Skip to main content Skip to navigation

MA999 2015/6

For reference, here is the entry for 2015/6:

12 Jan-21 Jan: Hugo van den Berg on Organismal energetics

Topics that will be covered: Metabolism and growth require an orchestration at the whole-organism level of, on the one hand, assimilation and disposition of nutrients, and, on the other hand, regulation of reserve mobilisation, rate of growth, level of basal metabolism, and food intake. Moreover, these processes must obey, collectively, fundamental physical constraints such as elemental conservation laws. Small wonder then that the neuronal and endocrine systems that regulate these processes in the mammalian system constitute a bewildering salmagondi of interlocking control loops. We discuss the minimal requirements that any reasonable mathematical model should satisfy and examine examples, within this minimal framework, of models at the "micro," "meso," and "macro" level of detail. We also discuss the issues of modularity (granularity) and the extent to which this can be adjusted at will - although these issues are to be discussed here in the context of organismal energetics, they arise in a wide variety of mathametical modelling contexts.

Useful resources include:

Chapter 6 in: Van den Berg Mathematical Models of Biological Systems Oxford University Press 2011

McNab The Physiological Ecology of Vertebrates: A View from Energetics Comstock Cornell 2002

Schmidt-Nielsen Animal Physiology: Adaptation and Environment Cambridge University Press 1975

Kooijman Dynamic Energy Budget Theory for Metabolic Organisation Cambridge University Press 2009

Van den Berg et al. (2015) Homeostatic regulation in physiological systems: A versatile Ansatz Math. Biosci. 268: 92-101

Pattaranit & van den Berg (2008) Mathematical models of energy homeostasis Roy Soc Interface 5: 1119-1135

Wang et al. (2012) Interaction of fast and slow dynamics in endocrine control systems with an application to beta-cell dynamics Math. Biosci. 235: 8018

26 Jan-4 Feb: Matthew Turner on Collective motion

Topics that will be covered: Review of collective motion in thermodynamic and animal systems. Metric and metric-free interactions. Exercises with coding approaches. Then either (i) interactive exercise in model building and research question refinement in collective effects or (ii) Stochastic dynamics - the Langevin and Fokker Planck equations.

Useful resources include:

Vicsek et al. (1995) Novel type of phase transition in a system of self-driven particles Phys Rev Lett

Giardina (2008) Collective behavior in animal groups: theoretical models and empirical studies HFSP J

Ballerini et al. (2008) Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence
from a field study PNAS

Lauga and Powers (2009) The hydrodynamics of swimming microorganisms Rep Prog Phys

Pearce et al. (2014) Role of projection in the control of bird flocks PNAS

Topaz and Bertozzi (2004) Swarming patters in a two dimensional kinematic model for biological groups SIAM J. Appl. Math.

Buhl et al. (2006) From Disorder to Order in Marching Locusts Science

Popkin (2016) The Physics of Life Nature 529, 16-18

T. Sanchez et al. (2012) Spontaneous motion in hierarchically assembled active matter Nature 491, 431

See also my slides in keynote or pdf and (perhaps) David Tong's lecture notes on kinetic theory and stochastic dynamics and/or the book by Frank Schweitzer on Amazon or in the library.

Click here for course material, including Python code.

9 Feb-18 Feb: Gareth Alexander on Soft Active Matter

Topics that will be covered: An introduction to modern research in soft active matter from the perspective of condensed matter physics. The focus will be on continuum hydrodynamic descriptions and the identification of generic behaviour. Applications will be drawn from active gels and the cell cytoskeleton, suspensions of motile microorganisms and active liquid crystals, active instabilities, and spontaneous flows.

Useful resources include:

J. Prost, F. Jülicher, and J.-F. Joanny (2015) Active gel physics Nature Physics 11, 111-117

S. Ramaswamy (2010) The Mechanics and Statistics of Active Matter Ann. Rev. Condens. Matter Phys. 1, 323-345

C. Marchetti et al. (2013) Hydrodynamics of soft active matter Rev. Mod. Phys. 85, 1143

T. Sanchez et al. (2012) Spontaneous motion in hierarchically assembled active matter Nature 491, 431-434

K. Kruse et al. (2004) Asters, Vortices, and Rotating Spirals in Active Gels of Polar Filaments Phys. Rev. Lett. 92, 078101

K. Kruse et al. (2005) Generic theory of active polar gels: a paradigm for cytoskeletal dynamics Eur. Phys. J. E 16, 5-16

Chapter 9 in: J. P. Sethna (2006) Entropy, Order Parameters, and Complexity Oxford University Press

23 Feb-3 Mar: Matt Keeling on Evolution

Topics that will be covered: Competition as a model of evolution; Pairwise invasibility plots; Evolutionary stable/singular strategies; Speciation; Evolution of Sex and The Red Queen hypothesis.

Some good references include:

Boots & Mealor. Local Interactions Select for Lower Pathogen Infectivity Science 2007

Boots, Hudson & Sasaki. Large Shifts in Pathogen Virulence Relate to Host Population Structure. Science 2004

Brannstrom & Festenberg. Hitchhiker's guide to Adaptive Dynamics.

Brennan Sexual Selection. Nature Education Knowledge 2010

Dieckmann & Doebeli. On the origin of species by sympatric speciation. Nature 1999

Gavrilets. Models of Speciation: What have we learned in 40 years? Evolution 2003

Ridley. The Advantage of Sex.

Servedio. Not Just a Theory—The Utility of Mathematical Models in Evolutionary Biology. PLOS Biology 2014

Waxman & Gavrilets. 20 Questions on Adaptive Dynamics. J. Evol. Biol. 2005

Van den Berg. Evolutionary Dynamics: The mathematics of genes and traits, Institute of Physics 2015

For more popular articles check out: Nova Evolution, New Scientist and the Natural History Museum.

2-13 Mar: oral presentations by students (20 minutes + 5 mins for questions)
Deadline for written literature reviews: 12.00 Monday 25 April 2015

Masters students for whom this is not advertised as a usual option are welcome to contact the module leader if interested in taking it.