Women in Mathematical Biology: Research Collaboration Workshop, NIMBioS, Knoxville, June 2015 (Association for Women in Mathematics Series Book 8)

Inspired by the Research Collaboration Workshop for Women in Mathematical Biology, this volume contains research and review articles that cover topics ranging from models of animal movement to the flow of blood cells in the embryonic heart. Hosted by the National Institute for Mathematics and Biological Synthesis (NIMBioS), the workshop brought together women working in biology and mathematics to form four research groups that encouraged multidisciplinary collaboration and lifetime connections in the STEM field. This volume introduces many of the topics from the workshop, including the aerodynamics of spider ballooning; sleep, circadian rhythms, and pain; blood flow regulation in the kidney; and the effects of antimicrobial therapy on gut microbiota and microbiota and Clostridium difficile. Perfect for students and researchers in mathematics and biology, the papers included in this volume offer an introductory glimpse at recent research in mathematical biology. . Read more... Abstract: Inspired by the Research Collaboration Workshop for Women in Mathematical Biology, this volume contains research and review articles that cover topics ranging from models of animal movement to the flow of blood cells in the embryonic heart. Read more... Preface 6 Contents 8 The Modulation of Pain by Circadian and Sleep-Dependent Processes: A Review of the Experimental Evidence 10 1 Introduction: A Vicious Cycle 11 2 What Is Pain? 12 3 The Relationship Between the Sleep Cycle and Pain Sensitivity in Humans 13 3.1 There Is a Daily Rhythm in Experimental Pain Sensitivity in Humans 14 3.2 Homeostatic Sleep Drive Increases Pain Sensitivity in Humans 17 3.3 A Cross-Species Comparison: Circadian Rhythms and Homeostatic Sleep Drive Influence Pain Sensitivity in Laboratory Rodents 23 4 Circadian Rhythms and Homeostatic Sleep Drive Modulate Pain Neural Circuitry 23 5 Discussion 25 References 27 Investigating Circadian Rhythmicity in Pain Sensitivity Usinga Neural Circuit Model for Spinal Cord Processing of Pain 31 1 The Neural Processing of Pain 32 1.1 Previous Models of Pain Processing 33 2 Mathematical Model 35 2.1 Equations of Time Evolution 35 2.1.1 Model Inputs from the Dorsal Root Ganglion 37 2.2 Firing Rate Response Functions 38 3 Model Validation 39 3.1 Pain Inhibition 40 3.2 Wind-Up 41 3.3 Neuropathy 44 4 Model with Descending Control from the Mid-Brain 47 4.1 Introduction 47 4.2 Amendments to Model 48 4.3 Model Validation 49 5 Conclusions and Future Work 50 References 54 A Two-Process Model for Circadian and Sleep-Dependent Modulation of Pain Sensitivity 57 1 Introduction 58 2 Background: Two-Process Model for Circadian Modulation of Sleep Timing 58 3 Two-Process Model for Pain Sensitivity 60 4 Model Predictions 63 4.1 Pain Sensitivity Under Sleep Deprivation 63 4.2 Pain Sensitivity Under Sleep Restriction 65 4.3 Pain Sensitivity Under Shift Work Schedules 66 5 Discussion 67 References 70 Introduction to Mathematical Modeling of Blood Flow Controlin the Kidney 71 1 Introduction 71 2 Myogenic Response 72 3 Tubuloglomerular Feedback 77 4 Applications 78 References 80 Modeling Autoregulation of the Afferent Arteriole of the Rat Kidney 82 1 Introduction 83 2 Mathematical Model 84 2.1 Single Cell Model 84 2.2 Multi-Cell Model 86 2.3 Numerical Method 87 3 Model Results 88 4 Discussion 93 Appendix 94 Transmembrane Ionic Transport 94 Ion and Charge Conservation Equations 94 Background Currents 95 Potassium Transport Pathways 95 Sodium Transport Pathways 97 Chloride Transport Pathways 98 Calcium Transport Pathways 99 Intracellular Ca2+ Dynamics 102 Calcium Buffers 102 Kinetics of Myosin Light Chain Phosphorylation 102 CaM Activation of MLCK 102 Rho-Kinase Inhibition of MLCP 104 MLCK- and MLCP-Dependent Phosphorylation of Myosin 104 Mechanical Behavior of Cell 105 References 106 Modeling Blood Flow and Oxygenation in a Diabetic Rat Kidney 108 1 Introduction 108 2 Mathematical Model 109 2.1 Renal Autoregulation 111 2.2 Solute Conservation 112 2.3 Oxygen Consumption 113 2.4 Modeling a Diabetic Kidney 114 3 Model Results 115 3.1 Renal Autoregulation in Diabetes 115 3.2 Renal Oxygenation in Diabetes 117 4 Discussion 118 References 119 Tracking the Distribution of a Solute Bolus in the Rat Kidney 121 1 Introduction 121 2 Mathematical Model 123 3 Model Results 128 3.1 Steady-State Results 128 3.2 Bolus Simulations in an Anti-Diuretic Kidney 130 3.3 Bolus Simulations in a Mildly Diuretic Kidney 137 4 Discussion 138 References 141 Mathematical Modeling of the Effects of Nutrient Competition and Bile Acid Metabolism by the Gut Microbiota on Colonization Resistance Against Clostridium difficile 143 1 Introduction 144 2 Model Development 146 2.1 Model of Microbial Interactions 148 2.2 Model of Bile Acid Interactions 149 2.3 Combined Model 150 3 Parameter Estimation 152 4 Model Dynamics 155 4.1 Microbial Interaction Model Dynamics 155 4.2 Bile Acid Model Dynamics 157 4.2.1 Sensitivity Analysis on Bile Acid Model 159 4.3 Combined Model Dynamics 159 4.3.1 Sensitivity Analysis on Combined Model 161 5 Discussion 162 References 165 Revisiting the Physics of Spider Ballooning 168 1 Ecology of Spider Dispersal 169 2 Relevant Physics 170 2.1 The Physical Parameter Space 170 2.2 Relevant Dimensionless Parameters 172 3 Meteorological Conditions Favoring Spider Ballooning 174 4 Previous Mechanical Models for Ballooning 175 4.1 Humphrey's Take-Off Model 175 4.2 Reynolds et al.'s Passive Dispersal Model 177 4.3 Thomas et al.'s Diffusion Model 178 4.4 Models Incorporating Electrostatics 179 5 Challenges, Open Questions, and Needs 180 References 181 Flying Spiders: Simulating and Modeling the Dynamicsof Ballooning 184 1 Introduction 185 2 Methods 187 2.1 Immersed Boundary Method 187 2.2 Spider Model 190 2.2.1 Numerical and Physical Parameters Used for Simulation 190 2.2.2 Dimensionless Parameters 191 2.2.3 Boundary and Flow Conditions 192 3 Results 192 3.1 Free Fall in a Quiescent Fluid 193 3.2 Free Fall with Background Flows 196 3.2.1 Uniform Background Flows 197 3.2.2 Free Fall in a Cavity Flow 202 3.3 Dynamics of Takeoff 205 3.3.1 Takeoff in Uniform Winds 206 3.3.2 Takeoff in a Cavity Flow 208 4 Conclusions 210 References 213 On the Dynamic Suction Pumping of Blood Cells in Tubular Hearts 216 1 Introduction 216 2 The Immersed Boundary Method 219 2.1 Equations of the Immersed Boundary Method 219 2.2 Numerical Algorithm 221 2.3 Model Geometry 222 2.3.1 Dynamic Suction Pumping Model 223 2.3.2 Peristalsis Model 224 2.3.3 Determining Biologically Relevant Parameter Values 226 3 Results 228 3.1 Dynamic Suction Pumping Results 228 3.2 Peristalsis Results 231 4 Conclusions 232 References 234 Undergraduate Research Highlight: Modeling Movement Behavior Among Interacting Species 237 1 Introduction 237 2 Methods 239 3 Metrics of System Motion 244 4 Case Studies 245 4.1 Case 1: Salamanders 246 4.2 Case 2: White Sharks 248 4.3 Case 3: Golden Perch 250 5 Discussion 251 6 Conclusions 253 References 253 Index 255 Front Matter ....Pages i-viii The Modulation of Pain by Circadian and Sleep-Dependent Processes: A Review of the Experimental Evidence (Megan Hastings Hagenauer, Jennifer A. Crodelle, Sofia H. Piltz, Natalia Toporikova, Paige Ferguson, Victoria Booth)....Pages 1-21 Investigating Circadian Rhythmicity in Pain Sensitivity Using a Neural Circuit Model for Spinal Cord Processing of Pain (Jennifer A. Crodelle, Sofia H. Piltz, Victoria Booth, Megan Hastings Hagenauer)....Pages 23-48 A Two-Process Model for Circadian and Sleep-Dependent Modulation of Pain Sensitivity (Natalia Toporikova, Megan Hastings Hagenauer, Paige Ferguson, Victoria Booth)....Pages 49-62 Introduction to Mathematical Modeling of Blood Flow Control in the Kidney (Anita T. Layton, Aurélie Edwards)....Pages 63-73 Modeling Autoregulation of the Afferent Arteriole of the Rat Kidney (Maria-Veronica Ciocanel, Tracy L. Stepien, Aurélie Edwards, Anita T. Layton)....Pages 75-100 Modeling Blood Flow and Oxygenation in a Diabetic Rat Kidney (Ioannis Sgouralis, Anita T. Layton)....Pages 101-113 Tracking the Distribution of a Solute Bolus in the Rat Kidney (Anita T. Layton)....Pages 115-136 Mathematical Modeling of the Effects of Nutrient Competition and Bile Acid Metabolism by the Gut Microbiota on Colonization Resistance Against Clostridium difficile (Arietta Fleming-Davies, Sara Jabbari, Suzanne L. Robertson, Tri Sri Noor Asih, Cristina Lanzas, Suzanne Lenhart et al.)....Pages 137-161 Revisiting the Physics of Spider Ballooning (Kimberly S. Sheldon, Longhua Zhao, Angela Chuang, Iordanka N. Panayotova, Laura A. Miller, Lydia Bourouiba)....Pages 163-178 Flying Spiders: Simulating and Modeling the Dynamics of Ballooning (Longhua Zhao, Iordanka N. Panayotova, Angela Chuang, Kimberly S. Sheldon, Lydia Bourouiba, Laura A. Miller)....Pages 179-210 On the Dynamic Suction Pumping of Blood Cells in Tubular Hearts (Nicholas A. Battista, Andrea N. Lane, Laura A. Miller)....Pages 211-231 Undergraduate Research Highlight: Modeling Movement Behavior Among Interacting Species (Anne Talkington)....Pages 233-250 Erratum (Anita T. Layton, Laura A. Miller)....Pages E1-E1 Back Matter ....Pages 251-252