58 research outputs found
Inferring the dynamics of underdamped stochastic systems
Many complex systems, ranging from migrating cells to animal groups, exhibit
stochastic dynamics described by the underdamped Langevin equation. Inferring
such an equation of motion from experimental data can provide profound insight
into the physical laws governing the system. Here, we derive a principled
framework to infer the dynamics of underdamped stochastic systems from
realistic experimental trajectories, sampled at discrete times and subject to
measurement errors. This framework yields an operational method, Underdamped
Langevin Inference (ULI), which performs well on experimental trajectories of
single migrating cells and in complex high-dimensional systems, including
flocks with Viscek-like alignment interactions. Our method is robust to
experimental measurement errors, and includes a self-consistent estimate of the
inference error
Physical models of bacterial chromosomes
The interplay between bacterial chromosome organization and functions such as
transcription and replication can be studied in increasing detail using novel
experimental techniques. Interpreting the resulting quantitative data, however,
can be theoretically challenging. In this minireview, we discuss how connecting
experimental observations to biophysical theory and modeling can give rise to
new insights on bacterial chromosome organization. We consider three flavors of
models of increasing complexity: simple polymer models that explore how
physical constraints, such as confinement or plectoneme branching, can affect
bacterial chromosome organization; bottom-up mechanistic models that connect
these constraints to their underlying causes, for instance chromosome
compaction to macromolecular crowding, or supercoiling to transcription; and
finally, data-driven methods for inferring interpretable and quantitative
models directly from complex experimental data. Using recent examples, we
discuss how biophysical models can both deepen our understanding of how
bacterial chromosomes are structured, and give rise to novel predictions about
bacterial chromosome organization.Comment: 9 pages, 2 figure
Learning dynamical models of single and collective cell migration: a review
Single and collective cell migration are fundamental processes critical for
physiological phenomena ranging from embryonic development and immune response
to wound healing and cancer metastasis. To understand cell migration from a
physical perspective, a broad variety of models for the underlying physical
mechanisms that govern cell motility have been developed. A key challenge in
the development of such models is how to connect them to experimental
observations, which often exhibit complex stochastic behaviours. In this
review, we discuss recent advances in data-driven theoretical approaches that
directly connect with experimental data to infer dynamical models of stochastic
cell migration. Leveraging advances in nanofabrication, image analysis, and
tracking technology, experimental studies now provide unprecedented large
datasets on cellular dynamics. In parallel, theoretical efforts have been
directed towards integrating such datasets into physical models from the single
cell to the tissue scale with the aim of conceptualizing the emergent behavior
of cells. We first review how this inference problem has been addressed in
freely migrating cells on two-dimensional substrates and in structured,
confining systems. Moreover, we discuss how data-driven methods can be
connected with molecular mechanisms, either by integrating mechanistic
bottom-up biophysical models, or by performing inference on subcellular degrees
of freedom. Finally, we provide an overview of applications of data-driven
modelling in developing frameworks for cell-to-cell variability in behaviours,
and for learning the collective dynamics of multicellular systems.
Specifically, we review inference and machine learning approaches to recover
cell-cell interactions and collective dynamical modes, and how these can be
integrated into physical active matter models of collective migration
Criticality and isostaticity in fiber networks
The rigidity of elastic networks depends sensitively on their internal
connectivity and the nature of the interactions between constituents. Particles
interacting via central forces undergo a zero-temperature rigidity-percolation
transition near the isostatic threshold, where the constraints and internal
degrees of freedom are equal in number. Fibrous networks, such as those that
form the cellular cytoskeleton, become rigid at a lower threshold due to
additional bending constraints. However, the degree to which bending governs
network mechanics remains a subject of considerable debate. We study disordered
fibrous networks with variable coordination number, both above and below the
central-force isostatic point. This point controls a broad crossover from
stretching- to bending-dominated elasticity. Strikingly, this crossover
exhibits an anomalous power-law dependence of the shear modulus on both
stretching and bending rigidities. At the central-force isostatic point---well
above the rigidity threshold---we find divergent strain fluctuations together
with a divergent correlation length , implying a breakdown of continuum
elasticity in this simple mechanical system on length scales less than .Comment: 6 pages, 5 figure
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