Mathematical Modelling for Biology, Health, and Environment

We present two generic SIR-like epidemic models with stochastic parameters, in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady-state, where the effective reproduction rate fluctuates close to the critical value one for a long period, as indeed observed for different epidemics. In the first model, the rate at which each individual becomes infected changes stochastically in time with a heavy-tailed steady state. The second model assumes a random scale-free interaction network, which is redrawn periodically. In both models, criticality is obtained through a self-organization mechanism and does not require any feedback between the state of the epidemic and the behaviour of individuals.

TBA

Phytoplankton, microscopic photosynthetic marine organisms, are vitally important for maintaining a habitable planet. These organisms have short lifetimes such that evolution is possible on the timescale of years. Experimental studies suggest that phytoplankton can rapidly evolve to climate changes. Adaptation is inherently a stochastic processes and the rate of adaptation will depend on many things including population size.  To understand phytoplankton adaptation, we must couple an understanding of how evolution acts on multi-trait phenotypes, with the impact of environmental fluctuations and transport of microbes by ocean currents on selection pressures. Ultimately, these stochastic, individual level dynamics then need to be incorporated into deterministic ecosystem models in order to understand and predict shifts in global carbon cycling. 

Bio: Naomi M. Levine is a Gabilan Assistant Professor at the University of Southern California where she holds joint appointments in the Departments of Marine and Environmental Biology, Quantitative and Computational Biology, and Earth Sciences. She received her B.A. in geosciences from Princeton University and her Ph.D. in chemical oceanography from the MIT-WHOI Joint Program. Levine’s research focuses on understanding the interactions between climate and marine microbial ecosystem composition and function. The Levine lab is developing innovative, interdisciplinary numerical models that allow them to understand how dynamics occurring at the scale of individual microbes impact large-scale ecosystem processes such as rates of global carbon cycling. Levine is an Alfred P. Sloan Research Fellow, a Simons Foundation Early Career Investigator and an NSF CAREER award recipient.

In this talk I will explore the potential pitfalls in calculating averages appropriately in different biological scenarios and suggest how to approach the problem in general. I consider averaging in foraging models, revisiting the “fallacy of averages” debate where different methods of working out payoff in foraging scenarios was considered. I will also look at related models including group sizes and how to measure them appropriately, and the problem of “length-biased” sampling from renewal theory. All of these problems are inter-related, with the correct selection of probability distributions central to the problem.

A key challenge for microbes is to locate nutrient hotspots amid nutrient deserts ill-suitable for growth. We will discuss several challenges and trade-offs involved in the search behavior. Specifically, I describe our work studying risk-reward trade-offs in search behavior, where we quantify the cost and benefit of bacterial motility to explain a behavioral dichotomy among marine bacteria. I use experiments to demonstrate how the chemotaxis pathway - used to navigate nutrient gradients - can amplify molecular noise to enhance their exploratory behavior even in areas without gradients. Finally, I will also explain how the interactions within chemosensory arrays - large signal-processing protein complexes - are tuned close to a critical point, on the border between order and chaos, and that this helps to leverage a sensory trade-off between response amplitude and speed.

Bio: Johannes Keegstra is a postdoctoral researcher based in the Environmental Microfluidics Group of Prof. Roman Stocker at ETH Zurich. He performed his PhD research in biophysics at the AMOLF research institute in Amsterdam, and before that studied physics in Delft and philosophy in Leiden. His work focusses microbes living in complex environments, linking molecular mechanisms to bacterial behaviour that affect biogeochemical cycles.

Antibiotic resistance is one of the major threats to human society prompting an urgent global response. Bacteria developed multiple strategies for antibiotic resistance by effectively reducing intracellular antibiotic concentrations or antibiotic binding affinities to their specific targets. In this talk, I will present a recently discovered pathway to antibiotic resistance that depends on the bacterial morphological transformation that promotes bacterial decrease of antibiotic influx to the cell. By analysing cell morphological data of different bacterial species under antibiotic stress, we find that bacterial cells robustly reduce the surface-to-volume ratio in response to most types of antibiotics. Using quantitative modelling we show that by reducing the surface-to-volume ratio, bacteria can effectively reduce intracellular antibiotic concentration by decreasing antibiotic influx. The model predicts that bacteria can also increase the surface-to-volume ratio to promote antibiotic dilution for membrane-targeting antibiotics, in agreement with data on membrane-transport inhibitors. Using the particular example of ribosome-targeting antibiotics, I will present a systems-level model for the regulation of cell shape under antibiotic stress and discuss feedback mechanisms that bacteria can harness to increase their fitness in the presence of antibiotics.

Bio: Nikola obtained PhD in theoretical and computational physics from Lehigh University in 2012. Nikola worked on experimental and theoretical aspects of bacterial adaptation to antibiotics during postdocs at Imperial College London, Edinburgh University and University College London. In 2022, Nikola became an independent group leader at Queen Mary University of London.

Understanding how spatial disorder affects the random search of a diffusing particle or agent is fundamental to a myriad of applications across disciplines. To quantify how spatial heterogeneities may affect the dynamics of first-passage processes, I consider diffusion occurring on a network, that is on a highly disordered environment. In most instances predicting the movement dynamics of an agent on networks has relied so far on estimates provided by stochastic simulations, rather than rigorous mathematical tools. To close this knowledge gap I have devised a general methodology to represent analytically the movement and search dynamics of a diffusing random walk on a graph, which is particularly convenient for sparse graphs. By considering small-world networks, I have uncovered the existence of a bi-modality regime in the time-dependence of the first-passage probability to hit a target node. By identifying the network features that give rise to the bi-modal regime, I challenge long-held beliefs on how the statistics of the so-called direct, intermediate, and indirect trajectories influence the shape of the resulting first-passage and first-absorption probabilities and the interpretation of their mean values.

How do living organisms move in their environment? While random walk models provide a foundation for understanding biological movement, they fall short in capturing the full complexity of movement patterns generated by living organisms. This study explores stochastic processes in two dimensions, defined in the Cartesian frame, and how they transform into a frame comoving with an organism. We argue that this comoving frame provides the correct description for the self-generated fluctuations of an organism leading to movement. By transforming stochastic equations of motion and by examining corresponding probability distributions and autocorrelations, we identify key features of these processes in the comoving frame. For the example of the generic Ornstein–Uhlenbeck process, we derive analytically two simple equations in the comoving frame that reproduce the stochastic behavior generated in the Cartesian frame. The talk will also discuss models of active Brownian particles and their corresponding stochastic dynamics in the comoving frame, highlighting the connection between self-propelled motion and stochasticity in biological systems by offering new insights into modeling active biological movement.

Ecologists often view changes in the species composition of an area as signs of damage that should be avoided and reversed. This thinking has influenced international agreements for the protection of aquatic biodiversity, such as the Ramsar Convention on Wetlands and the EU's Water Framework Directive. I will present recent work by Jacob O'Sullivan and myself  that shows that a simple two-parameter model can explain such changes as resulting from entirely natural processes. We find that the distribution of the number of sites occupied by species, the Occupancy Frequency Distribution, for three different groups of species consistently adheres to a simple log-series distribution. We explain this distribution in terms of a "birth-death" process, where "birth" corresponds to colonisations of patches and "death" to extirpations. The process implies a distribution for the time species persist in a collection of patches (which ecologists call a "metacommunity"), and this distribution agrees excellently with observations. The surprising finding that complex biological processes unfolding over decades in landscapes spanning tens of kilometres can be described by a simple mathematical model invite further mathematical study of such systems.

Short summary: I will tell a story of how quantitative thinking has helped us overcome experimental challenges in a synthetic yeast cooperative community.

About the speaker: Wenying has been trained in both Math and Biology as her majors and has worked with the evolution of synthetic yeast cooperative community and mathematical modelling of community dynamics in the past decades. We are very happy to have Wenying coming over to QMUL and share her exciting research with us. More info at https://iris.ucl.ac.uk/iris/browse/profile?upi=WSHOU61