18 research outputs found
Coordination of Cell Differentiation and Migration in Mathematical Models of Caudal Embryonic Axis Extension
Vertebrate embryos display a predominant head-to-tail body axis whose formation is associated with the progressive development of post-cranial structures from a pool of caudal undifferentiated cells. This involves the maintenance of active FGF signaling in this caudal region as a consequence of the restricted production of the secreted factor FGF8. FGF8 is transcribed specifically in the caudal precursor region and is down-regulated as cells differentiate and the embryo extends caudally. We are interested in understanding the progressive down-regulation of FGF8 and its coordination with the caudal movement of cells which is also known to be FGF-signaling dependent. Our study is performed using mathematical modeling and computer simulations. We use an individual-based hybrid model as well as a caricature continuous model for the simulation of experimental observations (ours and those known from the literature) in order to examine possible mechanisms that drive differentiation and cell movement during the axis elongation. Using these models we have identified a possible gene regulatory network involving self-repression of a caudal morphogen coupled to directional domain movement that may account for progressive down-regulation of FGF8 and conservation of the FGF8 domain of expression. Furthermore, we have shown that chemotaxis driven by molecules, such as FGF8 secreted in the stem zone, could underlie the migration of the caudal precursor zone and, therefore, embryonic axis extension. These mechanisms may also be at play in other developmental processes displaying a similar mode of axis extension coupled to cell differentiation
Self-organized Vortex State in Two-dimensional Dictyostelium Dynamics
We present results of experiments on the dynamics of Dictyostelium discoideum
in a novel set-up which constraints cell motion to a plane. After aggregation,
the amoebae collect into round ''pancake" structures in which the cells rotate
around the center of the pancake. This vortex state persists for many hours and
we have explicitly verified that the motion is not due to rotating waves of
cAMP. To provide an alternative mechanism for the self-organization of the
Dictyostelium cells, we have developed a new model of the dynamics of
self-propelled deformable objects. In this model, we show that cohesive energy
between the cells, together with a coupling between the self-generated
propulsive force and the cell's configuration produces a self-organized vortex
state. The angular velocity profiles of the experiment and of the model are
qualitatively similar. The mechanism for self-organization reported here can
possibly explain similar vortex states in other biological systems.Comment: submitted to PRL; revised version dated 3/8/9
Exponential Distribution of Locomotion Activity in Cell Cultures
In vitro velocities of several cell types have been measured using computer
controlled video microscopy, which allowed to record the cells' trajectories
over several days. On the basis of our large data sets we show that the
locomotion activity displays a universal exponential distribution. Thus, motion
resulting from complex cellular processes can be well described by an
unexpected, but very simple distribution function. A simple phenomenological
model based on the interaction of various cellular processes and finite ATP
production rate is proposed to explain these experimental results.Comment: 4 pages, 3 figure
Competing Patterns of Signaling Activity in Dictyostelium discoideum
Quantitative experiments are described on spatio-temporal patterns of
coherent chemical signaling activity in populations of {\it Dictyostelium
discoideum} amoebae. We observe competition between spontaneously firing
centers and rotating spiral waves that depends strongly on the overall cell
density. At low densities, no complete spirals appear and chemotactic
aggregation is driven by periodic concentric waves, whereas at high densities
the firing centers seen at early times nucleate and are apparently entrained by
spiral waves whose cores ultimately serve as aggregation centers. Possible
mechanisms for these observations are discussed.Comment: 10 pages, RevTeX, 4 ps figures, accepted in PR
Streaming instability of slime mold amoebae: An analytical model
During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed
Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
In a weakly excitable medium, characterized by a large threshold stimulus,
the free end of an isolated broken plane wave (wave tip) can either rotate
(steadily or unsteadily) around a large excitable core, thereby producing a
spiral pattern, or retract causing the wave to vanish at boundaries. An
asymptotic analysis of spiral motion and retraction is carried out in this
weakly excitable large core regime starting from the free-boundary limit of the
reaction-diffusion models, valid when the excited region is delimited by a thin
interface. The wave description is shown to naturally split between the tip
region and a far region that are smoothly matched on an intermediate scale.
This separation allows us to rigorously derive an equation of motion for the
wave tip, with the large scale motion of the spiral wavefront slaved to the
tip. This kinematic description provides both a physical picture and exact
predictions for a wide range of wave behavior, including: (i) steady rotation
(frequency and core radius), (ii) exact treatment of the meandering instability
in the free-boundary limit with the prediction that the frequency of unstable
motion is half the primary steady frequency (iii) drift under external actions
(external field with application to axisymmetric scroll ring motion in
three-dimensions, and spatial or/and time-dependent variation of excitability),
and (iv) the dynamics of multi-armed spiral waves with the new prediction that
steadily rotating waves with two or more arms are linearly unstable. Numerical
simulations of FitzHug-Nagumo kinetics are used to test several aspects of our
results. In addition, we discuss the semi-quantitative extension of this theory
to finite cores and pinpoint mathematical subtleties related to the thin
interface limit of singly diffusive reaction-diffusion models
Colloquium: Mechanical formalisms for tissue dynamics
The understanding of morphogenesis in living organisms has been renewed by
tremendous progressin experimental techniques that provide access to
cell-scale, quantitative information both on theshapes of cells within tissues
and on the genes being expressed. This information suggests that
ourunderstanding of the respective contributions of gene expression and
mechanics, and of their crucialentanglement, will soon leap forward.
Biomechanics increasingly benefits from models, which assistthe design and
interpretation of experiments, point out the main ingredients and assumptions,
andultimately lead to predictions. The newly accessible local information thus
calls for a reflectionon how to select suitable classes of mechanical models.
We review both mechanical ingredientssuggested by the current knowledge of
tissue behaviour, and modelling methods that can helpgenerate a rheological
diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and
tissue scale ("inter-cell") contributions. We recall the mathematical framework
developpedfor continuum materials and explain how to transform a constitutive
equation into a set of partialdifferential equations amenable to numerical
resolution. We show that when plastic behaviour isrelevant, the dissipation
function formalism appears appropriate to generate constitutive equations;its
variational nature facilitates numerical implementation, and we discuss
adaptations needed in thecase of large deformations. The present article
gathers theoretical methods that can readily enhancethe significance of the
data to be extracted from recent or future high throughput
biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few
corrections to the published version, all in Appendix D.2 devoted to large
deformation
Understanding regression of Hensen´s node and the caudal stem zone: a mathematical modelling approach
Poster presented at the Symposium on developmental biology from a cell biology and biophysics perspective, May 21-22, 2009, CNIC, Madrid.This work is funded by the Spanish MICINN
(BFU2005-2972) and by a collaborative grant from the University of Liverpool. A Wellcome Trust Research Training Fellowship in Mathematical Biology is also acknowledged.Spanish MICINNUniversity of LiverpoolWellcome Trust Research
Training Fellowship in Mathematical BiologyPeer reviewe