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Forthcoming events in this series
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Periodic patterning and growth analysis in the mammalian palate, a landmark-rich Turing system
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Spontaneous motility of actin-based cell fragments as a free-boundary problem
Abstract
We show that actin lamellar fragments extracted from cells, lacking
the complex machinery for cell crawling, are spontaneously motile due
solely to actin polymerization forces at the boundary. The motility
mechanism is associated to a morphological instability similar to the
problem of viscous fingering in Hele-Shaw cells, and does not require
the existence of a global polarization of the actin gel, nor the
presence of molecular motors, contrary to previous claims. We base our
study on the formulation of a 2d free-boundary problem and exploit
conformal mapping and center manifold projection techniques to prove
the nonlinear instability of the center of mass, and to find an exact
and simple relation between shape and velocity. A complex subcritical
bifurcation scenario into traveling solutions is unfolded. With the
help of high-precision numerical computation we show that the velocity
is exponentially small close to the bifurcation points, implying a
non-adiabatic mechanism. Examples of traveling solutions and their
stability are studied numerically. Extensions of the approach to more
realistic descriptions of actual biological systems are briefly
discussed.
REF: C. Blanch-Mercader and J. Casademunt, Physical Review Letters
110, 078102 (2013)
Mathematical models of cell polarization and migration
Design principles and dynamics in clocks, cell cycles and signals
Abstract
I will discuss two topics. Firstly, coupling of the circadian clock and cell cycle in mammalian cells. Together with the labs of Franck Delaunay (Nice) and Bert van der Horst (Rotterdam) we have developed a pipeline involving experimental and mathematical tools that enables us to track through time the phase of the circadian clock and cell cycle in the same single cell and to extend this to whole lineages. We show that for mouse fibroblast cell cultures under natural conditions, the clock and cell cycle phase-lock in a 1:1 fashion. We show that certain perturbations knock this coupled system onto another periodic state, phase-locked but with a different winding number. We use this understanding to explain previous results. Thus our study unravels novel phase dynamics of 2 key mammalian biological oscillators. Secondly, I present a radical revision of the Nrf2 signalling system. Stress responsive signalling coordinated by Nrf2 provides an adaptive response for protection against toxic insults, oxidative stress and metabolic dysfunction. We discover that the system is an autonomous oscillator that regulates its target genes in a novel way.
Exact representations of Susceptible-Infectious-Removed (SIR) epidemic dynamics on networks
Abstract
The majority of epidemic models fall into two categories: 1) deterministic models represented by differential equations and 2) stochastic models which can be evaluated by simulation. In this presentation I will discuss the precise connection between these models. Until recently, exact correspondence was only established in situations exhibiting large degrees of symmetry or for infinite populations.
I will consider SIR dynamics on finite static contact networks. I will give an overview of two provably exact deterministic representations of the underlying stochastic model for tree-like networks. These are the message passing description of Karrer and Newman and my pair-based moment closure representation. I will discuss relationship between the two representations and the relative merits of both.
STUDIES OF SINGLE CELL AND CELL POPULATION BEHAVIORS IN 3D CO-CULTURE MICROFLUIDIC SYSTEMS
Abstract
Recent years have seen rapid expansion of the capabilities
to recreate in vivo conditions using in vitro microfluidic assays.
A wide range of single cell and cell population behaviors can now
be replicated, controlled and imaged for detailed studies to gain
new insights. Such experiments also provide useful fodder for
computational models, both in terms of estimating model parameters
and for testing model-generated hypotheses. Our experiments have
focused in several different areas.
1) Single cell migration experiments in 3D collagen gels have
revealed that interstitial flow can lead to biased cell migration
in the upstream direction, with important implications to cancer
invasion. We show this phenomenon to be a consequence of
integrin-mediated mechanotransduction.
2) Endothelial cells seeded in fibrin gels form perfusable
vascular networks within 2-3 days through a process termed
“vasculogenesis”. The process by which cells sense their
neighbours, extend projections and form anastomoses, and
generate interconnected lumens can be observed through time-lapse
microscopy.
3) These vascular networks, once formed, can be perfused with
medium containing cancer cells that become lodged in the
smaller vessels and proceed to transmigrate across the endothelial
barrier and invade into the surrounding matrix. High resolution
imaging of this process reveals a fascinating sequence of events
involving interactions between a tumour cell, endothelial cells,
and underlying matrix. These three examples will be presented
with a view toward gaining new insights through computational
modelling of the associated phenomena.
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Recurrent Neural Networks in Modelling Biological Networks: Oscillatory p53 interaction dynamics
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Mechanical models to explore biological phenomena
Abstract
Mechanics plays an important role during several biological phenomena such as morphogenesis,
wound healing, bone remodeling and tumorogenesis. Each one of these events is triggered by specific
elementary cell deformations or movements that may involve single cells or populations of cells. In
order to better understand how cell behave and interact, especially during degenerative processes (i.e.
tumorogenesis and metastasis), it has become necessary to combine both numerical and experimental
approaches. Particularly, numerical models allow determining those parameters that are still very
difficult to experimentally measure such as strains and stresses.
During the last few years, I have developed new finite element models to simulate morphogenetic
movements in Drosophila embryo, limb morphogenesis, bone remodeling as well as single and
collective cell migration. The common feature of these models is the multiplicative decomposition of
the deformation gradient which has been used to take into account both the active and the passive
deformations undergone by the cells. I will show how this mechanical approach, firstly used in the
seventies by Lee and Mandel to describe large viscoelastic deformations, can actually be very
powerful in modeling the biological phenomena mentioned above.
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