Computational and experimental approaches to quantify protein binding interactions under confinement.

Crowded environments and confinement alter the interactions of adhesion proteins confined to membranes or narrow, crowded gaps at adhesive contacts. Experimental approaches and theoretical frameworks were developed to quantify protein binding constants in these environments. However, recent predictions and the complexity of some protein interactions proved challenging to address with prior experimental or theoretical approaches. This perspective highlights new methods developed by these authors that address these challenges. Specifically, single-molecule fluorescence resonance energy transfer and single-molecule tracking measurements were developed to directly image the binding/unbinding rates of membrane-tethered cadherins. Results identified predicted cis (lateral) interactions, which control cadherin clustering on membranes but were not detected in solution. Kinetic Monte Carlo simulations, based on a realistic model of cis cadherin interactions, were developed to extract binding/unbinding rate constants from heterogeneous single-molecule data. The extension of single-molecule fluorescence measurements to cis and trans (adhesive) cadherin interactions at membrane junctions identified unexpected cooperativity between cis and trans binding that appears to enhance intercellular binding kinetics. Comparisons of intercellular binding kinetics, kinetic Monte Carlo simulations, and single-molecule fluorescence data suggest a strategy to bridge protein binding kinetics across length scales. Although cadherin is the focus of these studies, the approaches can be extended to other intercellular adhesion proteins.

Combinatorial High-Throughput Screening of Complex Polymeric Enzyme Immobilization Supports.

Recent advances have demonstrated the promise of complex multicomponent polymeric supports to enable supra-biological enzyme performance. However, the discovery of such supports has been limited by time-consuming, low-throughput synthesis and screening. Here, we describe a novel combinatorial and high-throughput platform that enables rapid screening of complex and heterogeneous copolymer brushes as enzyme immobilization supports, named combinatorial high-throughput enzyme support screening (CHESS). Using a 384-well plate format, we synthesized arrays of three-component polymer brushes in the microwells using photoactivated surface-initiated polymerization and immobilized enzymes in situ. The utility of CHESS to identify optimal immobilization supports under thermally and chemically denaturing conditions was demonstrated usingBacillus subtilisLipase A (LipA). The identification of supports with optimal compositions was validated by immobilizing LipA on polymer-brush-modified biocatalyst particles. We further demonstrated that CHESS could be used to predict the optimal composition of polymer brushes a priori for the previously unexplored enzyme, alkaline phosphatase (AlkP). Our findings demonstrate that CHESS represents a predictable and reliable platform for dramatically accelerating the search of chemical compositions for immobilization supports and further facilitates the discovery of biocompatible and stabilizing materials.

Mechanisms of transport enhancement for self-propelled nanoswimmers in a porous matrix.

Micro/nanoswimmers convert diverse energy sources into directional movement, demonstrating significant promise for biomedical and environmental applications, many of which involve complex, tortuous, or crowded environments. Here, we investigated the transport behavior of self-propelled catalytic Janus particles in a complex interconnected porous void space, where the rate-determining step involves the escape from a cavity and translocation through holes to adjacent cavities. Surprisingly, self-propelled nanoswimmers escaped from cavities more than 20× faster than passive (Brownian) particles, despite the fact that the mobility of nanoswimmers was less than 2× greater than that of passive particles in unconfined bulk liquid. Combining experimental measurements, Monte Carlo simulations, and theoretical calculations, we found that the escape of nanoswimmers was enhanced by nuanced secondary effects of self-propulsion which were amplified in confined environments. In particular, active escape was facilitated by anomalously rapid confined short-time mobility, highly efficient surface-mediated searching for holes, and the effective abolition of entropic and/or electrostatic barriers at the exit hole regions by propulsion forces. The latter mechanism converted the escape process from barrier-limited to search-limited. These findings provide general and important insights into micro/nanoswimmer mobility in complex environments.

Cadherin cis and trans interactions are mutually cooperative.

Cadherin transmembrane proteins are responsible for intercellular adhesion in all biological tissues and modulate tissue morphogenesis, cell motility, force transduction, and macromolecular transport. The protein-mediated adhesions consist of adhesive trans interactions and lateral cis interactions. Although theory suggests cooperativity between cis and trans bonds, direct experimental evidence of such cooperativity has not been demonstrated. Here, the use of superresolution microscopy, in conjunction with intermolecular single-molecule Förster resonance energy transfer, demonstrated the mutual cooperativity of cis and trans interactions. Results further demonstrate the consequent assembly of large intermembrane junctions, using a biomimetic lipid bilayer cell adhesion model. Notably, the presence of cis interactions resulted in a nearly 30-fold increase in trans-binding lifetimes between epithelial-cadherin extracellular domains. In turn, the presence of trans interactions increased the lifetime of cis bonds. Importantly, comparison of trans-binding lifetimes of small and large cadherin clusters suggests that this cooperativity is primarily due to allostery. The direct quantitative demonstration of strong mutual cooperativity between cis and trans interactions at intermembrane adhesions provides insights into the long-standing controversy of how weak cis and trans interactions act in concert to create strong macroscopic cell adhesions.

Tuning Polymer Composition Leads to Activity-Stability Tradeoff in Enzyme-Polymer Conjugates.

Protein-polymer conjugation provides an opportune means to adjust the local environment of proteins and enhance protein stability, performance, and solubility. Although much attention has been focused on tuning protein-polymer interactions, the properties of polymer-modified proteins may also be altered by polymer-polymer interactions. Herein, we sought to better understand the influence of polymer-polymer interactions on Candida rugosa lipase, which was modified with random co-polymers composed of sulfobetaine methacrylate (SBMA) and poly(ethylene glycol) methacrylate (PEGMA). Our findings suggest that there is an apparent activity-stability tradeoff as a function of polymer composition. Specifically, as the ratio of SBMA to PEGMA increased, lipase stability was enhanced, whereas activity decreased. By tuning the monomer ratio, we showed that lipase productivity could be optimized. These findings are discussed in the context of complex enzyme-polymer and polymer-polymer interactions and ultimately may enable more informed conjugate designs and improved enzyme productivity in industrial biotransformations under harsh or extreme conditions.

Protein Desorption Kinetics Depends on the Timescale of Observation.

The presence of so-called reversible and irreversible protein adsorption on solid surfaces is well documented in the literature and represents the basis for the development of nanoparticles and implant materials to control interactions in physiological environments. Here, using a series of complementary single-molecule tracking approaches appropriate for different timescales, we show that protein desorption kinetics is much more complex than the traditional reversible-irreversible binary picture. Instead, we find that the surface residence time distribution of adsorbed proteins transitions from power law to exponential behavior when measured over a large range of timescales (10-2-106 s). A comparison with macroscopic results obtained using a quartz crystal microbalance suggested that macroscopic measurements have generally failed to observe such nonequilibrium phenomena because they are obscured by ensemble-averaging effects. These findings provide new insights into the complex phenomena associated with protein adsorption and desorption.

Faster Surface Ligation Reactions Improve Immobilized Enzyme Structure and Activity.

During integration into materials, the inactivation of enzymes as a result of their interaction with nanometer size denaturing "hotspots" on surfaces represents a critical challenge. This challenge, which has received far less attention than improving the long-term stability of enzymes, may be overcome by limiting the exploration of surfaces by enzymes. One way this may be accomplished is through increasing the rate constant of the surface ligation reaction and thus the probability of immobilization with reactive surface sites (i.e., ligation efficiency). Here, the connection between ligation reaction efficiency and the retention of enzyme structure and activity was investigated by leveraging the extremely fast reaction of strained trans-cyclooctene (sTCOs) and tetrazines (Tet). Remarkably, upon immobilization via Tet-sTCO chemistry, carbonic anhydrase (CA) retained 77% of its solution-phase activity, while immobilization via less efficient reaction chemistries, such as thiol-maleimide and azide-dibenzocyclooctyne, led to activity retention of only 46% and 27%, respectively. Dynamic single-molecule fluorescence tracking methods further revealed that longer surface search distances prior to immobilization (>0.5 µm) dramatically increased the probability of CA unfolding. Notably, the CA distance to immobilization was significantly reduced through the use of Tet-sTCO chemistry, which correlated with the increased retention of structure and activity of immobilized CA compared to the use of slower ligation chemistries. These findings provide an unprecedented insight into the role of ligation reaction efficiency in mediating the exploration of denaturing hotspots on surfaces by enzymes, which, in turn, may have major ramifications in the creation of functional biohybrid materials.

Chemically Triggered Changes in Mechanical Properties of Responsive Liquid Crystal Polymer Networks with Immobilized Urease.

Liquid crystal polymer networks (LCNs) are stimuli-responsive materials that can be programmed to realize spatial variation in mechanical response and undergo shape transformation. Herein, we report a process to introduce chemical specificity to the stimuli response of LCNs by integrating enzymes as molecular triggers. Specifically, the enzyme urease was immobilized in LCN films via acyl fluoride conjugation chemistry. Activity assays and confocal fluorescence imaging confirmed retention of urease activity after immobilization as well as widespread distribution of enzyme on the film. The addition of urea triggered a response in the LCN whereby newly generated ammonia reacted with free acyl fluorides to form benzamide moieties. These moieties were capable of dimerizing through the formation of supramolecular hydrogen bonds, which was reflected in a 4-fold increase in Young's modulus. Through dynamic mechanical analysis and calorimetry, we further confirmed that the degree of hydrogen bonding in the LCNs could be judiciously designed to fine-tune the mechanical properties and glass transition temperature. These findings demonstrate the untapped potential of biochemical mechanisms as molecular triggers in LCNs and open the door to the use of nucleophilic chemistries in modulating the mechanical properties of LCNs.

Nanoparticle Tracking to Probe Transport in Porous Media.

From the granular and fractured subsurface environment to highly engineered polymer membranes used in pharmaceutical purification, porous materials are ubiquitous in nature and industrial applications. In particular, porous media are used extensively in processes including water treatment, pharmaceutical sterilization, food/beverage processing, and heterogeneous catalysis, where hindered mass transport is either essential to the process or a necessary but undesirable limitation. Unfortunately, there are currently no universal models capable of predicting mass transport based on a description of the porous material because real porous materials are complex and because many coupled dynamic mechanisms (e.g., adsorption, steric effects, hydrodynamic effects, electrostatic interactions, etc.) give rise to the observed macroscopic transport phenomena.While classical techniques, like nuclear magnetic resonance and dynamic light scattering, provide useful information about mass transport in porous media at the ensemble level, they provide limited insight into the microscopic mechanisms that give rise to complex phenomena such as anomalous diffusion, hindered pore-space accessibility, and unexpected retention under flow, among many others. To address this issue, we have developed refractive index matching imaging systems, combined with single-particle tracking methods, allowing the direct visualization of single-particle motion within a variety of porous materials.In this Account, we summarize our recent efforts to advance the understanding of nanoparticle transport in porous media using single-particle tracking methods in both fundamental and applied scenarios. First, we describe the basic principles for two-dimensional and three-dimensional single-particle tracking in porous materials. Then, we provide concrete examples of nanoparticle transport in porous materials from two perspectives: (1) understanding fundamental elementary particle transport processes in porous media, including pore accessibility and cavity escape, which limit transport in porous media, and (2) facilitating applications in industrial processes, e.g., by understanding the mechanisms of particle fouling and remobilization in filtration membranes. Finally, we provide an outlook of opportunities associated with investigating other types of mass transport in confined environments using single-particle tracking methods, including electrophoretic and self-propelled motion.

Reduced Enzyme Dynamics upon Multipoint Covalent Immobilization Leads to Stability-Activity Trade-off.

The successful incorporation of enzymes into materials through multipoint covalent immobilization (MPCI) has served as the foundation for numerous advances in diverse fields, including biocatalysis, biosensing, and chemical weapons defense. Despite this success, a mechanistic understanding of the impact of this approach on enzyme stability has remained elusive, which is critical for realizing the full potential of MPCI. Here, we showed that the stabilization of lipase upon MPCI to polymer brush surfaces resulted from the rigidification of the enzyme with an increase in the number of enzyme-brush attachments. This was evident by a 10-fold decrease in the rates of enzyme unfolding and refolding as well as a reduction of the intrinsic fluctuations of the folded and unfolded states, which was measured by single-molecule (SM) Förster Resonance Energy Transfer imaging. Moreover, our results illuminate an important trade-off between stability and activity as a function of this decrease in structural dynamics of the immobilized lipase. Notably, as the thermal stability of lipase increased, as indicated by the temperature optimum for activity of the enzyme, the specific activity of lipase decreased. This decrease in activity was attributed to a reduction in the essential motions of the folded state that are required for catalytic turnover of substrate. These results provide direct evidence of this effect, which has long been a matter of speculation. Furthermore, our findings suggest that the retention of activity and stabilization of an enzyme may be balanced by tuning the extent of enzyme attachment.

Electrostatic Barriers to Nanoparticle Accessibility of a Porous Matrix.

Translocation from one cavity to another through a narrow constriction (i.e., a "hole") represents the fundamental elementary process underlying hindered mass transport of nanoparticles and macromolecules within many natural and synthetic porous materials, including intracellular environments. This process is complex and may be influenced by long-range (e.g., electrostatic) particle-wall interactions, transient adsorption/desorption, surface diffusion, and hydrodynamic effects. Here, we used a three-dimensional (3D) tracking method to explicitly visualize the process of nanoparticle diffusion within periodic porous nanostructures, where electrostatic interactions were mediated via ionic strength. The effects of electrostatic interactions on nanoparticle transport were surprisingly large. For example, an increase in the Debye length of only a few nanometers (in a material with a hole diameter of ∼100 nm) increased the mean cavity escape time 3-fold. A combination of computational and experimental analyses indicated that this hindered cavity escape was due to an electrostatic energy barrier in the region of the hole, which was quantitatively explained using DLVO theory. These findings explicitly demonstrate that the cavity escape process was barrier-limited and dominated by electrostatic effects.

Diffusive Escape of a Nanoparticle from a Porous Cavity.

Narrow escape from confinement through a nanochannel is the critical step of complex transport processes including size-exclusion-based separations, oil and gas extraction from the microporous subsurface environment, and ribonucleic acid translocation through nuclear pore complex channels. While narrow escape has been studied using theoretical and computational methods, experimental quantification is rare because of the difficulty in confining a particle into a microscopic space through a nanoscale hole. Here, we studied narrow escape in the context of continuous nanoparticle diffusion within the liquid-filled void space of an ordered porous material. Specifically, we quantified the spatial dependence of nanoparticle motion and the sojourn times of individual particles in the interconnected confined cavities of a liquid-filled inverse opal film. We found that nanoparticle motion was inhibited near cavity walls and cavity escape was slower than predicted by existing theories and random-walk simulations. A combined computational-experimental analysis indicated that translocation through a nanochannel is barrier controlled rather than diffusion controlled.

Standalone interferometry-based calibration of convex lens-induced confinement microscopy with nanoscale accuracy.

Strongly confined environments (confined dimensions between 1-100 nm) represent unique challenges and opportunities for understanding and manipulating molecular behavior due to the significant effects of electric double layers, high surface-area to volume ratios, and other phenomena at the nanoscale. Convex Lens-induced Confinement (CLiC) can be used to analyze the dynamics of individual molecules or particles confined in a planar slit geometry with continuously varying gap thickness. We describe an interferometry-based method for precise measurement of the slit pore geometry. Specifically, this approach permitted accurate characterization of separation distances as small as 5 nm, with 1 nm precision, without a priori knowledge or assumptions about the contact geometry, as well as a greatly simplified experimental setup that required only a lens, coverslip, and inverted microscope. The interferometry-based measurement of gap height offered a distinct advantage over conventional fluorescent dye-based methods; e.g., accurate interferometric height measurements were made at low gap heights regardless of solution conditions, while the concentration of fluorescent dye was significantly impacted by solution conditions such as ionic strength or pH. The accuracy of the interferometric measurements was demonstrated by comparing the experimentally measured concentration of a charged fluorescent dye as a function of gap thickness with dye concentration profiles calculated using Debye-Hückel theory. Accurate characterization of nanoscale gap thickness will enable researchers to study a variety of practical and biologically relevant systems within the CLiC geometry.

Single-Molecule Resolution of Antimicrobial Peptide Interactions with Supported Lipid A Bilayers.

The molecular interactions between antimicrobial peptides (AMPs) and lipid A-containing supported lipid bilayers were probed using single-molecule total internal reflection fluorescence microscopy. Hybrid supported lipid bilayers with lipid A outer leaflets and phospholipid (1,2-dioleoyl-sn-glycero-3-phosphoethanolamine (DOPE)) inner leaflets were prepared and characterized, and the spatiotemporal trajectories of individual fluorescently labeled LL37 and Melittin AMPs were determined as they interacted with the bilayer surfaces comprising either monophosphoryl or diphosphoryl lipid A (from Escherichia coli) to determine the impact of electrostatic interactions. Large numbers of trajectories were obtained and analyzed to obtain the distributions of surface residence times and the statistics of the spatial trajectories. Interestingly, the AMP species were sensitive to subtle differences in the charge of the lipid, with both peptides diffusing more slowly and residing longer on the diphosphoryl lipid A. Furthermore, the single-molecule dynamics indicated a qualitative difference between the behavior of AMPs on hybrid Lipid A bilayers and on those composed entirely of DOPE. Whereas AMPs interacting with a DOPE bilayer exhibited two-dimensional Brownian diffusion with a diffusion coefficient of ∼1.7 µm2/s, AMPs adsorbed to the lipid A surface exhibited much slower apparent diffusion (on the order of ∼0.1 µm2/s) and executed intermittent trajectories that alternated between two-dimensional Brownian diffusion and desorption-mediated three-dimensional flights. Overall, these findings suggested that bilayers with lipid A in the outer leaflet, as it is in bacterial outer membranes, are valuable model systems for the study of the initial stage of AMP-bacterium interactions. Furthermore, single-molecule dynamics was sensitive to subtle differences in electrostatic interactions between cationic AMPs and monovalent or divalent anionic lipid A moieties.

Nanoconfinement and Sansetsukon-like Nanocrawling Govern Fibrinogen Dynamics and Self-Assembly on Nanostructured Polymeric Surfaces.

Surface nanostructures are increasingly more employed for controlled protein assembly on functional nanodevices, in nanobiotechnology, and in nanobiomaterials. However, the mechanism and dynamics of how nanostructures induce order in the adsorbed protein assemblies are still enigmatic. Here, we use single-molecule mapping by accumulated probe trajectories and complementary atomic force microscopy to shed light on the dynamic of in situ assembly of human plasma fibrinogen (HPF) adsorbed on nanostructured polybutene-1 (PB-1) and nanostructured polyethylene (PE) surfaces. We found a distinct lateral heterogeneity of HPF-polymer nanostructure interface (surface occupancy, residence time, and diffusion coefficient) that allow identifying the interplay between protein topographical nanoconfinement, protein diffusion mechanism, and ordered protein self-assembly. The protein diffusion analysis revealed high-diffusion polarization without correlation to the anisotropic friction characteristic of the polymer surfaces. This suggests that HPF molecules confined on the nanosized PB-1 needle crystals and PE shish-kebab crystals, respectively, undergo partial detachment and diffuse via a Sansetsukon-like nanocrawling mechanism. This mechanism is based on the intrinsic flexibility of HPF in the coiled-coil regions. We conclude that nanostructured surfaces that encourage this characteristic surface mobility are more likely to lead to the formation of ordered protein assemblies and may be useful for advanced nanobiomaterials.

Connecting Protein Conformation and Dynamics with Ligand-Receptor Binding Using Three-Color Förster Resonance Energy Transfer Tracking.

Specific binding between biomolecules, i.e., molecular recognition, controls virtually all biological processes including the interactions between cells and biointerfaces, both natural and synthetic. Such binding often relies on the conformation of biomacromolecules, which can be highly heterogeneous and sensitive to environmental perturbations, and therefore difficult to characterize and control. An approach is demonstrated here that directly connects the binding kinetics and stability of the protein receptor integrin αvß3 to the conformation of the ligand fibronectin (FN), which are believed to control cellular mechanosensing. Specifically, we investigated the influence of surface-adsorbed FN structure and dynamics on αvß3 binding using high-throughput single-molecule three-color Förster resonance energy transfer (FRET) tracking methods. By controlling FN structure and dynamics through tuning surface chemistry, we found that as the conformational and translational dynamics of FN increased, the rate of binding, particularly to folded FN, and stability of the bound FN-αvß3 complex decreased significantly. These findings highlight the importance of the conformational plasticity and accessibility of the arginine-glycine-aspartic acid (RGD) binding site in FN, which, in turn, mediates cell signaling in physiological and synthetic environments.

Three-Dimensional Tracking of Interfacial Hopping Diffusion.

Theoretical predictions have suggested that molecular motion at interfaces-which influences processes including heterogeneous catalysis, (bio)chemical sensing, lubrication and adhesion, and nanomaterial self-assembly-may be dominated by hypothetical "hops" through the adjacent liquid phase, where a diffusing molecule readsorbs after a given hop according to a probabilistic "sticking coefficient." Here, we use three-dimensional (3D) single-molecule tracking to explicitly visualize this process for human serum albumin at solid-liquid interfaces that exert varying electrostatic interactions on the biomacromolecule. Following desorption from the interface, a molecule experiences multiple unproductive surface encounters before readsorption. An average of approximately seven surface collisions is required for the repulsive surfaces, decreasing to approximately two and a half for surfaces that are more attractive. The hops themselves are also influenced by long-range interactions, with increased electrostatic repulsion causing hops of longer duration and distance. These findings explicitly demonstrate that interfacial diffusion is dominated by biased 3D Brownian motion involving bulk-surface coupling and that it can be controlled by influencing short- and long-range adsorbate-surface interactions.

Surface-Mediated DNA Hybridization: Effects of DNA Conformation, Surface Chemistry, and Electrostatics.

Single-molecule Förster Resonance Energy Transfer (FRET) was used to study the dynamic association of mobile donor-labeled ssDNA oligonucleotides ("target") with covalently immobilized complementary acceptor-labeled ssDNA oligonucleotides ("probe"). While probe-target association events were resolved for all experiments, such FRET events were far more likely to occur in systems with complementarity and on hydrophobic, as compared to hydrophilic, surfaces. The distribution of donor-acceptor association-time intervals did not exhibit simple first-order kinetics, and when decomposed into a superposition of first-order processes, only a small fraction of events corresponded to a long-lived state that was presumed to represent true DNA hybridization, while the majority of association events were transient, representing nonspecific associations or partial hybridization. The structure of the DNA target and probe affected both the stability of the hybridized state, as well as the likelihood that an association between the two led to hybridization. In particular, the likelihood of hybridization decreased for longer target strands and for targets with stem-loop secondary structure. The presence of oligonucleotide secondary structure reduced the stability of hybridization, while greater complementarity increased stability of the hybridized state. Interestingly, increased ionic strength (i.e., greater electrostatic screening) increased the probability of hybridization but did not influence the lifetime of the hybridized state. Combined, these observations provide a nuanced view of surface-mediated DNA hybridization, where various factors independently influence the probability and stability of hybridization.

Cadherin Diffusion in Supported Lipid Bilayers Exhibits Calcium-Dependent Dynamic Heterogeneity.

Ca2+ ions are critical to cadherin ectodomain rigidity, which is required for the activation of adhesive functions. Therefore, changes in Ca2+ concentration, both in vivo and in vitro, can affect cadherin conformation and function. We employed single-molecule tracking to measure the diffusion of cadherin ectodomains tethered to supported lipid bilayers at varying Ca2+ concentrations. At a relatively high Ca2+ concentration of 2 mM, cadherin molecules exhibited a fast diffusion coefficient that was identical to that of individual lipid molecules in the bilayer (Dfast ≈ 3 µm2/s). At lower Ca2+ concentrations, where cadherin molecules were less rigid, the ensemble-average cadherin diffusion coefficient was systematically smaller. Individual cadherin trajectories were temporally heterogeneous, exhibiting alternating periods of fast and slow diffusion; the periods of slow diffusion (Dslow ≈ 0.1 µm2/s) were more prevalent at lower Ca2+ concentration. These observations suggested that more flexible cadherin ectodomains at lower Ca2+ concentration alternated between upright and lying-down conformations, where the latter interacted with more lipid molecules and experienced greater viscous drag.

Challenges in Predicting Protein-Protein Interactions from Measurements of Molecular Diffusivity.

Dynamic light scattering can be used to measure the diffusivity of a protein within a formulation. The dependence of molecular diffusivity on protein concentration (traditionally expressed in terms of the interaction parameter kD) is often used to infer whether protein-protein interactions are repulsive or attractive, resulting in solutions that are colloidally stable or unstable, respectively. However, a number of factors unrelated to intermolecular forces can also impact protein diffusion, complicating this interpretation. Here, we investigate the influence of multicomponent diffusion in a ternary protein-salt-water system on protein diffusion and kD in the context of Nernst-Planck theory. This analysis demonstrates that large changes in protein diffusivity with protein concentration can result even for hard-sphere systems in the absence of protein-protein interactions. In addition, we show that dynamic light scattering measurements of diffusivity made at low ionic strength cannot be reliably used to detect protein conformational changes. We recommend comparing experimentally determined kD values to theoretically predicted excluded-volume contributions, which will allow a more accurate assessment of protein-protein interactions.