34 research outputs found
Statistical Mechanics of a Cat's Cradle
It is believed that, much like a cat's cradle, the cytoskeleton can be
thought of as a network of strings under tension. We show that both regular and
random bond-disordered networks having bonds that buckle upon compression
exhibit a variety of phase transitions as a function of temperature and
extension. The results of self-consistent phonon calculations for the regular
networks agree very well with computer simulations at finite temperature. The
analytic theory also yields a rigidity onset (mechanical percolation) and the
fraction of extended bonds for random networks. There is very good agreement
with the simulations by Delaney et al. (Europhys. Lett. 2005). The mean field
theory reveals a nontranslationally invariant phase with self-generated
heterogeneity of tautness, representing ``antiferroelasticity''.Comment: 4 pages, 4 figure
The Interplay of Nonlinearity and Architecture in Equilibrium Cytoskeletal Mechanics
The interplay between cytoskeletal architecture and the nonlinearity of the
interactions due to bucklable filaments plays a key role in modulating the
cell's mechanical stability and affecting its structural rearrangements. We
study a model of cytoskeletal structure treating it as an amorphous network of
hard centers rigidly cross-linked by nonlinear elastic strings, neglecting the
effects of motorization. Using simulations along with a self-consistent phonon
method, we show that this minimal model exhibits diverse thermodynamically
stable mechanical phases that depend on excluded volume, crosslink
concentration, filament length and stiffness. Within the framework set by the
free energy functional formulation and making use of the random first order
transition theory of structural glasses, we further estimate the characteristic
densities for a kinetic glass transition to occur in this model system. Network
connectivity strongly modulates the transition boundaries between various
equilibrium phases, as well as the kinetic glass transition density.Comment: 17 pages, 18 figure
A coarse-grained model for synergistic action of multiple enzymes on cellulose
Background
Degradation of cellulose to glucose requires the cooperative action of three classes of enzymes, collectively known as cellulases. Endoglucanases randomly bind to cellulose surfaces and generate new chain ends by hydrolyzing β-1,4-D-glycosidic bonds. Exoglucanases bind to free chain ends and hydrolyze glycosidic bonds in a processive manner releasing cellobiose units. Then, β-glucosidases hydrolyze soluble cellobiose to glucose. Optimal synergistic action of these enzymes is essential for efficient digestion of cellulose. Experiments show that as hydrolysis proceeds and the cellulose substrate becomes more heterogeneous, the overall degradation slows down. As catalysis occurs on the surface of crystalline cellulose, several factors affect the overall hydrolysis. Therefore, spatial models of cellulose degradation must capture effects such as enzyme crowding and surface heterogeneity, which have been shown to lead to a reduction in hydrolysis rates. Results
We present a coarse-grained stochastic model for capturing the key events associated with the enzymatic degradation of cellulose at the mesoscopic level. This functional model accounts for the mobility and action of a single cellulase enzyme as well as the synergy of multiple endo- and exo-cellulases on a cellulose surface. The quantitative description of cellulose degradation is calculated on a spatial model by including free and bound states of both endo- and exo-cellulases with explicit reactive surface terms (e.g., hydrogen bond breaking, covalent bond cleavages) and corresponding reaction rates. The dynamical evolution of the system is simulated by including physical interactions between cellulases and cellulose. Conclusions
Our coarse-grained model reproduces the qualitative behavior of endoglucanases and exoglucanases by accounting for the spatial heterogeneity of the cellulose surface as well as other spatial factors such as enzyme crowding. Importantly, it captures the endo-exo synergism of cellulase enzyme cocktails. This model constitutes a critical step towards testing hypotheses and understanding approaches for maximizing synergy and substrate properties with a goal of cost effective enzymatic hydrolysis
Recurrent Signature Patterns in HIV-1 B Clade Envelope Glycoproteins Associated with either Early or Chronic Infections
Here we have identified HIV-1 B clade Envelope (Env) amino acid signatures from early in infection that may be favored at transmission, as well as patterns of recurrent mutation in chronic infection that may reflect common pathways of immune evasion. To accomplish this, we compared thousands of sequences derived by single genome amplification from several hundred individuals that were sampled either early in infection or were chronically infected. Samples were divided at the outset into hypothesis-forming and validation sets, and we used phylogenetically corrected statistical strategies to identify signatures, systematically scanning all of Env. Signatures included single amino acids, glycosylation motifs, and multi-site patterns based on functional or structural groupings of amino acids. We identified signatures near the CCR5 co-receptor-binding region, near the CD4 binding site, and in the signal peptide and cytoplasmic domain, which may influence Env expression and processing. Two signatures patterns associated with transmission were particularly interesting. The first was the most statistically robust signature, located in position 12 in the signal peptide. The second was the loss of an N-linked glycosylation site at positions 413–415; the presence of this site has been recently found to be associated with escape from potent and broad neutralizing antibodies, consistent with enabling a common pathway for immune escape during chronic infection. Its recurrent loss in early infection suggests it may impact fitness at the time of transmission or during early viral expansion. The signature patterns we identified implicate Env expression levels in selection at viral transmission or in early expansion, and suggest that immune evasion patterns that recur in many individuals during chronic infection when antibodies are present can be selected against when the infection is being established prior to the adaptive immune response
Bending stiff charged polymers: The electrostatic persistence length
Many charged polymers, including nucleic acids, are locally stiff. Their bending rigidity —quantified by the persistence length— depends crucially on Coulombic features, such as the ionic strength of the solution which offers a convenient experimental route for tuning the rigidity. While the classic Odijk-Skolnick-Fixman treatment fails for realistic parameter values, we derive a simple analytical formula for the electrostatic persistence length. It is shown to be in remarkable agreement with numerically obtained Poisson-Boltzmann theory results, thereby fully accounting for non-linearities, among which counter-ion condensation effects. Specified to double-stranded DNA, our work reveals that the widely used bare persistence length of 500 Å is overestimated by some 20%
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Statistical mechanics of a cat's cradle
It is believed that, much like a cat's cradle, the cytoskeleton can be thought of as a network of strings under tension. We show that both regular and random bond-disordered networks having bonds that buckle upon compression exhibit a variety of phase transitions as a function of temperature and extension. The results of self-consistent phonon calculations for the regular networks agree very well with computer simulations at finite temperature. The analytic theory also yields a rigidity onset ( mechanical percolation) and the fraction of extended bonds for random networks. There is very good agreement with the simulations by Delaney et al ( 2005 Europhys. Lett. 72 990). The mean field theory reveals a nontranslationally invariant phase with self-generated heterogeneity of tautness, representing 'antiferroelasticity'