Mariano Beguerisse Díaz

CV (04/05/2012)

I'm a postdoctoral researcher at Imperial College London working with with Sophia Yaliraki and Mauricio Barahona.

Research


The unifying theme of my research interests is the mathematical representation of biological and human made systems with a special focus on networks. Systems in a wide variety of disciplines can be abstracted by a network. Representing a system with a network has many advantages, perhaps the biggest is that their structure, and the processes that take place on them, can be precisely represented and studied mathematically.

Stomatal Closure


The main focus of my PhD research was the development of ordinary differential equations of stomatal closure. Stomata are tiny pores on the epidermis of plant leaves formed by two kidney-shaped guard cells (see picture above).
Stomata are important because they regulate the transpiration rate of the plant. If conditions are favourable (image A) the pores are open and the plant can exchange CO2 for oxygen and water. When the conditions become less favourable due to lack of light, drought or a pathogen attack, the cells deflate and the pore closes, minimising water loss (image B). The ability to regulate transpiration is essential to the survival and adaptation skills of the plant (they can't just run away when they decide they don't like their place anymore!). Two hormones, abscisic acid (ABA) and ethylene are known to initiate signalling events that culminate on the closing of the stomata. Intriguingly, when the two signals are present at the same time, the pores do not close. I'm trying to work out why.
Understanding the signalling mechanisms that lead to stomatal closure is fundamental to know how plants behave and how we can control them, especially in the face of climate change. It is also an ideal system to understand cellular signal transduction. The network of intracellular signalling components is large and rather complex (see top network for a substantial simplification), hence the need to model it mathematically to guide further experiments (which motivate new models, which motivate new experiments and so on).

In collaboration with Radhika Desikan, Mauricio Barahona, Marco Lizzul, and Mercedes Hernández.

Model reduction


I have worked on the reduction of differential equation models of activation cascades (see picture above). When these models meet certain conditions such as linearity and equal degradation, we can represent the entire cascade exactly with a single incomplete gamma function with three parameters, one of them being the length of the cascade which is useful when we want to estimate it from input/output data. Also if one of the nodes in the cascade has different deactivation rate, it's location in the cascade does not matter for the output, so it can be placed at the bottom and we can still represent the first n-1 proteins with the incomplete gamma function. Cascades with nonlinear dynamics and feedback loops can be approximated by incomplete gamma and hypergeometric functions. I'm interested in finding more exact solutions or approximations to different network motif-dynamics combinations.

In collaboration with Mauricio Barahona, Radhika Desikan, and Piers Ingram.
Read the draft of the paper here.

Parameter fitting


Differential equation models can have tens or even hundreds of parameters. Finding their value is a nontrivial task, and considerable efforts have been devoted to it. Usually, one looks for the combination of parameters that minimises the error (ie discrepancy between the model and data). I developed an optimisation method that takes ideas from local minimisation, Monte Carlo simulation and genetic algorithms to find parameters that minimise the error. This new method requires the user to provide prior distributions for the parameters, but it has the advantage that the priors do not need to contain the true value. Furthermore, the method requires very few simulations of points in the parameter space, resulting in accurate estimation of parameters in several models using simulated and laboratory data. The method is computationally not very expensive. In cases when calculating the error is costly, however, it may become impractical to use because the direct search method may need many computations of the error.

In collaboration with Mauricio Barahona, Baojun (Larry) Wang, and Radhika Desikan.
Read the draft of the paper here.
Code will be available.

Signal antagonism


I have played with little toy models of two signals that produce one response independently but none when combined (motivated from the stomatal ABA-ethylene antagonism, see picture above). Recently, one of these models was used in a limited resource scenario to study the activation and transport dynamics of proteins MAPK1 and MAPK2, and found that competition and antagonism can result when their activator, a MAPK-kinase, is present in limited amounts (paper under review).

In collaboration with Heather Harrington, Michał Komorowski, Michael Stumpf, and Gian Michele Ratto.
Read the draft of the paper here.

Previous research

Human dynamics

As a dissertation project for my MSc in Mathematical modelling and scientific computing, We studied the Netflix data set of DVD ratings, in particular structural properties of the network representation of the data and devised a growth model to describe how films acquire ratings and become popular. We showed that a simple model similar network rewiring models, based on preferential attachment (ie a "rich get richer" process) and random growth can explain some key structural features. We went further to investigate the rating patterns of Netflix users and found that they have bursts of activity. This finding is consistent with other studies that show bursts of activity in email and correspondence data sets.

In collaboration with Mason Porter and Jukka-Pekka Onnela.
Read the paper here.

Publications and papers in preparation

Papers

Submitted papers and papers in preparation

Study group reports

Contact

Mariano Beguerisse Díaz
Department of Mathematics
Department of Chemistry
Imperial College London
6M34 Huxley Building
South Kensington Campus
London SW7 2AZ, U.K.
m.beguerisse[-at-]imperial.ac.uk