65 research outputs found
Yangians in Integrable Field Theories, Spin Chains and Gauge-String Dualities
In the following dissertation, we explore the applicability of Yangian symmetry
to various integrable models, in particular, in relation with S-matrices.
One of the main themes in this dissertation is that, after a careful study of
the mathematics of the symmetry algebras one finds that in an integrable
model, one can directly reconstruct S-matrices just from the algebra. It has
been known for a long time that S-matrices in integrable models are fixed
by symmetry. However, Lie algebra symmetry, the Yang-Baxter equation,
crossing and unitarity, which are what constrains the S-matrix in integrable
models, are often taken to be separate, independent properties of the S-matrix.
Here, we construct scattering matrices purely from the Yangian,
showing that the Yangian is the right algebraic object to unify all required
symmetries of many integrable models. In particular, we reconstruct the
S-matrix of the principal chiral field, and, up to a CDD factor, of other
integrable field theories with su(n) symmetry. Furthermore, we study the
AdS/CFT correspondence, which is also believed to be integrable in the
planar limit. We reconstruct the S-matrices at weak and at strong coupling
from the Yangian or its classical limit.
This version of the thesis includes minor corrections following the viva on
17 September 2010
Hybrid approaches for multiple-species stochastic reaction-diffusion models
Reaction-diffusion models are used to describe systems in fields as diverse
as physics, chemistry, ecology and biology. The fundamental quantities in such
models are individual entities such as atoms and molecules, bacteria, cells or
animals, which move and/or react in a stochastic manner. If the number of
entities is large, accounting for each individual is inefficient, and often
partial differential equation (PDE) models are used in which the stochastic
behaviour of individuals is replaced by a description of the averaged, or mean
behaviour of the system. In some situations the number of individuals is large
in certain regions and small in others. In such cases, a stochastic model may
be inefficient in one region, and a PDE model inaccurate in another. To
overcome this problem, we develop a scheme which couples a stochastic
reaction-diffusion system in one part of the domain with its mean field
analogue, i.e. a discretised PDE model, in the other part of the domain. The
interface in between the two domains occupies exactly one lattice site and is
chosen such that the mean field description is still accurate there. This way
errors due to the flux between the domains are small. Our scheme can account
for multiple dynamic interfaces separating multiple stochastic and
deterministic domains, and the coupling between the domains conserves the total
number of particles. The method preserves stochastic features such as
extinction not observable in the mean field description, and is significantly
faster to simulate on a computer than the pure stochastic model.Comment: 38 pages, 8 figure
Mechanical and Systems Biology of Cancer
Mechanics and biochemical signaling are both often deregulated in cancer,
leading to cancer cell phenotypes that exhibit increased invasiveness,
proliferation, and survival. The dynamics and interactions of cytoskeletal
components control basic mechanical properties, such as cell tension,
stiffness, and engagement with the extracellular environment, which can lead to
extracellular matrix remodeling. Intracellular mechanics can alter signaling
and transcription factors, impacting cell decision making. Additionally,
signaling from soluble and mechanical factors in the extracellular environment,
such as substrate stiffness and ligand density, can modulate cytoskeletal
dynamics. Computational models closely integrated with experimental support,
incorporating cancer-specific parameters, can provide quantitative assessments
and serve as predictive tools toward dissecting the feedback between signaling
and mechanics and across multiple scales and domains in tumor progression.Comment: 18 pages, 3 figure
A mechanical modeling framework to study endothelial permeability
The inner lining of blood vessels, the endothelium, is made up of endothelial cells. Vascular endothelial (VE)-cadherin protein forms a bond with VE-cadherin from neighboring cells to determine the size of gaps between the cells and thereby regulate the size of particles that can cross the endothelium. Chemical cues such as thrombin, along with mechanical properties of the cell and extracellular matrix are known to affect the permeability of endothelial cells. Abnormal permeability is found in patients suffering from diseases including cardiovascular diseases, cancer, and COVID-19. Even though some of the regulatory mechanisms affecting endothelial permeability are well studied, details of how several mechanical and chemical stimuli acting simultaneously affect endothelial permeability are not yet understood. In this article, we present a continuum-level mechanical modeling framework to study the highly dynamic nature of the VE-cadherin bonds. Taking inspiration from the catch-slip behavior that VE-cadherin complexes are known to exhibit, we model the VE-cadherin homophilic bond as cohesive contact with damage following a traction-separation law. We explicitly model the actin cytoskeleton and substrate to study their role in permeability. Our studies show that mechanochemical coupling is necessary to simulate the influence of the mechanical properties of the substrate on permeability. Simulations show that shear between cells is responsible for the variation in permeability between bicellular and tricellular junctions, explaining the phenotypic differences observed in experiments. An increase in the magnitude of traction force due to disturbed flow that endothelial cells experience results in increased permeability, and it is found that the effect is higher on stiffer extracellular matrix. Finally, we show that the cylindrical monolayer exhibits higher permeability than the planar monolayer under unconstrained cases. Thus, we present a contact mechanics-based mechanochemical model to investigate the variation in the permeability of endothelial monolayer due to multiple loads acting simultaneously.</p
Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis
We propose a modelling framework to analyse the stochastic behaviour of
heterogeneous, multi-scale cellular populations. We illustrate our methodology
with a particular example in which we study a population with an
oxygen-regulated proliferation rate. Our formulation is based on an
age-dependent stochastic process. Cells within the population are characterised
by their age. The age-dependent (oxygen-regulated) birth rate is given by a
stochastic model of oxygen-dependent cell cycle progression. We then formulate
an age-dependent birth-and-death process, which dictates the time evolution of
the cell population. The population is under a feedback loop which controls its
steady state size: cells consume oxygen which in turns fuels cell
proliferation. We show that our stochastic model of cell cycle progression
allows for heterogeneity within the cell population induced by stochastic
effects. Such heterogeneous behaviour is reflected in variations in the
proliferation rate. Within this set-up, we have established three main results.
First, we have shown that the age to the G1/S transition, which essentially
determines the birth rate, exhibits a remarkably simple scaling behaviour. This
allows for a huge simplification of our numerical methodology. A further result
is the observation that heterogeneous populations undergo an internal process
of quasi-neutral competition. Finally, we investigated the effects of
cell-cycle-phase dependent therapies (such as radiation therapy) on
heterogeneous populations. In particular, we have studied the case in which the
population contains a quiescent sub-population. Our mean-field analysis and
numerical simulations confirm that, if the survival fraction of the therapy is
too high, rescue of the quiescent population occurs. This gives rise to
emergence of resistance to therapy since the rescued population is less
sensitive to therapy
Mesoscopic and continuum modelling of angiogenesis
Angiogenesis is the formation of new blood vessels from pre-existing ones in
response to chemical signals secreted by, for example, a wound or a tumour. In
this paper, we propose a mesoscopic lattice-based model of angiogenesis, in
which processes that include proliferation and cell movement are considered as
stochastic events. By studying the dependence of the model on the lattice
spacing and the number of cells involved, we are able to derive the
deterministic continuum limit of our equations and compare it to similar
existing models of angiogenesis. We further identify conditions under which the
use of continuum models is justified, and others for which stochastic or
discrete effects dominate. We also compare different stochastic models for the
movement of endothelial tip cells which have the same macroscopic,
deterministic behaviour, but lead to markedly different behaviour in terms of
production of new vessel cells.Comment: 48 pages, 13 figure
Effects of 3D Geometries on Cellular Gradient Sensing and Polarization
During cell migration, cells become polarized, change their shape, and move
in response to various internal and external cues. Cell polarization is defined
through the spatio-temporal organization of molecules such as PI3K or small
GTPases, and is determined by intracellular signaling networks. It results in
directional forces through actin polymerization and myosin contractions. Many
existing mathematical models of cell polarization are formulated in terms of
reaction-diffusion systems of interacting molecules, and are often defined in
one or two spatial dimensions. In this paper, we introduce a 3D
reaction-diffusion model of interacting molecules in a single cell, and find
that cell geometry has an important role affecting the capability of a cell to
polarize, or change polarization when an external signal changes direction. Our
results suggest a geometrical argument why more roundish cells can repolarize
more effectively than cells which are elongated along the direction of the
original stimulus, and thus enable roundish cells to turn faster, as has been
observed in experiments. On the other hand, elongated cells preferentially
polarize along their main axis even when a gradient stimulus appears from
another direction. Furthermore, our 3D model can accurately capture the effect
of binding and unbinding of important regulators of cell polarization to and
from the cell membrane. This spatial separation of membrane and cytosol, not
possible to capture in 1D or 2D models, leads to marked differences of our
model from comparable lower-dimensional models.Comment: 31 pages, 7 figure
p53 Orchestrates Cancer Metabolism:Unveiling Strategies to Reverse the Warburg Effect
Cancer cells exhibit significant alterations in their metabolism, characterised by a reduction in oxidative phosphorylation (OXPHOS) and an increased reliance on glycolysis, even in the presence of oxygen. This metabolic shift, known as the Warburg effect, is pivotal in fuelling cancer’s uncontrolled growth, invasion, and therapeutic resistance. While dysregulation of many genes contributes to this metabolic shift, the tumour suppressor gene p53 emerges as a master player. Yet, the molecular mechanisms remain elusive. This study introduces a comprehensive mathematical model, integrating essential p53 targets, offering insights into how p53 orchestrates its targets to redirect cancer metabolism towards an OXPHOS-dominant state. Simulation outcomes align closely with experimental data comparing glucose metabolism in colon cancer cells with wild-type and mutated p53. Additionally, our findings reveal the dynamic capability of elevated p53 activation to fully reverse the Warburg effect, highlighting the significance of its activity levels not just in triggering apoptosis (programmed cell death) post-chemotherapy but also in modifying the metabolic pathways implicated in treatment resistance. In scenarios of p53 mutations, our analysis suggests targeting glycolysis-instigating signalling pathways as an alternative strategy, whereas targeting solely synthesis of cytochrome c oxidase 2 (SCO2) does support mitochondrial respiration but may not effectively suppress the glycolysis pathway, potentially boosting the energy production and cancer cell viability
Single-Cell Migration in Complex Microenvironments: Mechanics and Signaling Dynamics
Cells are highly dynamic and mechanical automata powered by molecular motors that respond to external cues. Intracellular signaling pathways, either chemical or mechanical, can be activated and spatially coordinated to induce polarized cell states and directional migration. Physiologically, cells navigate through complex microenvironments, typically in three-dimensional (3D) fibrillar networks. In diseases, such as metastatic cancer, they invade across physiological barriers and remodel their local environments through force, matrix degradation, synthesis, and reorganization. Important external factors such as dimensionality, confinement, topographical cues, stiffness, and flow impact the behavior of migrating cells and can each regulate motility. Here, we review recent progress in our understanding of single-cell migration in complex microenvironments.National Cancer Institute (U.S.) (Grant No. 5U01CA177799)National Institutes of Health (U.S.) (Ruth L. Kirschstein National Research Service Award
The Yangian of sl(n|m) and the universal R-matrix
In this paper we study Yangians of sl(n|m) superalgebras. We derive the
universal R-matrix and evaluate it on the fundamental representation obtaining
the standard Yang R-matrix with unitary dressing factors. For m=0, we directly
recover up to a CDD factor the well-known S-matrices for relativistic
integrable models with su(N) symmetry. Hence, the universal R-matrix found
provides an abstract plug-in formula, which leads to results obeying
fundamental physical constraints: crossing symmetry, unitrarity and the
Yang-Baxter equation. This implies that the Yangian double unifies all desired
symmetries into one algebraic structure. In particular, our analysis is valid
in the case of sl(n|n), where one has to extend the algebra by an additional
generator leading to the algebra gl(n|n). We find two-parameter families of
scalar factors in this case and provide a detailed study for gl(1|1).Comment: 24 pages, 2 figure
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