Mathisca de Gunst: the math of the brain
‘In neurosciences, there are things you simply cannot investigate experimentally, whether because of ethical restrictions, because you don’t have the right tools, or perhaps because it is too much work or too expensive. In that case, modelling can be a solution.’
Trained as a mathematician, Mathisca de Gunst has been working on stochastic modelling and statistical analysis of biological phenomena ever since her PhD. Back then, she modelled the growth of plant cell populations in batch cultures. Later, she studied malignant cell growth and shifted her work towards topics from the neurosciences.
‘The idea behind modelling is to create a simplified version of reality. Having built a model, we can make statements about real situations which could not have been made otherwise’, De Gunst says. She explains that even though most groups on the Neuroscience Campus have the expertise to perform standard data analyses themselves, she is convinced that her group can contribute to the more involved statistical problems in many cases. ‘We keep track of the latest mathematical developments and are specialised in tackling the more complex statistical problems like integrating different types of data or dealing with high-dimensionality.’
As a successful example of ‘modelling on demand’, De Gunst mentions a recent project she undertook with neuroinformaticians Arjen van Ooyen and Jaap van Pelt. ‘We developed a mathematical model for the spiking patterns of neuronal ensembles over time. With multi-electrode arrays, Van Pelt had recorded spiking times of dissociated rat cortical cells. These data were used to estimate the parameters of the model. In the end, we were able to infer the connectivity pattern among the analysed cells. Another example is our work on gene regulatory networks with Guus Smit and Ronald van Kesteren. Using statistical and computational methods, we try to predict from experimental gene expression data as well as from information in relevant data bases which genes are involved in neuronal outgrowth. This is important, because it helps to determine which of the many possible experiments should be done in the lab in order to take a step forward in unravelling part of the complex mechanism that does or does not trigger outgrowth.’
Of course, De Gunst says, sometimes the type of modelling that is needed, has been done before, and not for every data analysis completely new methods need to be developed. ‘But still, every modelling situation is a new one, and most often the available tools do not suffice. For example, when working with data collected from rodents and humans, as we do, one cannot simply copy the methods that were used to solve similar problems for yeast. Together with the experimenters, we are constantly evaluating our methods, figuring out which parts work and which don’t, and then adjusting them until we are satisfied. And while doing this, we not only help advance biological knowledge, but step up our own knowledge as well.’
Hidden Markov models
Apart from working with other groups on their modelling and statistical challenges, De Gunst also publishes on topics that are purely mathematical. ‘Mostly, this theoretical research originates from our applied work.’ For example, De Gunst and a PhD student recently published on the asymptotic behaviour of Bayesian estimators for so called hidden Markov models in a mathematical journal. ‘We came to that subject while modelling ion channel kinetics.’ De Gunst hesitates while formulating the exact conclusion: ‘Under certain conditions, and with a sufficient number of observations, the distribution of a Bayesian estimator for the parameters of a hidden Markov model, resembles a particular normal distribution which is centred around the true value.’ Smiling, she adds: ‘Very theoretical indeed, but this is the combination I enjoy.’
De Gunst says that since becoming part of the Center for Neurogenomics and Cognitive Research (CNCR), she and her group have been collaborating with more and more research groups within the VU University Amsterdam and the VU University Medical Center. ‘And now, with the new Neuroscience Campus I hope and expect that this collaboration will intensify.’
Having worked on neuroscience applications for a couple of years now, De Gunst still sees many things to do here. Her fascination has been triggered. ‘This area is so large. There are many challenging statistical problems. One can work on so many different levels: from molecules and genes to cells, tissues and whole brain data. There’s years of very interesting work ahead of me.’
