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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research 8 What Determines How Organisms Behave in Their Worlds? Organisms as diverse as bacteria and humans shape their behaviors in response to particular environmental variables. Understanding life requires determining the rules that govern how organisms behave in their worlds, how they sense their environments, and how they use this information to change their behavior. Organisms do not passively wait for information from their environments; rather, their physiology is internally generated, by genetically determined rules, and input from the environment is used to alter the behavior of the organism. Much behavior is generated to actively explore the environment in search of specific sensory signals. For example, bacteria sense changes in the concentrations of chemicals in their environment and use these to govern their movements. The integration of sensory information into a form that can be processed by the organism, the nature of the processing machinery, the influence of the internal states of the organism, the influence of the experience on the future states of the organism, memory mechanisms, and many other issues have direct relevance to many different biological regimes, scales, and kinds of organisms. There is a remarkable potential for finding commonalities amid the diversity addressed by this question. Living organisms have an extraordinarily diverse set of tools for sensing the environment. Across the entire living world, the kinds of external cues that organisms can sense are extremely varied, ranging in intensity or power across the spectra of light and sound and across many orders of magnitude. Organisms are able to differentiate among thousands of chemicals by taste and smell and are sensitive to minute changes in temperature, pH, air speed, surface texture, and chemical concentrations. In short, there seem to be few
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research physical parameters that are not sensed by some living organism. Elephants hear sounds of much longer wavelength than humans and have specialized cells in their feet to sense seismic vibration. Their vibrational sense is specific enough to distinguish vibrations with different meanings, and the elephants react differently depending on whether the signal is coming from a familiar elephant or a stranger (O’Connell-Rodwell et al., in press). Plants acquire information about day length and temperature, and in temperate climates they use this to time their budding and flowering. Organisms from bacteria to humans use light and other cues to entrain circadian, or daily, rhythms so that these internally generated rhythms are synchronized to the fluctuations in their environment (Nakajima et al., 2005). The ability to detect different environmental signals and adjust behavior accordingly is evolutionarily ancient. Bacteria produce many small molecule signals that are used for communication both within and among species (Bassler and Losick, 2006). The realization that single-celled organisms—often perceived as “primitive” and “simple”—live in complex mixed-species communities and use a variety of chemical signals to detect community density and composition has stimulated a reexamination of our theories regarding the basic parameters of bacterial life. Theoretical approaches to understanding how organisms sense and respond are likely to be profitably employed across biological scales. The ability to receive and process external cues also plays a critical role in multicellular development. For a single fertilized egg to develop into a highly differentiated and organized multicellular organism, individual cells must receive cues about their location and future role in the organism to migrate to the right place and differentiate into the appropriate specialized cell. As each of the organism’s cells contain the same genetic material, the interplay between external cues, the triggering of various genetic pathways, and the subsequent modification of the cell to be able to respond to different external cues (e.g., by the expression of receptors or ion channels) results in an intricate and tightly regulated cascade that reliably produces a functional multicelled organism. Humans and other “higher animals” have complex brains that allow them to acquire information from the environment, compare this information with both memories of prior experience and internal models of the world, and then respond, often appropriately but in the case of humans too often inappropriately for the world of 2007. For example, many humans find themselves overeating, gambling, or otherwise engaging in counterproductive behaviors, as mechanisms that have evolved over millions of years for survival in simpler social and environmental circumstances are evoked by the stimuli and circumstances of today’s world. But humans are not the only organisms that may find themselves responding inappropriately in unusual environmental conditions. In the early winter of 2006-2007,
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research unseasonably warm temperatures in the northeastern United States led to many plants prematurely budding and flowering, only to be damaged when the normal cold weather finally came. At a still “higher” level of organization, organisms may self-associate into colonies, tribes, and other groupings in which individuals take on specialized roles to assess the environment, make decisions, and take action. For example, social insects, such as ants and bees, have fascinating patterns of divisions of labor that require not only that the individual animal acquire information for its own behavior but also that this information be communicated and shared in a larger population. BEHAVING IN THE WORLD: FIVE MULTISCALE QUESTIONS All living entities, be they cells within an organism, plants, bacteria, leeches, or humans, integrate information from their external and internal environments and respond, in most cases, appropriately. In this section, examples from a variety of biological organisms are used to address the following questions: How are external stimuli transduced into some kind of code that can be acted upon by the organism? How do these codes vary with the intensity, duration, and timing of the stimulus? How does the internal state of the organism influence the interpretation of sensory codes? How is past experience represented in the internal state of the organism? In other words, what kinds of memory mechanisms exist, how are they created, how long do they last, and how are they read out? How are representations of the external world combined with internally generated signals to allow the organism to integrate past and present stimuli to make decisions about relevant actions? How does memory influence decisionmaking? How are decisions used to implement specific actions? When are actions internally generated, and when are they triggered by specific events in the internal or external environment? SPECIFIC PROBLEMS, OPPORTUNITIES, AND CHALLENGES In each of the sections below, a few examples are given of how each question applies across biological scales, to illustrate how the same or very similar problems arise at levels ranging from the individual microbe or cell to a complex multicelled organism. Integrating knowledge across these scales will require much further study and further development of both theory and technology.
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research While these essential questions are easily recognized as central to the field of neuroscience, they are actually common to all biological systems, including plants, the immune system, bacteria, and fungi. Indeed “memory” is a fundamental feature of the immune system, and every living cell responds to environmental signals and encodes this information for eventual response. That said, more complex organisms require highly specialized nervous systems to do more and more complex computations to make more sophisticated responses to their environments. How are external stimuli transduced into some kind of “code” that can be read by the organism? How does this code vary with the intensity, duration, and timing of the stimulus? Cellular behavior is altered by signals from the cell’s surroundings. Different types of information can pass via mechanisms involving ion channels, gap junctions, or the initiation of intracellular signals resulting from binding or clustering of transmembrane proteins. Cells can also alter their environment, for example, by secreting proteins that are assembled into an extracellular matrix. That matrix can, in turn, influence intracellular organization such as the arrangement of the cytoskeleton. Cells can also communicate with their neighbors. For example, in plants, plasmodesmata allow cytosplasmic connections through cell walls. The cell’s reaction to external signals through these various mechanisms may differ depending on when the signal arrives (e.g., during darkness or light), how long the signal lasts (e.g., how long the temperature remains below freezing), and how strong the signal is (e.g., how many receptors are bound at the same time). In “higher” animals, many stimuli are detected initially by only a small minority of cells, and specialized endocrine and neuronal systems are used to coordinate the organism’s response to the stimulus. Animals have highly diverse and specialized sensory structures that allow them to turn a variety of such stimuli as light, sound, heat, body position, pH, and CO2 into neuronal signals that eventually are integrated with internally generated signals to result in behavior. Perhaps surprisingly, it has only been quite recently that the receptors for many of these environmental stimuli have even been identified. For example, a variety of transient receptor potential (TRP) channels that respond to heat or painful stimuli have only been recently identified (Julius and Basbaum, 2001; Ramsey et al., 2006), and while many signal transduction pathways are well characterized, those activated by many sensory modalities remain mysterious. A beautiful example of the interaction between physics and biology can be seen in elegant work elucidating the fundamental mechanism by which sound results in hair cell deformation and changes in membrane conductances (Hudspeth, 2001; Chan and Hudspeth, 2005a, b; Hudspeth, 2005; Keen and Hudspeth,
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research 2006; Lopez-Schier and Hudspeth, 2006; Kozlov et al., 2007). This work requires complex calculations of the forces accompanying the movements of molecules, as well as the technology to work with small and fragile biological preparations. As suggested in Chapter 7, information theory has been usefully applied in recent work on sensory processing to study how the sensory signal is encoded in spike trains (Fairhall et al., 2001; Lewen et al., 2001; Adelman et al., 2003; Thomson and Kristan, 2005). Most early studies of sensory processes used extremely simple, well-defined, and artificial stimuli, such as spots of light or pure tones. Because animals do not spend their lives experiencing pure, well-defined stimuli, investigators are beginning to ask how sensory systems respond to natural stimuli, which change in complex and unpredictable fashions. This is much more difficult than working with simpler stimuli, as it requires characterizing the properties of the stimuli and understanding how they are captured in a spike train or a series of spike trains. This is a very new area of investigation in which a theoretical approach might be helpful. Indeed, recent years have seen the impact of Bayesian statistics on problems of neural coding, illustrating the importance for biology of quantitatively trained investigators of all kinds. Responses to stimuli, whether artificial or natural, always show a degree of trial-to-trial variability in the responses of single neurons or groups of neurons to repeated presentations (Billimoria et al., 2006). Is this noise or is this an important feature of how the sensory world is represented? Indeed, working out the means by which different biological systems filter or sort different stimuli is another challenge. There are a number of important theoretical problems associated with understanding how noise in spike trains is dealt with by nervous systems. The field of sensory neurophysiology provides fascinating examples of the diversity of mechanisms that animals have evolved to sense their worlds (Box 8-1). For example, electric fish live in murky waters, where vision is essentially impossible, and use electrical discharges to locate their prey and each other (Zakon and Dunlap, 1999; Zakon et al., 2002; Bass and Zakon, 2005). Some bats capture prey with the help of wideband biosonar sounds that they emit and then use to calculate the distance to objects from the delay of echoes (Simmons et al., 2004). Sometimes the sensory response system involves more than one species. For example, the bobtail squid houses bioluminescent bacteria in specialized organs where they provide camouflage in different light conditions (Koropatnick et al., 2004). In fact, a large body of evidence is accumulating that most animals rely on a closely associated microbial community for a variety of functions, some of them sensory, such as alerting the organisms to the presence of pathogens, and detecting and degrading toxins. And, of course, there are many situations in nature whereby one species’ reaction
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research to environmental cues is interpreted and acted upon by other species (see Box 8-2). Whether these arrangements are cooperative or an example of animals expanding their own sensory repertoire to include the interpretation of other species’ signals is an interesting theoretical question. How does the internal state of the organism influence interpretation of the sensory “code”? Internal conditions also influence how cells react to stimuli. Internal conditions can vary depending on the stage of development of the organism or the types of contacts with neighboring cells. For example, signals from the Notch family of proteins cause distinct changes at two different stages in the development of the nematode C. elegans. During embryonic development, Notch signals lead to mesoderm induction, whereas during postembryonic development they lead to germ cell mitosis (Austin and Kimble, 1987). In Box 8-3 an example is given of plant seeds that express a sensitive light receptor when they are deprived of light; when the receptor is activated by even a brief light exposure, the seed begins to germinate. Across biological scales, the response to environmental cues can differ depending on the state of the cell or organism. Whether people experience a stimulus as painful depends to a large degree on prior history with the stimulus, expectation of its duration, and whether it is viewed as innocuous or as a portend of dire consequences. This is just one example that illustrates that internally generated neuronal activity plays important roles in shaping the processing and interpretation of sensory stimuli. Indeed, in a remarkable new study, the estimate is that internally generated activity is much more significant than the external stimulus in shaping the receptive fields of neurons responding to natural images (Fiser et al., 2004). This study is part of a newly developing area of research in which methods such as Bayesian inference are being used to understand visual processing and decision making (Ma et al., 2006). This is a very new area in neuroscience and one in which the use of theoretical methods for understanding the nervous system is needed. Circadian rhythms are found in organisms from bacteria to humans. A great deal is now known about the sequence of molecular events that gives rise to circadian rhythmicity (Allada et al., 2001; Hardin, 2005). Circadian rhythms, by definition, are internally generated, but are normally reset and entrained by light and other environmental cues (Stoleru et al., 2004). In all organisms, there are mechanisms by which information about light and other environmental cues is used to change the phase of the internally generated molecular clock (Gehring and Rosbash, 2003). Moreover, there are mechanisms by which the output of the molecular clock can be read out to trigger changes in behavior (Stoleru et al., 2005). The circadian system demonstrates that the state of intracellular signal transcriptional
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research Box 8-1 Animals as Engineers: Specialized Senses for Communication and Predation The Jamming Avoidance Response in Weakly Electric Fish If you are a fish living in muddy and murky waters, how do you locate your prey and your mate? The weakly electric gymnotoid fish such as Eigenmannia produce a very precise sinusoidal electric discharge (Heiligenberg, 1991). The fish use this discharge to navigate and locate their prey, as they sense reflections of the discharge by objects in their environment (Lewis and Maler, 2001). But remarkably, to avoid confounds produced by electric discharges of other fish, when two animals come into range of each other, if their discharges are close in frequency, which would effectively jam their signals, each fish alters the period of its discharge, so that the two animals now are operating at frequencies enough different so that they don’t interfere with each other. This has been termed the “jamming avoidance response” and is biological bandwidth sharing that allows multiple animals to navigate simultaneously. The jamming avoidance response of electric fish. Top trace, the frequency of the electric organ discharge, in response to a jamming signal turned on and off. The dotted line is the control signal in the absence of the perturbing influence. Modified from Metzner (1993). and translational mechanisms can directly alter an organism’s response to a stimulus. This is a counterexample to the common perception that organisms passively wait for input from the environment, rather than that behavior reflects an interaction between internal and external factors. There are many other examples of “counting” or “timing” mechanisms whereby cells
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research Bat Echolocation Like electric fish, bats hunt their prey under very difficult conditions. Bats hunt at night, in the absence of much light. Moreover, bats hunt rapidly moving objects, most notably moths and other flying insects that are moving in three dimensions in highly unpredictable trajectories. How then do bats successfully compute the appropriate trajectories to find their prey? Many species of bats produce and sense sonar, so again like the electric fish example above, the animal produces a signal and uses the disturbed reflection of the signal to find objects. Even more remarkably, bats compensate for the Doppler shift produced by the moving insect by changing the frequency of their own calls, to maintain the frequency of the reflected signal in the range at which the bat’s auditory system is optimally functional (Smotherman and Metzner, 2003). This “Doppler-shift compensation” behavior significantly enhances bats’ echolocation performance in their natural habitat. SOURCE: Auditory Adaptations for Prey Capture in Echolocating Bats, Vol. 70 by G. Neuweiler. Copyright 1990. Reproduced with permission of American Physiological Society via Copyright Clearance Center. Correlation between best foraging habitat and frequency of the bat’s calls. Modified from Neuweiler (1990). maintain a record of past events (see Box 8-4), and theoretical approaches may identify common features of these mechanisms. How is past experience represented in the internal state of the organism? In other words, what kinds of memory mechanisms exist, how are they created, how long do they last, and how are they “read out”?
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research Box 8-2 Taking Cues From Other Species Photo taken by Rayko Halitschke. A wild tobacco plant (front) growing next to sagebrush (background) in the Great Basin Desert in Utah. When damaged by insects, sagebrush releases a suite of chemicals that alert neighboring plants to the presence of the insects. The signal are not only picked up by other sagebrush, though. Wild tobacco plants growing within range of the chemical signals will also stimulate the defense mechanisms they use to repel plant-eating insects like caterpillars. SOURCE: Baldwin et al. (2006). In the broadest of terms, “memory” can be defined as a lasting trace of the prior history of the system’s experience. Memory can be seen in the immune system as evidence of prior exposure to antigen. In any cell, memory can be described as the state of all of the signal transduction and gene expression networks in a cell. In both the immune system and the nervous system, memory can be quite specific to the details of the experience that triggered the memory, and in both of these systems the “memory” can be quite long-lasting and may persist much longer than the lifetime of any of
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research Top row: The hornbill (left) and the Diana monkey (right). Bottom row: Leopard (left) and crowned eagle (right). Photo credits: Ben Wang, David Jenny, and the Peregrine Fund. Diana monkeys have two different, but very similar, predator warning calls for leopards and eagles. Hornbills, which are threatened by eagles, but not by leopards, respond only to the eagle warning cry. SOURCE: H. J. Rainey, K. Zuberbuhler, and P. J. Slater. Hornbills Can Distinguish Between Primate Alarm Calls. Proceedings of the Royal Society B Biological Sciences. 2004. 271:755-759. the molecules by which the memory is expressed. There is promise in theoretical approaches to studying the origin and maintenance of mechanisms by which organisms store and access information about the past. Understanding the storage of memory has been and continues to be one of the most intensively studied problems in neuroscience. Although the molecular and cellular mechanisms underlying stable changes in synaptic transmissions have progressed dramatically in the past decade (Kandel, 2001), even at the subcellular level, much remains to be understood that
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research Box 8-3 Germination of Weeds After Plowing When agricultural fields are plowed, many weeds germinate. Oddly, sometimes more weeds germinate if the fields are plowed during the day than if they are plowed at night. The reason appears to be that some seeds that have experienced a period of light deprivation up-regulate an extremely sensitive light receptor that can detect minute flashes of light and trigger germination (Scopel et al., 1991). Thus even a very brief exposure to sunlight during plowing primes these seeds for germination—an exposure that does not occur if fields are plowed at night. This mechanism may allow the plant to perceive when the soil has been disturbed and therefore favorable for growth. The phenomenon does not appear to be universal, with the effect of nighttime plowing varying according to the type of weed, the seeds’ dormancy status, seasonal variation in light, soil moisture levels, and method of plowing (Juroszek and Gerhards, 2004). Its existence, however, is an example of how the internal state of a cell (whether or not the sensitive light receptor is expressed) can affect how a signal is acted upon. Box 8-4 How Do Cicadas Know That 17 Years Have Passed? Residents of the eastern United States are familiar with the onslaught of cicadas that occurs every 17 years. The reason for this organism’s extreme life cycle may have its evolutionary roots in predator avoidance, but the mechanism appears to rely on using signals from the tree roots around which the cicada nymphs are developing. Each flowering cycle is detected by the cicada nymphs as an increase in sugars and proteins flowing to the roots; somehow the nymphs keep count of the number of cycles. In an experiment by Karban et al. (2000), 15-year-old nymphs were transplanted to the roots of trees that flowered twice per year. The nymphs emerged after two flowering cycles—during year 16 instead of year 17. will require new computational models, of both the molecules at the synapse (Korkin et al., 2006; Lisman, 1985; Lisman and Zhabotinsky, 2001; Miller et al., 2005) and the biochemical processing in dendritic spines. The volume of dendritic spines is small and the biochemistry that occurs in these restricted spaces takes place under conditions that defy the assumptions of most experiments done in the test tube in large volumes (see Chapter 5).
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research Therefore, it is not obvious how to apply the measurements done with purified proteins and known concentrations of solutes to enzymes anchored in the membrane in very small spaces (Shifman et al., 2006). For this reason, some are starting to employ Monte Carlo methods to study the organization of synapses and the biochemistry that is likely to be responsible for changes at the synapse (Franks et al., 2002; Coggan et al., 2005; Sosinsky et al., 2005). Understanding how memories are stored in neural networks is a topic that has and continues to attract a good deal of theoretical study. Starting with the early work by Hopfield and colleagues (Hopfield, 1982, 1984, 1987; Hopfield and Tank, 1986; Tank and Hopfield, 1987), many physicists have been attracted to neuroscience by the problem of the storage of memory in artificial neural networks (Abbott and Arian, 1987). Today, models of how the brain stores memory incorporate many more recently discovered biological details in order to understand memory storage in real biological networks. That said, there is a tremendous and continuing need for tandem experimental and theoretical studies of memory. Biological systems must be able to access and act on stored information (working memory) and to integrate information of different kinds across various time intervals. A number of recent studies on working memory have triggered a body of theoretical and experimental work on biological integrators (Seung et al., 2000). In this context, an integrator (like a capacitor in an electronic circuit that stores charge) is a mechanism that “builds up” over time and maintains information about the history of some event before it is reset. This work was stimulated by experiments in which recordings from monkeys doing working memory tasks showed sustained discharges (Fuster and Alexander, 1971). But there is a series of questions about the mechanisms used in long-term biological integrators that are relevant to a number of different biological systems. Many biological integrators routinely handle signals that persist for milliseconds, seconds, minutes, or even hours. These are time constants that are relatively easy to understand within the context of what is known about the storage of information in changes in membrane potential or buildup and decay of intracellular metabolites. Nonetheless, there are biological integrators that work over much longer times. For example, there is ample evidence in animals that the “sleep integrator” keeps track of how much sleep the animal gets over multiple days and that animals oversleep for several days to make up for the sleep debt incurred over days and weeks. Even more puzzling are data that suggest the existence of a long-term “caloric integrator” that keeps track over weeks and months of “energy debts” incurred by caloric restriction that causes animals to overeat after periods of caloric restriction and that contributes to the difficulties that dieters have in maintaining weight loss. It is completely unclear what
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research kinds of mechanisms would be needed to create such long-time constant integrators, and theoretical studies could help frame the question by asking whether cell-autonomous intracellular processes could, in principle, be sufficient or whether some kind of neuronal circuit would be needed. It is important to state that this kind of “memory” may be entirely different from memories that are needed for many other kinds of information storage, as these “integrator” processes can be reset at any time by the appropriate process. How are representations of the external world combined with internally generated signals to allow the organism to integrate past and present stimuli to make decisions about relevant actions? How does memory influence decision making? “Decisions” are made in all biological systems when stimuli result in some process moving past a threshold. This can be seen in the release of a hormone, an action potential, or a variety of other processes. Of course, animals can make more complex decisions, choosing or selecting among a variety of complex behaviors (Levi and Camhi, 2000). For example, should the leech swim or crawl under a set of circumstances (Esch et al., 2002; Briggman et al., 2005), or should a human walk to the post office or drive his or her car? Understanding how sets of different sensory inputs interact with the internal state of the nervous system to allow an animal to “decide” among a variety of different possible outcomes is an area of interest for study by both theorists and experimentalists (Lo and Wang, 2006; Ma et al., 2006). How are “decisions” used to implement specific actions? When are actions internally generated, and when are they triggered by specific events in the internal or external environment? Many conventional textbooks inadvertently leave the student with the notion that the nervous system is passively awaiting sensory input that will trigger a behavioral response. However, the nervous system is constantly active, and the challenge is to understand how this internally generated activity interacts with information from the environment. All regions of the brain show ongoing, internally generated spontaneous activity. Rhythmic motor patterns are generated by central pattern generating circuits (Marder and Calabrese, 1996; Marder and Bucher, 2001) that can produce rhythmic motor patterns in the absence of sensory input. The most crucial of these for life are the respiratory centers that drive breathing. Of course, sensory inputs modify the output of respiratory and other central pattern generating circuits, as is necessary for the animal to adapt its internally generated movements to its needs in the world.
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research Oscillations are not only important for rhythmic movements, but it is becoming clear that oscillatory processes are central to processing in virtually all brain regions (Buzsaki and Draguhn, 2004; Buhl and Buzsaki, 2005). For this reason, there is a large body of theoretical work being done, and still needed, to understand the roles of oscillatory processes in the circuits responsible for perception and cognition (Ermentrout, 1996; White et al., 1998; Sivan and Kopell, 2006). Equally needed are new studies that provide models for how voluntary movements are produced, as these will be the substrate for developing a variety of neuroprosthetic devices to enable movement. THE IMPORTANCE OF THRESHOLDS A characteristic feature of many of these biological processes is that they have specific thresholds, such that stimulus intensities below threshold fail to result in a response, while higher stimulus intensities produce responses. This kind of threshold is a characteristic feature of the action potential, the unit of most electrical signaling in the nervous system, but threshold behavior and amplification can also result from many signal transduction cascades, such as those triggered by hormones in individual cells. The action potential has a number of other important features: The relationship between membrane potential, time, and channel opening is highly nonlinear. Understanding multiple nonlinear processes that work together requires the use of computational and theoretical tools, as it is often impossible to predict intuitively the outcomes of interacting nonlinear processes without computing those outcomes directly. For this reason, it is now commonplace for neuroscientists and other biologists working to understand the interactions of nonlinear processes to construct formal models, with differing degrees of realism. As introduced in Chapter 2 (p. 28), one of the most thorny practical problems facing scientists who attempt to develop formal computational models of complex biological systems is the extent to which models should attempt to capture rich biological detail or the extent to which they can legitimately “reduce” the dimensionality of the problems to be studied. This is seen in a pronounced fashion in neuronal models, where individual model neurons may be represented extremely simply as a “firing rate,” or can be complex and detailed, anatomically realistic, multicompartmental models. Collaborations with mathematicians can help develop methods for dimension reduction in models. A great deal of additional theoretical work is needed to understand how much detail models must include to capture accurately the dynamics of the biological system in question.
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The Role of Theory in Advancing 21st-Century Biology: Catalyzing Transformative Research THEORY IN NEUROSCIENCE For a variety of historical reasons, research in neuroscience has long reflected combined experimental and theoretical approaches. For example, the Hodgkin-Huxley formulation of the action potential (Hodgkin and Huxley, 1952) remains as useful today as it was revolutionary at the time. At the same time, research in neuroscience has long been a source of insight for technological innovation. For example, the discovery that lateral inhibition in the Limulus eye resulted in contrast enhancement of visual images (Hartline and Ratliff, 1957, 1958) provided early information that aided in the development of computational algorithms for contrast enhancement. Likewise, many investigators interested in robotics have been inspired by the organization of insect and other invertebrate nervous systems and skeletal-muscular adaptations to locomotion (Chiel and Beer, 1997; Ayers and Witting, 2007). Today, neuroscience remains a field in which the interaction between theory and experimental work is rich. A large number of physicists and mathematicians have been drawn into computational neuroscience over the past 20 years, motivated by the sense that the brain poses one of the biggest mysteries left to solve and by their appreciation that understanding of computations in the brain can benefit from quantitative analyses and model building (Dayan and Abbott, 2001). Recognition of the deep evolutionary roots of sensory pathways provides opportunities for collaborative theoretical and experimental research combining neuroscience, microbiology, and plant and animal physiology.