UniKiel                MPG                UniLuebeck


Colloquium

Mathematics Meets Biology

This colloquium aims at highlighting interesting mathematical problems, methods and developments closely tied to applications in the life sciences, at fostering interdisciplinary discussion between the fields and at strengthening exchange between researchers interested in biomathematics, both theory and application. It takes place twice a year, once in Kiel and once in Lübeck.

Friday, 8 May, 3:15 pm, Department of Mathematics, CAU Kiel, Heinrich-Hecht-Platz 6, 24118 Kiel, Room EG024

3:15 pm Hether Harrington
(Max Planck Institute for Molecular Cell Biology and Genetics, Dresden) 		Topological Data Analysis for Multiscale Biology

Many processes in the life sciences are inherently multiscale and dynamic. Spatial structures and patterns vary across levels of organisation, from molecular to multi-cellular to multi-organism. With more sophisticated mechanistic models and data available, quantitative tools are needed to study their evolution in space and time. Topological data analysis (TDA) provides a multi-scale summary of data. I will review the main tools in topological data analysis and how single and multi-parameter persistent homology provide insights to biological system.
4:15 pm Coffee break
4:45 pm Susanna Röblitz
(Universität Bergen) 		Markov state modelling of stochastic gene-regulatory networks

Gene expression is a stochastic process, leading to cell-to-cell variation in mRNA and protein levels even in genetically identical cells under the same conditions. One reason for this noise is the low number of molecules involved in the process, such as a single gene or mRNA transcript, which makes molecular events like binding and decay inherently random and unpredictable. This randomness often results in complex multi-attractor dynamics, where attractors can be identified with committed and primed states in cell differentiation (cellular phenotypes). One way to describe the long-time behavior of such systems is to run stochastic simulations, but the occurrence of rare events typically demands very long and extensive simulations. In this presentation, I'll outline an alternative approach known as Markov state modeling (MSM). MSM enables the efficient simulation of rare events and provides a description of cellular phenotypes in terms of their gene expression and transition patterns.


Friday, 28 November, 3:15 pm, Ratzeburger Allee 160, 23562 Lübeck, Turmgebäde, Room H1

3:15 pm Daniele Avitabile
(Amsterdam Center for Dynamics and Computation of the Vrije Universiteit Amsterdam) 		Uncertainty quantification for neurobiological networks This talk presents a framework for forward uncertainty quantification problems in spatially-extended neurobiological networks. We will consider networks in which the cortex is represented as a continuum domain, and local neuronal activity evolves according to an integro-differential equation, collecting inputs nonlocally, from the whole cortex. These models are sometimes referred to as neural field equations. Large-scale brain simulations of such models are currently performed heuristically, and the numerical analysis of these problems is largely unexplored. In the first part of the talk I will summarise recent developments for the rigorous numerical analysis of projection schemes for deterministic neural fields, which sets the foundation for developing Finite-Element and Spectral schemes for large-scale problems. The second part of the talk will discuss the case of networks in the presence of uncertainties modelled with random data, in particular: random synaptic connections, external stimuli, neuronal firing rates, and initial conditions. Such problems give rise to random solutions, whose mean, variance, or other quantities of interest have to be estimated using numerical simulations. This so-called forward uncertainty quantification problem is challenging because it couples spatially nonlocal, nonlinear problems to large- dimensional random data. I will present a family of schemes that couple a spatial projector for the spatial discretisation, to stochastic collocation for the random data. We will analyse the time- dependent problem with random data and the schemes from a functional analytic viewpoint, and show that the proposed methods can achieve spectral accuracy, provided the random data is sufficiently regular. We will showcase the schemes using several examples.
4:15 pm Coffee break
4:45 pm Axel Hutt
(INRIA Nancy Center at University of Lorraine) 		Additive nose-induced system evolution (ANISE)

Experimental brain activity is known to show oscillations in specific frequency bands, which reflects neural information processing. For instance, strong oscillations at about 2Hz reflect tiredness and sleepiness, strong 40Hz oscillations indicate alertness. Changes of power in frequency bands indicate changes in information processing. Specifically, it has been observed that strong activity about 10Hz and 2Hz emerge in electroencephalographic activity (EEG) when a subject looses consciousness in general anaesthesia. Numerical simulations of stochastic neural models have shown that such a change can be reproduced by changing the variance of external additive Gaussian uncorrelated noise. At a first glance, this is surprising since additive noise is not supposed to affect a system’s oscillatory activity or stability. At first, the presentation shows how additive noise can affect a nonlinear system’s stability by applying stochastic center manifold analysis in non-delayed low-dimensional systems and delayed systems. An extension to stochastic randomly connected network models demonstrates that the observed effect also emerges in networks. Applying random matrix theory together with mean-field theory demonstrates how additive noise tunes the stability and oscillatory activity in such systems. In sum, the mathematical studies provide an explanation why the brain’s oscillatory activity changes with changing experimental conditions.



Previous talks:


Friday, 11 July, 3:15 pm, Ratzeburger Allee 160, 23562 Lübeck, Building 64, Banachraum Room 3.014

3:15 pm Denise Kühnert
(Robert-Koch-Institut, Wildau) 		Unraveling the Evolution and Transmission Dynamics of Infectious Pathogens

Understanding the evolution and transmission dynamics of infectious disease agents is important to public health. In order to infer pathogen transmission histories, phylodynamic methods fit stochastic population dynamic models to phylogenetic trees that are built based on alignments of viral sequences. These methods are broadly used but can be computationally expensive. We explore if machine learning and deep-learning models are suited, e.g. to infer phylodynamic parameters directly from the viral sequences and their sampling dates. This talk includes a range of different methods to understand the evolution and epidemiology of infectious disease agents over broad timescales - ranging from months and years to millennia.
4:15 pm Coffee break
4:45 pm Amaury Lambert
(Collège de France & Ecole Normale Supérieure, Paris) 		100 years after: Modernity and revival of Yule's "mathematical theory of evolution"

In 1925, the famous British statistician G.U. Yule published a paper entitled "A mathematical theory of evolution" that introduced the pure-birth process and is commonly cited as the first paper to deal with random tree models of phylogenies. We will discuss some historical aspects of this paper and of its legacy, including some overlooked aspects and common misattributions. We will then show how to generalize Yule's results on the frequency of genera of a given age and size (number of species) when species diversification within genera follows any integer-valued process, including species extinctions. Studying such macroevolutionary patterns in this broader context allows us to identify the cases where genus size has a power-law tail distribution, with new applications to urn schemes, in the vein of the famous paper by Simon (1955), future Nobel Memorial Prize in economic sciences (1978).


Friday, 6 June, 3:15 pm, Heinrich-Hecht-Platz 6, 24118 Kiel, Room EG024

3:15 pm Martin Vingron
(Max Planck Institute for Molecular Genetics, Berlin) 		Association plots and joint clustering and embedding of genes and cells

Single-cell transcriptome analysis poses many problems in visualizing and analyzing data. Based on the geometric interpretation of correspondence analysis biplots, we define “Association Plots” to depict genes that characterize ("are associated with") a cluster of cells. We further develop this geometric intuition into a clustering method for cells with their associated genes. The principles of this analysis are not restricted to single-cell transcriptomics, but should generally apply to data in the form of a contingency table.
4:15 pm Coffee break
4:45 pm Jana Wolf
(Max Delbrück Center for Molecular Medicine, Berlin) 		Modeling signal transduction at the interface of single-cell and population data

Signalling pathways and gene regulation are critically involved in cellular decisions about how to respond to external signals and they are frequently disrupted in tumour development. These pathways have been described by non-linear ODE systems that capture key proteins and regulatory interactions. While experimental settings and models initially focused on cell populations, the focus has recently shifted to single cells. This has revealed not only a wide range of dynamic phenomena but also considerable heterogeneity between cells. In this talk I will discuss how time-resolved data from single cells within populations can be used to derive quantitative signalling models and to decipher signal integration between pathways involved in the genotoxic stress response. We here use a subpopulation-based approach to describe the dynamics of single cells.




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