62 research outputs found
The Long and Viscous Road: Uncovering Nuclear Diffusion Barriers in Closed Mitosis
During Saccharomyces cerevisiae closed mitosis, parental identity is
sustained by the asymmetric segregation of ageing factors. Such asymmetry has
been hypothesized to occur via diffusion barriers, constraining protein lateral
exchange in cellular membranes. Diffusion barriers have been extensively
studied in the plasma membrane, but their identity and organization within the
nucleus remain unknown. Here, we propose how sphingolipid domains, protein
rings, and morphological changes of the nucleus may coordinate to restrict
protein exchange between nuclear lobes. Our spatial stochastic model is based
on several lines of experimental evidence and predicts that, while a
sphingolipid domain and a protein ring could constitute the barrier during
early anaphase; a sphingolipid domain spanning the bridge between lobes during
late anaphase would be entirely sufficient. Additionally, we explore the
structural organization of plausible diffusion barriers. Our work shows how
nuclear diffusion barriers in closed mitosis may be emergent properties of
simple nanoscale biophysical interactions.Comment: 21 pages, 6 figures and supplementary material (including 8
additional figures and a Table
A Selection Criterion for Patterns in Reaction-Diffusion Systems
Alan Turing's work in Morphogenesis has received wide attention during the
past 60 years. The central idea behind his theory is that two chemically
interacting diffusible substances are able to generate stable spatial patterns,
provided certain conditions are met. Turing's proposal has already been
confirmed as a pattern formation mechanism in several chemical and biological
systems and, due to their wide applicability, there is a great deal of interest
in deciphering how to generate specific patterns under controlled conditions.
However, techniques allowing one to predict what kind of spatial structure will
emerge from Turing systems, as well as generalized reaction-diffusion systems,
remain unknown. Here, we consider a generalized reaction diffusion system on a
planar domain and provide an analytic criterion to determine whether spots or
stripes will be formed. It is motivated by the existence of an associated
energy function that allows bringing in the intuition provided by phase
transitions phenomena. This criterion is proved rigorously in some situations,
generalizing well known results for the scalar equation where the pattern
selection process can be understood in terms of a potential. In more complex
settings it is investigated numerically. Our criterion can be applied to
efficiently design Biotechnology and Developmental Biology experiments, or
simplify the analysis of hypothesized morphogenetic models.Comment: 19 pages, 10 figure
Order Reduction of the Chemical Master Equation via Balanced Realisation
We consider a Markov process in continuous time with a finite number of
discrete states. The time-dependent probabilities of being in any state of the
Markov chain are governed by a set of ordinary differential equations, whose
dimension might be large even for trivial systems. Here, we derive a reduced
ODE set that accurately approximates the probabilities of subspaces of interest
with a known error bound. Our methodology is based on model reduction by
balanced truncation and can be considerably more computationally efficient than
the Finite State Projection Algorithm (FSP) when used for obtaining transient
responses. We show the applicability of our method by analysing stochastic
chemical reactions. First, we obtain a reduced order model for the
infinitesimal generator of a Markov chain that models a reversible,
monomolecular reaction. In such an example, we obtain an approximation of the
output of a model with 301 states by a reduced model with 10 states. Later, we
obtain a reduced order model for a catalytic conversion of substrate to a
product; and compare its dynamics with a stochastic Michaelis-Menten
representation. For this example, we highlight the savings on the computational
load obtained by means of the reduced-order model. Finally, we revisit the
substrate catalytic conversion by obtaining a lower-order model that
approximates the probability of having predefined ranges of product molecules.Comment: 12 pages, 6 figure
Simulating Stochastic Reaction-Diffusion Systems on and within Moving Boundaries
Chemical reactions inside cells are generally considered to happen within
fixed-size compartments. Needless to say, cells and their compartments are
highly dynamic. Thus, such stringent assumptions may not reflect biochemical
reality, and can highly bias conclusions from simulation studies. In this work,
we present an intuitive algorithm for particle-based diffusion in and on moving
boundaries, for both point particles and spherical particles. We first
benchmark in appropriate scenarios our proposed stochastic method against
solutions of partial differential equations, and further demonstrate that
moving boundaries can give rise to super diffusive motion as well as
time-inhomogeneous reaction rates. Finally, we conduct a numerical experiment
representing photobleaching of diffusing fluorescent proteins in dividing
Saccharomyces cerevisiae cells to demonstrate that moving boundaries might
cause important effects neglected in previously published studies.Comment: 22 pages, 7 figure
Asymmetrical inheritance of plasmids depends on dynamic cellular geometry and volume exclusion effects
The asymmetrical inheritance of plasmid DNA, as well as other cellular
components, has been shown to be involved in replicative aging. In
Saccharomyces cerevisiae, there is an ongoing debate regarding the mechanisms
underlying this important asymmetry. Currently proposed models suggest it is
established via diffusion, but differ on whether a diffusion barrier is
necessary or not. However, no study so far incorporated key aspects to
segregation, such as dynamic morphology changes throughout anaphase or plasmids
size. Here, we determine the distinct effects and contributions of individual
cellular variability, plasmid volume and moving boundaries in the asymmetric
segregation of plasmids. We do this by measuring cellular nuclear geometries
and plasmid diffusion rates with confocal microscopy, subsequently
incorporating this data into a growing domain stochastic spatial simulator. Our
modelling and simulations confirms that plasmid asymmetrical inheritance does
not require an active barrier to diffusion, and provides a full analysis on
plasmid size effects.Comment: 36 pages, 4 main figures, 8 figures and text supplementary material
Receptor dimer stabilization By hierarchical plasma membrane microcompartments regulates cytokine signaling
The interaction dynamics of signaling complexes is emerging as a key determinant that regulates the specificity of cellular responses. We present a combined experimental and computational study that quantifies the consequences of plasma membrane microcompartmentalization for the dynamics of type I interferon receptor complexes. By using long-term dual-color quantum dot (QD) tracking, we found that the lifetime of individual ligand-induced receptor heterodimers depends on the integrity of the membrane skeleton (MSK), which also proved important for efficient downstream signaling. By pair correlation tracking and localization microscopy as well as by fast QD tracking, we identified a secondary confinement within ~300-nm-sized zones. A quantitative spatial stochastic diffusion-reaction model, entirely parameterized on the basis of experimental data, predicts that transient receptor confinement by the MSK meshwork allows for rapid reassociation of dissociated receptor dimers. Moreover, the experimentally observed apparent stabilization of receptor dimers in the plasma membrane was reproduced by simulations of a refined, hierarchical compartment model. Our simulations further revealed that the two-dimensional association rate constant is a key parameter for controlling the extent of MSK-mediated stabilization of protein complexes, thus ensuring the specificity of this effect. Together, experimental evidence and simulations support the hypothesis that passive receptor confinement by MSK-based microcompartmentalization promotes maintenance of signaling complexes in the plasma membrane
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