No Arabic abstract
We study the space of all compact structures on a two-dimensional square lattice of size $N=6times6$. Each structure is mapped onto a vector in $N$-dimensions according to a hydrophobic model. Previous work has shown that the designabilities of structures are closely related to the distribution of the structure vectors in the $N$-dimensional space, with highly designable structures predominantly found in low density regions. We use principal component analysis to probe and characterize the distribution of structure vectors, and find a non-uniform density with a single peak. Interestingly, the principal axes of this peak are almost aligned with Fourier eigenvectors, and the corresponding Fourier eigenvalues go to zero continuously at the wave-number for alternating patterns ($q=pi$). These observations provide a stepping stone for an analytic description of the distribution of structural points, and open the possibility of estimating designabilities of realistic structures by simply Fourier transforming the hydrophobicities of the corresponding sequences.
When DNA molecules are heated they denature. This occurs locally so that loops of molten single DNA strands form, connected by intact double-stranded DNA pieces. The properties of this melting transition have been intensively investigated. Recently there has been a surge of interest in this question, caused by experiments determining the properties of partially bound DNA confined to nanochannels. But how does such confinement affect the melting transition? To answer this question we introduce, and solve a model predicting how confinement affects the melting transition for a simple model system by first disregarding the effect of self-avoidance. We find that the transition is smoother for narrower channels. By means of Monte-Carlo simulations we then show that a model incorporating self-avoidance shows qualitatively the same behaviour and that the effect of confinement is stronger than in the ideal case.
Advanced Monte Carlo simulations are used to study the effect of nano-slit confinement on metric and topological properties of model DNA chains. We consider both linear and circularised chains with contour lengths in the 1.2--4.8 $mu$m range and slits widths spanning continuously the 50--1250nm range. The metric scaling predicted by de Gennes blob model is shown to hold for both linear and circularised DNA up to the strongest levels of confinement. More notably, the topological properties of the circularised DNA molecules have two major differences compared to three-dimensional confinement. First, the overall knotting probability is non-monotonic for increasing confinement and can be largely enhanced or suppressed compared to the bulk case by simply varying the slit width. Secondly, the knot population consists of knots that are far simpler than for three-dimensional confinement. The results suggest that nano-slits could be used in nano-fluidic setups to produce DNA rings having simple topologies (including the unknot) or to separate heterogeneous ensembles of DNA rings by knot type.
Cytoskeletal motor proteins are involved in major intracellular transport processes which are vital for maintaining appropriate cellular function. The motor exhibits distinct states of motility: active motion along filaments, and effectively stationary phase in which it detaches from the filaments and performs passive diffusion in the vicinity of the detachment point due to cytoplasmic crowding. The transition rates between motion and pause phases are asymmetric in general, and considerably affected by changes in environmental conditions which influences the efficiency of cargo delivery to specific targets. By considering the motion of molecular motor on a single filament as well as a dynamic filamentous network, we present an analytical model for the dynamics of self-propelled particles which undergo frequent pause phases. The interplay between motor processivity, structural properties of filamentous network, and transition rates between the two states of motility drastically changes the dynamics: multiple transitions between different types of anomalous diffusive dynamics occur and the crossover time to the asymptotic diffusive or ballistic motion varies by several orders of magnitude. We map out the phase diagrams in the space of transition rates, and address the role of initial conditions of motion on the resulting dynamics.
A number of recently discovered protein structures incorporate a rather unexpected structural feature: a knot in the polypeptide backbone. These knots are extremely rare, but their occurrence is likely connected to protein function in as yet unexplored fashion. Our analysis of the complete Protein Data Bank reveals several new knots which, along with previously discovered ones, can shed light on such connections. In particular, we identify the most complex knot discovered to date in human ubiquitin hydrolase, and suggest that its entangled topology protects it against unfolding and degradation by the proteasome. Knots in proteins are typically preserved across species and sometimes even across kingdoms. However, we also identify a knot which only appears in some transcarbamylases while being absent in homologous proteins of similar structure. The emergence of the knot is accompanied by a shift in the enzymatic function of the protein. We suggest that the simple insertion of a short DNA fragment into the gene may suffice to turn an unknotted into a knotted structure in this protein.
We study by Small Angle Neutron Scattering (SANS) the structure of Hyaluronan -Lysozyme complexes. Hyaluronan (HA) is a polysaccharide of 9 nm intrinsic persistence length that bears one negative charge per disaccharide monomer (Mmol = 401.3 g/mol); two molecular weights, Mw = 6000 and 500 000 Da were used. The pH was adjusted at 4.7 and 7.4 so that lysozyme has a global charge of +10 and + 8 respectively. The lysozyme concentration was varied from 3 to 40 g/L, at constant HA concentration (10 g/L). At low protein concentration, samples are monophasic and SANS experiments reveal only fluctuations of concentration although, at high protein concentration, clusters are observed by SANS in the dense phase of the diphasic samples. In between, close to the onset of the phase separation, a distinct original scattering is observed. It is characteristic of a rod-like shape, which could characterize single complexes involving one or a few polymer chains. For the large molecular weight (500 000) the rodlike rigid domains extend to much larger length scale than the persistence length of the HA chain alone in solution and the range of the SANS investigation. They can be described as a necklace of proteins attached along a backbone of diameter one or a few HA chains. For the short chains (Mw ~ 6000), the rod length of the complexes is close to the chain contour length (~ 15 nm).