4,493 research outputs found
Neutral networks of genotypes: Evolution behind the curtain
Our understanding of the evolutionary process has gone a long way since the
publication, 150 years ago, of "On the origin of species" by Charles R. Darwin.
The XXth Century witnessed great efforts to embrace replication, mutation, and
selection within the framework of a formal theory, able eventually to predict
the dynamics and fate of evolving populations. However, a large body of
empirical evidence collected over the last decades strongly suggests that some
of the assumptions of those classical models necessitate a deep revision. The
viability of organisms is not dependent on a unique and optimal genotype. The
discovery of huge sets of genotypes (or neutral networks) yielding the same
phenotype --in the last term the same organism--, reveals that, most likely,
very different functional solutions can be found, accessed and fixed in a
population through a low-cost exploration of the space of genomes. The
'evolution behind the curtain' may be the answer to some of the current puzzles
that evolutionary theory faces, like the fast speciation process that is
observed in the fossil record after very long stasis periods.Comment: 7 pages, 7 color figures, uses a modification of pnastwo.cls called
pnastwo-modified.cls (included
Random Network Behaviour of Protein Structures
Geometric and structural constraints greatly restrict the selection of folds
adapted by protein backbones, and yet, folded proteins show an astounding
diversity in functionality. For structure to have any bearing on function, it
is thus imperative that, apart from the protein backbone, other tunable degrees
of freedom be accountable. Here, we focus on side-chain interactions, which
non-covalently link amino acids in folded proteins to form a network structure.
At a coarse-grained level, we show that the network conforms remarkably well to
realizations of random graphs and displays associated percolation behavior.
Thus, within the rigid framework of the protein backbone that restricts the
structure space, the side-chain interactions exhibit an element of randomness,
which account for the functional flexibility and diversity shown by proteins.
However, at a finer level, the network exhibits deviations from these random
graphs which, as we demonstrate for a few specific examples, reflect the
intrinsic uniqueness in the structure and stability, and perhaps specificity in
the functioning of biological proteins.Comment: Expanded version available in Molecular BioSystem
Erratum: Signal propagation in proteins and relation to equilibrium fluctuations (PLoS Computational Biology (2007) 3, 9, (e172) DOI: 10.1371/journal.pcbi.0030172))
Elastic network (EN) models have been widely used in recent years for describing protein dynamics, based on the premise that the motions naturally accessible to native structures are relevant to biological function. We posit that equilibrium motions also determine communication mechanisms inherent to the network architecture. To this end, we explore the stochastics of a discrete-time, discrete-state Markov process of information transfer across the network of residues. We measure the communication abilities of residue pairs in terms of hit and commute times, i.e., the number of steps it takes on an average to send and receive signals. Functionally active residues are found to possess enhanced communication propensities, evidenced by their short hit times. Furthermore, secondary structural elements emerge as efficient mediators of communication. The present findings provide us with insights on the topological basis of communication in proteins and design principles for efficient signal transduction. While hit/commute times are information-theoretic concepts, a central contribution of this work is to rigorously show that they have physical origins directly relevant to the equilibrium fluctuations of residues predicted by EN models
Chance and Necessity in Evolution: Lessons from RNA
The relationship between sequences and secondary structures or shapes in RNA
exhibits robust statistical properties summarized by three notions: (1) the
notion of a typical shape (that among all sequences of fixed length certain
shapes are realized much more frequently than others), (2) the notion of shape
space covering (that all typical shapes are realized in a small neighborhood of
any random sequence), and (3) the notion of a neutral network (that sequences
folding into the same typical shape form networks that percolate through
sequence space). Neutral networks loosen the requirements on the mutation rate
for selection to remain effective. The original (genotypic) error threshold has
to be reformulated in terms of a phenotypic error threshold. With regard to
adaptation, neutrality has two seemingly contradictory effects: It acts as a
buffer against mutations ensuring that a phenotype is preserved. Yet it is
deeply enabling, because it permits evolutionary change to occur by allowing
the sequence context to vary silently until a single point mutation can become
phenotypically consequential. Neutrality also influences predictability of
adaptive trajectories in seemingly contradictory ways. On the one hand it
increases the uncertainty of their genotypic trace. At the same time neutrality
structures the access from one shape to another, thereby inducing a topology
among RNA shapes which permits a distinction between continuous and
discontinuous shape transformations. To the extent that adaptive trajectories
must undergo such transformations, their phenotypic trace becomes more
predictable.Comment: 37 pages, 14 figures; 1998 CNLS conference; high quality figures at
http://www.santafe.edu/~walte
Rigidity and flexibility of biological networks
The network approach became a widely used tool to understand the behaviour of
complex systems in the last decade. We start from a short description of
structural rigidity theory. A detailed account on the combinatorial rigidity
analysis of protein structures, as well as local flexibility measures of
proteins and their applications in explaining allostery and thermostability is
given. We also briefly discuss the network aspects of cytoskeletal tensegrity.
Finally, we show the importance of the balance between functional flexibility
and rigidity in protein-protein interaction, metabolic, gene regulatory and
neuronal networks. Our summary raises the possibility that the concepts of
flexibility and rigidity can be generalized to all networks.Comment: 21 pages, 4 figures, 1 tabl
Stochastic dynamics of model proteins on a directed graph
A method for reconstructing the energy landscape of simple polypeptidic
chains is described. We show that we can construct an equivalent representation
of the energy landscape by a suitable directed graph. Its topological and
dynamical features are shown to yield an effective estimate of the time scales
associated with the folding and with the equilibration processes. This
conclusion is drawn by comparing molecular dynamics simulations at constant
temperature with the dynamics on the graph, defined by a temperature dependent
Markov process. The main advantage of the graph representation is that its
dynamics can be naturally renormalized by collecting nodes into "hubs", while
redefining their connectivity. We show that both topological and dynamical
properties are preserved by the renormalization procedure. Moreover, we obtain
clear indications that the heteropolymers exhibit common topological
properties, at variance with the homopolymer, whose peculiar graph structure
stems from its spatial homogeneity. In order to obtain a clear distinction
between a "fast folder" and a "slow folder" in the heteropolymers one has to
look at kinetic features of the directed graph. We find that the average time
needed to the fast folder for reaching its native configuration is two orders
of magnitude smaller than its equilibration time, while for the bad folder
these time scales are comparable. Accordingly, we can conclude that the
strategy described in this paper can be successfully applied also to more
realistic models, by studying their renormalized dynamics on the directed
graph, rather than performing lengthy molecular dynamics simulations.Comment: 15 pages, 12 figure
Understanding Hydrogen-Bond Patterns in Proteins using a Novel Statistical Model
Proteins are built from basic structural elements and their systematic characterization is of interest. Searching for recurring patterns in protein contact maps, we found several network motifs, patterns that occur more frequently in experimentally determined protein contact maps than in randomized contact maps with the same properties. Some of these network motifs correspond to sub-structures of alpha helices, including topologies not previously recognized in this context. Other motifs characterize beta-sheets, again some of which appear to be novel. This topological characterization of patterns serves as a tool to characterize proteins, and to reveal a high detailed differences map for comparing protein structures solved by X-ray crystallography, NMR and molecular dynamics (MD) simulations. Both NMR and MD show small but consistent differences from the crystal structures of the same proteins, possibly due to the pair-wise energy functions used. Network motifs analysis can serve as a base for many-body energy statistical energy potential, and suggests a dictionary of basic elements of which protein secondary structure is made
Solitonic State in Microscopic Dynamic Failures
Onset of permanent deformation in crystalline materials under a sharp
indenter tip is accompanied by nucleation and propagation of defects. By
measuring the spatio-temporal strain field nearthe indenter tip during
indentation tests, we demonstrate that the dynamic strain history at the moment
of a displacement burst carries characteristics of formation and interaction of
local excitations, or solitons. We show that dynamic propagation of multiple
solitons is followed by a short time interval where the propagating fronts can
accelerate suddenly. As a result of such abrupt local accelerations, duration
of the fast-slip phase of a failure event is shortened. Our results show that
formation and annihilation of solitons mediate the microscopic fast weakening
phase, during which extreme acceleration and collision of solitons lead to
non-Newtonian behavior and Lorentz contraction, i.e., shortening of solitons
characteristic length. The results open new horizons for understanding dynamic
material response during failure and, more generally, complexity of earthquake
sources
- …