30 research outputs found
Formal derivation of dissipative particle dynamics from first principles
We show that the Markovian approximation assumed in current particle-based coarse-grained techniques, like dissipative particle dynamics, is unreliable in situations in which sound plays an important role. As an example we solve analytically and numerically the dynamics of coarse-grained harmonic systems by using first principle methods, showing the presence of long-lived memory kernels. This effect raises questions about the connection of these approaches at their current form to molecular dynamics.The European Union and the EPSR
Inhomogeneous multiscale dynamics in harmonic lattices
We use projection operators to address the coarse-grained multiscale problem in harmonic systems. Stochastic equations of motion for the coarse-grained variables with an inhomogeneous level of coarse graining in both time and space are presented. In contrast to previous approaches that typically start with thermodynamic averages the key element of our approach is the use of a projection matrix chosen both for its physical appeal in analogy to mechanical stability theory and for its algebraic properties. We show that thermodynamic equilibrium can be recovered and obtain the fluctuation dissipation theorema posteriori. All system-specific information can be computed from a series of feasible molecular dynamics simulations. We recover previous results in the literature and show how this approach can be used to extend the quasicontinuum approach and comment on implications for dissipative particle dynamics type of methods. Contrary to what is assumed in the latter models the stochastic process of all coarse-grained variables is not necessarily Markovian even though the variables are slow. Our approach is applicable to any system in which the coarse-grained regions are linear. As an example we apply it to the dynamics of a single mesoscopic particle in the infinite one-dimensional harmonic chain.EU growth project SENTIMATS under Contract No. G5RD-CT-200
The directional contact distance of two ellipsoids: Coarse-grained potentials for anisotropic interactions
Copyright @ 2005 American Institute of Physics.We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons with Gay-Berne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given.This research has been supported by GlaxoSmith-Klin
Great cities look small
Great cities connect people; failed cities isolate people. Despite the
fundamental importance of physical, face-to-face social-ties in the functioning
of cities, these connectivity networks are not explicitly observed in their
entirety. Attempts at estimating them often rely on unrealistic
over-simplifications such as the assumption of spatial homogeneity. Here we
propose a mathematical model of human interactions in terms of a local strategy
of maximising the number of beneficial connections attainable under the
constraint of limited individual travelling-time budgets. By incorporating
census and openly-available online multi-modal transport data, we are able to
characterise the connectivity of geometrically and topologically complex
cities. Beyond providing a candidate measure of greatness, this model allows
one to quantify and assess the impact of transport developments, population
growth, and other infrastructure and demographic changes on a city. Supported
by validations of GDP and HIV infection rates across United States metropolitan
areas, we illustrate the effect of changes in local and city-wide
connectivities by considering the economic impact of two contemporary inter-
and intra-city transport developments in the United Kingdom: High Speed Rail 2
and London Crossrail. This derivation of the model suggests that the scaling of
different urban indicators with population size has an explicitly mechanistic
origin.Comment: 19 pages, 8 figure
The stability of a graph partition: A dynamics-based framework for community detection
Recent years have seen a surge of interest in the analysis of complex
networks, facilitated by the availability of relational data and the
increasingly powerful computational resources that can be employed for their
analysis. Naturally, the study of real-world systems leads to highly complex
networks and a current challenge is to extract intelligible, simplified
descriptions from the network in terms of relevant subgraphs, which can provide
insight into the structure and function of the overall system.
Sparked by seminal work by Newman and Girvan, an interesting line of research
has been devoted to investigating modular community structure in networks,
revitalising the classic problem of graph partitioning.
However, modular or community structure in networks has notoriously evaded
rigorous definition. The most accepted notion of community is perhaps that of a
group of elements which exhibit a stronger level of interaction within
themselves than with the elements outside the community. This concept has
resulted in a plethora of computational methods and heuristics for community
detection. Nevertheless a firm theoretical understanding of most of these
methods, in terms of how they operate and what they are supposed to detect, is
still lacking to date.
Here, we will develop a dynamical perspective towards community detection
enabling us to define a measure named the stability of a graph partition. It
will be shown that a number of previously ad-hoc defined heuristics for
community detection can be seen as particular cases of our method providing us
with a dynamic reinterpretation of those measures. Our dynamics-based approach
thus serves as a unifying framework to gain a deeper understanding of different
aspects and problems associated with community detection and allows us to
propose new dynamically-inspired criteria for community structure.Comment: 3 figures; published as book chapte
Prediction of protein allosteric signalling pathways and functional residues through paths of optimised propensity
Allostery commonly refers to the mechanism that regulates protein activity
through the binding of a molecule at a different, usually distal, site from the
orthosteric site. The omnipresence of allosteric regulation in nature and its
potential for drug design and screening render the study of allostery
invaluable. Nevertheless, challenges remain as few computational methods are
available to effectively predict allosteric sites, identify signalling pathways
involved in allostery, or to aid with the design of suitable molecules
targeting such sites. Recently, bond-to-bond propensity analysis has been shown
successful at identifying allosteric sites for a large and diverse group of
proteins from knowledge of the orthosteric sites and its ligands alone by using
network analysis applied to energy-weighted atomistic protein graphs. To
address the identification of signalling pathways, we propose here a method to
compute and score paths of optimised propensity that link the orthosteric site
with the identified allosteric sites, and identifies crucial residues that
contribute to those paths. We showcase the approach with three well-studied
allosteric proteins: h-Ras, caspase-1, and 3-phosphoinositide-dependent
kinase-1 (PDK1). Key residues in both orthosteric and allosteric sites were
identified and showed agreement with experimental results, and pivotal
signalling residues along the pathway were also revealed, thus providing
alternative targets for drug design. By using the computed path scores, we were
also able to differentiate the activity of different allosteric modulators