Precise boundary element computation of protein transport properties: Diffusion tensors, specific volume, and hydration

Computational simulations of bispecific T cell engagers by a multiscale model

The use of bispecific antibodies as T cell engagers can bypass the normal T cell receptor-major histocompatibility class interaction, redirect the cytotoxic activity of T cells, and lead to highly efficient tumor cell killing. However, this immunotherapy also causes significant on-target off-tumor toxicologic effects, especially when it is used to treat solid tumors. To avoid these adverse events, it is necessary to understand the fundamental mechanisms involved in the physical process of T cell engagement. We developed a multiscale computational framework to reach this goal. The framework combines simulations on the intercellular and multicellular levels. On the intercellular level, we simulated the spatial-temporal dynamics of three-body interactions among bispecific antibodies, CD3 and tumor-associated antigens (TAAs). The derived number of intercellular bonds formed between CD3 and TAAs was further transferred to the multicellular simulations as the input parameter of adhesive density between cells. Through the simulations under various molecular and cellular conditions, we were able to gain new insights into how to adopt the most appropriate strategy to maximize the drug efficacy and avoid the off-target effect. For instance, we discovered that the low antibody-binding affinity resulted in the formation of large clusters at the cell-cell interface, which could be important to control the downstream signaling pathways. We also tested different molecular architectures of the bispecific antibody and suggested the existence of an optimal length in regulating the T cell engagement. Overall, the current multiscale simulations serve as a proof-of-concept study to help in the future design of new biological therapeutics.

Identification of motif-based interactions between SARS-CoV-2 protein domains and human peptide ligands pinpoint antiviral targets

The virus life cycle depends on host-virus protein-protein interactions, which often involve a disordered protein region binding to a folded protein domain. Here, we used proteomic peptide phage display (ProP-PD) to identify peptides from the intrinsically disordered regions of the human proteome that bind to folded protein domains encoded by the SARS-CoV-2 genome. Eleven folded domains of SARS-CoV-2 proteins were found to bind 281 peptides from human proteins, and affinities of 31 interactions involving eight SARS-CoV-2 protein domains were determined (KD ∼ 7-300 μM). Key specificity residues of the peptides were established for six of the interactions. Two of the peptides, binding Nsp9 and Nsp16, respectively, inhibited viral replication. Our findings demonstrate how high-throughput peptide binding screens simultaneously identify potential host-virus interactions and peptides with antiviral properties. Furthermore, the high number of low-affinity interactions suggest that overexpression of viral proteins during infection may perturb multiple cellular pathways.

How does the same ligand activate signaling of different receptors in TNFR superfamily: a computational study

TNFα is a highly pleiotropic cytokine inducing inflammatory signaling pathways. It is initially presented on plasma membrane of cells (mTNFα), and also exists in a soluble variant (sTNFα) after cleavage. The ligand is shared by two structurally similar receptors, TNFR1 and TNFR2. Interestingly, while sTNFα preferentially stimulates TNFR1, TNFR2 signaling can only be activated by mTNFα. How can two similar receptors respond to the same ligand in such a different way? We employed computational simulations in multiple scales to address this question. We found that both mTNFα and sTNFα can trigger the clustering of TNFR1. The size of clusters induced by sTNFα is constantly larger than the clusters induced by mTNFα. The systems of TNFR2, on the other hand, show very different behaviors. Only when the interactions between TNFR2 are very weak, mTNFα can trigger the receptors to form very large clusters. Given the same weak binding affinity, only small oligomers were obtained in the system of sTNFα. Considering that TNF-mediated signaling is modulated by the ligand-induced clustering of receptors on cell surface, our study provided the mechanistic foundation to the phenomenon that different isoforms of the ligand can lead to highly distinctive signaling patterns for its receptors.

Revisiting macromolecular hydration with HullRadSAS

Hydration of biological macromolecules is important for their stability and function. Historically, attempts have been made to describe the degree of macromolecular hydration using a single parameter over a narrow range of values. Here, we describe a method to calculate two types of hydration: surface shell water and entrained water. A consideration of these two types of hydration helps to explain the "hydration problem" in hydrodynamics. The combination of these two types of hydration allows accurate calculation of hydrodynamic volume and related macromolecular properties such as sedimentation and diffusion coefficients, intrinsic viscosities, and the concentration-dependent non-ideality identified with sedimentation velocity experiments.

Dissecting the general mechanisms of protein cage self-assembly by coarse-grained simulations

The development of artificial protein cages has recently gained massive attention due to their promising application prospect as novel delivery vehicles for therapeutics. These nanoparticles are formed through a process called self-assembly, in which individual subunits spontaneously arrange into highly ordered patterns via non-covalent but specific interactions. Therefore, the first step toward the design of novel engineered protein cages is to understand the general mechanisms of their self-assembling dynamics. Here we have developed a new computational method to tackle this problem. Our method is based on a coarse-grained model and a diffusion-reaction simulation algorithm. Using a tetrahedral cage as test model, we showed that self-assembly of protein cage requires of a seeding process in which specific configurations of kinetic intermediate states are identified. We further found that there is a critical concentration to trigger self-assembly of protein cages. This critical concentration allows that cages can only be successfully assembled under a persistently high concentration. Additionally, phase diagram of self-assembly has been constructed by systematically testing the model across a wide range of binding parameters. Finally, our simulations demonstrated the importance of protein's structural flexibility in regulating the dynamics of cage assembly. In summary, this study throws lights on the general principles underlying self-assembly of large cage-like protein complexes and thus provides insights to design new nanomaterials.

Understanding the functional role of membrane confinements in TNF-mediated signaling by multiscale simulations

The interaction between TNFα and TNFR1 is essential in maintaining tissue development and immune responses. While TNFR1 is a cell surface receptor, TNFα exists in both soluble and membrane-bound forms. Interestingly, it was found that the activation of TNFR1-mediated signaling pathways is preferentially through the soluble form of TNFα, which can also induce the clustering of TNFR1 on plasma membrane of living cells. We developed a multiscale simulation framework to compare receptor clustering induced by soluble and membrane-bound ligands. Comparing with the freely diffusive soluble ligands, we hypothesize that the conformational dynamics of membrane-bound ligands are restricted, which affects the clustering of ligand-receptor complexes at cell-cell interfaces. Our simulation revealed that only small clusters can form if TNFα is bound on cell surface. In contrast, the clustering triggered by soluble TNFα is more dynamic, and the size of clusters is statistically larger. We therefore demonstrated the impact of membrane-bound ligand on dynamics of receptor clustering. Moreover, considering that larger TNFα-TNFR1 clusters is more likely to provide spatial platform for downstream signaling pathway, our studies offer new mechanistic insights about why the activation of TNFR1-mediated signaling pathways is not preferred by membrane-bound form of TNFα.

Multiphysics Modeling and Simulation of Subcutaneous Injection and Absorption of Biotherapeutics: Model Development

PURPOSE

Many monoclonal antibodies (mAbs) are administered via subcutaneous (SC) injection. Local transport and absorption kinetics and mechanisms, however, remain poorly understood. A multiphysics computational model was developed to simulate the injection and absorption processes of a protein solution in the SC tissue.

METHODS

Quantitative relationships among tissue properties and transport behaviors of an injected solution were described by respective physical laws. SC tissue was treated as a 3-dimensional homogenous, poroelastic medium, in which vasculatures and lymphatic vessels were implicitly treated. Tissue deformation was considered, and interstitial fluid flow was modeled by Darcy's law. Transport of the drug mass was described based on diffusion and advection, which was integrated with tissue mechanics and interstitial fluid dynamics.

RESULTS

Injection and absorption of albumin and IgG solutions were simulated. Upon injection, a sharp rise in tissue pressure, porosity, and fluid velocity could be observed at the injection tip. Largest tissue deformation appeared at the model surface. Transport of drug mass out of the injection zone was minimal. Absorption by local lymphatics was found to last several weeks.

CONCLUSIONS

A bottom-up method was developed to simulate drug transport and absorption of protein solutions in skin tissue base on physical principles. The results appear to match experimental observations.

A multiscale study on the mechanisms of spatial organization in ligand-receptor interactions on cell surfaces

The binding of cell surface receptors with extracellular ligands triggers distinctive signaling pathways, leading into the corresponding phenotypic variation of cells. It has been found that in many systems, these ligand-receptor complexes can further oligomerize into higher-order structures. This ligand-induced oligomerization of receptors on cell surfaces plays an important role in regulating the functions of cell signaling. The underlying mechanism, however, is not well understood. One typical example is proteins that belong to the tumor necrosis factor receptor (TNFR) superfamily. Using a generic multiscale simulation platform that spans from atomic to subcellular levels, we compared the detailed physical process of ligand-receptor oligomerization for two specific members in the TNFR superfamily: the complex formed between ligand TNFα and receptor TNFR1 versus the complex formed between ligand TNFβ and receptor TNFR2. Interestingly, although these two systems share high similarity on the tertiary and quaternary structural levels, our results indicate that their oligomers are formed with very different dynamic properties and spatial patterns. We demonstrated that the changes of receptor’s conformational fluctuations due to the membrane confinements are closely related to such difference. Consistent to previous experiments, our simulations also showed that TNFR can preassemble into dimers prior to ligand binding, while the introduction of TNF ligands induced higher-order oligomerization due to a multivalent effect. This study, therefore, provides the molecular basis to TNFR oligomerization and reveals new insights to TNFR-mediated signal transduction. Moreover, our multiscale simulation framework serves as a prototype that paves the way to study higher-order assembly of cell surface receptors in many other bio-systems.

Using Coarse-Grained Simulations to Characterize the Mechanisms of Protein-Protein Association

The formation of functionally versatile protein complexes underlies almost every biological process. The estimation of how fast these complexes can be formed has broad implications for unravelling the mechanism of biomolecular recognition. This kinetic property is traditionally quantified by association rates, which can be measured through various experimental techniques. To complement these time-consuming and labor-intensive approaches, we developed a coarse-grained simulation approach to study the physical processes of protein–protein association. We systematically calibrated our simulation method against a large-scale benchmark set. By combining a physics-based force field with a statistically-derived potential in the simulation, we found that the association rates of more than 80% of protein complexes can be correctly predicted within one order of magnitude relative to their experimental measurements. We further showed that a mixture of force fields derived from complementary sources was able to describe the process of protein–protein association with mechanistic details. For instance, we show that association of a protein complex contains multiple steps in which proteins continuously search their local binding orientations and form non-native-like intermediates through repeated dissociation and re-association. Moreover, with an ensemble of loosely bound encounter complexes observed around their native conformation, we suggest that the transition states of protein–protein association could be highly diverse on the structural level. Our study also supports the idea in which the association of a protein complex is driven by a “funnel-like” energy landscape. In summary, these results shed light on our understanding of how protein–protein recognition is kinetically modulated, and our coarse-grained simulation approach can serve as a useful addition to the existing experimental approaches that measure protein–protein association rates.

A Multiscale Computational Model for Simulating the Kinetics of Protein Complex Assembly

Proteins fulfill versatile biological functions by interacting with each other and forming high-order complexes. Although the order in which protein subunits assemble is important for the biological function of their final complex, this kinetic information has received comparatively little attention in recent years. Here we describe a multiscale framework that can be used to simulate the kinetics of protein complex assembly. There are two levels of models in the framework. The structural details of a protein complex are reflected by the residue-based model, while a lower-resolution model uses a rigid-body (RB) representation to simulate the process of complex assembly. These two levels of models are integrated together, so that we are able to provide the kinetic information about complex assembly with both structural details and computational efficiency.

Companion Simulations and Modeling to NMR-Based Dynamical Studies of Proteins

NMR-based studies of protein dynamics and molecular simulations have a synergistic relationship. Molecular simulations, in combination with interpretative theoretical models, leverage the dynamical information obtained from NMR. They provide the concrete physical schema underlying the quantities measured by NMR, and help extend the range of applications beyond the strictly dynamic properties. NMR data in turn provide concrete data to test and improve the potential functions used for simulation of dynamics of proteins. The concept of time correlation functions is central to the understanding of many dynamical processes. Their evaluation through atomistic simulations is discussed, with application to different dynamical quantities measured by NMR. While advances in computers have made such atomistic simulations almost routine, the companion use of simple interpretive models is stressed, to provide not just numbers but physical insight.

GRPY: An Accurate Bead Method for Calculation of Hydrodynamic Properties of Rigid Biomacromolecules

Two main problems that arise in the context of hydrodynamic bead modeling are an inaccurate treatment of bead overlaps and the necessity of using volume corrections when calculating intrinsic viscosity. We present a formalism based on the generalized Rotne-Prager-Yamakawa approximation that successfully addresses both of these issues. The generalized Rotne-Prager-Yamakawa method is shown to be highly effective for the calculation of transport properties of rigid biomolecules represented as assemblies of spherical beads of different sizes, both overlapping and nonoverlapping. We test the method on simple molecular shapes as well as real protein structures and compare its performance with other computational approaches.

HullRad: Fast Calculations of Folded and Disordered Protein and Nucleic Acid Hydrodynamic Properties

Hydrodynamic properties are useful parameters for estimating the size and shape of proteins and nucleic acids in solution. The calculation of such properties from structural models informs on the solution properties of these molecules and complements corresponding structural studies. Here we report, to our knowledge, a new method to accurately predict the hydrodynamic properties of molecular structures. This method uses a convex hull model to estimate the hydrodynamic volume of the molecule and is orders of magnitude faster than common methods. It works well for both folded proteins and ensembles of conformationally heterogeneous proteins and for nucleic acids. Because of its simplicity and speed, the method should be useful for the modification of computer-generated, intrinsically disordered protein ensembles and ensembles of flexible, but folded, molecules in which rapid calculation of experimental parameters is needed. The convex hull method is implemented in a Python script called HullRad. The use of the method is facilitated by a web server and the code is freely available for batch applications.

General principles of binding between cell surface receptors and multi-specific ligands: A computational study

The interactions between membrane receptors and extracellular ligands control cell-cell and cell-substrate adhesion, and environmental responsiveness by representing the initial steps of cell signaling pathways. These interactions can be spatial-temporally regulated when different extracellular ligands are tethered. The detailed mechanisms of this spatial-temporal regulation, including the competition between distinct ligands with overlapping binding sites and the conformational flexibility in multi-specific ligand assemblies have not been quantitatively evaluated. We present a new coarse-grained model to realistically simulate the binding process between multi-specific ligands and membrane receptors on cell surfaces. The model simplifies each receptor and each binding site in a multi-specific ligand as a rigid body. Different numbers or types of ligands are spatially organized together in the simulation. These designs were used to test the relation between the overall binding of a multi-specific ligand and the affinity of its cognate binding site. When a variety of ligands are exposed to cells expressing different densities of surface receptors, we demonstrated that ligands with reduced affinities have higher specificity to distinguish cells based on the relative concentrations of their receptors. Finally, modification of intramolecular flexibility was shown to play a role in optimizing the binding between receptors and ligands. In summary, our studies bring new insights to the general principles of ligand-receptor interactions. Future applications of our method will pave the way for new strategies to generate next-generation biologics.

In order to adapt to surrounding environments, multiple signaling pathways have been evolved in cells. The first step of these pathways is to detect external stimuli, which is conducted by the dynamic interactions between cell surface receptors and extracellular ligands. As a result, recognition of extracellular ligands by cell surface receptors is an indispensable component of many physiological or pathological activities. In both natural selection and drug design, the presence of multiple binding sites in extracellular ligand complexes (so-called multi-specific ligands) is a common strategy to target different receptors on surface of the same cell. Such spatial organization of ligand binding sites can elaborately modulate the downstream signaling pathways. However, our understanding to the interactions between multi-specific ligands and membrane receptors is largely limited by the fact that these interactions are difficult to quantify and they have only been successfully measured in a very small number of cases in vivo. Using a simple computational model, we can realistically simulate the binding process between specially designed multi-specific ligands and membrane receptors on cell surfaces. This study therefore provides a useful pathway to unravel basic mechanisms of ligand-receptor interactions and design principles for new drug candidates.

Predicting Protein-protein Association Rates using Coarse-grained Simulation and Machine Learning

Protein–protein interactions dominate all major biological processes in living cells. We have developed a new Monte Carlo-based simulation algorithm to study the kinetic process of protein association. We tested our method on a previously used large benchmark set of 49 protein complexes. The predicted rate was overestimated in the benchmark test compared to the experimental results for a group of protein complexes. We hypothesized that this resulted from molecular flexibility at the interface regions of the interacting proteins. After applying a machine learning algorithm with input variables that accounted for both the conformational flexibility and the energetic factor of binding, we successfully identified most of the protein complexes with overestimated association rates and improved our final prediction by using a cross-validation test. This method was then applied to a new independent test set and resulted in a similar prediction accuracy to that obtained using the training set. It has been thought that diffusion-limited protein association is dominated by long-range interactions. Our results provide strong evidence that the conformational flexibility also plays an important role in regulating protein association. Our studies provide new insights into the mechanism of protein association and offer a computationally efficient tool for predicting its rate.

The unusual internal motion of the villin headpiece subdomain

The thermostable 36-residue subdomain of the villin headpiece (HP36) is the smallest known cooperatively folding protein. Although the folding and internal dynamics of HP36 and close variants have been extensively studied, there has not been a comprehensive investigation of side-chain motion in this protein. Here, the fast motion of methyl-bearing amino acid side chains is explored over a range of temperatures using site-resolved solution nuclear magnetic resonance deuterium relaxation. The squared generalized order parameters of methyl groups extensively spatially segregate according to motional classes. This has not been observed before in any protein studied using this methodology. The class segregation is preserved from 275 to 305 K. Motions detected in Helix 3 suggest a fast timescale of conformational heterogeneity that has not been previously observed but is consistent with a range of folding and dynamics studies. Finally, a comparison between the order parameters in solution with previous results based on solid-state nuclear magnetic resonance deuterium line shape analysis of HP36 in partially hydrated powders shows a clear disagreement for half of the sites. This result has significant implications for the interpretation of data derived from a variety of approaches that rely on partially hydrated protein samples.

Hydrodynamic Modeling and Its Application in AUC

The hydrodynamic parameters measured in an AUC experiment, s(20,w) and D(t)(20,w)(0), can be used to gain information on the solution structure of (bio)macromolecules and their assemblies. This entails comparing the measured parameters with those that can be computed from usually "dry" structures by "hydrodynamic modeling." In this chapter, we will first briefly put hydrodynamic modeling in perspective and present the basic physics behind it as implemented in the most commonly used methods. The important "hydration" issue is also touched upon, and the distinction between rigid bodies versus those for which flexibility must be considered in the modeling process is then made. The available hydrodynamic modeling/computation programs, HYDROPRO, BEST, SoMo, AtoB, and Zeno, the latter four all implemented within the US-SOMO suite, are described and their performance evaluated. Finally, some literature examples are presented to illustrate the potential applications of hydrodynamics in the expanding field of multiresolution modeling.

Hard sphere-like glass transition in eye lens α-crystallin solutions

We study the equilibrium liquid structure and dynamics of dilute and concentrated bovine eye lens α-crystallin solutions, using small-angle X-ray scattering, static and dynamic light scattering, viscometry, molecular dynamics simulations, and mode-coupling theory. We find that a polydisperse Percus-Yevick hard-sphere liquid-structure model accurately reproduces both static light scattering data and small-angle X-ray scattering liquid structure data from α-crystallin solutions over an extended range of protein concentrations up to 290 mg/mL or 49% vol fraction and up to ca. 330 mg/mL for static light scattering. The measured dynamic light scattering and viscosity properties are also consistent with those of hard-sphere colloids and show power laws characteristic of an approach toward a glass transition at α-crystallin volume fractions near 58%. Dynamic light scattering at a volume fraction beyond the glass transition indicates formation of an arrested state. We further perform event-driven molecular dynamics simulations of polydisperse hard-sphere systems and use mode-coupling theory to compare the measured dynamic power laws with those of hard-sphere models. The static and dynamic data, simulations, and analysis show that aqueous eye lens α-crystallin solutions exhibit a glass transition at high concentrations that is similar to those found in hard-sphere colloidal systems. The α-crystallin glass transition could have implications for the molecular basis of presbyopia and the kinetics of molecular change during cataractogenesis.

Linking 3D and 2D binding kinetics of membrane proteins by multiscale simulations

Membrane proteins are among the most functionally important proteins in cells. Unlike soluble proteins, they only possess two translational degrees of freedom on cell surfaces, and experience significant constraints on their rotations. As a result, it is currently challenging to characterize the in situ binding of membrane proteins. Using the membrane receptors CD2 and CD58 as a testing system, we developed a multiscale simulation framework to study the differences of protein binding kinetics between 3D and 2D environments. The association and dissociation processes were implemented by a coarse-grained Monte-Carlo algorithm, while the dynamic properties of proteins diffusing on lipid bilayer were captured from all-atom molecular dynamic simulations. Our simulations show that molecular diffusion, linker flexibility and membrane fluctuations are important factors in adjusting binding kinetics. Moreover, by calibrating simulation parameters to the measurements of 3D binding, we derived the 2D binding constant which is quantitatively consistent with the experimental data, indicating that the method is able to capture the difference between 3D and 2D binding environments. Finally, we found that the 2D dissociation between CD2 and CD58 is about 100-fold slower than the 3D dissociation. In summary, our simulation framework offered a generic approach to study binding mechanisms of membrane proteins.

Elucidating molecular motion through structural and dynamic filters of energy-minimized conformer ensembles

Complex RNA structures are constructed from helical segments connected by flexible loops that move spontaneously and in response to binding of small molecule ligands and proteins. Understanding the conformational variability of RNA requires the characterization of the coupled time evolution of interconnected flexible domains. To elucidate the collective molecular motions and explore the conformational landscape of the HIV-1 TAR RNA, we describe a new methodology that utilizes energy-minimized structures generated by the program “Fragment Assembly of RNA with Full-Atom Refinement (FARFAR)”. We apply structural filters in the form of experimental residual dipolar couplings (RDCs) to select a subset of discrete energy-minimized conformers and carry out principal component analyses (PCA) to corroborate the choice of the filtered subset. We use this subset of structures to calculate solution T₁ and T_1ρ relaxation times for ¹³C spins in multiple residues in different domains of the molecule using two simulation protocols that we previously published. We match the experimental T₁ times to within 2% and the T_1ρ times to within less than 10% for helical residues. These results introduce a protocol to construct viable dynamic trajectories for RNA molecules that accord well with experimental NMR data and support the notion that the motions of the helical portions of this small RNA can be described by a relatively small number of discrete conformations exchanging over time scales longer than 1 μs.

Solution properties of γ-crystallins: hydration of fish and mammal γ-crystallins

Lens γ crystallins are found at the highest protein concentration of any tissue, ranging from 300 mg/mL in some mammals to over 1000 mg/mL in fish. Such high concentrations are necessary for the refraction of light, but impose extreme requirements for protein stability and solubility. γ-crystallins, small stable monomeric proteins, are particularly associated with the lowest hydration regions of the lens. Here, we examine the solvation of selected γ-crystallins from mammals (human γD and mouse γS) and fish (zebrafish γM2b and γM7). The thermodynamic water binding coefficient B₁ could be probed by sucrose expulsion, and the hydrodynamic hydration shell of tightly bound water was probed by translational diffusion and structure-based hydrodynamic boundary element modeling. While the amount of tightly bound water of human γD was consistent with that of average proteins, the water binding of mouse γS was found to be relatively low. γM2b and γM7 crystallins were found to exhibit extremely low degrees hydration, consistent with their role in the fish lens. γM crystallins have a very high methionine content, in some species up to 15%. Structure-based modeling of hydration in γM7 crystallin suggests low hydration is associated with the large number of surface methionine residues, likely in adaptation to the extremely high concentration and low hydration environment in fish lenses. Overall, the degree of hydration appears to balance stability and tissue density requirements required to produce and maintain the optical properties of the lens in different vertebrate species.

Improving the thermal, radial, and temporal accuracy of the analytical ultracentrifuge through external references

Sedimentation velocity (SV) is a method based on first principles that provides a precise hydrodynamic characterization of macromolecules in solution. Due to recent improvements in data analysis, the accuracy of experimental SV data emerges as a limiting factor in its interpretation. Our goal was to unravel the sources of experimental error and develop improved calibration procedures. We implemented the use of a Thermochron iButton temperature logger to directly measure the temperature of a spinning rotor and detected deviations that can translate into an error of as much as 10% in the sedimentation coefficient. We further designed a precision mask with equidistant markers to correct for instrumental errors in the radial calibration that were observed to span a range of 8.6%. The need for an independent time calibration emerged with use of the current data acquisition software (Zhao et al., Anal. Biochem., 437 (2013) 104-108), and we now show that smaller but significant time errors of up to 2% also occur with earlier versions. After application of these calibration corrections, the sedimentation coefficients obtained from 11 instruments displayed a significantly reduced standard deviation of approximately 0.7%. This study demonstrates the need for external calibration procedures and regular control experiments with a sedimentation coefficient standard.

Holographic measurements of anisotropic three-dimensional diffusion of colloidal clusters

We measure all nonzero elements of the three-dimensional diffusion tensor D for clusters of colloidal spheres to a precision of 1% or better using digital holographic microscopy. We study both dimers and triangular trimers of spheres, for which no analytical calculations of the diffusion tensor exist. We observe anisotropic rotational and translational diffusion arising from the asymmetries of the clusters. In the case of the three-particle triangular cluster, we also detect a small but statistically significant difference in the rotational diffusion about the two in-plane axes. We attribute this difference to weak breaking of threefold rotational symmetry due to a small amount of particle polydispersity. Our experimental measurements agree well with numerical calculations and show how diffusion constants can be measured under conditions relevant to colloidal self-assembly, where theoretical and even numerical prediction is difficult.

Recorded scan times can limit the accuracy of sedimentation coefficients in analytical ultracentrifugation

We report systematic and large inaccuracies in the recorded elapsed time in data files from the analytical ultracentrifuge, leading to overestimates of the sedimentation coefficients of up to 10%. This far exceeds previously considered factors contributing to the uncertainty in this parameter and has significant ramifications for derived parameters such as hydrodynamic shape and molar mass estimates. The source of this error is currently unknown, but we found it to be quantitatively consistent across different instruments, increasing with rotor speed. Furthermore, its occurrence appears to correlate with the use of the latest data acquisition software from the manufacturer, in use in some of our laboratories for nearly 2 years. Many of the recently published sedimentation coefficients may need to be reexamined. The problem can be easily recognized by comparing the file timestamps provided by the operating system with the elapsed scan times recorded within the data files. Therefore, we implemented a routine in SEDFIT that can automatically examine the data files, alert the user to significant discrepancies, and correct the scan times accordingly. This eliminates errors in the recorded scan times.

Hydrodynamic modelling of protein conformation in solution: ELLIPS and HYDRO

The last three decades has seen some important advances in our ability to represent the conformation of proteins in solution on the basis of hydrodynamic measurements. Advances in theoretical modeling capabilities have been matched by commensurate advances in the precision of hydrodynamic measurements. We consider the advances in whole-body (simple ellipsoid-based) modeling—still useful for providing an overall idea of molecular shape, particularly for those systems where only a limited amount of data is available—and outline the ELLIPS suite of algorithms which facilitates the use of this approach. We then focus on bead modeling strategies, particularly the surface or shell–bead approaches and the HYDRO suite of algorithms. We demonstrate how these are providing great insights into complex issues such as the conformation of immunoglobulins and other multi-domain complexes.

Overview of current methods in sedimentation velocity and sedimentation equilibrium analytical ultracentrifugation

Modern computational strategies have allowed for the direct modeling of the sedimentation process of heterogeneous mixtures, resulting in sedimentation velocity (SV) size-distribution analyses with significantly improved detection limits and strongly enhanced resolution. These advances have transformed the practice of SV, rendering it the primary method of choice for most existing applications of analytical ultracentrifugation (AUC), such as the study of protein self- and hetero-association, the study of membrane proteins, and applications in biotechnology. New global multisignal modeling and mass conservation approaches in SV and sedimentation equilibrium (SE), in conjunction with the effective-particle framework for interpreting the sedimentation boundary structure of interacting systems, as well as tools for explicit modeling of the reaction/diffusion/sedimentation equations to experimental data, have led to more robust and more powerful strategies for the study of reversible protein interactions and multiprotein complexes. Furthermore, modern mathematical modeling capabilities have allowed for a detailed description of many experimental aspects of the acquired data, thus enabling novel experimental opportunities, with important implications for both sample preparation and data acquisition. The goal of the current unit is to describe the current tools for the study of soluble proteins, detergent-solubilized membrane proteins and their interactions by SV and SE.

Free energy of conformational transition paths in biomolecules: the string method and its application to myosin VI

A set of techniques developed under the umbrella of the string method is used in combination with all-atom molecular dynamics simulations to analyze the conformation change between the prepowerstroke (PPS) and rigor (R) structures of the converter domain of myosin VI. The challenges specific to the application of these techniques to such a large and complex biomolecule are addressed in detail. These challenges include (i) identifying a proper set of collective variables to apply the string method, (ii) finding a suitable initial string, (iii) obtaining converged profiles of the free energy along the transition path, (iv) validating and interpreting the free energy profiles, and (v) computing the mean first passage time of the transition. A detailed description of the PPS↔R transition in the converter domain of myosin VI is obtained, including the transition path, the free energy along the path, and the rates of interconversion. The methodology developed here is expected to be useful more generally in studies of conformational transitions in complex biomolecules.

Dimeric states of neural- and epithelial-cadherins are distinguished by the rate of disassembly

Epithelial- and neural-cadherins are specifically localized at synapses in neurons which can change the shape and contact surface on a time scale of seconds to months. We have focused our studies on the role of the extracellular domains of cadherins in the dynamics of synapses. The kinetics of dimer disassembly of the first two extracellular domains of E- and N-cadherin, ECAD12 and NCAD12, were studied with analytical size exclusion chromatography and sedimentation velocity. NCAD12 forms three different dimers that are distinguished by assembly conditions and kinetics of dissociation. ECAD12 dimer disassembles rapidly regardless of the calcium concentration, whereas the disassembly of NCAD12 dimers was strongly dependent on calcium concentration. In addition to the apo- and saturated-dimeric forms of NCAD12, there is a third dimeric form that is a slow exchange dimer. This third dimeric form for NCAD12, formed by decalcification of the calcium-saturated dimer, was kinetically trapped in apo-conditions and did not disassemble over a period of months. Sedimentation velocity experiments showed that this dimer, upon addition of calcium, had similar weighted averages as a calcium-saturated dimer. These studies provide evidence that the kinetics of dimer disassembly of the extracellular domains may be a major contributor to the morphological dynamics of synapses in vivo.

Recent advances in macromolecular hydrodynamic modeling

The modern implementation of the boundary element method [23] has ushered unprecedented accuracy and precision for the solution of the Stokes equations of hydrodynamics with stick boundary conditions. This article begins by reviewing computations with the program BEST of smooth surface objects such as ellipsoids, the dumbbell, and cylinders that demonstrate that the numerical solution of the integral equation formulation of hydrodynamics yields very high precision and accuracy. When BEST is used for macromolecular computations, the limiting factor becomes the definition of the molecular hydrodynamic surface and the implied effective solvation of the molecular surface. Studies on 49 different proteins, ranging in molecular weight from 9 to over 400kDa, have shown that a model using a 1.1Å thick hydration layer describes all protein transport properties very well for the overwhelming majority of them. In addition, this data implies that the crystal structure is an excellent representation of the average solution structure for most of them. In order to investigate the origin of a handful of significant discrepancies in some multimeric proteins (about -20% observed in the intrinsic viscosity), the technique of Molecular Dynamics simulation (MD) has been incorporated into the research program. A preliminary study of dimeric α-chymotrypsin using approximate implicit water MD is presented. In addition I describe the successful validation of modern protein force fields, ff03 and ff99SB, for the accurate computation of solution structure in explicit water simulation by comparison of trajectory ensemble average computed transport properties with experimental measurements. This work includes small proteins such as lysozyme, ribonuclease and ubiquitin using trajectories around 10ns duration. We have also studied a 150kDa flexible monoclonal IgG antibody, Trastuzumab, with multiple independent trajectories encompassing over 320ns of simulation. The close agreement within experimental error of the computed and measured properties allows us to conclude that MD does produce structures typical of those in solution, and that flexible molecules can be properly described using the method of ensemble averaging over a trajectory. We review similar work on the study of a transfer RNA molecule and DNA oligomers that demonstrate that within 3% a simple uniform hydration model 1.1Å thick provides agreement with experiment for these nucleic acids. In the case of linear oligomers, the precision can be improved close to 1% by a non-uniform hydration model that hydrates mainly in the DNA grooves, in agreement with high resolution X-ray diffraction. We conclude with a vista on planned improvements for the BEST program to decrease its memory requirements and increase its speed without sacrificing accuracy.

Construction, MD simulation, and hydrodynamic validation of an all-atom model of a monoclonal IgG antibody

At 150 kDa, antibodies of the IgG class are too large for their structure to be determined with current NMR methodologies. Because of hinge-region flexibility, it is difficult to obtain atomic-level structural information from the crystal, and questions regarding antibody structure and dynamics in solution remain unaddressed. Here we describe the construction of a model of a human IgG1 monoclonal antibody (trastuzumab) from the crystal structures of fragments. We use a combination of molecular-dynamics (MD) simulation, continuum hydrodynamics modeling, and experimental diffusion measurements to explore antibody behavior in aqueous solution. Hydrodynamic modeling provides a link between the atomic-level details of MD simulation and the size- and shape-dependent data provided by hydrodynamic measurements. Eight independent 40 ns MD trajectories were obtained with the AMBER program suite. The ensemble average of the computed transport properties over all of the MD trajectories agrees remarkably well with the value of the translational diffusion coefficient obtained with dynamic light scattering at 20 degrees C and 27 degrees C, and the intrinsic viscosity measured at 20 degrees C. Therefore, our MD results likely represent a realistic sampling of the conformational space that an antibody explores in aqueous solution.

Orientational and translational dynamics of polyether/water solutions

Optical heterodyne-detected optical Kerr effect (OHD-OKE) experiments and pulsed field-gradient spin-echo NMR (PFGSE-NMR) experiments were performed to measure the rotational and translational diffusion constants of a polyether, tetraethylene glycol dimethyl ether (TEGDE), in binary mixtures with water over concentrations ranging from pure TEGDE to approaching infinite dilution. In addition, hydrodynamic calculations of the rotational and translational diffusion constants for several rigid TEGDE conformations in the neat liquid and in the infinitely dilute solution were performed to supplement the experimental data. The rotational relaxation data follow the Debye-Stokes-Einstein (DSE) equation within experimental error over the entire water concentration range. The agreement with the DSE equation indicates that there is no significant structural change of the polyether as the water content is changed. In contrast to the rotational dynamics, the translational diffusion data show a distinct deviation from Stokes-Einstein (SE) behavior. As the water content of the mixture is reduced, the translational diffusion rate decreases less rapidly than the increase in viscosity alone predicts until the water/TEGDE mole ratio of 7:1 is reached. Upon further reduction of water content, the translational diffusion tracks the viscosity. Comparison of the translational data with the rotational data and the hydrodynamic computations shows that the translational dynamics cannot be explained by a molecular shape change and that the low water fraction solutions are the ones that deviate from hydrodynamic behavior. A conjecture is presented as a possible explanation for the different behaviors of the rotational and translational dynamics.

Proton-driven assembly of the Rous Sarcoma virus capsid protein results in the formation of icosahedral particles

In a mature and infectious retroviral particle, the capsid protein (CA) forms a shell surrounding the genomic RNA and the replicative machinery of the virus. The irregular nature of this capsid shell precludes direct atomic resolution structural analysis. CA hexamers and pentamers are the fundamental building blocks of the capsid, however the pentameric state, in particular, remains poorly characterized. We have developed an efficient in vitro protocol for studying the assembly of Rous sarcoma virus (RSV) CA that involves mild acidification and produces structures modeling the authentic viral capsid. These structures include regular spherical particles with T = 1 icosahedral symmetry, built from CA pentamers alone. These particles were subject to cryoelectron microscopy (cryo-EM) and image processing, and a pseudo-atomic model of the icosahedron was created by docking atomic structures of the constituent CA domains into the cryo-EM-derived three-dimensional density map. The N-terminal domain (NTD) of CA forms pentameric turrets, which decorate the surface of the icosahedron, while the C-terminal domain (CTD) of CA is positioned underneath, linking the pentamers. Biophysical analysis of the icosahedral particle preparation reveals that CA monomers and icosahedra are the only detectable species and that these exist in reversible equilibrium at pH 5. These same acidic conditions are known to promote formation of a RSV CA CTD dimer, present within the icosahedral particle, which facilitates capsid assembly. The results are consistent with a model in which RSV CA assembly is a nucleation-limited process driven by very weak protein-protein interactions.

Prediction of the rotational tumbling time for proteins with disordered segments

For well-structured, rigid proteins, the prediction of rotational tumbling time (tau(c)) using atomic coordinates is reasonably accurate, but is inaccurate for proteins with long unstructured sequences. Under physiological conditions, many proteins contain long disordered segments that play important regulatory roles in fundamental biological events including signal transduction and molecular recognition. Here we describe an ensemble approach to the boundary element method that accurately predicts tau(c) for such proteins by introducing two layers of molecular surfaces whose correlated velocities decay exponentially with distance. Reliable prediction of tau(c) will help to detect intra- and intermolecular interactions and conformational switches between more ordered and less ordered states of the disordered segments. The method has been extensively validated using 12 reference proteins with 14 to 103 disordered residues at the N- and/or C-terminus and has been successfully employed to explain a set of published results on a system that incorporates a conformational switch.

Stagnation of flow in protein cavities by boundary element microhydrodynamics

In this work, we apply the boundary element method to describe the fluid velocity profiles in pockets in protein surfaces that are crucial to their function as enzymes. First, we study a simplified model, that of a dimpled sphere, in order to properly interpret the behavior in more complex surfaces such as proteins. In that case, we are able to observe the difference between an unphysical sharp edge for the dimple and a smooth edge. The sharp edge produces extra dissipation in the fluid, accounting for much more friction for all types of body motions. We were able to observe the direct correlation of the stagnation depth with the depth of the dimple in this simple case, allowing us to interpret this feature in a similar fashion for proteins. We have found that the fluid in the protein pockets translates with the body, irrespective of the direction body motion, for a distance comparable to the size of the pocket, and that such stagnation volumes are larger for motions parallel to the pocket axis. Outside of these pockets, the fluid velocity profile decays to that of the surrounding fluid far away from the protein (taken to be zero in our case, for convenience), as the Oseen tensor requires. We have also found that there is weak local motion of fluid inside of the pockets, with velocities about 1% of those of the body. This study suggests that there may be a role for the hydrodynamics of solvent inside of pockets for the transport of substrates to protein active sites. If solvent is effectively stagnant inside of a pocket, then transport must occur by diffusion near the pocket surface even if the fluid around the protein is stirred. The weak local motions inside of the pocket may also be relevant in this transport process, but these may be easily overwhelmed by any electrostatic interactions that are likely present at active sites.

Modeling the sequence-dependent diffusion coefficients of short DNA molecules

A boundary element model for the computation of sequence-dependent hydrodynamic properties of short DNA molecules is introduced. The hydrated surface is modeled as a curved tube of uniform radius with ends capped by hemispheres, and the axis of the tube is a general space curve whose length and curvature are determined locally by the sequence using a rigid basepair model of double-helical DNA with parameters based on x-ray crystallography. Diffusion coefficients for families of random and periodic DNA sequences are computed and compared with theories for straight tubes and experimental data. Our results indicate that sequence-dependent curvature can have a measurable impact on both the translational and rotational diffusion coefficients, even for relatively short fragments of lengths less than about 150 basepairs, and that previous estimates of the hydrated radius of DNA are likely to be underestimates. Moreover, our results suggest a possible method for refining the rigid basepair model parameters for DNA in solution as well as the hydrated radius.

Simulation of nitroxide electron paramagnetic resonance spectra from brownian trajectories and molecular dynamics simulations

A simulated continuous wave electron paramagnetic resonance spectrum of a nitroxide spin label can be obtained from the Fourier transform of a free induction decay. It has been previously shown that the free induction decay can be calculated by solving the time-dependent stochastic Liouville equation for a set of Brownian trajectories defining the rotational dynamics of the label. In this work, a quaternion-based Monte Carlo algorithm has been developed to generate Brownian trajectories describing the global rotational diffusion of a spin-labeled protein. Also, molecular dynamics simulations of two spin-labeled mutants of T4 lysozyme, T4L F153R1, and T4L K65R1 have been used to generate trajectories describing the internal dynamics of the protein and the local dynamics of the spin-label side chain. Trajectories from the molecular dynamics simulations combined with trajectories describing the global rotational diffusion of the protein are used to account for all of the dynamics of a spin-labeled protein. Spectra calculated from these combined trajectories correspond well to the experimental spectra for the buried site T4L F153R1 and the helix surface site T4L K65R1. This work provides a framework to further explore the modeling of the dynamics of the spin-label side chain in the wide variety of labeling environments encountered in site-directed spin labeling studies.

Structure of the nucleocapsid-binding domain from the mumps virus polymerase; an example of protein folding induced by crystallization

The human pathogen mumps virus, like all paramyxoviruses, encodes a polymerase responsible for virally directed RNA synthesis. The template for the polymerase is the nucleocapsid, a filamentous protein-RNA complex harboring the viral genome. Interaction of the polymerase and the nucleocapsid is mediated by a small domain tethered to the end of the phosphoprotein (P), one of the polymerase subunits. We report the X-ray crystal structure of this region of mumps virus P (the nucleocapsid-binding domain, or NBD, amino acids 343-391). The mumps P NBD forms a compact bundle of three alpha-helices within the crystal, a fold apparently conserved across the Paramyxovirinae. In solution, however, the domain exists in the molten globule state. This is demonstrated through application of differential scanning calorimetry, circular dichroism spectroscopy, NMR spectroscopy, and dynamic light scattering. While the mumps P NBD is compact and has persistent secondary structure, it lacks a well-defined tertiary structure under normal solution conditions. It can, however, be induced to fold by addition of a stabilizing methylamine cosolute. The domain provides a rare example of a molten globule that can be crystallized. The structure that is stabilized in the crystal represents the fully folded state of the domain, which must be transiently realized during binding to the viral nucleocapsid. While the intermolecular forces that govern the polymerase-nucleocapsid interaction appear to be different in measles, mumps, and Sendai viruses, for each of these viruses, polymerase translocation involves the coupled binding and folding of protein domains. In all cases, we suggest that this will result in a weak-affinity protein complex with a short lifetime, which allows the polymerase to take rapid steps forward.