Molecular rigidity and enthalpy-entropy compensation in DNA melting

Understanding Relaxation in the Kob-Andersen Liquid Based on Entropy, String, Shoving, Localization, and Parabolic Models

We assess the validity of a range of models of glass formation based on molecular dynamics simulation results of the Kob-Andersen (KA) model system under a wide range of constant volume and constant pressure conditions. These models include the Adam-Gibbs model emphasizing configurational entropy, the string model emphasizing collective particle exchange motion, the shoving model emphasizing material elasticity, the localization model emphasizing dynamical free volume, and parabolic models based on the ideas of dynamic facilitation and, alternatively, the hypothesis that glass formation involves an avoided critical point. We demonstrate that these seemingly disparate models all provide a reasonable description of structural relaxation and diffusion data for the KA model system under all simulation conditions considered. Hence, the present study points to some unity in our understanding of the relationship between leading models of glass formation, supporting inferences drawn from previous studies of polymeric glass-forming liquids.

Methodical evaluation of Boyle temperatures using Mayer sampling Monte Carlo with application to polymers in implicit solvent

The Boyle temperature, TB, for an n-segment polymer in solution is the temperature where the second osmotic virial coefficient, A2, is zero. This characteristic is of interest for its connection to the polymer condensation critical temperature, particularly for n → ∞. TB can be measured experimentally or computed for a given model macromolecule. For the latter, we present and examine two approaches, both based on the Mayer-sampling Monte Carlo (MSMC) method, to calculate Boyle temperatures as a function of model parameters. In one approach, we use MSMC calculations to search for TB, as guided by the evaluation of temperature derivatives of A2. The second approach involves numerical integration of an ordinary differential equation describing how TB varies with a model parameter, starting from a known TB. Unlike general MSMC calculations, these adaptations are appealing because they neither invoke a reference for the calculation nor use special averages needed to avoid bias when computing A2 directly. We demonstrate these methods by computing TB lines for off-lattice linear Lennard-Jones polymers as a function of chain stiffness, considering chains of length n ranging from 2 to 512 monomers. We additionally perform calculations of single-molecule radius of gyration Rg and determine the temperatures Tθ, where linear scaling of Rg2 with n is observed, as if the polymers were long random-walk chains. We find that Tθ and TB seem to differ by 6% in the n → ∞ limit, which is beyond the statistical uncertainties of our computational methodology. However, we cannot rule out systematic error relating to our extrapolation procedure as being the source of this discrepancy.

Mechanical response of double-stranded DNA: Bend, twist, and overwind

We employed all-atom molecular dynamics simulations to explore the mechanical response of bending, twisting, and overwinding for double-stranded DNA (dsDNA). We analyzed the bending and twisting deformations, as well as their stiffnesses, using the tilt, roll, and twist modes under stretching force. Findings indicate that the roll and twist angles vary linearly with the stretching force but show opposite trends. The tilt, roll, and twist elastic moduli are considered constants, while the coupling between roll and twist modes slightly decreases under stretching force. The effect of the stretching force on the roll and twist modes, including both their deformations and elasticities, exhibits sequence-dependence, with symmetry around the base pair step. Furthermore, we examined the overwinding path and mechanism of dsDNA from the perspective of the stiffness matrix, based on the tilt, roll, and twist modes. The correlations among tilt, roll, and twist angles imply an alternative overwinding pathway via twist-roll coupling when dsDNA is stretched, wherein entropic contribution prevails.

Influence of temperature on bend, twist and twist-bend coupling of dsDNA

The temperature-dependent bend and twist elasticities of dsDNA, as well as their couplings, were explored through all-atom molecular dynamics simulations. Three rotational parameters, tilt, roll, and twist, were employed to assess the bend and twist elasticities through their stiffness matrix. Our analysis indicates that the bend and twist stiffnesses decrease as the temperature rises, primarily owing to entropic influences stemming from thermodynamic fluctuations. Furthermore, the couplings between these rotational parameters also exhibit a decline with increasing temperature, although the roll-twist coupling displays greater strength than the tilt-roll and tilt-twist couplings, attributed to its more robust correction component. We elucidated the influence of temperature on bend and twist elasticities based on the comparisons between various models and existing data.

Photoacid-macroion assemblies: how photo-excitation switches the size of nano-objects

Electrostatic self-assembly of photoacids with oppositely charged macroions yields supramolecular nano-objects in aqueous solutions, whose size is controlled through light irradiation. Nano-assemblies are formed due to electrostatic attractions and mutual hydrogen bonding of the photoacids. Irradiation with UV light leads to the deprotonation of the photoacid and, consequently, a change in particle size. Overall, the hydrodynamic radii of the well-defined photoacid-macroion nano-objects lie between 130 and 370 nm. For a set of photoacids, we determine the acidity constants in the ground and excited state, discuss the sizes of photoacid-macroion nano-objects (by dynamic and static light scattering), their composition and the particle shapes (by small-angle neutron scattering), and relate their charge characteristics to size, structure and shape. We investigate the association thermodynamics and relate nanoscale structures to thermodynamics and, in turn, thermodynamics to molecular features, particularly the ionization energy of the photoacid hydroxyl group proton. Structure-directing effects completely differ from those for previously investigated systems, with hydrogen bonding and entropic effects playing a major role herein. This combined approach allows developing a comprehensive understanding of assembly formation and photo-response, anchored in molecular parameters (pKa, ionization energy, substituent group location), charge characteristics, and the association enthalpy and entropy. This fundamental understanding again paves the way for tailoring application solutions with novel photoresponsive materials.

Molecular Dynamics Simulation of the Influence of Temperature and Salt on the Dynamic Hydration Layer in a Model Polyzwitterionic Polymer PAEDAPS

We investigate the hydration of poly(3-[2-(acrylamido) ethyldimethylammonio] propanesulfonate) over a range of temperatures in pure water and with the inclusion of 0.1 mol/L NaCl using atomistic molecular dynamics simulation. Drawing on concepts drawn from the field of glass-forming liquids, we use the Debye-Waller parameter () for describing the water mobility gradient around the polybetaine backbone extending to an overall distance ≈18 Å. The water mobility in this layer is defined through the mean-square water molecule displacement at a time on the order of water's β-relaxation time. The brushlike topology of polybetaines leads to two regions in the dynamic hydration layer. The inner region of ≈10.5 Å is explored by pendant group conformational motions, and the outer region of ≈7.5 Å represents an extended layer of reduced water mobility relative to bulk water. The dynamic hydration layer extends far beyond the static hydration layer, adjacent to the polymer.

Designing Multimodal ON-OFF Nanoswitches of DNA-Functionalized Nanoparticles by Stimuli-Responsive Polymers

It is a challenging task to realize highly reversible ON-OFF nanoswitches over a wide range of temperatures, which emerge as a versatile toolbox for use in nanobiotechnology. Herein, nanoparticles (NPs) bifunctionalized by DNA strands and stimuli-responsive polymers are proposed to construct multimodal ON-OFF nanoswitches by the coarse-grained model. The successful achievement of multimodal ON-OFF nanoswitches for bifunctionalized NPs at lower temperatures is attributed to the synergistic effects of the contraction and expansion configurations of stimuli-responsive polymers, combined with the hybridization-dehybridization event of DNA strands. Importantly, our simulations isolate the conditions of programmable self-assembly of bifunctionalized NPs to realize the multimodal ON-OFF nanoswitches by the changes of temperature and chain rigidity. In addition, it is found that the bifunctionalized NPs in the ON state display anisotropic and patchy features due to an introduction of stimuli-responsive polymers. Our simulation results provide fundamental insights on qualitative predictions of ON/OFF states of DNA-based NPs, which can aid in realizing a set of ON-OFF nanoswitches by the rational design of functionalization molecules.

The Nature of the Enthalpy-Entropy Compensation and "Exotic" Arrhenius Parameters in the Denaturation Kinetics of Proteins

Protein unfolding is a ubiquitous process responsible for the loss of protein functionality (denaturation), which, in turn, can be accompanied by the death of cells and organisms. The nature of enthalpy-entropy compensation (EEC) in the kinetics of protein unfolding is a subject of debate. In order to investigate the nature of EEC, the "completely loose" transition state (TS) model has been applied to calculate the Arrhenius parameters for the unfolding of polyglycine dimers as a model process. The calculated Arrhenius parameters increase with increasing dimer length and demonstrate enthalpy-entropy compensation. It is shown that EEC results from the linear correlations of enthalpy and entropy of activation with dimer length, which are derived directly from the properties of the transition state. It is shown that EEC in solvated (hydrated, etc.) proteins is a direct consequence of EEC in proteins themselves. The suggested model allows us also to reproduce and explain "exotic" very high values of the pre-exponential factor measured for the proteins unfolding, which are drastically higher than those known for unimolecular reactions of organic molecules. A similar approach can be applied to analyzing the nature of EEC phenomena observed in other areas of chemistry.

Solution properties of spherical gold nanoparticles with grafted DNA chains from simulation and theory

There has been a rapidly growing interest in the use of functionalized Au nanoparticles (NPs) as platforms in multiple applications in medicine and manufacturing. The sensing and targeting characteristics of these NPs, and the realization of precisely organized structures in manufacturing applications using such NPs, depend on the control of their surface functionalization. NP functionalization typically takes the form of polymer grafted layers, and a detailed knowledge of the chemical and structural properties of these layers is required to molecularly engineer the particle characteristics for specific applications. However, the prediction and experimental determination of these properties to enable the rational engineering of these particles is a persistent problem in the development of this class of materials. To address this situation, molecular dynamic simulations were performed based on a previously established coarse-grained single-stranded DNA (ssDNA) model to determine basic solution properties of model ssDNA-grafted NP-layers under a wide range of conditions. In particular, we emphasize the calculation of the hydrodynamic radius for ssDNA-grafted Au NPs as a function of structural parameters such as ssDNA length, NP core size, and surface coverage. We also numerically estimate the radius of gyration and the intrinsic viscosity of these NPs, which in combination with hydrodynamic radius estimates, provide valuable information about the fluctuating structure of the grafted polymer layers. We may then understand the origin of the commonly reported variation in effective NP "size" by different measurement methods, and then exploit this information in connection to material design and characterization in connection with the ever-growing number of applications utilizing polymer-grafted NPs.

DNA Bending Force Facilitates Z-DNA Formation under Physiological Salt Conditions

Z-DNA, a noncanonical helical structure of double-stranded DNA (dsDNA), plays pivotal roles in various biological processes, including transcription regulation. Mechanical stresses on dsDNA, such as twisting and stretching, help to form Z-DNA. However, the effect of DNA bending, one of the most common dsDNA deformations, on Z-DNA formation is utterly unknown. Here, we show that DNA bending induces the formation of Z-DNA, that is, more Z-DNA is formed as the bending force becomes stronger. We regulated the bending force on dsDNA by using D-shaped DNA nanostructures. The B-Z transition was observed by single-molecule fluorescence resonance energy transfer. We found that as the bending force became stronger, Z-DNA was formed at lower Mg²⁺ concentrations. When dsDNA contained cytosine methylations, the B-Z transition occurred at 78 mM Mg²⁺ (midpoint) in the absence of the bending force. However, the B-Z transition occurred at a 28-fold lower Mg²⁺ concentration (2.8 mM) in the presence of the bending force. Monte Carlo simulation suggested that the B-Z transition stabilizes the bent form via the formation of the B-Z junction with base extrusion, which effectively releases the bending stress on DNA. Our results clearly show that the bending force facilitates the B-Z transition under physiological salt conditions.

Thermodynamics of Point Defects in Solids and Relation with the Bulk Properties: Recent Results

For several decades, the crucial question has arisen as to whether there exists any direct interconnection between the thermodynamic parameters of point defects in solids with the bulk properties of the solid under investigation. To answer this important question, an interrelation of the defect Gibbs energy gi in solids with bulk properties has been proposed almost half a century ago. Considering that gi corresponds to an isobaric and isothermal process, this interrelation states that, for different processes (defect formation, self-diffusion activation, and heterodiffusion), gi is proportional to the isothermal bulk modulus B and the mean volume per atom Ω, termed cBΩ model. Here, we review several challenging applications of this interrelation that appeared during the last decade (2011–2021), including high pressure diamond anvil measurements, high Tc superconductors, nuclear fuels, and materials for micro-electronics devices, applications of usefulness in Geophysics and Seismology, a problem of major technological interest, search for compositions of better target properties in Cu-Co-Si alloys via machine learning as well as two independent studies on the physical origin of this interrelation that has been further strengthened during the last few years.

Melting of confined DNA: static and dynamic properties

We study dsDNA (double strand DNA) melting in detail within varying strip-like confinement in a two-dimensional lattice model. The interplay between reduced configurational entropy and attractive base-pairing energy results in a non-monotonic melting profile of DNA. Structural transitions associated with confined DNA melting reveal a stretched or extended state for very strong confinement. By using the exact enumeration method, we investigate the emergence of a local denatured zone e.g. bubbles during DNA melting. The survival time of a single bubble within varying strip width is studied from the Fokker-Planck formalism by considering the bubble size as a reaction co-ordinate. We show that a simple lattice model can capture the sequence heterogeneity effect on DNA melting and bubble dynamics within the strip. Different time scales of bubble zipping for different DNA sequences are found, which may have potential applications in denaturation mapping.

Influence of network defects on the conformational structure of nanogel particles: From "closed compact" to "open fractal" nanogel particles

We propose an approach to generate a wide range of randomly branched polymeric structures to gain general insights into how polymer topology encodes a configurational structure in solution. Nanogel particles can take forms ranging from relatively symmetric sponge-like compact structures to relatively anisotropic open fractal structures observed in some nanogel clusters and in some self-associating polymers in solutions, such as aggrecan solutions under physiologically relevant conditions. We hypothesize that this broad "spectrum" of branched polymer structures derives from the degree of regularity of bonding in the network defining these structures. Accordingly, we systematically introduce bonding defects in an initially perfect network having a lattice structure in three and two topological dimensions corresponding to "sponge" and "sheet" structures, respectively. The introduction of bonding defects causes these "closed" and relatively compact nanogel particles to transform near a well-defined bond percolation threshold into "open" fractal objects with the inherent anisotropy of randomly branched polymers. Moreover, with increasing network decimation, the network structure of these polymers acquires other configurational properties similar to those of randomly branched polymers. In particular, the mass scaling of the radius of gyration and its eigenvalues, as well as hydrodynamic radius, intrinsic viscosity, and form factor for scattering, all undergo abrupt changes that accompany these topological transitions. Our findings support the idea that randomly branched polymers can be considered to be equivalent to perforated sheets from a "universality class" standpoint. We utilize our model to gain insight into scattering measurements made on aggrecan solutions.

The initiation of shear band formation in deformed metallic glasses from soft localized domains

It has long been thought that shear band (SB) formation in amorphous solids initiates from relatively "soft" regions in the material in which large-scale non-affine deformations become localized. The test of this hypothesis requires an effective means of identifying "soft" regions and their evolution as the material is deformed to varying degrees, where the metric of "softness" must also account for the effect of temperature on local material stiffness. We show that the mean square atomic displacement on a caging timescale ⟨u²⟩, the "Debye-Waller factor," provides a useful method for estimating the shear modulus of the entire material and, by extension, the material stiffness at an atomic scale. Based on this "softness" metrology, we observe that SB formation indeed occurs through the strain-induced formation of localized soft regions in our deformed metallic glass free-standing films. Unexpectedly, the critical strain condition for SB formation occurs when the softness (⟨u²⟩) distribution within the emerging soft regions approaches that of the interfacial region in its undeformed state, initiating an instability with similarities to the transition to turbulence. Correspondingly, no SBs arise when the material is so thin that the entire material can be approximately described as being "interfacial" in nature. We also quantify relaxation in the glass and the nature and origin of highly non-Gaussian particle displacements in the dynamically heterogeneous SB regions at times longer than the caging time.

Activation free energy gradient controls interfacial mobility gradient in thin polymer films

We examine the mobility gradient in the interfacial region of substrate-supported polymer films using molecular dynamics simulations and interpret these gradients within the string model of glass-formation. No large gradients in the extent of collective motion exist in these simulated films, and an analysis of the mobility gradient on a layer-by-layer basis indicates that the string model provides a quantitative description of the relaxation time gradient. Consequently, the string model indicates that the interfacial mobility gradient derives mainly from a gradient in the high-temperature activation enthalpy ΔH₀ and entropy ΔS₀ as a function of depth z, an effect that exists even in the high-temperature Arrhenius relaxation regime far above the glass transition temperature. To gain insight into the interfacial mobility gradient, we examined various material properties suggested previously to influence ΔH₀ in condensed materials, including density, potential and cohesive energy density, and a local measure of stiffness or u²(z)^-3/2, where u²(z) is the average mean squared particle displacement at a caging time (on the order of a ps). We find that changes in local stiffness best correlate with changes in ΔH₀(z) and that ΔS₀(z) also contributes significantly to the interfacial mobility gradient, so it must not be neglected.

Comparison of Huggins Coefficients and Osmotic Second Virial Coefficients of Buffered Solutions of Monoclonal Antibodies

The Huggins coefficient kH is a well-known metric for quantifying the increase in solution viscosity arising from intermolecular interactions in relatively dilute macromolecular solutions, and there has been much interest in this solution property in connection with developing improved antibody therapeutics. While numerous kH measurements have been reported for select monoclonal antibodies (mAbs) solutions, there has been limited study of kH in terms of the fundamental molecular interactions that determine this property. In this paper, we compare measurements of the osmotic second virial coefficient B22, a common metric of intermolecular and interparticle interaction strength, to measurements of kH for model antibody solutions. This comparison is motivated by the seminal work of Russel for hard sphere particles having a short-range "sticky" interparticle interaction, and we also compare our data with known results for uncharged flexible polymers having variable excluded volume interactions because proteins are polypeptide chains. Our observations indicate that neither the adhesive hard sphere model, a common colloidal model of globular proteins, nor the familiar uncharged flexible polymer model, an excellent model of intrinsically disordered proteins, describes the dependence of kH of these antibodies on B22. Clearly, an improved understanding of protein and ion solvation by water as well as dipole-dipole and charge-dipole effects is required to understand the significance of kH from the standpoint of fundamental protein-protein interactions. Despite shortcomings in our theoretical understanding of kH for antibody solutions, this quantity provides a useful practical measure of the strength of interprotein interactions at elevated protein concentrations that is of direct significance for the development of antibody formulations that minimize the solution viscosity.

Lattice theory for binding of linear polymers to a solid substrate from polymer melts: I. Influence of chain connectivity on molecular binding and adsorption

Most theories of the binding of molecules to surfaces or for the association between molecules treat the binding species as structureless entities and neglect their rigidity and the changes in their stiffness induced by the binding process. The binding species are also taken to be "ideal," meaning that the existence of van der Waals interactions and changes in these interactions upon molecular binding are also neglected. An understanding of the thermodynamics of these multifunctional molecular binding processes has recently come into focus in the context of the molecular binding of complex molecules, such as dendrimers and DNA grafted nanoparticles, to surfaces where the degree of binding cooperativity and selectivity, as well as the location of the binding transition, are found to be sensitive to the number of binding units constrained to a larger scale polymeric scaffold. We address the fundamental problem of molecular binding by extending classical Langmuir theory to describe the particular example of the reversible binding of semiflexible polymer chains to a solid substrate under melt conditions. The polymer chains are assumed to have a variable number N of binding units (segments) and to exhibit variable bending energies and van der Waals interactions in the bulk and on the surface, in addition to strong directional interactions with the surface. The resulting generalized Langmuir theory is applied to the examination of the influence of the chain connectivity of ideal polymers on the surface coverage Θ, transition binding temperature T_1/2 at which Θ = 1/2, and on the derivative |dΘ/dT|_T=T1/2 and the constant volume specific heat of binding, C_v ^bind, measures of the cooperativity and "sharpness" of the binding transition, respectively. Paper II is devoted to the impact of the van der Waals attractive interactions and chain stiffness on the reversible binding of nonideal polymer chains to a solid surface, including the enthalpy-entropy compensation phenomenon observed experimentally in many molecular and particle binding processes.

Lattice theory for binding of linear polymers to a solid substrate from polymer melts. II. Influence of van der Waals interactions and chain semiflexibility on molecular binding and adsorption

The polymeric Langmuir theory, developed in Paper I [J. Dudowicz et al., J. Chem. Phys. 151, 124706 (2019)], is employed to investigate the influence of van der Waals interactions and chain rigidity on the thermodynamics of the reversible molecular binding to interfaces in one component polymer fluids (polymer melts). Both van der Waals interactions and chain stiffness are found to influence the temperature variation of the surface coverage Θ, the binding transition itself, and the cooperativity of molecular binding. Re-entrancy of the surface coverage Θ(T) is found to arise when the intermolecular interactions are sufficiently attractive to cause a liquid-vapor like phase separation in the interfacial region, a phenomenon that can occur in the binding of both small molecules and polymer chains to surfaces.

Influence of knot complexity on glass-formation in low molecular mass ring polymer melts

We perform molecular dynamics simulations on a coarse-grained polymer melt to study the dynamics of glass-formation in ring polymer melts of variable knot complexity. After generating melts of non-concatenated polymeric rings having a range of minimum crossing number values, mc, we compute the coherent intermediate scattering function, the segmental α-relaxation time, fragility, and the glass transition temperature as a function of mc. Variation of knot complexity is found to have a pronounced effect on the dynamics of polymer melts since both molecular rigidity and packing are altered, primary physical factors governing glass-formation in polymeric materials.

Lattice theory of competitive binding: Influence of van der Waals interactions on molecular binding and adsorption to a solid substrate from binary liquid mixtures

The reversible binding of molecules to surfaces is one of the most fundamental processes in condensed fluids, with obvious applications in the molecular separation of materials, chromatographic characterization, and material processing. Motivated in particular by the ubiquitous occurrence of binding processes in molecular biology and self-assembly, we have developed a lattice type theory of competitive molecular binding to solid substrates from binary mixtures of two small molecule liquids that interact between themselves by van der Waals forces in addition to exhibiting binding interactions with the solid surface. The derived theory, in contrast to previously existing theoretical frameworks, enables us to investigate the influence of van der Waals interactions on interfacial binding and selective molecular adsorption. For reference, the classic Langmuir theory of adsorption is recovered when all van der Waals interaction energies between the molecules in the bulk liquid phase and those on the surface are formally set to zero. Illustrative calculations are performed for the binding of molecules to a solid surface from pure liquids and from their binary mixtures. The properties analyzed include the surface coverage θ, the binding transition temperature T_bind, the individual surface coverages, θ_A and θ_C, and the relative surface coverages, σ_AC≡θ_A/θ_C or σ_CA≡θ_C/θ_A. The latter two quantities coincide with the degrees of adsorption directly determined from experimental adsorption measurements. The Langmuir theory is shown to apply formally under a wide range of conditions where the original enthalpies (Δh or Δh_A and Δh_C) and entropies (Δs or Δs_A and Δs_C) of the binding reactions are simply replaced by their respective "effective" counterparts (Δh_eff or Δh_A^eff and Δh_C^eff and Δs_eff or Δs_A^eff and Δs_C^eff), whose values depend on the strength of der Waals interactions and of the "bare" free energy parameters (Δh or Δh_A and Δh_C, and Δs or Δs_A and Δs_C). Numerous instances of entropy-enthalpy compensation between these effective free energy parameters follow from our calculations, confirming previous reports on this phenomenon obtained from experimental studies of molecular binding processes in solution.

Fiber Network Formation in Semi-Flexible Polymer Solutions: An Exploratory Computational Study

The formation of gels through the bundling of semi-flexible polymer chains into fiber networks is ubiquitous in diverse manufactured and natural materials, and, accordingly, we perform exploratory molecular dynamics simulations of a coarse-grained model of semi-flexible polymers in a solution with attractive lateral interchain interactions to understand essential features of this type of gel formation. After showing that our model gives rise to fibrous gels resembling real gels of this kind, we investigate how the extent of fiber bundling influences the "melting" temperature, T m , and the emergent rigidification of model bundled fibers having a fixed number of chains, N, within them. Based on our preliminary observations, we suggest the fiber size is kinetically selected by a reduced thermodynamic driving force and a slowing of the dynamics within the fibers associated with their progressive rigidification with the inclusion of an increasing number of chains in the bundle.