The entropic cost of polymer confinement

Hierarchical single-crystal-to-single-crystal transformations of a monomer to a 1D-polymer and then to a 2D-polymer

Designing and synthesizing flawless two-dimensional polymers (2D-Ps) via meticulous molecular preorganization presents an intriguing yet challenging frontier in research. We report here the single-crystal-to-single-crystal (SCSC) synthesis of a 2D-P via thermally induced topochemical azide-alkyne cycloaddition (TAAC) reaction. A designed monomer incorporating two azide and two alkyne units is synthesized. The azide and alkyne groups are preorganized in the monomer crystal in reactive geometries for polymerizations in two orthogonal directions. On heating, the polymerizations proceed in a hierarchical manner; at first, the monomer reacts regiospecifically in a SCSC fashion to form a 1,5-triazolyl-linked 1D polymer (1D-P), which upon further heating undergoes another SCSC polymerization to a 2D-P through a second regiospecific TAAC reaction forming 1,4-triazolyl-linkages. Two different linkages in orthogonal directions make this an architecturally attractive 2D-P, as determined, at atomic resolution, by single-crystal X-ray diffraction. The 2D-P reported here is thermally stable in view of the robust triazole-linkages and can be exfoliated as 2D-sheets.

B-Cell Epitope Prediction for Antipeptide Paratopes with the HAPTIC2/HEPTAD User Toolkit (HUT)

B-cell epitope prediction is key to developing peptide-based vaccines and immunodiagnostics along with antibodies for prophylactic, therapeutic and/or diagnostic use. This entails estimating paratope binding affinity for variable-length peptidic sequences subject to constraints on both paratope accessibility and antigen conformational flexibility, as described herein for the HAPTIC2/HEPTAD User Toolkit (HUT). HUT comprises the Heuristic Affinity Prediction Tool for Immune Complexes 2 (HAPTIC2), the HAPTIC2-like Epitope Prediction Tool for Antigen with Disulfide (HEPTAD) and the HAPTIC2/HEPTAD Input Preprocessor (HIP). HIP enables tagging of residues (e.g., in hydrophobic blobs, ordered regions and glycosylation motifs) for exclusion from downstream analyses by HAPTIC2 and HEPTAD. HAPTIC2 estimates paratope binding affinity for disulfide-free disordered peptidic antigens (by analogy between flexible-ligand docking and protein folding), from terms attributed to compaction (in view of sequence length, charge and temperature-dependent polyproline-II helical propensity), collapse (disfavored by residue bulkiness) and contact (with glycine and proline regarded as polar residues that hydrogen bond with paratopes). HEPTAD analyzes antigen sequences that each contain two cysteine residues for which the impact of disulfide pairing is estimated as a correction to the free-energy penalty of compaction. All of HUT is freely accessible online ( https://freeshell.de/~badong/hut.htm ).

Into the dynamics of rotaxanes at atomistic resolution

Mechanically-interlocked molecules (MIMs) are at the basis of artificial molecular machines and are attracting increasing interest for various applications, from catalysis to drug delivery and nanoelectronics. MIMs are composed of mechanically-interconnected molecular sub-parts that can move with respect to each other, imparting these systems innately dynamical behaviors and interesting stimuli-responsive properties. The rational design of MIMs with desired functionalities requires studying their dynamics at sub-molecular resolution and on relevant timescales, which is challenging experimentally and computationally. Here, we combine molecular dynamics and metadynamics simulations to reconstruct the thermodynamics and kinetics of different types of MIMs at atomistic resolution under different conditions. As representative case studies, we use rotaxanes and molecular shuttles substantially differing in structure, architecture, and dynamical behavior. Our computational approach provides results in agreement with the available experimental evidence and a direct demonstration of the critical effect of the solvent on the dynamics of the MIMs. At the same time, our simulations unveil key factors controlling the dynamics of these systems, providing submolecular-level insights into the mechanisms and kinetics of shuttling. Reconstruction of the free-energy profiles from the simulations reveals details of the conformations of macrocycles on the binding site that are difficult to access via routine experiments and precious for understanding the MIMs' behavior, while their decomposition in enthalpic and entropic contributions unveils the mechanisms and key transitions ruling the intermolecular movements between metastable states within them. The computational framework presented herein is flexible and can be used, in principle, to study a variety of mechanically-interlocked systems.

Pressure of Linear and Ring Polymers Confined in a Cavity

Nanoscale confinement of polymers in a cavity is central to a variety of biological and nanotechnology processes. Using the discrete WLC model we simulate the compression of flexible and semiflexible polymers of linear and ring topology in a closed cavity. Simulation reveals that polymer pressure inside the cavity increases with the chain stiffness but is practically unaffected by the chain topology. For flexible polymers, the computed dependence of pressure on the cavity size and polymer concentration is consistent with the scaling behavior expected for bulk polymers in a good solvent. However, the scaling behavior of semiflexible polymers is only in partial agreement with the theory prediction, with discrepancies arising from a continuous transition between regimes in chains of moderate lengths. The computed segment density profiles endorse the propensity of semiflexible polymers to concentrate beneath the cavity surface and thus elevate the pressure. The compaction of polymers by compression into the disordered globule or growing toroidal structure is documented.

Confinement free energy for a polymer chain: Corrections to scaling

Spatial confinement of a polymer chain results in a reduction of conformational entropy. For confinement of a flexible N-mer chain in a planar slit or cylindrical pore (confining dimension D), a blob model analysis predicts the asymptotic scaling behavior ΔF/N ∼ D^-γ with γ ≈ 1.70, where ΔF is the free energy increase due to confinement. Here, we extend this scaling analysis to include the variation of local monomer density upon confinement giving ΔF/N ∼ D^-γ(1 - h(N, D)), where the correction-to-scaling term has the form h ∼ D^y/N^Δ with exponents y = 3 - γ ≈ 1.30 and Δ = 3/γ - 1 ≈ 0.76. To test these scaling predictions, we carry out Wang-Landau simulations of confined and unconfined tangent-hard-sphere chains (bead diameter σ) in the presence of a square-well trapping potential. The fully trapped chain provides a common reference state, allowing for an absolute determination of the confinement free energy. Our simulation results for 32 ≤ N ≤ 1024 and 3 ≤ D/σ ≤ 14 are well-described by the extended scaling relation giving exponents of γ = 1.69(1), y = 1.25(2), and Δ = 0.75(6).

Prediction of Variable-Length B-Cell Epitopes for Antipeptide Paratopes Using the Program HAPTIC

BACKGROUND

B-cell epitope prediction for antipeptide antibody responses enables peptide-based vaccine design and related translational applications. This entails estimating epitopeparatope binding free-energy changes from antigen sequence; but attempts to do so assuming uniform epitope length (e.g., of hexapeptide sequences, each spanning a typical paratope diameter when fully extended) have neglected empirically established variation in epitope length.

OBJECTIVE

This work aimed to develop a sequence-based physicochemical approach to variablelength B-cell epitope prediction for antipeptide paratopes recognizing flexibly disordered targets.

METHODS

Said approach was developed by analogy between epitope-paratope binding and protein folding modeled as polymer collapse, treating paratope structure implicitly. Epitope-paratope binding was thus conceptually resolved into processes of epitope compaction, collapse and contact, with epitope collapse presenting the main entropic barrier limiting epitope length among nonpolyproline sequences. The resulting algorithm was implemented as a computer program, namely the Heuristic Affinity Prediction Tool for Immune Complexes (HAPTIC), which is freely accessible via an online interface (http://badong.freeshell.org/haptic.htm). This was used in conjunction with published data on representative known peptide immunogens.

RESULTS

HAPTIC predicted immunodominant epitope sequences with lengths limited by penalties for both compaction and collapse, consistent with known paratope-bound structures of flexibly disordered epitopes. In most cases, the predicted association constant was greater than its experimentally determined counterpart but below the predicted upper bound for affinity maturation in vivo.

CONCLUSION

HAPTIC provides a physicochemically plausible means for estimating the affinity of antipeptide paratopes for sterically accessible and flexibly disordered peptidic antigen sequences by explicitly considering candidate B-cell epitopes of variable length.

Modulation of DNA conformation in electrolytic nanodroplets

The behavior of deoxyribonucleic acid (DNA) molecules in confinement is of profound importance in various bioengineering and medical applications. In the present study, all-atom molecular dynamics simulation is utilized to investigate the transition of the double-strand DNA (dsDNA) conformation in the electrolytic nanodroplet. Three typical conformations, i.e., C-shaped, folded S-shaped, and double C-shaped, are observed for different droplet sizes and ionic concentrations. To reveal the physics underlying this phenomenon, the characteristics of the dsDNA molecules, such as the overcharging intensity, the end-to-end distance, the radius of gyration, etc. are analyzed in detail based on the numerical results. It is found that the transition can be ascribed to the buckling of the polymer molecules under the compression due to the confinement of the nanodroplet, and it can be modulated by the ionic concentration in the electrolyte. Generally, nanoscale confinement dominates dsDNA behavior over the electrostatic effects in smaller nanodroplets, while the latter becomes more important for larger nanodroplets. This competition results in the persistence length increasing with the nanodroplet radii. Based on these discussions, a non-dimensional elasto-capillary number μ is proposed to classify the dsDNA conformations into three regions.

A Rotavirus Virus-Like Particle Confined Palladium Nanoreactor and Its Immobilization on Graphene Oxide for Catalysis

Abstract

In this work, a new viral protein cage based nanoreactor was successfully constructed via encapsulating Tween 80 stabilized palladium nanoparticles (NPs) into rotavirus capsid VP2 virus-like particles (i.e. Pd@VP2). The effects of stabilizers including CTAB, SDS, Tween 80 and PVP on controlling the particle size of Pd NPs were investigated. They were further immobilized on graphene oxide (i.e. Pd@VP2/GO) by a simple mixing method. Some characterizations including FT-IR and XPS were conducted to study adsorption mode of Pd@VP2 on GO sheets. Their catalytic performance was estimated in the reduction of 4-nitrophenol (4-NP). Results showed that Tween 80 stabilized Pd NPs with the molar ratio of Pd to Tween 80 at 1:0.1 possessed the smallest size and the best stability as well. They were encapsulated into viral protein cages (mean size 49 ± 0.26 nm) to assemble confined nanoreactors, most of which contained 1-2 Pd NPs (mean size 8.15 ± 0.26 nm). As-prepared Pd@VP2 indicated an enhanced activity (apparent reaction rate constant k _app  = (3.74 ± 0.10) × 10^-3 s^-1) for the reduction of 4-NP in comparison to non-confined Pd-Tween80 colloid (k _app  = (2.20 ± 0.06) × 10^-3 s^-1). It was logically due to confinement effects of Pd@VP2 including high dispersion of Pd NPs and high effective concentration of substrates in confined space. Pd@VP2 were further immobilized on GO surface through C-N bond. Pd@VP2/GO exhibited good reusability after recycling for four runs, confirming the strong anchoring effects of GO on Pd@VP2.

Graphic Abstract

Efficient Separation of Nucleic Acids with Different Secondary Structures by Metal-Organic Frameworks

We report the use of metal-organic frameworks (MOFs) for the selective separation of nucleic acids (DNA and RNA) with different secondary structures through size, shape, length, and capability of conformational transition. Three MOFs with precisely controlled pore environments, Co-IRMOF-74-II, -III, and -IV, composed of Co²⁺ and organic linkers (II, III, and IV), respectively, were used for the inclusion of nucleic acid into their pores from the solution. This was proven to be a spontaneous process from disordered free state to restricted ordered state via circular dichroism (CD) spectroscopy. Three critical factors were identified for their inclusion: (1) size selection induced by steric hindrance, (2) conformation transition energy selection induced by stability, and (3) molecular weight selection. These selection rules were used to extract nucleic acids with flexible and unstable secondary structures from complex mixtures of multiple nucleic acids, leaving those with rigid and stable secondary structures in the mother liquor. This provides the possibility to separate and enrich nucleic acids in bulk through their different structure feature, which is highly desirable in genome-wide structural measurement of nucleic acids. Unlike methods that rely on specific binding antibodies or ligand, this MOF method is capable of selecting all kinds of nucleic acids with similar secondary structure features; therefore, it is suitable for the handling of a large variety and quantity of nucleic acids at the same time. This method also has the potential to gather information about the folding stability of biomolecules with secondary structures.

Separation Phenomena in Tailored Micro- and Nanofluidic Environments

Separations of bioanalytes require robust, effective, and selective migration phenomena. However, due to the complexity of biological matrices such as body fluids or tissue, these requirements are difficult to achieve. The separations field is thus constantly evolving to develop suitable methods to separate biomarkers and fractionate biospecimens for further interrogation of biomolecular content. Advances in the field of microfabrication allow the tailored generation of micro- and nanofluidic environments. These can be exploited to induce interactions and dynamics of biological species with the corresponding geometrical features, which in turn can be capitalized for novel separation approaches. This review provides an overview of several unique separation applications demonstrated in recent years in tailored micro- and nanofluidic environments. These include electrokinetic methods such as dielectrophoresis and electrophoresis, but also rather nonintuitive ratchet separation mechanisms, continuous flow separations, and fractionations such as deterministic lateral displacement, as well as methods employing entropic forces for separation.

DNA Conformational Changes Play a Force-Generating Role during Bacteriophage Genome Packaging

Motors that move DNA, or that move along DNA, play essential roles in DNA replication, transcription, recombination, and chromosome segregation. The mechanisms by which these DNA translocases operate remain largely unknown. Some double-stranded DNA (dsDNA) viruses use an ATP-dependent motor to drive DNA into preformed capsids. These include several human pathogens as well as dsDNA bacteriophages-viruses that infect bacteria. We previously proposed that DNA is not a passive substrate of bacteriophage packaging motors but is instead an active component of the machinery. We carried out computational studies on dsDNA in the channels of viral portal proteins, and they reveal DNA conformational changes consistent with that hypothesis. dsDNA becomes longer ("stretched") in regions of high negative electrostatic potential and shorter ("scrunched") in regions of high positive potential. These results suggest a mechanism that electrostatically couples the energy released by ATP hydrolysis to DNA translocation: The chemical cycle of ATP binding, hydrolysis, and product release drives a cycle of protein conformational changes. This produces changes in the electrostatic potential in the channel through the portal, and these drive cyclic changes in the length of dsDNA as the phosphate groups respond to the protein's electrostatic potential. The DNA motions are captured by a coordinated protein-DNA grip-and-release cycle to produce DNA translocation. In short, the ATPase, portal, and dsDNA work synergistically to promote genome packaging.

Density fields for branching, stiff networks in rigid confining regions

We develop a formalism to describe the equilibrium distributions for segments of confined branched networks consisting of stiff filaments. This is applicable to certain situations of cytoskeleton in cells, such as for example actin filaments with branching due to the Arp2/3 complex. We develop a grand ensemble formalism that enables the computation of segment density and polarisation profiles within the confines of the cell. This is expressed in terms of the solution to nonlinear integral equations for auxiliary functions. We find three specific classes of behaviour depending on filament length, degree of branching and the ratio of persistence length to the dimensions of the geometry. Our method allows a numerical approach for semi-flexible filaments that are networked.

Confinement-Induced Ordering and Self-Folding of Cellulose Nanofibrils

Cellulose is a pervasive polymer, displaying hierarchical lengthscales and exceptional strength and stiffness. Cellulose's complex organization, however, also hinders the detailed understanding of the assembly, mesoscopic properties, and structure of individual cellulose building blocks. This study combines nanolithography with atomic force microscopy to unveil the properties and structure of single cellulose nanofibrils under weak geometrical confinement. By statistical analysis of the fibril morphology, it emerges that confinement induces both orientational ordering and self-folding of the fibrils. Excluded volume simulations reveal that this effect does not arise from a fibril population bias applied by the confining slit, but rather that the fibril conformation itself changes under confinement, with self-folding favoring fibril's free volume entropy. Moreover, a nonstochastics angular bending probability of the fibril kinks is measured, ruling out alternating amorphous-crystalline regions. These findings push forward the understanding of cellulose nanofibrils and may inspire the design of functional materials based on fibrous templates.

The entropic force generated by intrinsically disordered segments tunes protein function

Protein structures are dynamic and can explore a large conformational landscape^1,2. Only some of these structural substates are important for protein function (such as ligand binding, catalysis and regulation)^3-5. How evolution shapes the structural ensemble to optimize a specific function is poorly understood^3,4. One of the constraints on the evolution of proteins is the stability of the folded 'native' state. Despite this, 44% of the human proteome contains intrinsically disordered peptide segments greater than 30 residues in length⁶, the majority of which have no known function^7-9. Here we show that the entropic force produced by an intrinsically disordered carboxy terminus (ID-tail) shifts the conformational ensemble of human UDP-α-D-glucose-6-dehydrogenase (UGDH) towards a substate with a high affinity for an allosteric inhibitor. The function of the ID-tail does not depend on its sequence or chemical composition. Instead, the affinity enhancement can be accurately predicted based on the length of the intrinsically disordered segment, and is consistent with the entropic force generated by an unstructured peptide attached to the protein surface^10-13. Our data show that the unfolded state of the ID-tail rectifies the dynamics and structure of UGDH to favour inhibitor binding. Because this entropic rectifier does not have any sequence or structural constraints, it is an easily acquired adaptation. This model implies that evolution selects for disordered segments to tune the energy landscape of proteins, which may explain the persistence of intrinsic disorder in the proteome.

Self-Avoiding Wormlike Chain Confined in a Cylindrical Tube: Scaling Behavior

Within a confining tube section, the multithreads of a strongly confined, backfolding polymer exert the excluded-volume repulsions on each other and produce physical properties that are very different from those of a confined ideal chain. The conformational properties of a such confined wormlike chain are of fundamental interest and are also practically useful in understanding the DNA confinement problems. Here, the excluded-volume effects are added to the standard wormlike-chain model by a self-consistent field theory. The numerical solutions are examined in light of their scaling properties.

Stretching and compression of DNA by external forces under nanochannel confinement

Mechanical deformation of dsDNA molecules inside square nanochannels is investigated using simulations based on a coarse-grained model of DNA. The combined action of confinement and weak external forces is explored in a variety of confinement regimes, including the transition zone relevant to nanofluidic experiments. The computed free energy and force profiles are markedly affected by the channel size. Effective elastic softening of confined DNA molecules relative to the bulk DNA is observed in the channels of intermediate widths. The extension of DNA from its bulk equilibrium length in nanofluidic devices is resolved into contributions from the passive extension due to confinement and from the active stretching induced by force. Potential implications of the very different energy costs computed for the two extension modes (extension by confinement takes much more free energy than stretching by force) for behavior of DNA in nanofluidic chips are indicated.

Evidence for the extended de Gennes regime of a semiflexible polymer in slit confinement

We use off-lattice, pruned-enriched Rosenbluth method (PERM) simulations to compute the confinement free energy of a real wormlike chain of effective width w and persistence length lp in a slit of height H. For slit heights much larger than the persistence length of the polymer and much smaller than the thermal blob size, the excess free energy of the confined chain is consistent with a modified version of the scaling theory for the extended de Gennes regime in a channel that reflects the blob statistics in slit confinement. Explicitly, for channel sizes [Formula: see text], the difference between the confinement free energy of the real chain and that of an ideal chain scales like w/H.

Conformational Properties of a Back-Folding Wormlike Chain Confined in a Cylindrical Tube

When a semiflexible chain is confined in a narrow cylindrical tube, the formation of a polymer hairpin is a geometrical conformation that accompanies an exponentially large local free energy and, hence, is a relatively rare event. Numerical solutions of the hairpin distribution functions for persistence-length-to-tube-radius ratios over a wide range are obtained in high precision, by using the Green's function approach for the wormlike-chain model. The crossover region between the narrow and moderately narrow tubes is critically investigated in terms of the hairpin free energy, global persistence length, mean hairpin-tip distance from the tube axis, and hairpin-plane orientational properties. Accurate representations of the solutions by simple interpolation formulae are suggested.

Scaling, crumpled wires, and genome packing in virions

The packing of a genome in virions is a topic of intense current interest in biology and biological physics. The area is dominated by allometric scaling relations that connect, e.g., the length of the encapsulated genome and the size of the corresponding virion capsid. Here we report scaling laws obtained from extensive experiments of packing of a macroscopic wire within rigid three-dimensional spherical and nonspherical cavities that can shed light on the details of the genome packing in virions. We show that these results obtained with crumpled wires are comparable to those from a large compilation of biological data from several classes of virions.

Role of tau in the spatial organization of axonal microtubules: keeping parallel microtubules evenly distributed despite macromolecular crowding

Opposing views have been proposed regarding the role of tau, the principal microtubule-associated protein in axons. On the one hand, tau forms cross-bridges at the interface between microtubules and induces microtubule bundling in neurons. On the other hand, tau is also considered a polymer brush which efficiently separates microtubules. In mature axons, microtubules are indeed arranged in parallel arrays and are well separated from each other. To reconcile these views, we developed a mechanistic model based on in vitro and cellular approaches combined to analytical and numerical analyses. The results indicate that tau forms long-range cross-bridges between microtubules under macromolecular crowding conditions. Tau cross-bridges prevent the redistribution of tau away from the interface between microtubules, which would have occurred in the polymer brush model. Consequently, the short-range attractive force between microtubules induced by macromolecular crowding is avoided and thus microtubules remain well separated from each other. Interestingly, in this unified model, tau diffusion on microtubules enables to keep microtubules evenly distributed in axonal sections at low tau levels.

Synthesis of semicrystalline nanocapsular structures obtained by Thermally Induced Phase Separation in nanoconfinement

Phase separation of a polymer solution exhibits a peculiar behavior when induced in a nanoconfinement. The energetic constraints introduce additional interactions between the polymer segments that reduce the number of available configurations. In our work, this effect is exploited in a one-step strategy called nanoconfined-Thermally Induced Phase Separation (nc-TIPS) to promote the crystallization of polymer chains into nanocapsular structures of controlled size and shell thickness. This is accomplished by performing a quench step of a low-concentrated PLLA-dioxane-water solution included in emulsions of mean droplet size <500 nm acting as nanodomains. The control of nanoconfinement conditions enables not only the production of nanocapsules with a minimum mean particle diameter of 70 nm but also the tunability of shell thickness and its crystallinity degree. The specific properties of the developed nanocapsular architectures have important implications on release mechanism and loading capability of hydrophilic and lipophilic payload compounds.

Computational virology: From the inside out

Viruses typically pack their genetic material within a protein capsid. Enveloped viruses also have an outer membrane made up of a lipid bilayer and membrane-spanning glycoproteins. X-ray diffraction and cryoelectron microscopy provide high resolution static views of viral structure. Molecular dynamics (MD) simulations may be used to provide dynamic insights into the structures of viruses and their components. There have been a number of simulations of viral capsids and (in some cases) of the inner core of RNA or DNA packaged within them. These simulations have generally focussed on the structural integrity and stability of the capsid and/or on the influence of the nucleic acid core on capsid stability. More recently there have been a number of simulation studies of enveloped viruses, including HIV-1, influenza A, and dengue virus. These have addressed the dynamic behaviour of the capsid, the matrix, and/or of the outer envelope. Analysis of the dynamics of the lipid bilayer components of the envelopes of influenza A and of dengue virus reveals a degree of biophysical robustness, which may contribute to the stability of virus particles in different environments. Significant computational challenges need to be addressed to aid simulation of complex viruses and their membranes, including the need to integrate structural data from a range of sources to enable us to move towards simulations of intact virions. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

DNA Scrunching in the Packaging of Viral Genomes

The motors that drive double-stranded DNA (dsDNA) genomes into viral capsids are among the strongest of all biological motors for which forces have been measured, but it is not known how they generate force. We previously proposed that the DNA is not a passive substrate but that it plays an active role in force generation. This "scrunchworm hypothesis" holds that the motor proteins repeatedly dehydrate and rehydrate the DNA, which then undergoes cyclic shortening and lengthening motions. These are captured by a coupled protein-DNA grip-and-release cycle to rectify the motion and translocate the DNA into the capsid. In this study, we examined the interactions of dsDNA with the dodecameric connector protein of bacteriophage ϕ29, using molecular dynamics simulations on four different DNA sequences, starting from two different conformations (A-DNA and B-DNA). In all four simulations starting with the protein equilibrated with A-DNA in the channel, we observed transitions to a common, metastable, highly scrunched conformation, designated A*. This conformation is very similar to one recently reported by Kumar and Grubmüller in much longer MD simulations on B-DNA docked into the ϕ29 connector. These results are significant for four reasons. First, the scrunched conformations occur spontaneously, without requiring lever-like protein motions often believed to be necessary for DNA translocation. Second, the transition takes place within the connector, providing the location of the putative "dehydrator". Third, the protein has more contacts with one strand of the DNA than with the other; the former was identified in single-molecule laser tweezer experiments as the "load-bearing strand". Finally, the spontaneity of the DNA-protein interaction suggests that it may play a role in the initial docking of DNA in motors like that of T4 that can load and package any sequence.

Thermal Destabilization of Collagen Matrix Hierarchical Structure by Freeze/Thaw

This study aims to characterize and understand the effects of freezing on collagen structures and functionality. Specifically, thermodynamic destabilization of collagen at molecular- and fibril-levels by combination of low temperatures and freezing were experimentally characterized using modulated differential scanning calorimetry. In order to delineate the effects of sub-zero temperature and water-ice phase change, we hypothesized that the extent of destabilization can be determined based on post-thaw heat induced thermal denaturation of collagen. It is found that thermal denaturation temperature of collagen in hydrogel decreases by 1.4–1.6°C after freeze/thaw while no such decrease is observed in the case of molecular solution. The destabilization is predominantly due to ice formation. Exposure to low temperatures in the absence of ice has only minimal effect. Calorimetry measurements combined with morphological examination of collagen matrices by scanning electron microscopy suggest that freezing results in destabilization of collagen fibrils due to expansion of intrafibrillar space by ice formation. This fibril-level damage can be alleviated by use of cryoprotectant DMSO at concentrations as low as 0.5 M. A theoretical model explaining the change in collagen post-thaw thermal stability by freezing-induced fibril expansion is also proposed.

Coexistence of coil and globule domains within a single confined DNA chain

The highly charged DNA chain may be either in an extended conformation, the coil, or condensed into a highly dense and ordered structure, the toroid. The transition, also called collapse of the chain, can be triggered in different ways, for example by changing the ionic conditions of the solution. We observe individual DNA molecules one by one, kept separated and confined inside a protein shell (the envelope of a bacterial virus, 80 nm in diameter). For subcritical concentrations of spermine (4+), part of the DNA is condensed and organized in a toroid and the other part of the chain remains uncondensed around. Two states coexist along the same DNA chain. These ‘hairy’ globules are imaged by cryo-electron microscopy. We describe the global conformation of the chain and the local ordering of DNA segments inside the toroid.

Confinement and partitioning of a single polymer chain in a dense array of nanoposts

We present a Brownian dynamics simulation study on the confinement and partitioning of a single, flexible polymer chain in a dense array of nanoposts with different sizes and separations, especially, when the volume of an interstitial space formed among four nanoposts is less than the volume of the polymer chain. As the interstitial volume decreases by either increasing the nanopost diameter or decreasing the separation between nanoposts, the chain conformation becomes elongated in the direction parallel to the nanoposts. Interestingly, however, the degree of chain elongation varies in a non-monotonic fashion as the interstitial volume decreases while keeping the passage width between two nanoposts constant at a small value. We calculate the free energy of chain partitioning over several interstitial spaces from the partitioning probability, and find that the non-monotonic dependence of the chain elongation results from an interplay between the confinement-driven chain elongation along the direction parallel to the nanoposts and the chain spreading perpendicular to the nanoposts by partitioning chain segments over several interstitial spaces. These results present the possibility of utilizing a dense array of nanoposts as a template to control polymer conformations.

Self-assembled phases of block copolymer blend thin films

The patterns formed by self-assembled thin films of blended cylindrical and lamellar polystyrene-b-poly(methyl methacrylate) block copolymers can be either a spatially uniform, single type of nanostructure or separate, coexisting regions of cylinders and lamellae, depending on fractional composition and molecular weight ratio of the blend constituents. In blends of block copolymers with different molecular weights, the morphology of the smaller molecular weight component more strongly dictates the resulting pattern. Although molecular scale chain mixing distorts microdomain characteristic length scales from those of the pure components, even coexisting morphologies exhibit the same domain spacing. We quantitatively account for the phase behavior of thin-film blends of cylinders and lamellae using a physical, thermodynamic model balancing the energy of chain distortions with the entropy of mixing.

Free energy of a long semiflexible polymer confined in a spherical cavity

The free energy and conformational properties of a wormlike chain confined inside a spherical surface are investigated. We show that in the weak-confinement limit, the wormlike chain model exactly reproduces the confinement properties of a Gaussian chain; in such a case the confinement entropy dominates the free energy; in the strong-confinement limit, the free energy is dominated by the bending energy of the chain, which is forced to wrap around the confining surface. We also present a numerical solution within the crossover region between the two limits, solving the differential equation that the probability distribution function satisfies.

Nonequilibrium dynamics and ultraslow relaxation of confined DNA during viral packaging

Many viruses use molecular motors that generate large forces to package DNA to near-crystalline densities inside preformed viral proheads. Besides being a key step in viral assembly, this process is of interest as a model for understanding the physics of charged polymers under tight 3D confinement. A large number of theoretical studies have modeled DNA packaging, and the nature of the molecular dynamics and the forces resisting the tight confinement is a subject of wide debate. Here, we directly measure the packaging of single DNA molecules in bacteriophage phi29 with optical tweezers. Using a new technique in which we stall the motor and restart it after increasing waiting periods, we show that the DNA undergoes nonequilibrium conformational dynamics during packaging. We show that the relaxation time of the confined DNA is >10 min, which is longer than the time to package the viral genome and 60,000 times longer than that of the unconfined DNA in solution. Thus, the confined DNA molecule becomes kinetically constrained on the timescale of packaging, exhibiting glassy dynamics, which slows the motor, causes significant heterogeneity in packaging rates of individual viruses, and explains the frequent pausing observed in DNA translocation. These results support several recent hypotheses proposed based on polymer dynamics simulations and show that packaging cannot be fully understood by quasistatic thermodynamic models.

Comment on the letter by A. Ben-Shaul: "entropy, energy, and bending of DNA in viral capsids"

The conformational entropic penalty associated with packaging double-stranded DNA into viral capsids remains an issue of contention. So far, models based on a continuum approximation for DNA have either left the question unexamined, or they have assumed that the entropic penalty is negligible, following an early analysis by Riemer and Bloomfield. In contrast, molecular-dynamics (MD) simulations using bead-and-spring models consistently show a large penalty. A recent letter from Ben-Shaul attempts to reconcile the differences. While the letter makes some valid points, the issue of how to include conformational entropy in the continuum models remains unresolved. In this Comment, I show that the free energy decomposition from continuum models could be brought into line with the decomposition from the MD simulations with two adjustments. First, the entropy from Flory-Huggins theory should be replaced by the estimate of the entropic penalty given in Ben-Shaul's letter, which corresponds closely to that from the MD simulations. Second, the DNA-DNA repulsions are well described by the empirical relationship given by the Cal Tech group, but the strength of these should be reduced by about half, using parameters based on the Rau-Parsegian experiments, rather than treating them as "fitting parameters (tuned) to fit the data from (single molecule pulling) experiments."

Entropy, energy, and bending of DNA in viral capsids

Inspired by novel single-molecule and bulk solution measurements, the physics underlying the forces and pressures involved in DNA packaging into bacteriophage capsids became the focus of numerous recent theoretical models. These fall into two general categories: Continuum-elastic theories (CT), and simulation studies-mostly of the molecular dynamics (MD) genre. Both types of models account for the dependence of the force, and hence the packaging free energy (ΔF), on the loaded DNA length, but differ markedly in interpreting their origin. While DNA confinement entropy is a dominant contribution to ΔF in the MD simulations, in the CT theories this role is fulfilled by interstrand repulsion, and there is no explicit entropy term. The goal of this letter is to resolve this apparent contradiction, elucidate the origin of the entropic term in the MD simulations, and point out its tacit presence in the CT treatments.