Catalyzing Inquiry at the Interface of Computing and Biology (2005) / Chapter Skim
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5 Computational Modeling and Simulation as Enablers for Biological Discovery
5 Computational Modeling and Simulation as Enablers for Biological Discovery
Pages 117-204
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From page 117... ...
. In biological phenomena, what is interesting and significant is usually a set of relationships -- from the interaction of two molecules to the behavior of a population in its environment.
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One of the earliest quantitative biological models involved ecology: the Lotka-Volterra model of species competition and predator-prey relationships described in Section 5.2.4. In the context of cell biology, models and simulations are used to examine the structure and dynamics of a cell or organism's function, rather than the characteristics of isolated parts of a cell or organism.2 Such models must consider stochastic and deterministic processes, complex pleiotropy, robustness through redundancy, modular design, alternative pathways, and emergent behavior in biological hierarchy.
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From page 119... ...
Feedback is very important, and it is this feedback, along with the global -- or, loosely speaking, genomic-scale -- nature of the inquiry that characterizes much of 21st century biology. 5.2 WHY BIOLOGICAL MODELS CAN BE USEFUL In the last decade, mathematical modeling has gained stature and wider recognition as a useful tool in the life sciences.
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Finally, modeling presumes that the researcher can both identify the important state variables and obtain the quantitative data relevant to those variables.4 Computational models apply to specific biological phenomena (e.g., organisms, processes) and are used for a number of purposes as described below.
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2, 1926. The Lotka-Volterra model is a set of coupled differential equations that relate the densities of prey and predator given parameters involving the predator-free rate of prey population increase, the normalized rate at which predators can successfully remove prey from the population, the normalized rate at which predators reproduce, and the rate at which predators die.
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Specifically, models can be used alongside experiments to help optimize experimental design, thereby saving time and resources. Simple models
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Models can help link observations to quantities that are not experimentally accessible. At the scale of a few millimeters, Marée and Hogeweg recently developed9 a computational model based on a cellular automaton for the behavior of the social amoeba Dictyostelium discoideum.
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On the other hand, the notorious difficulties of making accurate weather predictions point to the need for caution in adopting the conclusions even of classical models, especially for more than short-term predictions, as one might expect from mathematically chaotic systems. 5.2.12 Models Expand the Range of Questions That Can Meaningfully Be Asked12 For much of life science research, questions of purpose arise about biological phenomena.
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From page 125... ...
On the other hand, the forms and structures of graphical models are generally inadequate to express much detail, which might well be necessary for mechanistic models. In general, qualitative models do not account for mechanisms, but they can sometimes be developed or analyzed in an automated manner.
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They do not provide detailed insight into mechanism, although power law models form the basis for a large class of metabolic control analyses and dynamic simulations. Computational models -- simulations -- represent the other end of the modeling spectrum.
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and can also predict new phenomena not explicitly represented in but nevertheless consistent with existing datasets. Note also that when a simulation seeks to capture essential elements in some oversimplified and idealized fashion, it is unrealistic to expect the simulation to make detailed predictions about specific biological phenomena.
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More detailed models require a detailed consideration of chemical or physical mechanisms involved (i.e., these models are mechanistic27 )
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These allow a model builder the flexibility to mix modeling paradigms to describe different portions of a complex system. For example, in a hybrid model, a signal transduction pathway might be described by a set of differential equations, and this pathway could be linked to a graphical model of the genetic regulatory network that it influences.
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remains one of the difficulties that every modeler faces sooner or later. As modelers know well, even qualitative analysis of simple models depends on knowing which "leading-order terms" are to be kept on which time scales.
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Because biological phenomena are the result of an evolutionary process that simply uses what is available, many biological phenomena are simply cobbled together and in no sense can be regarded as the "simplest" way to accomplish something. As noted in Footnote 28, there is a tension between the need to capture details faithfully in a model and the desire to simplify those details so as to arrive at a representation that can be analyzed, understood fully, and converted into scientific "knowledge." There are numerous ways of reducing models that are well known in applied mathematics communities.
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From page 132... ...
(For example, the modeling of genetic regulatory networks can be complicated by the fact that although the data may show that a certain gene is expressed under certain circumstances, the biological function being served may not depend on the expression of that gene.) On the other hand, this robustness may also mean that a flawed understanding of detailed processes incorporated into a model that does explain survival responses and behavior will not be reflected in the model's output.34 Simulation models are essentially computer programs and hence suffer from all of the problems that plague software development.
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a novel approach to modeling biological phenomena. It utilizes in a direct and powerful way the mechanisms by which raw biological data are amassed, and smoothly captures that data within tools designed by computer scientists for the design and analysis of complex reactive systems.
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Berman, "Statistical Models for Discerning Protein Structures Containing the DNA-binding Helix-Turn-Helix Motif," Journal of Molecular Biology 330(1)
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With a classification model created, the entire Protein Data Bank of experimentally measured structures was searched and new examples of the motif were found that have no detected sequence homology with previously known examples. Two such examples are Esa1 histone acetyltransferase and isoflavone 4-O-methyltransferase.
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From page 136... ...
, the scoring function approach shows substantial improvements over the other methods. 5.4.1.4 Computational Analysis and Recognition of Functional and Structural Sites in Protein Structures40 Structural genomics initiatives are producing a great increase in protein three-dimensional structures determined by X-ray and nuclear magnetic resonance technologies as well as those predicted by computational methods.
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The expected surfeit of protein structures provides an opportunity to develop computational methods for collectively examining multiple biological structures and extracting key biophysical and biochemical features, as well as methods for automatically recognizing these features in new protein structures. Wei and Altman have developed an automated system known as FEATURE that statistically studies the important functional and structural sites in protein structures such as active sites, binding sites, disulfide bonding sites, and so forth.
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The column shows properties that are statistically significantly different (at p-value cutoff of 0.01) in at least one volume between known examples of calcium binding sites and those of control nonsites.
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5.4.2 Cell Biology and Physiology 5.4.2.1 Cellular Modeling and Simulation Efforts Cellular simulation requires a theoretical framework for analyzing the interactions of molecular components, of modules made up of those components, and of systems in which such modules are linked to carry out a variety of functions. The theoretical goal is to quantitatively organize, analyze, and interpret complex data on cell biological processes, and experiments provide images, biochemical and electrophysiological data on the initial concentrations, kinetic rates, and transport properties of the molecules and cellular structures that are presumed to be the key components of a cellular event.41 A simulation embeds the relevant rate laws and rate constants for the biochemical transformations being modeled.
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. More general tools, such as Mathematica and MATLAB or other systems that can be used for solving systems of differential or stochastic-differential equations, can be used to develop simulations, and because these tools are commonly used by many researchers, their use facilitates the transfer of models among different researchers.
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In addition, BioSPICE provides a number of simulation engines with the capability to simulate ordinary, stochastic, and partial differential equations and other tools that support stability and bifurcation analysis and qualitative reasoning that combines proba bilistic and temporal logic. SOURCE: Sri Kumar, Defense Advanced Research Projects Agency, June 30, 2003.
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From page 142... ...
Most of these genes were taken from Mycoplasma genitalium, the organism with the smallest known chromosome (the complete genome sequence is 580 kilobases) .48 E-CELL has also been used to construct a computer model of the human erythrocyte,49 to estimate a gene regulatory network and signaling 48M.
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Miyoshi et al., "Estimation of Genetic Networks of the Circadian Rhythm in Cyanobacterium Using the E-CELL system," poster session, presented at US-Japan Joint Workshop on Systems Biology of Useful Microorganisms, September 6-18, 2002, Keio University, Yamagata, Japan, available at http://nedo-doe.jtbcom.co.jp/abstracts/35.pdf.
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These results open the possibility of using adaptive evolution of entire metabolic networks to realize metabolic states that have been determined a priori based on in silico analysis."55 Simulation models can also be used to test design ideas for engineering networks in cells. For example, very simple models have been used to provide insight into a genetic oscillator and a switch in E
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Endy and Yin in using their T7 model to propose a pharmaceutical strategy for preventing both T7 propagation and the development of drug resistance through mutation.57 Given observed cell behavior, simulation models can be used to suggest the necessity of a given regulatory motif or the sufficiency of known interactions to produce the phenomenon. For example, Qi et al.
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A network of such complexity, with multiple feedback loops, cannot be understood thoroughly by casual intuition. Instead, the network is converted into a set of nonlinear differential equations, and the physiological implications of these equations are studied.59 Numerical simulation of the equations (Figure 5.6)
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The bifurcation diagram in Figure 5.7 presents recurrent solutions (steady states and limit cycle oscillations) of the differential equations as functions of cell size.
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used this information to build their computational models.60 Two important metabolic enzymes, glucose-6-phosphate dehydrogenase (G6PD) and pyruvate kinase (PK)
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Thus, in silico modeling of biological processes may aid in analysis and prediction of SNPs and pathophysiological conditions. 5.4.2.4 Spatial Inhomogeneities in Cellular Development Simulation models can be used to provide insight into the significance of spatial inhomogeneities.
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Mechanical interactions, which resolve collisions and accommodate the stretching of protein-protein linkages, follow Newton's laws. The model is based on a large set of differential equations that determine how the relevant state variables change with time.
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that diffused to its receptor on the endoplasmic reticulum, leading to calcium release. Using the Virtual Cell software environment, they assembled a simulation model of this phenomenon.66 The model contained details of the relevant receptor distributions (via immunofluorescence)
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. In particular, the proteins that comprise any given cell type are different from those of other cell types, even though the genomic information is the same in both.
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is based on the notion that some genes can have regulatory effects on others.73 In reality, the network of connections between genes that regulate and genes that are regulated is highly complex. In an attempt to gain insight into genetic regulatory networks from a gross oversimplification, Kaufmann proposed that actual genetic regulatory networks might be modeled as randomly connected Boolean networks.74 Kaufmann's model made several simplifying assumptions: 70E.F.
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Yet, it may provide insight into biological order that emerges from the structure of the genetic regulatory network itself. Simulations of the operation of this model yielded interesting behavior, which depends on the values of N and K
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More work will be needed to investigate these possibilities.76 Box 5.10 provides one view on experimental work that might be relevant. To illustrate the potential value of Boolean networks as a model for genetic regulatory networks, consider their application to understanding the etiology of cancer.77 Specifically, cancer is 76This point is discussed further in Section 5.4.2.2 and the references therein.
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This might be tested by cloning exogenous promoters upstream of a modest number of randomly chosen genes to transiently activate them, or by using inhibitory RNA to transiently inactivate a gene's RNA products, and following the trajectory of gene activities in unperturbed cells over time and perturbed cells where the gene's activity is transiently altered, using DNA chips to assess whether the states of activity be come more similar.
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From page 157... ...
5.4.3.3 Genetic Regulation as Circuits Genetic networks can also be modeled as electrical circuits.81 In some ways, the electrical circuit analogy is almost irresistible, as can be seen from a glance at any of the known regulatory pathways: the tangle of links and nodes could easily pass for a circuit diagram of Intel's latest Pentium chip. For example, McAdams and Shapiro described the regulatory network that governs the course of a -phage infection in E
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Because critical molecules are often present in the cell in extremely small quantities, to take the most notable example, certain critical reactions are subject to large statistical fluctuations, meaning that they proceed in fits and starts, much more erratically than their electrical counterparts. 5.4.3.4 Combinatorial Synthesis of Genetic Networks83 Guet et al.
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Because genetic networks are nonlinear (and stochastic as well) , the unknown details of interactions between components might be of crucial importance to understanding their functions.
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160 CATALYZING INQUIRY Fatty Acid Degradation Network Fatty acid degradation Cytoplasm Lipid biosynthesis Cell wall Neither Membrane Membrane and cell wall Membrane and cytoplasm FIGURE 5.9 Fatty acid degradation network. SOURCE: Courtesy of Christian Forst, Los Alamos National Laboratories, December 8, 2004.
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The rapid growth in biological databases; models of cells, tissues, and organs; and the development of powerful computing hardware and algorithms have made it possible to explore functionality in a quantitative manner all the way from the level of genes to the physiological function of whole organs and regulatory systems."87 5.4.4.1 Multiscale Physiological Modeling88 Physiological modeling is the modeling of biological units at a level of aggregation larger than that of an individual cell. Biological units can be successively decomposed into subunits (e.g., an organism may consist of subsystems for circulatory, pulmonary, digestive, and cognitive function; a digestive 86S.
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Because they are based on first principles, they impose constraints on the space of possible organismic models. Functionally integrative models are strongly data-driven and therefore data-intensive, and are needed to bridge the multiple time and space scales of substructures within an organism without leaving the problem computationally intractable.
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From page 163... ...
A medical application of simulation models in immunology has been to evaluate the effects of revaccinating someone yearly for influenza. Because of the phenomenon of immune memory, a vaccine that is too similar to a prior year's vaccine will be eliminated rapidly by the immune response (a negative interference effect)
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· Atomic model, in which molecules are represented in terms of the positions of their constituent atoms in crystallographic structures. (Such data can be found in public repositories such as the Protein Data Bank.)
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Seamans, and T.J. Sejnowski, "Neurocomputational Models of Working Memory," Nature Neuroscience 3(Supplement)
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Furthermore, blood cells and heart cells are themselves part of a collective of other blood cells and heart cells; thus, the structure within which an individual cell is embedded is relevant. An integrated computational model of the heart would bring together all of the relevant physiological processes (Box 5.14)
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Perelson, "Mathematical and Computational Challenges in Population Biology and Ecosystems Science," Science 275(5298)
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. Predictive computational models of various processes at almost every individual level of the hierarchy have been based on physicochemical first principles.
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Huber, "Integrative Biological Modelling in Silico," pp. 4-19 in `In Silico' Simulation of Biological Processes No.
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They incorporated these changes sequentially into the computational model and used the model to predict the functional consequences of each alteration of gene expression in this disease. Results show that the minimal HF [heart failure]
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· Patterns of electrical current flow in the heart are computed using reaction-diffusion equations on a grid of deforming material points which access systems of ordinary differential equations representing the cellular processes underlying the cardiac action potential; these result in representations of the activation wavefronts that spread around the heart and initiate contraction. · Coronary blood flow is computed based on the Navier-Stokes equations in a system of branching blood vessels embedded in the deforming myocardium and the delivery of oxygen and metabolites is coupled to the energy-dependent cellular processes.
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From page 172... ...
172 CATALYZING INQUIRY 5.4.5 Neuroscience In recent years, neuroscience has expanded its horizons beyond the microstructure of the brain-neurons, synapses, neurotransmitters, and the like -- to focus on the brain's large-scale cognitive architecture. Drawing on dramatic advances in mapping techniques, such as functional magnetic resonance imaging (MRI)
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From page 173... ...
modeling of psychological processes is the primary focus. Computational neuroscience provides the basis for testing models of the nervous system's functional processes and their mechanisms, and computational modeling at several levels of detail is important, depending on the purposes of a given effort.
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Effector sites and surface positions are mapped spatially, and the encounters during ligand diffu sion are detected. Bulk solution rate constants are converted into Monte Carlo probabilities so that the diffus ing ligands can undergo stochastic chemical interactions with individual binding sites such as receptor pro teins, enzymes, and transporters.
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Bartol, Jr., "Monte Carlo Methods for Simulating Realistic Synaptic Microphysiology Using MCell," pp. 87-127 in Computational Neuroscience: Realistic Modeling for Experimentalists, E
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Using this set of differential equations, certain essential features of neural behavior can be modeled. For example, assuming appro
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:5900-5920, 1997. priate parameter values, a constant input current larger than a certain critical value and turned on at a given instant of time results in the potential difference across the membrane taking the form of a regular spike train -- which is reminiscent of how a real neuron fires.
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Dynamical systems theory provides a conceptual framework for characterizing rhythms. This theory explains why there are only a small number of dynamical mechanisms that initiate or terminate bursts of action potentials, and it provides the foundations for algorithms that compute parameter space maps delineating regions with different dynamical behaviors.
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From page 179... ...
This is accomplished by the concurrent potentiation of excitatory and inhibitory transmission, implemented as changes in ion channel properties in biophysically detailed models and "summarized" as a change in the gain of the sigmoidal activation function in connectionist models. These mechanisms can be used to simulate the effects of DA on performance in cognitive tasks that rely on PFC function.
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. Before block of synaptic transmission, the neuron bursts in synchrony with the inspiratory phase of network activity as monitored by the inspiratory discharge recorded on the hypoglossal (XII)
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neuroanatomy, and electrophysiology, and correlation of the observations made through these various techniques has led to the development of computational models of synaptic microphysiology. However, the scope of previous modeling attempts has been limited by available computing power, modeling framework, and lack of high-resolution three-dimensional ultrastructural data in an appropriate machine representation.
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From page 182... ...
Coggan et al. have developed and used a suite of such computational tools to build a realistic computational model of nicotinic synaptic transmission based on serial electron tomograms of a chick ciliary ganglion somatic spine mat.105 The chick ciliary ganglion somatic spine mat is a complex system with more than one type of neurotransmitter receptor, possible alternative locations for transmitter release, and a tortuous synaptic geometry that includes a spine mat and calyx-type nerve terminal.
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7. Specification of the reaction mechanisms and kinetic rate constants governing the mass action kinetics interaction of neurotransmitter and effector molecules -- this is accomplished using MCell MDL.
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Bulk solution rate constants are con verted into Monte Carlo probabilities so that the diffusing ligands can undergo stochastic chemical interactions with individual binding sites such as receptor proteins, enzymes, and transporters. These interactions are governed by user-specified reaction mechanisms.
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, receptor molecules (tiny blue particles on membrane surface) , and several neurotransmitter release sites (red spheres)
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at each of 550 distinct vesicular release sites. The mEPSC amplitudes are indicated by the diameter of the yellow spherical glyph and demonstrate a strong dependence on location and underlying geometry.
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Using largedeformation brain mapping tools in computational anatomy, researchers can define, visualize, and measure the volume and shape of the hippocampus. These methods allow for precise assessment of changes in hippocampal formation.
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with 18 healthy elderly and 15 younger control subjects. Hippocampal volume loss and shape deformities observed in subjects with DAT distinguished them from both elderly and younger control subjects.
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These shape changes occurred in a pattern distinct from the pattern seen in DAT and were not associated with substantial volume loss. These assessments indicate that hippocampal volume and shape derived from computational anatomy large deformation brain mapping tools may be useful in distinguishing early DAT from healthy aging.
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Mathematically modeling the response to this perturbation using a system of ordinary differential equations that kept track of the concentrations of infected cells and HIV, and fitting the experimental data to the model, revealed a plethora of new features of HIV infection. Figure 5.19.1 shows that after therapy is initiated at time 0, levels of HIV RNA (a surrogate for virus)
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This fact suggests that drug treatment regimes must target multiple binding sites, and hence combination drug therapy is likely to be more effective because drug-resistant variants must then be the result of multiple errors in the replication process (which occur much less frequently)
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Hastings, and A.S. Perelson, "Mathematical and Computational Challenges in Population Biology and Ecosystems Science," Science 275(5298)
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In these fields, data have been relatively difficult to collect in ways that relate directly to mathematical or computational models, although this has been changing over the past 10 years. Thus, both fields have relied heavily on theory to advance their insights.
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From page 194... ...
New techniques and the availability of more powerful computers have also led to the development of highly detailed models in which a wide variety of components and mechanisms can be incorporated. Among these are individual unit models that attempt to follow every individual in a population over time, thereby providing insight into dynamical behavior (Box 5.22)
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"The challenge, then, is to develop mechanistic models that begin from what is understood about the interactions of the individual units, and to use computation and analysis to explain emergent behavior in terms of the statistical mechanics of ensembles of such units." Such models must extrapolate from the effects of change on individual plants and animals to changes in the distribution of individuals over longer time scales and broader space scales and hence in community-level patterns and the fluxes of nutrients. 5.4.8.2.1 Reconstruction of the Saccharomyces Phylogenetic Tree Although the basic structure and mechanisms underlying evolution and genetics are known in principle, there are many complexities that force researchers into computational approaches in order to gain insight.
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Perelson, "Mathematical and Computational Challenges in Population Biology and Ecosystems Science," Science 275(5298)
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From page 197... ...
The above system was modeled in closed form based on a set of coupled differential equations; this model was successful in reproducing the essential qualitative features described above.111 In 1990, this model was extended by Dwyer et al. to incorporate more biologically plausible features.112 For example, the evolution of rabbit and virus reacting to each other was modeled explicitly.
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From page 198... ...
One important tool underlying these efforts is the Adaptive Evolution Database (TAED) , a phylogenetically organized database that gathers information related to coding sequence evolution.115 This database is designed to both provide high-quality gene families with multiple sequence alignments and phylogenetic trees for chordates and embryophytes and to enable answers to the question, "What makes each species unique at the molecular genomic level?
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From page 199... ...
In 1971, Eigen found an explicit relationship between the size of a stable genome and the error rate inherent in its replication, specifically that the size of the genome was inversely proportional to the per-nucleotide replication error rate.119 Thus, for a genome of length L to be reasonably stable over successive generations, the maximum tolerable error rate in replication could be no more than 1/L per nucleotide. However, more precise replication mechanisms tend to be more complex.
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Perelson, "Mathematical and Computational Challenges in Population Biology and Ecosystems Science," Science 275(5298)
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The species life history (available for each of nine tree species) provides the relationship between radial growth rates as a function of its local light environment and is based on empirically estimated life-history information.
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Nonlinear dynamics and bifurcation theory provide some of the most well-developed applied mathematical techniques and offer great successes in illuminating simple nonlinear systems of differential equations. But they are inadequate in many situations, as illustrated by the fact that understanding global stability in systems larger than four equations is prohibitively hard, if not unrealistic.
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In general, traditional modeling approaches require the derivation of macroscopic equations that govern the time evolution of a system. With these equations in hand (usually partial differential equations (PDEs)
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From page 204... ...
On the other hand, progress in software development and engineering over the last several decades has not been nearly as dramatic as progress in hardware capability, and there appears to be no magic bullets on the horizon that will revolutionize the software development process. This is not to say that good software engineering does not or should not play a role in the development of computational models.
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