Mathematical Biology and Medicine

Seminar: 3pm Monday 15 May, MALL
Mario Castro (Madrid)
The physics of cauliflowers Some fascinating natural shapes present cauliflower-like structures. Surfaces of thin films, turbulent and combustion fronts, geological formations or biological systems are strikingly similar in spite of their diversity. In all cases, one can recognize a typical motif independently of the scale of observation. These appealing morphologies combine two apparently contradictory features: a hierarchical (fractal) structure and disorder (randomness). Fractal geometry is a useful tool to describe natural shapes but, to gain physical insight a theoretical framework that captures the way that they can be produced is needed. We present a compact dynamical equation for evolving surfaces that produces cauliflower-like structures and has a large degree of universality. This nonlinear equation allows us to identify non-locality, nonconservation and randomness, as the main mechanisms controlling the formation of these ubiquitous shapes. To test our theory at different scales, we have grown thin film nano-structures by Chemical Vapor Deposition and measured the scaling properties of (centimeter size) cauliflower plants. Besides, control of the expermental system also allows us to control the patterns and produce experimental observations of first and second order "phase"-transitions reminiscent of statistical mechanics systems but in a non-equilibrium context.

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Current and recent visitors

   
   
  • Joe Gillard and Tom Laws
  • Mario Castro works on mathematical models of systems where fluctuations are relevant (cellular and receptor immunology) and on pattern formation in spatially extended systems (from tumor cell modeling to cauliflower morphogenesis or nano-structuring). The figure shows comparisons of different mathematical models with real experiments.
  • Madhulika Mishra (IISc Bangalore)
  • Narmada Sambaturu (IISc Bangalore)
  • Sathya Baarathi (IISc Bangalore)
  • Shamik Majumdar (IISc Bangalore)
Applications for research leading to a PhD are welcome. Please apply here, naming a potential project and supervisor. Sample projects are as follows:
  • Analysis of high-throughput genomic data applied to diseases such as cancer
    Arief Gusnanto, Charles Taylor, Jeanine Houwing-Duistermaat
    Statistical modelling of copy number alteration in cancer: using statistical methodology to discover patterns within the genomic copy number alteration profiles in cancer patients and how the pattern can be utilised for improved prediction of cancer survival and patients' clinical characteristics.
    Genetic association in complex diseases and cancer: a collaboration with research groups in the School of Medicine to perform fine mapping around a previously identified location to identify genetic variants that are associated with cancer.
  • Mathematical immunology
    Grant Lythe and Carmen Molina-París
    Development of stochastic mathematical and computational models of the immune system in health and disease, of intra-cellular signalling to understand cell fate, and development of diffusive motion models of cell-cell interactions and receptor-ligand interactions.
  • Modelling biodiversity and ecosystems
    Sandro Azaele
    In this project you will be developing mathematical and computational tools for modeling spatial and temporal patterns in ecosystems, understanding their principal drivers across different scales, at population and community level. This will also help developing methodologies for upscaling biodiversity information from fine-scale sampling.
  • Modelling evolution on molecular and macroscopic scales
    Mauro Mobilia
    Inspired by recent results in biology, and also in behavioural sciences, we will combine notions of non-linear dynamics and evolutionary game together with the theory of stochastic processes and numerical simulations to investigate how noise and mobility influences the formation of coherent patterns.
  • Modelling of biomolecules
    Oliver Harlen and Daniel Read, in collaboration with the Astbury Centre
    Simulating the motions of large biomolecules such molecular motors and also soft colloidal particles, entities that are large enough to be beyond the scope of atomistic simulations (that model the motion of individual atoms), but small enough to be affected by thermal fluctuations (Brownian motion).

Recent programs, conferences and workshops