BIOMAT 2007: International Symposium on Mathematical and Computational Biology, Armac ʹa o dos Bu zios, Rio de Janeiro, Brazil, 24-29 Novermber 2007

The present volume contains the contributions of the keynote speakers of the BIOMAT 2007 Symposium as well as selected contributed papers in the areas of mathematical biology, biological physics, biophysics and bioinformatics. It contains new results on some aspects of Lotka-Volterra equations, the proposal of using differential geometry to model neurosurgical tools, recent data on epidemiological modeling, pattern recognition and comprehensive reviews on the structure of proteins, the folding problem and the influence of Allee effects on population dynamics.This book contains some original results on the growth of gliomas: the role played by membrane channels on activity-dependent modulation of spike transmission; a proposal for reconsidering the concept of gene and the understanding of the mechanisms responsible for gene expression; a differential geometric approach to the influence of the drying effect on the dynamics of pods of Leguminosae; the comparison of agent-based models with the approach of differential equations on the study of selection mechanisms in germinal centers; and the synchronization phenomenon for protocell systems driven by linear kinetic equations. Preface......Page 9 Editorial Board of the BIOMAT Consortium......Page 8 Protein Structure and Function......Page 10 1. Introduction......Page 11 2.1. The protein chain......Page 13 2.3. Hydrophobic effect......Page 14 2.4. Folding stages......Page 16 3.1. Stochastic variable......Page 17 3.2. Brownian motion......Page 18 4. CSAW......Page 19 5. Implementation of CSAW......Page 20 6. Exploratory Runs......Page 22 7. Folding Pathways and Energy Landscape......Page 23 8. Nucleation and Growth of an Alpha Helix......Page 24 9. All-atom Model......Page 25 10. Discussion and Outlook......Page 28 References......Page 31 1. Introduction......Page 32 2.1. Variable Definitions for Re-ordering......Page 35 2.2. Objective Functions......Page 36 2.3.1. Network Flow Model: Dense Data Matrices......Page 37 2.3.2. TSP Model: Dense Data Matrices......Page 40 2.3.3. Assignment Problem Model: Sparse Data Matrices......Page 41 3.1. Metabolite Concentration Data: Dense Data Matrix......Page 44 3.1.1. Results for Other Biclustering Algorithms......Page 48 3.2. Colon Cancer Data: Dense Data Matrix......Page 49 3.3. Percent Inhibition Data: Sparse Data Matrix......Page 50 3.3.1. Iterative Synthesis Strategy......Page 51 4. Conclusions......Page 55 References......Page 56 1. Distance Based Protein Modeling......Page 60 2.1. Problems with Exact Distances......Page 65 2.2. Problems with Sparse Distances......Page 67 2.3. Problems with Inexact Distances......Page 69 3. The Geometric Buildup Approach......Page 71 3.1. The General Algorithm......Page 72 3.2. Control of Numerical Errors......Page 75 3.3. Rigid vs. Unique Buildup......Page 78 3.4. Tolerance of Inexact Distances......Page 84 4. Concluding Remarks......Page 91 References......Page 95 1. Introduction......Page 99 2. Methods......Page 101 2.1. Curvatures to curve......Page 103 2.2. Curves from atomic models......Page 104 2.4. Polyhelices......Page 107 2.5. Embedding methods......Page 108 3. Fold Space Exploration......Page 110 3.1. Protein Quality Functions......Page 111 3.2. The fold spaces of polyhelices......Page 112 3.3. Modeling helical bundle and -barrel membrane proteins......Page 115 4. Protein Design......Page 116 4.1. Creation of structure specification and optimization tools......Page 117 5. Continuum Mechanics of Biological Structures......Page 118 5.1. Continuum elastic theory of coiled-coils......Page 119 5.2. Modeling the open and closed states of the CusCFBA bacterial efflux complex......Page 120 5.3. Modeling oligomerization states of Adiponectin......Page 121 Acknowledgments......Page 124 References......Page 125 Mathematical and computational modeling of physiological disorders: A case study of the IUPS human physiome project and aneurysmal models. Alexander R. Oshmyansky, Philip K. Maini......Page 129 1. Seizure Modelling......Page 130 2. Combining Geometry with Cellular Automata......Page 131 3. Using Cellular Manifolds to Model Seizures......Page 132 4. Example and Qualitative Comparison to Actual Data......Page 133 References......Page 134 1. Introduction......Page 138 2. Telescoping Levels of Magnification: From Simple to Complex......Page 139 2.1. Porridge is too cold: The simple approach......Page 140 2.2. Porridge is too hot: The complicated approach......Page 141 2.3. Porridge is just right: The middle approach......Page 142 2.3.1. Patient-specific glioma growth dynamics: invasion (D) and proliferation (p)......Page 144 2.3.2. Differential migration: a new way to eat porridge of two distinct densities......Page 145 Acknowledgments......Page 150 References......Page 151 1. Introduction......Page 154 2. Mucosal Wave Model......Page 155 3. Small Approximation......Page 157 4. General Case for Arbitrary......Page 159 5. Conditions for the Oscillation Onset......Page 160 References......Page 162 1.1. Background......Page 164 2. Model......Page 166 3.1. Simulation of the excitability and action potentials of the reduced T cell model......Page 173 3.2. Activity-dependent spike transmission failure from peripheral neuritic compartment to somatic compartment: inuence of membrane kinetics......Page 174 3.3. Activity-dependent spike transmission failure from peripheral neuritic compartment to somatic compartment: inuence of ionic channel density distribution......Page 179 3.4. Activity-dependent spike transmission failure from peripheral neuritic compartment to somatic compartment: inuence of synaptic noise......Page 181 4.1. Activity-dependent modulation of spike transmission......Page 184 4.2. Activity-dependent modulation of spike transmission: effects of membrane channel kinetic, channel density and noise......Page 185 References......Page 186 1.1. What are Allee effects?......Page 189 2.1. Models of component Allee effects......Page 191 2.2. From component to demographic Allee effects......Page 194 3. Demographic Allee Effects and Metapopulation Dynamics......Page 197 3.2. Allee effects in metapopulations......Page 198 3.3. Allee effects and invasion dynamics......Page 201 4.1. Allee effects and predator-prey dynamics......Page 204 4.2. Allee effects and host-parasite dynamics......Page 207 5. Concluding Remarks......Page 210 References......Page 212 The decoupling & solution of logistic & classical two-species Lotka-Volterra dynamics with variable production rates. Charles E. M. Pearce, Roy B. Leipnik......Page 218 2. Euler Substitution and Separation......Page 219 3. Equal Production Rates......Page 221 4. Separated Dynamics......Page 222 5. The Painleve Property......Page 223 7. Classical Case, Variable Rates......Page 224 8. Classical Lotka-Volterra System......Page 226 References......Page 230 Allee effect, emigration and immigration in a class of predator-prey models. Eduardo Gonzalez-Olivares , Jaime Mena-Lorca, Hector Meneses-Alcay, Betsabe Gonzalez-Yanez, Jose D. Flores......Page 232 1. Introduction......Page 233 2. The Model......Page 234 2.1. Immigration......Page 235 2.2. Emigration......Page 237 3. Main Results......Page 239 4. Discussion......Page 253 References......Page 254 Epidemic predictions and predictability in complex environments. Vittoria Colizza, Alain Barrat, Marc Barth elemy, Alessandro Vespignani......Page 257 1. Complexity and Epidemic Modeling......Page 258 2. Meta-population Models: Integrating Several Levels of Complexity......Page 259 2.1. Predictability......Page 261 3. SARS: Risk Assessment Analysis and Forecast Reliability......Page 263 4. Conclusions......Page 266 References......Page 267 1. Introduction......Page 269 2. Model for the West Nile Virus......Page 270 2.1. Model for the spatially homogeneous WNV propagation dynamics......Page 271 2.2. Model for the spatial dynamics of WNV......Page 272 3. Travelling Waves Solution......Page 276 4. Conclusion......Page 281 References......Page 282 1. Introduction......Page 284 2. Modeling of Complex Systems......Page 285 3. Mathematical Models of Biological Control in Population Systems......Page 287 4. Biological Pest Control Strategies......Page 291 4.1. Scenario 1: One prey – one predator Lotka – Volterra model......Page 293 4.1.1. Inundative biological control......Page 294 4.1.2. Inoculative biological control......Page 295 4.2.1. Inundative biological control......Page 297 4.2.2. Inoculative biological control......Page 298 4.3. Scenario 3: Two preys – two predators Lotka-Volterra model......Page 299 5. Concluding Remarks......Page 300 References......Page 301 1. Introduction......Page 303 2. Mathematical Formulation......Page 304 2.1. The Hopf bifurcation......Page 305 2.2. Turing instabilities for the stable steady state......Page 309 2.3. Asymptotic analysis for Turing-Hopf instabilities......Page 311 3.1. The Schnakenberg model......Page 312 3.2. A predator-prey model with stable periodic solution......Page 316 3.3. Topological normal form for the Hopf Bifurcation......Page 320 4. Conclusions......Page 321 References......Page 322 1. Introduction......Page 324 2.2. Grasshopper survey......Page 326 2.4. Mathematical models......Page 327 3. Results......Page 328 4. Discussion......Page 331 References......Page 333 1. Introduction......Page 335 2. Function of Noise?......Page 337 3. What Are Genes Anyway?......Page 339 4. Regulation by RNA......Page 340 5. Elusive Networks: Many More Layers......Page 342 6. Space Matters......Page 344 7. Concluding Remarks......Page 347 References......Page 348 1. Introduction......Page 356 2. Smooth Curve Through an Ordered Set of Points......Page 357 3. Elementary Theory of Geodesic Curves in R3......Page 360 4. Techniques of Solution......Page 361 5. Geodesic Curves Along Steiner Points......Page 364 References......Page 366 1. Introduction......Page 368 2. Selection in Germinal Centres......Page 369 3. Differential Equations for Germinal Centres......Page 371 4. Agent-based Model for Germinal Centres......Page 375 5. Biological Conclusions......Page 378 6. Methodological Conclusions......Page 379 References......Page 380 1. Introduction......Page 383 2. Surface Reaction Models of Protocells......Page 386 3. Synchronization in Linear Surface–reaction Models......Page 388 4. Eigenvalues and Eigenvectors......Page 390 5. Conclusions......Page 397 References......Page 402 Index......Page 403 Protein structure and function. Systems protein folding as a physical stochastic process / Kerson Huang. Optimal methods for re-ordering data matrices in systems biology and drug discovery applications / Peter A. DiMaggio Jr. [und weitere]. The solution of the distance geometry problem in protein modeling via geometric buildup / Di Wu, Zhijun Wu, Yaxiang Yuan. The differential geometry of proteins and its applications to structure de-termination / Alain Goriely, Andrew Hausrath, Sébastien Neukirch -- Modeling physiological disorders. Mathematical and computational modeling of physiological disorders: a case study of the IUPS human physiome project and aneurysmal models / Alexander R. Oshmyansky, Philip K. Maini. Modeling the growth and invasion of gliomas, from simple to complex: the Goldie Locks paradigm / Russell Rockne [und weitere]. Advanced-delay differential equation for aeroelastic oscillations in physiol-ogy / Jorge C. Lucero. Geometry, activity-dependent mechanisms, membrane kinetics and channel density distribution interplay in single neuron plasticity. A computational study / Enrico Cataldo [und weitere] -- Population dynamics. Models of Allee effects and their implications for population and community dynamics / Ludek Berec. The decoupling & solution of logistic & classical two-species Lotka-Volterra dynamics with variable production rates / Charles E.M. Pearce, Roy B. Leipnik. Allee effect, emigration and immigration in a class of predator-prey models / Eduardo González-Olivares [und weitere] -- Epidemiological modeling. Epidemic predictions and predictability in complex environments / Vittoria Colizza [und weitere]. Assessing the spatial propagation ofWest Nile virus / Norberto A. Maidana, Hyun M. Yang. Management of complex systems: modeling the biological pest control / Marat Rafikov, José Manoel Balthazar, Hubertus F. von Bremen -- Biological and chemical pattern recognition. On TuringHopf instabilities in reaction-diffusion systems / Mariano Rodríguez Ricard. Grasshopper density population classification with neural networks / Isaias Chairez Hernández [und weiteren] -- Modeling of biosystems. A story of growing confusion: genes and their regulation / Sonja J. Prohaska, Peter F. Stadler. Geodesic curves for biomolecular structure modelling / Rubem P. Mondaini, Roberto A.C. Prata. Agent-based models or differential equations: two ways to learn about selection mechanisms in germinal centres / Michael Meyer-Hermann. Synchronization phenomena in protocell models / Alessandro Filisetti [und weiteren] The present volume contains the contributions of the keynote speakers of the BIOMAT 2007 Symposium as well as selected contributed papers in the areas of mathematical biology, biological physics, biophysics and bioinformatics. It contains new results on some aspects of LotkaVolterra equations, the proposal of using differential geometry to model neurosurgical tools, recent data on epidemiological modeling, pattern recognition and comprehensive reviews on the structure of proteins, the folding problem and the influence of Allee effects on population dynamics. This book contains some original results on the growth of gliomas: the role played by membrane channels on activity-dependent modulation of spike transmission; a proposal for reconsidering the concept of gene and the understanding of the mechanisms responsible for gene expression; a differential geometric approach to the influence of the drying effect on the dynamics of pods of Leguminosae; the comparison of agent-based models with the approach of differential equations on the study of selection mechanisms in germinal centers; and the synchronization phenomenon for protocell systems driven by linear kinetic equations. The present volume contains the contributions of the keynote speakers of the BIOMAT 2007 Symposium as well as selected contributed papers in the areas of mathematical biology, biological physics, biophysics and bioinformatics. It contains new results on some aspects of LotkaئVolterra equations, the proposal of using differential geometry to model neurosurgical tools, recent data on epidemiological modeling, pattern recognition and comprehensive reviews on the structure of proteins, the folding problem and the influence of Allee effects on population dynamics. This book contains some original results on the growth of gliomas: the role played by membrane channels on activity-dependent modulation of spike transmission; a proposal for reconsidering the concept of gene and the understanding of the mechanisms responsible for gene expression; a differential geometric approach to the influence of the drying effect on the dynamics of pods of Leguminosae; the comparison of agent-based models with the approach of differential equations on the study of selection mechanisms in germinal centers; and the synchronization phenomenon for protocell systems driven by linear kinetic equations Population dynamics. Models of Allee effects and their implications for population and community dynamics / Ludek Berec. The decoupling & solution of logistic & classical two-species Lotka-Volterra dynamics with variable production rates / Charles E. M. Pearce, Roy B. Leipnik. Allee effect, emigration and immigration in a class of predator-prey models / Eduardo Gonza lez-Olivares ... [et al.] Epidemiological modeling. Epidemic predictions and predictability in complex environments / Vittoria Colizza ... [et al.]. Assessing the spatial propagation ofWest Nile virus / Norberto A. Maidana, Hyun M. Yang. Management of complex systems: modeling the biological pest control / Marat Rafikov, Jose Manoel Balthazar, Hubertus F. von Bremen Biological and chemical pattern recognition. On TuringHopf instabilities in reaction-diffusion systems / Mariano Rodri guez Ricard. Grasshopper density population classification with neural networks / Isaias Chairez Herna ndez ... [et al.]