108 research outputs found
Stability of graph communities across time scales
The complexity of biological, social and engineering networks makes it
desirable to find natural partitions into communities that can act as
simplified descriptions and provide insight into the structure and function of
the overall system. Although community detection methods abound, there is a
lack of consensus on how to quantify and rank the quality of partitions. We
show here that the quality of a partition can be measured in terms of its
stability, defined in terms of the clustered autocovariance of a Markov process
taking place on the graph. Because the stability has an intrinsic dependence on
time scales of the graph, it allows us to compare and rank partitions at each
time and also to establish the time spans over which partitions are optimal.
Hence the Markov time acts effectively as an intrinsic resolution parameter
that establishes a hierarchy of increasingly coarser clusterings. Within our
framework we can then provide a unifying view of several standard partitioning
measures: modularity and normalized cut size can be interpreted as one-step
time measures, whereas Fiedler's spectral clustering emerges at long times. We
apply our method to characterize the relevance and persistence of partitions
over time for constructive and real networks, including hierarchical graphs and
social networks. We also obtain reduced descriptions for atomic level protein
structures over different time scales.Comment: submitted; updated bibliography from v
Uncovering allosteric pathways in caspase-1 with Markov transient analysis and multiscale community detection
Allosteric regulation at distant sites is central to many cellular processes.
In particular, allosteric sites in proteins are a major target to increase the
range and selectivity of new drugs, and there is a need for methods capable of
identifying intra-molecular signalling pathways leading to allosteric effects.
Here, we use an atomistic graph-theoretical approach that exploits Markov
transients to extract such pathways and exemplify our results in an important
allosteric protein, caspase-1. Firstly, we use Markov Stability community
detection to perform a multiscale analysis of the structure of caspase-1 which
reveals that the active conformation has a weaker, less compartmentalised
large-scale structure as compared to the inactive conformation, resulting in
greater intra-protein coherence and signal propagation. We also carry out a
full computational point mutagenesis and identify that only a few residues are
critical to such structural coherence. Secondly, we characterise explicitly the
transients of random walks originating at the active site and predict the
location of a known allosteric site in this protein quantifying the
contribution of individual bonds to the communication pathway between the
active and allosteric sites. Several of the bonds we find have been shown
experimentally to be functionally critical, but we also predict a number of as
yet unidentified bonds which may contribute to the pathway. Our approach offers
a computationally inexpensive method for the identification of allosteric sites
and communication pathways in proteins using a fully atomistic description.Comment: 14 pages, 8 figure
Protein multi-scale organization through graph partitioning and robustness analysis: Application to the myosin-myosin light chain interaction
Despite the recognized importance of the multi-scale spatio-temporal
organization of proteins, most computational tools can only access a limited
spectrum of time and spatial scales, thereby ignoring the effects on protein
behavior of the intricate coupling between the different scales. Starting from
a physico-chemical atomistic network of interactions that encodes the structure
of the protein, we introduce a methodology based on multi-scale graph
partitioning that can uncover partitions and levels of organization of proteins
that span the whole range of scales, revealing biological features occurring at
different levels of organization and tracking their effect across scales.
Additionally, we introduce a measure of robustness to quantify the relevance of
the partitions through the generation of biochemically-motivated surrogate
random graph models. We apply the method to four distinct conformations of
myosin tail interacting protein, a protein from the molecular motor of the
malaria parasite, and study properties that have been experimentally addressed
such as the closing mechanism, the presence of conserved clusters, and the
identification through computational mutational analysis of key residues for
binding.Comment: 13 pages, 7 Postscript figure
Driving current through single organic molecules
We investigate electronic transport through two types of conjugated
molecules. Mechanically controlled break-junctions are used to couple thiol
endgroups of single molecules to two gold electrodes. Current-voltage
characteristics (IVs) of the metal-molecule-metal system are observed. These
IVs reproduce the spatial symmetry of the molecules with respect to the
direction of current flow. We hereby unambigously detect an intrinsic property
of the molecule, and are able to distinguish the influence of both the molecule
and the contact to the metal electrodes on the transport properties of the
compound system.Comment: 4 pages, 5 figure
Current-Driven Conformational Changes, Charging and Negative Differential Resistance in Molecular Wires
We introduce a theoretical approach based on scattering theory and total
energy methods that treats transport non-linearities, conformational changes
and charging effects in molecular wires in a unified way. We apply this
approach to molecular wires consisting of chain molecules with different
electronic and structural properties bonded to metal contacts. We show that
non-linear transport in all of these systems can be understood in terms of a
single physical mechanism and predict that negative differential resistance at
high bias should be a generic property of such molecular wires.Comment: 9 pages, 4 figure
ab initio modeling of open systems: charge transfer, electron conduction, and molecular switching of a C_{60} device
We present an {\it ab initio} analysis of electron conduction through a
molecular device. Charge transfer from the device electrodes to the
molecular region is found to play a crucial role in aligning the lowest
unoccupied molecular orbital (LUMO) of the to the Fermi level of the
electrodes. This alignment induces a substantial device conductance of . A gate potential can inhibit charge transfer and
introduce a conductance gap near , changing the current-voltage
characteristics from metallic to semi-conducting, thereby producing a field
effect molecular current switch
Fullerene-based molecular nanobridges: A first-principles study
Building upon traditional quantum chemistry calculations, we have implemented
an {\em ab-initio} method to study the electrical transport in nanocontacts. We
illustrate our technique calculating the conductance of C molecules
connected in various ways to Al electrodes characterized at the atomic level.
Central to a correct estimate of the electrical current is a precise knowledge
of the local charge transfer between molecule and metal which, in turn,
guarantees the correct positioning of the Fermi level with respect to the
molecular orbitals. Contrary to our expectations, ballistic transport seems to
occur in this system.Comment: 4 pages in two-column forma
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