Aggregation - Growth - Fragmentation Phenomena arising in biology

Thursday, June 17 at 02:15am (PDT)
Thursday, June 17 at 10:15am (BST)
Thursday, June 17 06:15pm (KST)

SMB2021 SMB2021 Follow Wednesday (Thursday) during the "MS17" time block.
Share this


Magali Tournus (Ecole Centrale Marseille, France), Marie Doumic (INRIA Paris, France), Miguel Escobedo (Universidad del País Vasco, Spain)


Fragmentation, growth and coagulation or aggregation are phenomena that are observed in many biological systems. We can cite among others : cells that grow and divide during mitosis, microtubules that grow via the addition of monomers and divide brutally during what is called a catastrophe, amyloid fibrils that are involved in neurodegenerative diseases and whose growth and division contitute the main propagation strategy. Mathematical models have been proposed to describe a general system of particules that udergo fragmentation, growth and/or coagulation. We aim to gather here specialists of such models. The types of questions that will be raised in this minisymposium are -inverse problems, or how to recover some information on the particles under study (parameter values), -control theory, or how to combat protein aggregation via drug administration. All these questions involve mathematical models of growth, aggregation and fragmentation, and their answers use powerful mathematical tools. Half of the speakers we selected are mathematicians with a deep interest in biological issues and who have tight collaborations with biophysicists or biologists, the other half consists in a theoretical biophysicist, and an experimental biophysicist with a deep understanding of the modern mathematical tools that can be used to extract information from experiments.

Thomas C T Michaels

(Department of Physics and Astronomy, University College London, UK)
"Spatiotemporal control of filamentous protein aggregation"
Liquid cellular compartments form in the cyto- or nucleoplasm and can regulate aberrant filamentous protein aggregation. Yet, the mechanisms by which these compartments affect protein aggregation remain unknown. Here, we combine kinetic theory of protein aggregation and liquid-liquid phase separation to study the spatial control of irreversible protein aggregation in the presence of liquid compartments. We find that even for weak interactions aggregates strongly partition into the liquid compartment. Aggregate partitioning is caused by a positive feedback mechanism of aggregate nucleation and growth driven by a flux maintaining the phase equilibrium between the compartment and its surrounding. Our model establishes a link between specific aggregating systems and the physical conditions maximizing aggregate partitioning into the compartment. The underlying mechanism of aggregate partitioning could be used to confine cytotoxic protein aggregates inside droplet-like compartments but may also represent a common mechanism to spatially control irreversible chemical reactions in general.

Alex Watson

(University College London, UK)
"Growth-fragmentation and quasi-stationary methods"
A growth-fragmentation is a stochastic process representing cells with continuously growing mass and sudden fragmentation. Growth-fragmentations are used to model cell division and protein polymerisation in biophysics. A topic of wide interest is whether or not these models settle into an equilibrium, in which the number of cells is growing exponentially and the distribution of cell sizes approaches some fixed asymptotic profile. In this work, we present a new spine-based approach to this question, in which a cell lineage is singled out according to a suitable selection of offspring at each generation, with death of the spine occurring at size-dependent rate. The quasi-stationary behaviour of this spine process translates to the equilibrium behaviour, on average, of the growth-fragmentation. We present some Foster-Lyapunov-type conditions for this to hold.

Wei-Feng Xue

(School of Biosciences, University of Kent, UK)
"The division of amyloid fibrils – Experimental analysis and future challenges"
The division of amyloid protein fibrils is required for the propagation of the amyloid state, and is an important contributor to their stability, pathogenicity and normal function. Here, I will present our experimental work on resolving amyloid division and biological impact of their size distributions. By applying new theoretical results emerging from collaboration with mathematicians, these experiments to profile the dynamical stability towards breakage for different amyloid types using AFM imaging reveal particular differences in the division properties of disease- and non-disease related amyloid. Here, the disease associated amyloid formed from alpha-synuclein show lowered intrinsic stability towards breakage and increased likelihood of shedding smaller particles compared with non-disease related amyloid models. Our results enable the comparison of protein filaments’ intrinsic dynamic stabilities, and suggest mapping stability differences of polymorphic amyloid structures as an important challenge to resolve in unravelling their toxic and infectious potentials.

Magali Tournus

(Ecole Centrale Marseille, France)
" Recovering the parameters of the fragmentation equation"
We consider a suspension of particles that undergo fragmentation. We address the question of estimating the fragmentation parameters – i.e. the division rate B(x) and the fragmentation kernel k(y,x) – from measurements of the size particles distribution at various times. This is a natural question for any application where the sizes of the particles are measured experimentally whereas the fragmentation rates are unknown. The application that drives our work is the study of mechanical properties of amyloid fibrils that undergo fragmentation (are the mechanical properties related to toxicity?). In this talk, I will present the biological questions that motivate our work and the new experiments performed by Wei-Feng Xue team at Canterbury, then I will explain why the inverse problem is well posed under reasonable assumptions, and I will focus on how we can recover the fragmentation rate and kernel in practice.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.