction of a large number of components [36]. Hopfield's network consisted of simple equivalent components, and the network had little structure. Nonetheless, new collective properties spontaneously emerged. This had been anticipated by Anderson: “We expect to encounter fascinating and, I believe, very fundamental questions at each stage in fitting together less complicated pieces into the more complicated system and understanding the basically new types of behavior which can result” [1]. As Aristotle put it, “In the case of all things which have several parts and in which the whole is not, as it were, a mere heap, but the totality is something besides the parts, there is a cause of unity.” [37]. Interactions among multiple scales also may give rise to new phenomena. Let us consider just a few classical examples. The first one dates back to 1869, when Maxwell solved the problem of anomalous dispersion of a monochromatic electromagnetic wave of the frequency ω interacting with the transmitting media whose electrons have the intrinsic frequency ω₀ [38–40]. In essence, this theory links the macroscopically observed refraction and absorption to the microscopic oscillations of electrons. Another example concerns spatial scales and comes from nonlinear waves in elastic media with microstructure [41]. Microstructure induces the spatial dispersion that, together with nonlinearity, gives rise to a striking new type of nonlinear waves – solitons, described by the macroscopic Korteweg–de Vries (KdV) equation. These examples indicate that both collective behavior and the effect of multiple scales may separately lead to changes in the nature of a system. Therefore, the integration of multiscaling and collective dynamics (iMCD), the paradigm advocated here, takes into account the convoluted interplay between these two factors, thus providing a broad, inclusive way of describing emergence and adaptivity of complex systems.

Besides furnishing a theoretical perspective, modeling based on iMCD will also be important for how Systems Biology and Systems Neuroscience collect experimental data. In neuroscience, for example, it will soon be possible to record from thousands of neurons, but for studies of a particular phenomenon, it is important to know from which (and from how many) neurons the spikes should be recorded (see, for example, Refs [35,42,43]).

Moreover, the iMCD paradigm, being comprehensive, will help to grasp and interpret this flood of experimental/simulated data. Indeed, one primarily detects what he/she is looking for (“The decisive point is not observation but expectation” as Popper put it [44]), and even when there is something unforeseen and a model proves to be inadequate, it is the comprehensiveness of the modeling that helps one to spot the unanticipated.² In addition to providing useful technical tools, multiscaling is in fact a way of thinking. For example, let us take a look at the so-called model equations. The KdV equation mentioned above is just one example of such equations which describe a large number of physical, chemical, technical, and biological phenomena. These equations include the nonlinear Schrödinger equation, the sine–Gordon equation, the Ginzburg–Landau equation, and so on [39,45,46]. Their derivation, which utilizes multiple space/time scales essential to a phenomenon, has led to advances in the understanding of diverse phenomena and also to the establishment of new, rich branches of research in physics and applied mathematics. In other words, multiscaling is not only a mathematical language common to various disciplines, but, more importantly, a way of thinking.

Even though multiscale analysis is probably the oldest among the above-mentioned unifying concepts of the book, it is less universally recognized as a powerful, indispensable framework for describing complex natural phen...

Table of contents

• Cover
• Reviews of Nonlinear Dynamics and Complexity
• Title Page
• Copyright
• List of Contributors
• Preface
• Chapter 1: Introduction: Multiscale Analysis – Modeling, Data, Networks, and Nonlinear Dynamics
• Part One: Multiscale Analysis
• Part Two: Nonlinear Dynamics: Genelets and Synthetic Biochemical Circuits
• Part Three: Nonlinear Dynamics: the Brain and the Heart
• Index