387,444 research outputs found
Origin of complexity in multicellular organisms
Through extensive studies of dynamical system modeling cellular growth and
reproduction, we find evidence that complexity arises in multicellular
organisms naturally through evolution. Without any elaborate control mechanism,
these systems can exhibit complex pattern formation with spontaneous cell
differentiation. Such systems employ a `cooperative' use of resources and
maintain a larger growth speed than simple cell systems, which exist in a
homogeneous state and behave 'selfishly'. The relevance of the diversity of
chemicals and reaction dynamics to the growth of a multicellular organism is
demonstrated. Chaotic biochemical dynamics are found to provide the
multi-potency of stem cells.Comment: 6 pages, 2 figures, Physical Review Letters, 84, 6130, (2000
Population growth and persistence in a heterogeneous environment: the role of diffusion and advection
The spatio-temporal dynamics of a population present one of the most
fascinating aspects and challenges for ecological modelling. In this article we
review some simple mathematical models, based on one dimensional
reaction-diffusion-advection equations, for the growth of a population on a
heterogeneous habitat. Considering a number of models of increasing complexity
we investigate the often contrary roles of advection and diffusion for the
persistence of the population. When it is possible we demonstrate basic
mathematical techniques and give the critical conditions providing the survival
of a population, in simple systems and in more complex resource-consumer models
which describe the dynamics of phytoplankton in a water column.Comment: Introductory review of simple conceptual models. 45 pages, 15 figures
v2: minor change
BlenX-based compositional modeling of complex reaction mechanisms
Molecular interactions are wired in a fascinating way resulting in complex
behavior of biological systems. Theoretical modeling provides a useful
framework for understanding the dynamics and the function of such networks. The
complexity of the biological networks calls for conceptual tools that manage
the combinatorial explosion of the set of possible interactions. A suitable
conceptual tool to attack complexity is compositionality, already successfully
used in the process algebra field to model computer systems. We rely on the
BlenX programming language, originated by the beta-binders process calculus, to
specify and simulate high-level descriptions of biological circuits. The
Gillespie's stochastic framework of BlenX requires the decomposition of
phenomenological functions into basic elementary reactions. Systematic
unpacking of complex reaction mechanisms into BlenX templates is shown in this
study. The estimation/derivation of missing parameters and the challenges
emerging from compositional model building in stochastic process algebras are
discussed. A biological example on circadian clock is presented as a case study
of BlenX compositionality
Fixed Points and Attractors of Reactantless and Inhibitorless Reaction Systems
Reaction systems are discrete dynamical systems that model biochemical
processes in living cells using finite sets of reactants, inhibitors, and
products. We investigate the computational complexity of a comprehensive set of
problems related to the existence of fixed points and attractors in two
constrained classes of reaction systems, in which either reactants or
inhibitors are disallowed. These problems have biological relevance and have
been extensively studied in the unconstrained case; however, they remain
unexplored in the context of reactantless or inhibitorless systems.
Interestingly, we demonstrate that although the absence of reactants or
inhibitors simplifies the system's dynamics, it does not always lead to a
reduction in the complexity of the considered problems.Comment: 29 page
Effective dynamics along given reaction coordinates, and reaction rate theory
In molecular dynamics and related fields one considers dynamical descriptions of complex systems in full (atomic) detail. In order to reduce the overwhelming complexity of realistic systems (high dimension, large timescale spread, limited computational resources) the projection of the full dynamics onto some reaction coordinates is examined in order to extract statistical information like free energies or reaction rates. In this context, the effective dynamics that is induced by the full dynamics on the reaction coordinate space has attracted considerable attention in the literature. In this article, we contribute to this discussion: we first show that if we start with an ergodic diffusion process whose invariant measure is unique then these properties are inherited by the effective dynamics. Then, we give equations for the effective dynamics, discuss whether the dominant timescales and reaction rates inferred from the effective dynamics are accurate approximations of such quantities for the full dynamics, and compare our findings to results from approaches like Mori–Zwanzig, averaging, or homogenization. Finally, by discussing the algorithmic realization of the effective dynamics, we demonstrate that recent algorithmic techniques like the “equation-free” approach and the “heterogeneous multiscale method” can be seen as special cases of our approach
Stochastic dynamics of macromolecular-assembly networks
The formation and regulation of macromolecular complexes provides the
backbone of most cellular processes, including gene regulation and signal
transduction. The inherent complexity of assembling macromolecular structures
makes current computational methods strongly limited for understanding how the
physical interactions between cellular components give rise to systemic
properties of cells. Here we present a stochastic approach to study the
dynamics of networks formed by macromolecular complexes in terms of the
molecular interactions of their components. Exploiting key thermodynamic
concepts, this approach makes it possible to both estimate reaction rates and
incorporate the resulting assembly dynamics into the stochastic kinetics of
cellular networks. As prototype systems, we consider the lac operon and phage
lambda induction switches, which rely on the formation of DNA loops by proteins
and on the integration of these protein-DNA complexes into intracellular
networks. This cross-scale approach offers an effective starting point to move
forward from network diagrams, such as those of protein-protein and DNA-protein
interaction networks, to the actual dynamics of cellular processes.Comment: Open Access article available at
http://www.nature.com/msb/journal/v2/n1/full/msb4100061.htm
Computationally-efficient stochastic cluster dynamics method for modeling damage accumulation in irradiated materials
An improved version of a recently developed stochastic cluster dynamics (SCD)
method {[}Marian, J. and Bulatov, V. V., {\it J. Nucl. Mater.} \textbf{415}
(2014) 84-95{]} is introduced as an alternative to rate theory (RT) methods for
solving coupled ordinary differential equation (ODE) systems for irradiation
damage simulations. SCD circumvents by design the curse of dimensionality of
the variable space that renders traditional ODE-based RT approaches inefficient
when handling complex defect population comprised of multiple (more than two)
defect species. Several improvements introduced here enable efficient and
accurate simulations of irradiated materials up to realistic (high) damage
doses characteristic of next-generation nuclear systems. The first improvement
is a procedure for efficiently updating the defect reaction-network and event
selection in the context of a dynamically expanding reaction-network. Next is a
novel implementation of the -leaping method that speeds up SCD
simulations by advancing the state of the reaction network in large time
increments when appropriate. Lastly, a volume rescaling procedure is introduced
to control the computational complexity of the expanding reaction-network
through occasional reductions of the defect population while maintaining
accurate statistics. The enhanced SCD method is then applied to model defect
cluster accumulation in iron thin films subjected to triple ion-beam
(, and \text{H\ensuremath{{}^{+}}})
irradiations, for which standard RT or spatially-resolved kinetic Monte Carlo
simulations are prohibitively expensive
Theory of Robustness of Irreversible Differentiation in a Stem Cell System: Chaos hypothesis
Based on extensive study of a dynamical systems model of the development of a
cell society, a novel theory for stem cell differentiation and its regulation
is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell
systems - stochastic differentiation of stem cells and the robustness of a
system due to regulation of this differentiation - are found to be general
properties of a system of interacting cells exhibiting chaotic intra-cellular
reaction dynamics and cell division, whose presence does not depend on the
detail of the model. It is found that stem cells differentiate into other cell
types stochastically due to a dynamical instability caused by cell-cell
interactions, in a manner described by the Isologous Diversification theory.
This developmental process is shown to be stable not only with respect to
molecular fluctuations but also with respect to removal of cells. With this
developmental process, the irreversible loss of multipotency accompanying the
change from a stem cell to a differentiated cell is shown to be characterized
by a decrease in the chemical diversity in the cell and of the complexity of
the cellular dynamics. The relationship between the division speed and this
loss of multipotency is also discussed. Using our model, some predictions that
can be tested experimentally are made for a stem cell system.Comment: 31 pages, 10 figures, submitted to Jour. Theor. Bio
A scalable computational framework for establishing long-term behavior of stochastic reaction networks
Reaction networks are systems in which the populations of a finite number of
species evolve through predefined interactions. Such networks are found as
modeling tools in many biological disciplines such as biochemistry, ecology,
epidemiology, immunology, systems biology and synthetic biology. It is now
well-established that, for small population sizes, stochastic models for
biochemical reaction networks are necessary to capture randomness in the
interactions. The tools for analyzing such models, however, still lag far
behind their deterministic counterparts. In this paper, we bridge this gap by
developing a constructive framework for examining the long-term behavior and
stability properties of the reaction dynamics in a stochastic setting. In
particular, we address the problems of determining ergodicity of the reaction
dynamics, which is analogous to having a globally attracting fixed point for
deterministic dynamics. We also examine when the statistical moments of the
underlying process remain bounded with time and when they converge to their
steady state values. The framework we develop relies on a blend of ideas from
probability theory, linear algebra and optimization theory. We demonstrate that
the stability properties of a wide class of biological networks can be assessed
from our sufficient theoretical conditions that can be recast as efficient and
scalable linear programs, well-known for their tractability. It is notably
shown that the computational complexity is often linear in the number of
species. We illustrate the validity, the efficiency and the wide applicability
of our results on several reaction networks arising in biochemistry, systems
biology, epidemiology and ecology. The biological implications of the results
as well as an example of a non-ergodic biological network are also discussed.Comment: 31 pages, 9 figure
Molecular dynamics at water interfaces: from astrophysical to biochemical applications
This PhD thesis investgates the chemical and physical interactions between water and systems of different sizes. The first section illustrates the chemical context of the projects and methodological basis used.
The second part studies the dynamics and reactivity of small systems of astrochemical interest on top of water ice, at each step the complexity of the model is increased. Initially the ice surface is characterized, then different aspects of the reaction are examined.
The final part explores the interactions between water molecules and two different proteins, to understand water’s role as solvent and how it influences protein macromolecule
dynamics.
The appendix includes a discussion on the interatomic interaction of water and the contribution apported in CHARMM software package are presented
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