Crowding induced self-assembly and enthalpy-entropy compensation

Universalized and robust length separation of carbon and boron nitride nanotubes with improved polymer depletion-based fractionation

Partitioning nanoparticles by shape and dimension is paramount for advancing nanomaterial standardization, fundamental colloidal investigations, and technologies such as biosensing and digital electronics. Length-separation methods for single-walled carbon nanotubes (SWCNTs) have historically incurred trade-offs in precision and mass throughput, and boron nitride nanotubes (BNNTs) are a rapidly emerging material analogue. We extend and detail a polymer precipitation-based method to fractionate populations of either nanotube type at significant mass scale for four distinct nanotube sources of increasing average diameter (0.7 nm to >2 nm). Such separations result in a supernant phase containing shorter nanotubes and a pellet phase containing the longer nanotubes, with the threshold length for depletion decreasing with increasing polymer concentration. Cross-comparison through analytical ultracentrifugation, spectroscopy, and microscopy versus applied polymer concentration show tailorable and precise length fractionation for 100 nm through >1 μm rod lengths, with fractionation also designable to remove non-nanotube impurities. The threshold length of depletion is further found to increase for decreasing nanotube diameter at fixed polymer concentration, a finding consistent with scaling attributable to nanotube radial excluded volume. The capabilities demonstrated herein promise to significantly advance nanotube implementation within the scientific community.

Wettability-modulated behavior of polymers under varying degrees of nano-confinement

Extreme confinement in nanochannels results in unconventional equilibrium and flow behavior of polymers. The underlying flow physics dictating such paradigms remains far from being understood and more so if the confining substrate is composed of two-dimensional materials, such as graphene. In this study, we conducted systematic molecular dynamics simulations to explore the effect of wettability, confinement, and chain length on polymer flow through graphene-like nanochannels. Altering the wetting properties of these membranes that structurally represent graphene results in substantial changes in the behavior of polymers of disparate chain lengths. Longer hydrocarbon chains (n-dodecane) exhibit negligible wettability-dependent structuring in narrower nanochannels compared to shorter chains (n-hexane) culminating in higher average velocities and interfacial slippage of n-dodecane under less wettable conditions. We demonstrate that the wettability compensation comes from chain entanglement attributed to entropic factors. This study reveals a delicate balance between wettability-dependent enthalpy and chain-length-dependent entropy, resulting in a unique nanoscale flow paradigm, thus not only having far-reaching implications in the superior discernment of polymeric flow in sub-micrometer regimes but also potentially revolutionizing various applications in the oil industry, including innovative oil transport, oil extraction, ion transport polymers, and separation membranes.

Influence of Nonspecific Interactions on Protein Associations: Implications for Biochemistry In Vivo

The cellular interior is composed of a variety of microenvironments defined by distinct local compositions and composition-dependent intermolecular interactions. We review the various types of nonspecific interactions between proteins and between proteins and other macromolecules and supramolecular structures that influence the state of association and functional properties of a given protein existing within a particular microenvironment at a particular point in time. The present state of knowledge is summarized, and suggestions for fruitful directions of research are offered. Expected final online publication date for the Annual Review of Biochemistry, Volume 91 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Thermodynamics and ordering kinetics in asymmetric PS-b-PMMA block copolymer thin films

The ordering kinetics of standing cylinder-forming polystyrene-block-poly(methyl methacrylate) block copolymers (molecular weight: 39 kg mol^-1) close to the order-disorder transition is experimentally investigated following the temporal evolution of the correlation length at different annealing temperatures. The growth exponent of the grain-coarsening process is determined to be 1/2, signature of a curvature-driven ordering mechanism. The measured activation enthalpy and the resulting Meyer-Neldel temperature for this specific copolymer along with the data already known for PS-b-PMMA block copolymers in strong segregation limit allow investigation of the interplay between the ordering kinetics and the thermodynamic driving force during the grain coarsening. These findings unveil various phenomena concomitantly occurring during the thermally activated ordering kinetics at segmental, single chain, and collective levels.

A comparative study of semi-flexible linear and ring polymer conformational change in an anisotropic environment

We adopt a Langevin-dynamics based simulation to systematically study the conformational change of a semi-flexible probed polymer in a rod crowding environment. Two topologically different probed polymer types, linear and ring polymers, are specifically considered. Our results unravel the significance of the interplay of probed polymer's semi-flexibility and crowding anisotropy. Firstly, both ring and linear polymers show a non-trivial dimensional change including nonmonotonicity and collapse-swelling crossover as their stiffness increases. Secondly, we modulate rod crowder length to investigate the anisotropic effect. We reveal that the formation of an ordered parallel arrangement of the environment can effectively lead to a remarkable stretching effect on the probed polymer. The coupling between the crowding anisotropy-induced stretching and the polymer stiffness can account for the unusual swelling behavior. Lastly, nonmonotonic swelling and shape change of the ring polymer are analyzed. We find out that the ring polymer is subject to most pronounced swelling at robust stiffness. Moreover, the maximum prolate shape is also observed at the same robust location.

Clusterization of self-propelled particles in a two-component system

We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated.

Confinement and Crowding Effects on Folding of a Multidomain Y-Family DNA Polymerase

Proteins in vivo endure highly various interactions from the luxuriant surrounding macromolecular cosolutes. Confinement and macromolecular crowding are the two major effects that should be considered while comparing the results of protein dynamics from in vitro to in vivo. However, efforts have been largely focused on single domain protein folding up to now, and the quantifications of the in vivo effects in terms of confinements and crowders on modulating the structure and dynamics as well as the physical understanding of the underlying mechanisms on multidomain protein folding are still challenging. Here we developed a topology-based model to investigate folding of a multidomain Y-family DNA polymerase (DPO4) within spherical confined space and in the presence of repulsive and attractive crowders. We uncovered that the entropic component of the thermodynamic driving force led by confinements and repulsive crowders increases the stability of folded states relative to the folding intermediates and unfolded states, while the enthalpic component of the thermodynamic driving force led by attractive crowders gives rise to the opposite effects with less stability. We found that the shapes of DPO4 conformations influenced by the confinements and the crowders are quite different even when only the entropic component of the thermodynamic driving force is considered. We uncovered that under all in vivo conditions, the folding cooperativity of DPO4 decreases compared to that in bulk. We showed that the loss of folding cooperativity can promote the sequential domain-wise folding, which was widely found in cotranslational multidomain protein folding, and effectively prohibit the backtracking led by topological frustrations during multidomain protein folding processes.

Revealing the dynamics and energetics of interaction of a cationic biological photosensitizer within a bile salt aggregate

The present investigation reports a detailed characterization of the interaction of a cationic photosensitizer, phenosafranin (PSF) with sodium deoxycholate (NaDC) bile salt aggregates based on spectroscopic and calorimetric techniques. Our explicit spectroscopic results not only establish the occurrence of PSF-NaDC binding interaction, but also reveal marked lowering of micropolarity at the interaction site (E_T(30) = 55.97 kcal mol^-1 in the presence of NaDC as compared to E_T(30) = 63.1 kcal mol^-1 in bulk aqueous buffer). A thorough mathematical analysis of the fluorescence depolarization results based on the two-step and wobbling in cone model yields critical insight into the complex rotational relaxation dynamics of the bound drug. The impartation of motional restriction on the PSF molecules within the bile salt aggregates is evidenced from enhancement of average rotational correlation time from <τ_r> = 136 ps in aqueous buffer to 1.11 ns with added NaDC (8.0 mM). This is further supported from a high value of the generalized order parameter (S = 0.81) as well as the diffusion coefficient (D_w = 1.40 × 10¹² s^-1). Furthermore, our extensive calorimetric investigation unveils the complicated thermodynamics of the interaction process in terms of predominant entropic contribution over the enthalpic part in the lower temperature regime (TΔS = 18.84 ± 1.13 kJ mol^-1, ΔH = -5.82 ± 0.35 kJ mol^-1 at 288 K) with subsequent reversal of the relative contributions with increasing temperature (TΔS = 7.54 ± 0.39 kJ mol^-1, ΔH = - 17.09 ± 0.90 kJ mol^-1 at 318 K). The instrumental role of the hydrophobic effect underlying the PSF-NaDC interaction is characterized by a negative heat capacity change (ΔC_p = -364 J mol^-1 K^-1). An intriguing thermodynamic feature in terms of enthalpy-entropy compensation (with increasing temperature ΔG remains almost constant while ΔH and TΔS vary significantly) aptly corroborates the aforesaid argument and establishes an appreciable hydrophobic contribution to the overall binding energies.

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.

Measuring and Manipulating the Adhesion of Graphene

We present a technique to precisely measure the surface energies between two-dimensional materials and substrates that is simple to implement and allows exploration of spatial and chemical control of adhesion at the nanoscale. As an example, we characterize the delamination of single-layer graphene from monolayers of pyrene tethered to glass in water and maximize the work of separation between these surfaces by varying the density of pyrene groups in the monolayer. Control of this energy scale enables high-fidelity graphene-transfer protocols that can resist failure under sonication. Additionally, we find that the work required for graphene peeling and readhesion exhibits a dramatic rate-independent hysteresis, differing by a factor of 100. This work establishes a rational means to control the adhesion of 2D materials and enables a systematic approach to engineer stimuli-responsive adhesives and mechanical technologies at the nanoscale.

Energy Renormalization Method for the Coarse-Graining of Polymer Viscoelasticity

Developing temperature transferable coarse-grained (CG) models is essential for the computational prediction of polymeric glass-forming (GF) material behavior, but their dynamics are often greatly altered from those of all-atom (AA) models mainly because of the reduced fluid configurational entropy under coarse-graining. To address this issue, we have recently introduced an energy renormalization (ER) strategy that corrects the activation free energy of the CG polymer model by renormalizing the cohesive interaction strength ε as a function of temperature T, i.e., ε(T), thus semiempirically preserving the T-dependent dynamics of the AA model. Here we apply our ER method to consider-in addition to T-dependency-the frequency f-dependent polymer viscoelasticity. Through smallamplitude oscillatory shear molecular dynamics simulations, we show that changing the imposed oscillation f on the CG systems requires changes in ε values (i.e., ε(T, f)) to reproduce the AA viscoelasticity. By accounting for the dynamic fragility of polymers as a material parameter, we are able to predict ε(T, f) under coarse-graining in order to capture the AA viscoelasticity, and consequently the activation energy, across a wide range of T and f in the GF regime. Specifically, we showcase our achievements on two representative polymers of distinct fragilities, polybutadiene (PB) and polystyrene (PS), and show that our CG models are able to sample viscoelasticity up to the megahertz regime, which approaches state-of-the-art experimental resolutions, and capture results sampled via AA simulations and prior experiments.

Molecular rigidity and enthalpy-entropy compensation in DNA melting

Enthalpy-entropy compensation (EEC) is observed in diverse molecular binding processes of importance to living systems and manufacturing applications, but this widely occurring phenomenon is not sufficiently understood from a molecular physics standpoint. To gain insight into this fundamental problem, we focus on the melting of double-stranded DNA (dsDNA) since measurements exhibiting EEC are extensive for nucleic acid complexes and existing coarse-grained models of DNA allow us to explore the influence of changes in molecular parameters on the energetic parameters by using molecular dynamics simulations. Previous experimental and computational studies have indicated a correlation between EEC and changes in molecular rigidity in certain binding-unbinding processes, and, correspondingly, we estimate measures of DNA molecular rigidity under a wide range of conditions, along with resultant changes in the enthalpy and entropy of binding. In particular, we consider variations in dsDNA rigidity that arise from changes of intrinsic molecular rigidity such as varying the associative interaction strength between the DNA bases, the length of the DNA chains, and the bending stiffness of the individual DNA chains. We also consider extrinsic changes of molecular rigidity arising from the addition of polymer additives and geometrical confinement of DNA between parallel plates. All our computations confirm EEC and indicate that this phenomenon is indeed highly correlated with changes in molecular rigidity. However, two distinct patterns relating to how DNA rigidity influences the entropy of association emerge from our analysis. Increasing the intrinsic DNA rigidity increases the entropy of binding, but increases in molecular rigidity from external constraints decreases the entropy of binding. EEC arises in numerous synthetic and biological binding processes and we suggest that changes in molecular rigidity might provide a common origin of this ubiquitous phenomenon in the mutual binding and unbinding of complex molecules.

Macromolecular Crowding In Vitro, In Vivo, and In Between

Biochemical processes take place in heterogeneous and highly volume-occupied or crowded environments that can considerably influence the reactivity and distribution of participating macromolecules. We summarize here the thermodynamic consequences of excluded-volume and long-range nonspecific intermolecular interactions for macromolecular reactions in volume-occupied media. In addition, we summarize and compare the information content of studies of crowding in vitro and in vivo. We emphasize the importance of characterizing the behavior not only of labeled tracer macromolecules but also the composition and behavior of unlabeled macromolecules in the immediate vicinity of the tracer. Finally, we propose strategies for extending quantitative analyses of crowding in simple model systems to increasingly complex media up to and including intact cells.

Elucidating Electrostatic Self-Assembly: Molecular Parameters as Key to Thermodynamics and Nanoparticle Shape

The rational design of supramolecular nanoparticles by self-assembly is a crucial field of research due to the wide applications and the possibility of control through external triggers. Understanding the shape-determining factors is the key for tailoring nanoparticles with desired properties. Here, we show how the thermodynamics of the interaction control the shape of the nanoparticle. We highlight the connection between the molecular structure of building blocks, the interaction strength, and the nanoassembly shape. Nanoparticles are prepared by electrostatic self-assembly of cationic polyelectrolyte dendrimers of different generations and oppositely charged multivalent organic dyes relying on the combination of electrostatic and π-π interactions. Different building blocks have been used to vary interaction strength, geometric constraints, and charge ratio, providing insights into the assembly process. The nanoassembly structure has been characterized using atomic force microscopy, static light scattering, small angle neutron scattering, and UV-vis spectroscopy. We show that the isotropy/anisotropy of the nanoassemblies is related to the dye valency. Isothermal titration calorimetry has been used to investigate both dye-dye and dye-dendrimer interaction. The existence of a threshold value in entropy and enthalpy change separating isotropic and anisotropic shapes for both interactions has been demonstrated. The effects of the dye molecular structure on the interaction thermodynamics and therefore on the nanoparticle structure have been revealed using molecular modeling. The polar surface area of the dye molecule takes a key role in the dye self-interaction. This study opens the possibility for a priori shape determination knowing the building blocks structure and their interactions.

Direct insight into the nonclassical hydrophobic effect in bile salt:β-cyclodextrin interaction: role of hydrophobicity in governing the prototropism of a biological photosensitizer

The interaction of norharmane with bile salts is reported along with the evidence for nonclassical hydrophobic effect in bile salt:β-cyclodextrin interaction.

Quantitative relations between cooperative motion, emergent elasticity, and free volume in model glass-forming polymer materials

The study of glass formation is largely framed by semiempirical models that emphasize the importance of progressively growing cooperative motion accompanying the drop in fluid configurational entropy, emergent elasticity, or the vanishing of accessible free volume available for molecular motion in cooled liquids. We investigate the extent to which these descriptions are related through computations on a model coarse-grained polymer melt, with and without nanoparticle additives, and for supported polymer films with smooth or rough surfaces, allowing for substantial variation of the glass transition temperature and the fragility of glass formation. We find quantitative relations between emergent elasticity, the average local volume accessible for particle motion, and the growth of collective motion in cooled liquids. Surprisingly, we find that each of these models of glass formation can equally well describe the relaxation data for all of the systems that we simulate. In this way, we uncover some unity in our understanding of glass-forming materials from perspectives formerly considered as distinct.

Kinetic and density functional theory (DFT) studies of in vitro reactions of acrylamide with the thiols: captopril, l-cysteine, and glutathione

In vitro kinetic studies with DFT computations to explain the potential of acrylamide metabolism/toxicity with thiols in vivo.

Further Development of the FFT-based Method for Atomistic Modeling of Protein Folding and Binding under Crowding: Optimization of Accuracy and Speed

Recently, we (Qin, S.; Zhou, H. X. J. Chem. Theory Comput.2013, 9, 4633–4643) developed the FFT-based method for Modeling Atomistic Proteins–crowder interactions, henceforth FMAP. Given its potential wide use for calculating effects of crowding on protein folding and binding free energies, here we aimed to optimize the accuracy and speed of FMAP. FMAP is based on expressing protein–crowder interactions as correlation functions and evaluating the latter via fast Fourier transform (FFT). The numerical accuracy of FFT improves as the grid spacing for discretizing space is reduced, but at increasing computational cost. We sought to speed up FMAP calculations by using a relatively coarse grid spacing of 0.6 Å and then correcting for discretization errors. This strategy was tested for different types of interactions (hard-core repulsion, nonpolar attraction, and electrostatic interaction) and over a wide range of protein–crowder systems. We were able to correct for the numerical errors on hard-core repulsion and nonpolar attraction by an 8% inflation of atomic hard-core radii and on electrostatic interaction by a 5% inflation of the magnitudes of protein atomic charges. The corrected results have higher accuracy and enjoy a speedup of more than 100-fold over those obtained using a fine grid spacing of 0.15 Å. With this optimization of accuracy and speed, FMAP may become a practical tool for realistic modeling of protein folding and binding in cell-like environments.

Temporal variation of a protein folding energy landscape in the cell

Chemical reaction rate coefficients and free energies are usually time-independent quantities. Protein folding in vitro is one such reaction with a fixed energy landscape. However, in the milieu of the cell, the energy landscape can be modulated in space and time by fluctuations in the intracellular environment such as cytoskeletal rearrangements, changes in biomolecule concentrations, and large scale cellular reorganization. We studied the time dependence of the folding landscape of a FRET-labeled enzyme, yeast phosphoglycerate kinase (PGK-FRET). Living U2OS cells served as our test tube, and the mammalian cell cycle, a process strictly regulated in time, served as our clock. We found that both the rate of folding and the thermodynamic stability of PGK-FRET are cell cycle-dependent. We also assayed folding rates of PGK-FRET in spatial proximity to and far away from mitotic chromosomes. Our results show that expedited folding in DNA-rich regions cannot account for the faster rate of PGK-FRET folding in mitotic cells.

Phase field method for nonequilibrium dynamics of reversible self-assembly systems

Phase field methods are extended to describe the nonequilibrium dynamics of reversible self-assembly systems, an extension that is complicated by the mutual coupling of many non-conserved order parameters into a set of highly nonlinear partial differential equations. Further complications arise because the sum of all non-conserved order parameters equals a conserved order parameter. The theory is developed for the simplest model of reversible self-assembly in which no additional constraints are imposed on the self-assembly process since the extension to treat more complex self-assembly models is straightforward. Specific calculations focus on the time evolution of the cluster size distribution for a free association system that is rapidly dropped from one ordered state to a more ordered state within the one-phase region. The dynamics proceed as expected, thereby providing validation of the theory which is also capable of treating systems with spatial inhomogeneities.

Quinary protein structure and the consequences of crowding in living cells: leaving the test-tube behind

Although the importance of weak protein-protein interactions has been understood since the 1980s, scant attention has been paid to this "quinary structure". The transient nature of quinary structure facilitates dynamic sub-cellular organization through loose grouping of proteins with multiple binding partners. Despite our growing appreciation of the quinary structure paradigm in cell biology, we do not yet understand how the many forces inside the cell--the excluded volume effect, the "stickiness" of the cytoplasm, and hydrodynamic interactions--perturb the weakest functional protein interactions. We discuss the unresolved problem of how the forces in the cell modulate quinary structure, and to what extent the cell has evolved to exert control over the weakest biomolecular interactions. We conclude by highlighting the new experimental and computational tools coming on-line for in vivo studies, which are a critical next step if we are to understand quinary structure in its native environment.

Protein-protein interactions in a crowded environment

Protein-protein interactions are important in many essential biological functions, such as transcription, translation, and signal transduction. Much progress has been made in understanding protein-protein association in dilute solution via experimentation and simulation. Cells, however, contain various macromolecules, such as DNA, RNA, proteins, among many others, and a myriad of non-specific interactions (usually weak) are present between these cellular constituents. In this review article, we describe the important developments in recent years that have furthered our understanding and even allowed prediction of the consequences of macromolecular crowding on protein-protein interactions. We outline the development of our crowding theory that can predict the change in binding free energy due to crowding quantitatively for both repulsive and attractive protein-crowder interactions. One of the most important findings from our recent work is that weak attractive interactions between crowders and proteins can actually destabilize protein complex formation as opposed to the commonly assumed stabilizing effect predicted based on traditional crowding theories that only account for the entropic-excluded volume effects. We also discuss the implications of macromolecular crowding on the population of encounter versus specific native complex.

Crowding induced entropy-enthalpy compensation in protein association equilibria

A statistical mechanical theory is presented to predict the effects of macromolecular crowding on protein association equilibria, accounting for both excluded volume and attractive interactions between proteins and crowding molecules. Predicted binding free energies are in excellent agreement with simulation data over a wide range of crowder sizes and packing fractions. It is shown that attractive interactions between proteins and crowding agents counteract the stabilizing effects of excluded volume interactions. A critical attraction strength, for which there is no net effect of crowding, is approximately independent of the crowder packing fraction.

Lattice cluster theory of associating telechelic polymers. III. Order parameter and average degree of self-assembly, transition temperature, and specific heat

The lattice cluster theory of strongly interacting, structured polymer fluids is applied to determine the thermodynamic properties of solutions of telechelic polymers that may associate through bifunctional end groups. Hence, this model represents a significant albeit natural extension of a diverse array of prior popular equilibrium polymerization models in which structureless "bead" monomers associate into chain-like clusters under equilibrium conditions. In particular, the thermodynamic description of the self-assembly of linear telechelic chains in small molecule solvents (initiated in Paper II) is systematically extended through calculations of the order parameter Φ and average degree <N> of self-assembly, the self-assembly transition temperature T(p), and the specific heat C(V) of solutions of telechelic molecules. Special focus is placed on examining how molecular and thermodynamic parameters, such as the solution composition φ, temperature T, microscopic interaction energies (ε(s) and ε), and length M of individual telechelic chains, influence the computed thermodynamic quantities that are commonly used to characterize self-assembling systems.

The Fundamental Role of Flexibility on the Strength of Molecular Binding

Non-covalent molecular association underlies a diverse set of biologically and technologically relevant phenomena, including the action of drugs on their biomolecular targets and self- and supra-molecular assembly processes. Computer models employed to model binding frequently use interaction potentials with atomistic detail while neglecting the thermal molecular motions of the binding species. However, errors introduced by this simplification and, more broadly, the thermodynamic consequences of molecular flexibility on binding, are little understood. Here, we isolate the fundamental relationship of molecular flexibility to binding thermodynamics via simulations of simplified molecules with a wide range of flexibilities but the same interaction potential. Disregarding molecular motion is found to generate large errors in binding entropy, enthalpy and free energy, even for molecules that are nearly rigid. Indeed, small decreases in rigidity markedly reduce affinity for highly rigid molecules. Remarkably, precisely the opposite occurs for more flexible molecules, for which increasing flexibility leads to stronger binding affinity. We also find that differences in flexibility suffice to generate binding specificity: for example, a planar surface selectively binds rigid over flexible molecules. Intriguingly, varying molecular flexibility while keeping interaction potentials constant leads to near-linear enthalpy-entropy compensation over a wide range of flexibilities, with the unexpected twist that increasing flexibility produces opposite changes in entropy and enthalpy for molecules in the flexible versus the rigid regime. Molecular flexibility is thus a crucial determinant of binding affinity and specificity and variations in flexibility can lead to strong yet non-intuitive consequences.

Molecular structure encodes nanoscale assemblies: understanding driving forces in electrostatic self-assembly

Supramolecular nanoparticles represent a key field in recent research as their synthesis through self-assembly is straightforward and they often can respond to external triggers. A fundamental understanding of structure-directing factors is highly desirable for a targeted structure design. This contribution demonstrates a quantitative relation between the size of supramolecular self-assembled nanoparticles and the free energy of association. Nanoparticles are prepared by electrostatic self-assembly of cationic polyelectrolyte dendrimers as model macroions and oppositely charged di- and trivalent organic dye molecules relying on the combination of electrostatic and π-π-interactions. A systematic set of sulfonate-group carrying azo-dyes was synthesized. Light scattering and ζ-potential measurements on the resulting nanoparticles yield hydrodynamic radii between 20 nm < R(H) < 50 nm and positive ζ-potential values indicating a positive particle charge. Studies on dye self-aggregation and dendrimer-dye association by isothermal titration calorimetry (ITC) and UV-vis spectroscopy allow for the correlation of the thermodynamic parameters of dendrimer-dye association with the size of the particles, showing that at least a free energy gain of ΔG ≈ - 32 kJ mol(-1) is necessary to induce dendrimer interconnection. Structural features of the azo dyes causing these to favor or prevent nanoparticle formation have been identified. The dye-dye-interaction was found to be the key factor in particle size control. A simple model yields a quantitative relation between the free energy and the particle sizes, allowing for predicting the latter based on thermodynamic measurements. Hence, a set of different molecular "building bricks" can be defined where the choice of building block determines the resulting assembly size.

Molecular-crowding-induced clustering of DNA-wrapped carbon nanotubes for facile length fractionation

Emerging applications require single-wall carbon nanotubes (SWCNTs) of well-defined length. Yet the use of length-defined SWCNTs is limited, in part due to the lack of an easily accessible materials preparation method. Here, we present a new strategy for SWCNT length fractionation based on molecular crowding induced cluster formation. We show that the addition of polyethylene glycol (PEG) as a crowding agent into DNA-wrapped SWCNT dispersion leads to the formation of reversible, nematic, and rodlike microclusters, which can be collected by gentle centrifugation. Since shorter SWCNTs form clusters at higher polyethylene glycol concentration, gradual increase in PEG concentration results in length fractionated SWCNTs. Using atomic force microscopy (AFM) we show that fractions with average lengths of 60-500 nm and standard deviations of 30-40% can be obtained. The concept of molecular-crowding-based fractionation should be applicable to other nanoparticle dispersions.

Quantitative characterization of temperature-independent and temperature-dependent protein-protein interactions in highly nonideal solutions

The interaction among each of three dilute "tracer" proteins (bovine serum albumin, superoxide dismutase, and ovomucoid) at a concentration of 2 mg/mL and each of two "crowder" proteins (ovomucoid and BSA) at concentrations up to 100 mg/mL was characterized by analysis of dependence of the equilibrium gradients of both tracer and crowder upon the concentration of crowder. The equilibrium gradients of both crowder proteins were found to be independent of temperature over the range 5-37 °C. The equilibrium gradients of tracer BSA and ovomucoid in the complementary crowder species were likewise found to be independent of temperature over this range, indicating that interaction among these tracers and crowders is predominantly repulsive and essentially entirely entropic in nature. The equilibrium gradient of tracer SOD in BSA was also found to be independent of temperature over this range, but the gradient of tracer SOD in ovomucoid depended significantly upon temperature in a manner indicating a significant enthalpic (attractive) component of the overall interaction between SOD and ovomucoid. The experimental data are analyzed using model-free expansions of the thermodynamic activity coefficients of tracer and crowder in powers of the concentration of crowder and using approximate statistical thermodynamic models based upon highly simplified descriptions of molecular structure and interactions. Detailed analysis of the results indicates a relatively small contribution of nonspecific attraction to the total protein-protein interaction, which is dominated by steric repulsion.

Surfactant two-dimensional self-assembly under confinement

Confinement-induced structural rearrangements in supported self-assembled surfactant layers in aqueous salt solutions are investigated using classical density functional theory. The systematic study of the influence of the nature of electrolyte revealed that 2:1 electrolyte stabilizes the hemicylindrical configuration of ionic surfactant layers, while a confinement-induced transition to a tilted monolayer configuration was found in symmetric 1:1 and 2:2 electrolytes. On the basis of this study, we formulate a general model for the energetics of structural rearrangements in supported surfactant layers. This model provides a basis for directed self-assembly of surfactant templates with desired structure and stability for scalable synthesis of nanocomposite functional materials, templated crystal growth, and biomolecule adsorption.

Attractive protein-polymer interactions markedly alter the effect of macromolecular crowding on protein association equilibria

The dependence of the fluorescence of catalase upon the concentration of added superoxide dismutase (SOD) indicates that SOD binds to saturable sites on catalase. The affinity of SOD for these sites varies with temperature, and with the concentration of each of three nominally inert polymeric additives--dextran 70, Ficoll 70, and polyethylene glycol 2000. At room temperature (25.0 degrees C) and higher, the addition of high concentrations of polymer is found to significantly enhance the affinity of SOD for catalase, but with decreasing temperature the enhancing effect of polymer addition diminishes, and at 8.0 degrees C, addition of polymer has little or no effect on the affinity of SOD for catalase. The results presented here provide the first experimental evidence for the existence of competition between a repulsive excluded volume interaction between protein and polymer, which tends to enhance association of dilute protein, and an attractive interaction between protein and polymer, which tends to inhibit protein association. The net effect of high concentrations of polymer upon protein associations depends upon the relative strength of these two types of interactions at the temperature of measurement, and may vary significantly between different proteins and/or polymers.