Seminars

Abstract: Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance of the vesicle to the calcium channels determines the fusion probability and consequently the postsynaptic signal. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. For all these process components, stochastic effects are widely recognized to play an important role. In this talk, I will present our recent efforts on how to describe and structurally understand neurotransmission dynamics using stochastic modeling approaches. Starting with a linear reaction scheme, a method to directly compute the exact first- and second-order moments of the filtered output signal is proposed. For a modification of the model including explicit recovery steps, the stochastic dynamics are compared to the mean-field approximation in terms of reaction rate equations. Finally, we reflect on spatial extensions of the model, as well as on their approximation by hybrid methods.

References:

- A. Ernst, C. Schütte, S. Sigrist, S. Winkelmann. Mathematical Biosciences, 343, 108760, 2022.

- A. Ernst, N. Unger, C. Schütte, A. Walter, S. Winkelmann. Under Review. https://arxiv.org/abs/2302.01635

Data-driven modeling and deep learning present powerful tools that are opening up new paradigms and opportunities in the understanding, discovery, and design of soft and biological materials. I will describe our recent applications of deep representational learning to expose the sequence-function relationship within homologous protein families and to use these principles for the data-driven design and experimental testing of synthetic proteins with elevated function. I will then describe an approach based on latent space simulators to learn ultra-fast surrogate models of protein folding and biomolecular assembly by stacking three specialized deep learning networks to (i) encode a molecular system into a slow latent space, (ii) propagate dynamics in this latent space, and (iii) generatively decode a synthetic molecular trajectory.

The Omicron BA.1 variant of SARS-CoV-2 was more transmissible and less severe than the preceding Delta variant, including in hosts without previous infection or vaccination.  To investigate why this was the case, we conducted in vitro replication experiments in human nasal and lung cells, then constructed and fitted ODE models of varying levels of complexity to the data, using Markov chain Monte Carlo methods.  Our results fitting a simple model suggest that the basic reproduction number and growth rate are higher for Omicron in nasal cells, and higher for Delta in lung cells. As growth in nasal cells is thought to correspond to transmissibility and growth in lung cells is thought to correspond to severity, these results are consistent with epidemiological and clinical observations.  We then fitted a more complex model, including different virus entry pathways and the immune response, to the data, to understand the mechanisms leading to higher infectivity for Omicron in nasal cells. This work paves the way for using within-host mathematical models to analyse experimental data and understand the transmission potential of future variants. 

While presenting the results of this study, I will use them to open a wider discussion on common problems in mathematical biology, such as the situations in which complex models are preferable to simpler models; when it is appropriate to fix model parameters; and how to present results which are contingent on unidentifiable parameters.

We study the positional information conferred by the morphogens Sonic Hedgehog and BMP in neural tube patterning. We use the mathematics of information theory to quantify the information that cells use to decide their fate. We study the encoding, recoding and decoding that take place as the morphogen gradient is formed, triggers a nuclear response and determines cell fates using a gene regulatory network.