Sequence and Temperature Dependence of the End-to-End Collision Dynamics of Single-Stranded DNA

Intramolecular collision dynamics play an essential role in biomolecular folding and function and, increasingly, in the performance of biomimetic technologies. To date, however, the quantitative studies of dynamics of single-stranded nucleic acids have been limited. Thus motivated, here we investigate the sequence composition, chain-length, viscosity, and temperature dependencies of the end-to-end collision dynamics of single-stranded DNAs. We find that both the absolute collision rate and the temperature dependencies of these dynamics are base-composition dependent, suggesting that base stacking interactions are a significant contributor. For example, whereas the end-to-end collision dynamics of poly-thymine exhibit simple, linear Arrhenius behavior, the behavior of longer poly-adenine constructs is more complicated. Specifically, 20- and 25-adenine constructs exhibit biphasic temperature dependencies, with their temperature dependences becoming effectively indistinguishable from that of poly-thymine above 335 K for 20-adenines and 328 K for 25-adenines. The differing Arrhenius behaviors of poly-thymine and poly-adenine and the chain-length dependence of the temperature at which poly-adenine crosses over to behave like poly-thymine can be explained by a barrier friction mechanism in which, at low temperatures, the energy barrier for the local rearrangement of poly-adenine becomes the dominant contributor to its end-to-end collision dynamics.     

Human erythrocyte spectrin dimer intrinsic viscosity: temperature dependence and implications for the molecular basis of the erythrocyte membrane free energy

We have determined experimentally the temperature dependence of human erythrocyte spectrin dimer intrinsic viscosity at shear rates 8-12 s-1 using a Cartesian diver viscometer. We find that the intrinsic viscosity decreases from 43 +/- 3 ml/g at 4 degrees C to 34 +/- 3 ml/g when the temperature is increased to 38 degrees C. Our results show that spectrin dimers are flexible worm-like macromolecules with persistence length about 20 nm and that the mean square end-to-end distance for this worm-like macromolecules decreases when the temperature is increased. This implies that the spectrin dimer internal energy decreases when the end-to-end distance is increased and that the free energy increase associated with making the end-to-end distance longer than the equilibrium value for the free molecules is of entropic origin. The temperature dependence of the erythrocyte membrane shear modulus reported previously in the literature therefore appears mainly to be due to temperature dependent alterations in the membrane skeleton topology.     

Conformational Dynamics of Titin PEVK Explored with FRET Spectroscopy

The proline-, glutamate-, valine-, and lysine-rich (PEVK) domain of the giant muscle protein titin is thought to be an intrinsically unstructured random-coil segment. Various observations suggest, however, that the domain may not be completely devoid of internal interactions and structural features. To test the validity of random polymer models for PEVK, we determined the mean end-to-end distances of an 11- and a 21-residue synthetic PEVK peptide, calculated from the efficiency of the fluorescence resonance energy transfer (FRET) between an N-terminal intrinsic tryptophan donor and a synthetically added C-terminal IAEDANS acceptor obtained in steady-state and time-resolved experiments. We find that the contour-length scaling of mean end-to-end distance deviates from predictions of a purely statistical polymer chain. Furthermore, the addition of guanidine hydrochloride decreased, whereas the addition of salt increased the FRET efficiency, pointing at the disruption of structure-stabilizing interactions. Increasing temperature between 10 and 50°C increased the normalized FRET efficiency in both peptides but with different trajectories, indicating that their elasticity and conformational stability are different. Simulations suggest that whereas the short PEVK peptide displays an overall random structure, the long PEVK peptide retains residual, loose helical configurations. Transitions in the local structure and dynamics of the PEVK domain may play a role in the modulation of passive muscle mechanics.     

DNA translocation governed by interactions with solid-state nanopores

We investigate the voltage-driven translocation dynamics of individual DNA molecules through solid-state nanopores in the diameter range 2.7-5 nm. Our studies reveal an order of magnitude increase in the translocation times when the pore diameter is decreased from 5 to 2.7 nm, and steep temperature dependence, nearly threefold larger than would be expected if the dynamics were governed by viscous drag. As previously predicted for an interaction-dominated translocation process, we observe exponential voltage dependence on translocation times. Mean translocation times scale with DNA length by two power laws: for short DNA molecules, in the range 150-3500 bp, we find an exponent of 1.40, whereas for longer molecules, an exponent of 2.28 dominates. Surprisingly, we find a transition in the fraction of ion current blocked by DNA, from a length-independent regime for short DNA molecules to a regime where the longer the DNA, the more current is blocked. Temperature dependence studies reveal that for increasing DNA lengths, additional interactions are responsible for the slower DNA dynamics. Our results can be rationalized by considering DNA/pore interactions as the predominant factor determining DNA translocation dynamics in small pores. These interactions markedly slow down the translocation rate, enabling higher temporal resolution than observed with larger pores. These findings shed light on the transport properties of DNA in small pores, relevant for future nanopore applications, such as DNA sequencing and genotyping.     

Simulation of Polymer Solutions by Dissipative Particle Dynamics

Abstract

Dissipative Particle Dynamics (DPD) is employed to model the dynamics and rheology of polymer solutions, and suspensions of spherical particles with adsorbed polymers. Static and dynamic scaling relationships for the variation of radius of gyration and relaxation time with polymer chain length are reviewed, demonstrating that the DPD polymer solution model correctly represents the effects of hydrodynamic interaction and excluded volume. Rheological simulations for both polymer solutions and polymer-sphere suspensions predict Newtonian viscosities at low shear rate followed by shear-thinning behavior as a reduced shear rate of unity is approached. Both the Newtonian viscosity and the extent of shear-thinning are greatly enhanced in the case of good solvents, compared to the viscosity curves for polymers and polymer-spheres structures dissolved in theta solvents and poor solvents.     

The end-to-end distance of RNA as a randomly self-paired polymer

In this paper, we present the end-to-end distance of randomly self-paired polymers (RSPPs). We define a randomly self-paired polymer as a linear polymer each of whose monomers has a probability, f(0<f<1), of pairing with any other one monomer. The RSPP model is inspired by numerous observations that the ends of RNAs are in close proximity. We use this model to explain this proximity. The prediction made by the RSPP model is consistent with these observations. Mapping an RNA with a length of 1000 nucleotides and a pairing fraction of 0.6 onto our RSPP model, for example, we predict an expected end-to-end distance of about 14 unpaired bases. We have also found that the expected end-to-end distance of the RSPP scales roughly as the 1/4 power of its total length.     

Molecular basis for the effect of urea and guanidinium chloride on the dynamics of unfolded polypeptide chains

Chemical denaturants are frequently used to unfold proteins and to characterize mechanisms and transition states of protein folding reactions. The molecular basis of the effect of urea and guanidinium chloride (GdmCl) on polypeptide chains is still not well understood. Models for denaturant--protein interaction include both direct binding and indirect changes in solvent properties. Here we report studies on the effect of urea and GdmCl on the rate constants (k(c)) of end-to-end diffusion in unstructured poly(glycine-serine) chains of different length. Urea and GdmCl both lead to a linear decrease of lnk(c) with denaturant concentration, as observed for the rate constants for protein folding. This suggests that the effect of denaturants on chain dynamics significantly contributes to the denaturant-dependence of folding rate constants for small proteins. We show that this linear dependency is the result of two additive non-linear effects, namely increased solvent viscosity and denaturant binding. The contribution from denaturant binding can be quantitatively described by Schellman's weak binding model with binding constants (K) of 0.62(+/-0.01)M(-1) for GdmCl and 0.26(+/-0.01)M(-1) for urea. In our model peptides the number of binding sites and the effect of a bound denaturant molecule on chain dynamics is identical for urea and GdmCl. The results further identify the polypeptide backbone as the major denaturant binding site and give an upper limit of a few nanoseconds for residence times of denaturant molecules on the polypeptide chain.     

Mechanical properties ofChlorella cell walls as determined by the suspension method

The so-called suspension method was employed to measure the mechanical properties ofChlorella cell walls. This method worked well for the present sample. The ratio of compressibility of the cell wall to that of water was 0.62 at room temperature at frequencies of 1.5 and 2.0 MH_z. Temperature dependence of compressibility was similar to that of many polymer samples. A difference of compressibility was observed at two different stages of the cell cycle ofChlorella, but any difference of volume viscosity was not as obvious. The more extensive the enlargement growth of the cell, the larger was the compressibility. The existence of a relaxation mechanism in the order of microseconds was postulated from measurements of the frequency dependence of the attenuation of sound waves.     

Structural analysis of telechelic polymer solution using dissipative particle dynamics simulations

A telechelic polymer is an amphiphilic polymer that can form micellar structures when dissolved in water. A telechelic polymer solution shows viscoelastic behaviour owing to the formation of characteristic networks, i.e. loops, bridges and dangling chains. For industrial purposes, telechelic polymers have many applications as thickening agents, such as in paints and cosmetics. Thus, it is desirable to predict and control the rheological properties of telechelic polymers. However, detailed studies at the molecular level have not yet been performed. In this study, I use the dissipative particle dynamics (DPD) method to investigate the relationship between the characteristic structural properties and the molecular structure in telechelic polymer solutions. I show that the morphology of telechelic polymer solutions depends on the concentration and chain length, the distribution of the end-to-end distance, the mean square end-to-end distance, the mean square radius of gyration and the time-averaged mean square displacement. Although an effect of entanglement is important for properties of polymer melts, the polymer chain composed of DPD particles cannot reproduce it. Therefore, I compare telechelic polymer solutions with and without the segmental repulsive potential (SRP), which can simulate the effect of entanglement in DPD simulations. The results indicate that it is necessary to include the SRP in DPD simulations to correctly analyse the behaviour of telechelic polymer solutions.     

Hydrogen-Bond Driven Loop-Closure Kinetics in Unfolded Polypeptide Chains

Characterization of the length dependence of end-to-end loop-closure kinetics in unfolded polypeptide chains provides an understanding of early steps in protein folding. Here, loop-closure in poly-glycine-serine peptides is investigated by combining single-molecule fluorescence spectroscopy with molecular dynamics simulation. For chains containing more than 10 peptide bonds loop-closing rate constants on the 20–100 nanosecond time range exhibit a power-law length dependence. However, this scaling breaks down for shorter peptides, which exhibit slower kinetics arising from a perturbation induced by the dye reporter system used in the experimental setup. The loop-closure kinetics in the longer peptides is found to be determined by the formation of intra-peptide hydrogen bonds and transient β-sheet structure, that accelerate the search for contacts among residues distant in sequence relative to the case of a polypeptide chain in which hydrogen bonds cannot form. Hydrogen-bond-driven polypeptide-chain collapse in unfolded peptides under physiological conditions found here is not only consistent with hierarchical models of protein folding, that highlights the importance of secondary structure formation early in the folding process, but is also shown to speed up the search for productive folding events.     

Persistence of structured populations in random environments

Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.     

An experimental study of GFP-based FRET, with application to intrinsically unstructured proteins

We have experimentally studied the fluorescence resonance energy transfer (FRET) between green fluorescent protein (GFP) molecules by inserting folded or intrinsically unstructured proteins between CyPet and Ypet. We discovered that most of the enhanced FRET signal previously reported for this pair was due to enhanced dimerization, so we engineered a monomerizing mutation into each. An insert containing a single fibronectin type III domain (3.7 nm end-to-end) gave a moderate FRET signal while a two-domain insert (7.0 nm) gave no FRET. We then tested unstructured proteins of various lengths, including the charged-plus-PQ domain of ZipA, the tail domain of alpha-adducin, and the C-terminal tail domain of FtsZ. The structures of these FRET constructs were also studied by electron microscopy and sedimentation. A 12 amino acid linker and the N-terminal 33 amino acids of the charged domain of the ZipA gave strong FRET signals. The C-terminal 33 amino acids of the PQ domain of the ZipA and several unstructured proteins with 66-68 amino acids gave moderate FRET signals. The 150 amino acid charged-plus-PQ construct gave a barely detectable FRET signal. FRET efficiency was calculated from the decreased donor emission to estimate the distance between donor and acceptor. The donor-acceptor distance varied for unstructured inserts of the same length, suggesting that they had variable stiffness (persistence length). We conclude that GFP-based FRET can be useful for studying intrinsically unstructured proteins, and we present a range of calibrated protein inserts to experimentally determine the distances that can be studied.     

Solution properties of viilian, the exopolysaccharide from Lactococcus lactis subsp. cremoris SBT 0495

The exopolysaccharide (EPS) "viilian" was isolated from a large-batch fermentation of Lactococcus lactis subsp. cremoris SBT 0495. After applying a newly developed purification procedure, pure viilian with a weight-averaged molar mass of 2.64 x 10(3) kg/mol was obtained in a yield of 0.6 g/L culture broth. The native EPS, as well as lower molar mass fractions obtained by sonication of the native polymer, were studied by capillary viscometry and size-exclusion chromatography (SEC) coupled to multiangle laser light scattering detection (MALLS). From the viscosity data at various ionic strengths, we extracted a Mark-Houwink-Kuhn-Sakurada exponent a = 0.79, and a Smidsrod B value of 0.03. By application of the Hearst, Bohdanecky, and Odijk models for stiff polymer coils, in connection to the experimental viscosity data, we established the characteristic ratio to be C(infinity) = 44 and the intrinsic persistence length q(0) = 11.5 nm. The rms radii of gyration predicted from each of the models were in good agreement with the experimental radii (e.g., (1/2)(w) = 162 nm for native viilian in 0.2M NaNO(3)), as determined by SEC-MALLS. In addition, the Odijk model predicts correct ionic strength-linear charge density dependence of the rms radius of gyration. From the combined viscosity and SEC-MALLS experiments we concluded that, in dilute aqueous solutions, viilian behaves as an intermediately stiff, random coil polyelectrolyte system.Copyright 2000 John Wiley & Sons, Inc.     

Quantification of the spatial aspect of chaotic dynamics in biological and chemical systems

The need to study spatio-temporal chaos in a spatially extended dynamical system which exhibits not only irregular, initial-value sensitive temporal behavior but also the formation of irregular spatial patterns, has increasingly been recognized in biological science. While the temporal aspect of chaotic dynamics is usually characterized by the dominant Lyapunov exponent, the spatial aspect can be quantified by the correlation length. In this paper, using the diffusion-reaction model of population dynamics and considering the conditions of the system stability with respect to small heterogeneous perturbations, we derive an analytical formula for an ‘intrinsic length’ which appears to be in a very good agreement with the value of the correlation length of the system. Using this formula and numerical simulations, we analyze the dependence of the correlation length on the system parameters. We show that our findings may lead to a new understanding of some well-known experimental and field data as well as affect the choice of an adequate model of chaotic dynamics in biological and chemical systems.     

DNA condensation by TmHU studied by optical tweezers,AFM and molecular dynamics simulations

The compaction of DNA by the HU protein from Thermotoga maritima (TmHU) is analysed on a single-molecule level by the usage of an optical tweezers-assisted force clamp. The condensation reaction is investigated at forces between 2 and 40 pN applied to the ends of the DNA as well as in dependence on the TmHU concentration. At 2 and 5 pN, the DNA compaction down to 30% of the initial end-to-end distance takes place in two regimes. Increasing the force changes the progression of the reaction until almost nothing is observed at 40 pN. Based on the results of steered molecular dynamics simulations, the first regime of the length reduction is assigned to a primary level of DNA compaction by TmHU. The second one is supposed to correspond to the formation of higher levels of structural organisation. These findings are supported by results obtained by atomic force microscopy.     

Direct demonstration of actin filament annealing in vitro

Direct electron microscopic examination confirms that short actin filaments rapidly anneal end-to-end in vitro, leading over time to an increase in filament length at steady state. During annealing of mixtures of native unlabeled filaments and glutaraldehyde-fixed filaments labeled with myosin subfragment-1, the structural polarity within heteropolymers is conserved absolutely. Annealing does not appear to require either ATP hydrolysis or the presence of exogenous actin monomers, suggesting that joining occurs through the direct association of filament ends. During recovery from sonication the initial rate of annealing is consistent with a second-order reaction involving the collision of two filament ends with an apparent annealing rate constant of 10(7) M-1s-1. This rapid phase lasts less than 10 s and is followed by a slow phase lasting minutes to hours. Annealing is calculated to contribute minimally to filament elongation during the initial stages of self-assembly. However, the rapid rate of annealing of sonicated fixed filaments observed in vitro suggests that it may be an efficient mechanism for repairing breaks in filaments and that annealing together with polymer-severing mechanisms may contribute significantly to the dynamics and function of actin filaments in vivo.     

Molecular dynamics studies of polyethylene oxide and polyethylene glycol: hydrodynamic radius and shape anisotropy

A revision (C35r) to the CHARMM ether force field is shown to reproduce experimentally observed conformational populations of dimethoxyethane. Molecular dynamics simulations of 9, 18, 27, and 36-mers of polyethylene oxide (PEO) and 27-mers of polyethylene glycol (PEG) in water based on C35r yield a persistence length λ = 3.7 Å, in quantitative agreement with experimentally obtained values of 3.7 Å for PEO and 3.8 Å for PEG; agreement with experimental values for hydrodynamic radii of comparably sized PEG is also excellent. The exponent υ relating the radius of gyration and molecular weight of PEO from the simulations equals 0.515 ± 0.023, consistent with experimental observations that low molecular weight PEG behaves as an ideal chain. The shape anisotropy of hydrated PEO is 2.59:1.44:1.00. The dimension of the middle length for each of the polymers nearly equals the hydrodynamic radius R_h obtained from diffusion measurements in solution. This explains the correspondence of R_h and R_p, the pore radius of membrane channels: a polymer such as PEG diffuses with its long axis parallel to the membrane channel, and passes through the channel without substantial distortion.     

Dissipative particle dynamics simulation on the properties of the oil/water/surfactant system in the absence and presence of polymer

Dissipative particle dynamics is used to simulate the oil/water/surfactant system in the absence and presence of polymer. Structural properties, interfacial properties, and their dependence on the surfactant concentration, polymer concentration and oil/water ratio were investigated. The snapshots illustrate the variation of the structure of oil/water/surfactant system. In the presence of polymer, the interface is supersaturated at a lower surfactant concentration. The end-to-end distance increases with surfactant concentration and polymer chains but shows weak dependence on the oil/water ratio. The peak of density grows higher with surfactant concentration, but it is not affected by oil/water ratio. The density profiles of polymer grow higher with polymer chains, indicating that most of the polymer chains stay at the interface for stability. Interfacial thickness shows an adsorption of polymer/surfactant complexes at the interface, where the polymer is in an extended conformation at the interface. The formation of polymer/surfactant complexes is favourable for the decrease of oil/water interfacial tension.     

Encapsulation of a polymer by an icosahedral virus

The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated with encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.