Microscopic diffusion and hydrodynamic interactions of hemoglobin in red blood cells

Testing mixing rules for structural and dynamical quantities in multi-component crowded protein solutions

Crowding effects significantly influence the phase behavior and the structural and dynamic properties of the concentrated protein mixtures present in the cytoplasm of cells or in the blood serum. This poses enormous difficulties for our theoretical understanding and our ability to predict the behavior of these systems. While the use of course grained colloid-inspired models allows us to reproduce the key physical solution properties of concentrated monodisperse solutions of individual proteins, we lack corresponding theories for complex polydisperse mixtures. Here, we test the applicability of simple mixing rules in order to predict solution properties of protein mixtures. We use binary mixtures of the well-characterized bovine eye lens proteins α and γB crystallin as model systems. Combining microrheology with static and dynamic scattering techniques and observations of the phase diagram for liquid-liquid phase separation, we show that reasonably accurate descriptions are possible for macroscopic and mesoscopic signatures, while information on the length scale of the individual protein size requires more information on cross-component interaction.

Effects of Crowding and Cosolutes on Biomolecular Function at Extreme Environmental Conditions

The extent of the effect of cellular crowding and cosolutes on the functioning of proteins and cells is manifold and includes the stabilization of the biomolecular systems, the excluded volume effect, and the modulation of molecular dynamics. Simultaneously, it is becoming increasingly clear how important it is to take the environment into account if we are to shed light on biological function under various external conditions. Many biosystems thrive under extreme conditions, including the deep sea and subseafloor crust, and can take advantage of some of the effects of crowding. These relationships have been studied in recent years using various biophysical techniques, including neutron and X-ray scattering, calorimetry, FTIR, UV-vis and fluorescence spectroscopies. Combining knowledge of the structure and conformational dynamics of biomolecules under extreme conditions, such as temperature, high hydrostatic pressure, and high salinity, we highlight the importance of considering all results in the context of the environment. Here we discuss crowding and cosolute effects on proteins, nucleic acids, membranes, and live cells and explain how it is possible to experimentally separate crowding-induced effects from other influences. Such findings will contribute to a better understanding of the homeoviscous adaptation of organisms and the limits of life in general.

Contraction of the rigor actomyosin complex drives bulk hemoglobin expulsion from hemolyzing erythrocytes

Erythrocyte ghost formation via hemolysis is a key event in the physiological clearance of senescent red blood cells (RBCs) in the spleen. The turnover rate of millions of RBCs per second necessitates a rapid efflux of hemoglobin (Hb) from RBCs by a not yet identified mechanism. Using high-speed video-microscopy of isolated RBCs, we show that electroporation-induced efflux of cytosolic ATP and other small solutes leads to transient cell shrinkage and echinocytosis, followed by osmotic swelling to the critical hemolytic volume. The onset of hemolysis coincided with a sudden self-propelled cell motion, accompanied by cell contraction and Hb-jet ejection. Our biomechanical model, which relates the Hb-jet-driven cell motion to the cytosolic pressure generation via elastic contraction of the RBC membrane, showed that the contributions of the bilayer and the bilayer-anchored spectrin cytoskeleton to the hemolytic cell motion are negligible. Consistent with the biomechanical analysis, our biochemical experiments, involving extracellular ATP and the myosin inhibitor blebbistatin, identify the low abundant non-muscle myosin 2A (NM2A) as the key contributor to the Hb-jet emission and fast hemolytic cell motion. Thus, our data reveal a rapid myosin-based mechanism of hemolysis, as opposed to a much slower diffusive Hb efflux.

Short-Time Transport Properties of Bidisperse Suspensions of Immunoglobulins and Serum Albumins Consistent with a Colloid Physics Picture

The crowded environment of biological systems such as the interior of living cells is occupied by macromolecules with a broad size distribution. This situation of polydispersity might influence the dependence of the diffusive dynamics of a given tracer macromolecule in a monodisperse solution on its hydrodynamic size and on the volume fraction. The resulting size dependence of diffusive transport crucially influences the function of a living cell. Here, we investigate a simplified model system consisting of two constituents in aqueous solution, namely, of the proteins bovine serum albumin (BSA) and bovine polyclonal gamma-globulin (Ig), systematically depending on the total volume fraction and ratio of these constituents. From high-resolution quasi-elastic neutron spectroscopy, the separate apparent short-time diffusion coefficients for BSA and Ig in the mixture are extracted, which show substantial deviations from the diffusion coefficients measured in monodisperse solutions at the same total volume fraction. These deviations can be modeled quantitatively using results from the short-time rotational and translational diffusion in a two-component hard sphere system with two distinct, effective hydrodynamic radii. Thus, we find that a simple colloid picture well describes short-time diffusion in binary mixtures as a function of the mixing ratio and the total volume fraction. Notably, the self-diffusion of the smaller protein BSA in the mixture is faster than the diffusion in a pure BSA solution, whereas the self-diffusion of Ig in the mixture is slower than in the pure Ig solution.

Passive and active tracer dynamics in polymer solutions with isotropic-to-nematic phase transition

Macromolecular crowding plays a crucial role in determining the dynamics in a living cell. We adopt Langevin dynamics simulations to investigate the anomalous diffusion dynamics of passive and active particles in a solution of polymer chains with tunable stiffness. The solution's anisotropic feature is modulated by changing both the polymer stiffness and volume fraction, where isotropic-to-nematic phase transition is involved. Our results demonstrate the significant impact of polymer flexibility on the dynamics of both passive and active probes. The distinct diffusion mechanism for an active particle is clarified by the interplay between polymer stiffness, crowdedness and activity. Polymer stiffness leads to a global inhibition effect on passive particle diffusion. The diffusion coefficient exhibits an intriguing non-monotonic variation at increasing polymer stiffness, which is due to the fact that the alignment of polymer chains is beneficial for diffusion along the nematic direction but unfavorable for that in the direction perpendicular to it. In sharp contrast, polymer stiffness plays a dominant role in facilitating active particle diffusion. Self-propulsion of the particle can utilize stiffness-induced elastic interactions more efficiently, which promotes its mobility in both directions. Meanwhile, an active particle might have a stronger ability to take advantage of the polymer alignment, contributing substantially enhanced diffusivity. In addition, the diffusion coefficient of an active particle is subject to a tendency of degeneration against varying volume fraction. This counter-intuitive behavior is due to the contrasting factors that increasing crowdedness induces a lower particle speed but a longer persistent motion time.

Conformational dynamics of a multidomain protein by neutron scattering and computational analysis

The flexible conformations of a multidomain protein are responsible for its biological functions. Although MurD, a 47-kDa protein that consists of three domains, sequentially changes its domain conformation from an open form to a closed form through a semiclosed form in its enzymatic reaction, the domain dynamics in each conformation remains unclear. In this study, we verify the conformational dynamics of MurD in the corresponding three states (apo and ATP- and inhibitor-bound states) with a combination of small-angle x-ray and neutron scattering (SAXS and SANS), dynamic light scattering (DLS), neutron backscattering (NBS), neutron spin echo (NSE) spectroscopy, and molecular dynamics (MD) simulations. Applying principal component analysis of the MD trajectories, twisting and open-closed domain modes are identified as the major collective coordinates. The deviations of the experimental SAXS profiles from the theoretical calculations based on the known crystal structures become smaller in the ATP-bound state than in the apo state, and a further decrease is evident upon inhibitor binding. These results suggest that domain motions of the protein are suppressed step by step of each ligand binding. The DLS and NBS data yield collective and self-translational diffusion constants, respectively, and we used them to extract collective domain motions in nanometer and nanosecond scales from the NSE data. In the apo state, MurD shows both twisting and open-closed domain modes, whereas an ATP binding suppresses twisting domain motions, and a further reduction of open-closed mode is seen in the inhibitor-binding state. These observations are consistent with the structure modifications measured by the small-angle scattering as well as the MD simulations. Such changes in the domain dynamics associated with the sequential enzymatic reactions should be related to the affinity and reaction efficiency with a ligand that binds specifically to each reaction state.

Brownian Dynamics Simulations of Proteins in the Presence of Surfaces: Long-Range Electrostatics and Mean-Field Hydrodynamics

Simulations of macromolecular diffusion and adsorption in confined environments can offer valuable mechanistic insights into numerous biophysical processes. In order to model solutes at atomic detail on relevant time scales, Brownian dynamics simulations can be carried out with the approximation of rigid body solutes moving through a continuum solvent. This allows the precomputation of interaction potential grids for the solutes, thereby allowing the computationally efficient calculation of forces. However, hydrodynamic and long-range electrostatic interactions cannot be fully treated with grid-based approaches alone. Here, we develop a treatment of both hydrodynamic and electrostatic interactions to include the presence of surfaces by modeling grid-based and long-range interactions. We describe its application to simulate the self-association and many-molecule adsorption of the well-characterized protein hen egg-white lysozyme to mica-like and silica-like surfaces. We find that the computational model can recover a number of experimental observables of the adsorption process and provide insights into their determinants. The computational model is implemented in the Simulation of Diffusional Association (SDA) software package.

Lytic and sublytic effects of gossypol on red blood cells and thymocytes

Gossypol is a natural polyphenol presently considered as a promising biological phytochemical with a range of activities including anticancer. We examined volume regulation-dependent effects of gossypol using erythrocytes and thymic lymphocytes. Gossypol effectively lysed human red blood cells (RBC) with a half-maximal concentration of 67.4 ± 1.6 μmol/L and in a non-colloid osmotic manner. Sublytic gossypol doses of 1-10 μmol/L significantly protected RBC from osmotic hemolysis, but potentiated their sensitivity to the colloid-osmotic lysis induced by a pore-former nystatin. When added to the thymocytes suspension, gossypol caused a strong depression of the ability of cells to restore their volume under hypoosmotic stress with a half-maximal activity at 2.1 ± 0.3 μmol/L. Gossypol suppressed regulatory volume decrease under experimental conditions, when cationic permeability was controlled by gramicidin D, and volume recovery depended mainly on anionic conductance, suggesting that the polyphenol inhibits the swelling-induced anion permeability. In direct patch-clamp experiments, gossypol inhibited the volume-sensitive outwardly rectifying (VSOR) chloride channel in thymocytes and in human HCT116 and HeLa cells, possibly by a mechanism when gossypol molecule with a radius close to the size of channel pore plugs into the narrowest portion of the native VSOR chloride channel. Micromolar gossypol suppressed proliferation of thymocytes, HCT116 and HeLa cells. VSOR blockage may represent new mechanism of anticancer activity of gossypol in addition to its action as a BH3-mimetic.

Crowding in the Eye Lens: Modeling the Multisubunit Protein β-Crystallin with a Colloidal Approach

We present a multiscale characterization of aqueous solutions of the bovine eye lens protein β_H crystallin from dilute conditions up to dynamical arrest, combining dynamic light scattering, small-angle x-ray scattering, tracer-based microrheology, and neutron spin echo spectroscopy. We obtain a comprehensive explanation of the observed experimental signatures from a model of polydisperse hard spheres with additional weak attraction. In particular, the model predictions quantitatively describe the multiscale dynamical results from microscopic nanometer cage diffusion over mesoscopic micrometer gradient diffusion up to macroscopic viscosity. Based on a comparative discussion with results from other crystallin proteins, we suggest an interesting common pathway for dynamical arrest in all crystallin proteins, with potential implications for the understanding of crowding effects in the eye lens.

Effect of red blood cell shape changes on haemoglobin interactions and dynamics: a neutron scattering study

By using a combination of experimental neutron scattering techniques, it is possible to obtain a statistical perspective on red blood cell (RBC) shape in suspensions, and the inter-relationship with protein interactions and dynamics inside the confinement of the cell membrane. In this study, we examined the ultrastructure of RBC and protein-protein interactions of haemoglobin (Hb) in them using ultra-small-angle neutron scattering and small-angle neutron scattering (SANS). In addition, we used the neutron backscattering method to access Hb motion on the ns time scale and Å length scale. Quasi-elastic neutron scattering (QENS) experiments were performed to measure diffusive motion of Hb in RBCs and in an RBC lysate. By using QENS, we probed both internal Hb dynamics and global protein diffusion, on the accessible time scale and length scale by QENS. Shape changes of RBCs and variation of intracellular Hb concentration were induced by addition of the Na⁺-selective ionophore monensin and the K⁺-selective one, valinomycin. The experimental SANS and QENS results are discussed within the framework of crowded protein solutions, where free motion of Hb is obstructed by mutual interactions.

Multiscale modeling of hemolysis during microfiltration

In this paper, we propose a multiscale numerical algorithm to simulate the hemolytic release of hemoglobin (Hb) from red blood cells (RBCs) flowing through sieves containing micropores with mean diameters smaller than RBCs. Analyzing the RBC damage in microfiltration is important in the sense that it can quantify the sensitivity of human erythrocytes to mechanical hemolysis while they undergo high shear rate and high deformation. Here, the numerical simulations are carried out via lattice Boltzmann method and spring connected network (SN) coupled by an immersed boundary method. To predict the RBC sublytic damage, a sub-cellular damage model derived from molecular dynamic simulations is incorporated in the cellular solver. In the proposed algorithm, the local RBC strain distribution calculated by the cellular solver is used to obtain the pore radius on the RBC membrane. Index of hemolysis (IH) is calculated by resorting to the resulting pore radius and solving a diffusion equation considering the effects of steric hinderance and increased hydrodynamic drag due to the size of the hemoglobin molecule. It should be mentioned that current computational hemolysis models usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged RBCs. These empirical correlations contain ad hoc parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis under different conditions. In contrast to the available hemolysis model, the proposed algorithm does not have any empirical parameters. Therefore, it can predict the IH in microfilter with different sieve pore sizes and filtration pressures. Also, in contrast to empirical correlations in which the Hb release is related to shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and hemoglobin release. In this paper, the cellular solver is validated by simulating optical tweezers experiment, shear flow experiment as well as an experiment to measure RBC deformability in a very narrow microchannel. Moreover, the shape of a single RBC at the rupture moment is compared with corresponding experimental data. Finally, to validate the damage model, the results obtained from our parametric study on the role of filtration pressure and sieve pore size in Hb release are compared with experimental data. Numerical results are in good agreement with experimental data. Similar to the corresponding experiment, the numerical results confirm that hemolysis increases with increasing the filtration pressure and reduction in pore size on the sieve. While in experiment, the RBC pore size cannot be measured, the numerical results can quantify the RBC pore size. The numerical results show that at the sieve pore size of 2.2 μm above 25 cm Hg, RBC pore size is above 75 nm and RBCs experience rupture. More importantly, the results demonstrate that the proposed approach is independent from the operating conditions and it can estimate the hemolysis in a wide range of filtration pressure and sieve pore size with reasonable accuracy.

Prediction of mechanical hemolysis in medical devices via a Lagrangian strain-based multiscale model

This work introduces a new Lagrangian strain-based model to predict the shear-induced hemolysis in biomedical devices. Current computational models for device-induced hemolysis usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged red blood cells (RBCs). These empirical correlations contain parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis in a general device. The proposed algorithm does not have any empirical parameters, thus can presumably be used for hemolysis prediction in various blood-wetting medical devices. In contrast to empirical correlations in which the Hb release is related to the shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and Hb release. In this approach, once the steady-state numerical solution of blood flow in the device is obtained under a prescribed operating condition, sample path lines are traced from the inlet of the device to the outlet to calculate the history of the shear stress tensor. In solving the fluid flow, it is assumed that RBCs do not have any influence on the flow pattern. Along each path line, shear stress tensor will be input into a coarse-grained (CG) RBC model to calculate the RBC deformation. Then the correlations obtained from molecular dynamics (MD) simulations are applied to relate the local areal RBC deformation to the perforated area on the RBC membrane. Finally, Hb released out of transient pores is calculated over each path line via a diffusion equation considering the effects of the steric hindrance and increased hydrodynamic drag due to the size of the Hb molecule. The total index of hemolysis (IH) is calculated by integration of released Hb over all the path lines in the computational domain. Hemolysis generated in the Food and Drug Administration (FDA) nozzle and two blood pumps, that is, a CentriMag blood pump (a centrifugal pump) and HeartMate II (an axial pump), for different flow regimes including the laminar and turbulent flows are calculated via the proposed algorithm. In all the simulations, the numerical predicted IH is close to the range of experimental data. The results promisingly indicate that this multiscale approach can be used as a tool for predicting hemolysis and optimizing the hematologic design of other types of blood-wetting devices.

In situ absorbance measurements: a new means to study respiratory electron transfer in chemolithotrophic microorganisms

Absorbance measurements on intact chemolithotrophic microorganisms that respire aerobically on soluble iron are described that used a novel integrating cavity absorption meter to eliminate the effects of light scattering on the experimental results. Steady state kinetic measurements on ferric iron production by intact cells revealed that the Michaelis Menten equation described the initial rates of product formation for at least 8 different chemolithotrophic microorganisms in 6 phyla distributed equally among the archaea and the Gram negative and Gram positive eubacteria. Cell-monitored turnover measurements during aerobic respiration on soluble iron by the same 12 intact microorganisms revealed six different patterns of iron-dependent absorbance changes, suggesting that there may be at least six different sets of prosthetic groups and biomolecules that can accomplish aerobic respiration on soluble iron. Detailed kinetic studies revealed that the 3-component iron respiratory chain of Acidithiobacillus ferrooxidans functioned as an ensemble with a single macroscopic rate constant when the iron-reduced proteins were oxidized in the presence of excess molecular oxygen. The principal member of this 3-component system was a cupredoxin called rusticyanin that was present in the periplasm of At. ferrooxidans at an approximate concentration of 350 mg/mL, an observation that provides new insights into the crowded environments in the periplasms of Gram negative eubacteria that conduct electrons across their periplasm. The ability to conduct direct spectrophotometric measurements under noninvasive physiological conditions represents a new and powerful approach to examine the rates and extents of biological events in situ without disrupting the complexity of the live cellular environment.

Understanding mAb aggregation during low pH viral inactivation and subsequent neutralization

Monoclonal antibodies (mAbs) and related recombinant proteins continue to gain importance in the treatment of a great variety of diseases. Despite significant advances, their manufacturing can still present challenges owing to their molecular complexity and stringent regulations with respect to product purity, stability, safety, and so forth. In this context, protein aggregates are of particular concern due to their immunogenic potential. During manufacturing, mAbs routinely undergo acidic treatment to inactivate viral contamination, which can lead to their aggregation and thereby to product loss. To better understand the underlying mechanism so as to propose strategies to mitigate the issue, we systematically investigated the denaturation and aggregation of two mAbs at low pH as well as after neutralization. We observed that at low pH and low ionic strength, mAb surface hydrophobicity increased whereas molecular size remained constant. After neutralization of acidic mAb solutions, the fraction of monomeric mAb started to decrease accompanied by an increase on average mAb size. This indicates that electrostatic repulsion prevents denatured mAb molecules from aggregation under acidic pH and low ionic strength, whereas neutralization reduces this repulsion and coagulation initiates. Limiting denaturation at low pH by d-sorbitol addition or temperature reduction effectively improved monomer recovery after neutralization. Our findings might be used to develop innovative viral inactivation procedures during mAb manufacturing that result in higher product yields.

The first study on the impact of osmolytes in whole cells of high temperature-adapted microorganisms

The hyperthermophilic piezophile, Thermococcus barophilus displays a strong stress response characterized by the accumulation of the organic osmolyte, mannosylglycerate during growth under sub-optimal pressure conditions (0.1 MPa). Taking advantage of this known effect, the impact of osmolytes in piezophiles in an otherwise identical cellular context was investigated, by comparing T. barophilus cells grown under low or optimal pressures (40 MPa). Using neutron scattering techniques, we studied the molecular dynamics of live cells of T. barophilus at different pressures and temperatures. We show that in the presence of osmolytes, cells present a higher diffusion coefficient of hydration water and an increase of bulk water motions at a high temperature. In the absence of osmolytes, the T. barophilus cellular dynamics is more responsive to high temperature and high hydrostatic pressure. These results therefore give clear evidence for a protecting effect of osmolytes on proteins.

Evolutionary drivers of protein shape

Diffusional motion within the crowded environment of the cell is known to be crucial to cellular function as it drives the interactions of proteins. However, the relationships between protein diffusion, shape and interaction, and the evolutionary selection mechanisms that arise as a consequence, have not been investigated. Here, we study the dynamics of triaxial ellipsoids of equivalent steric volume to proteins at different aspect ratios and volume fractions using a combination of Brownian molecular dynamics and geometric packing. In general, proteins are found to have a shape, approximately Golden in aspect ratio, that give rise to the highest critical volume fraction resisting gelation, corresponding to the fastest long-time self-diffusion in the cell. The ellipsoidal shape also directs random collisions between proteins away from sites that would promote aggregation and loss of function to more rapidly evolving nonsticky regions on the surface, and further provides a greater tolerance to mutation.

Dynamics of proteins in solution

The dynamics of proteins in solution includes a variety of processes, such as backbone and side-chain fluctuations, interdomain motions, as well as global rotational and translational (i.e. center of mass) diffusion. Since protein dynamics is related to protein function and essential transport processes, a detailed mechanistic understanding and monitoring of protein dynamics in solution is highly desirable. The hierarchical character of protein dynamics requires experimental tools addressing a broad range of time- and length scales. We discuss how different techniques contribute to a comprehensive picture of protein dynamics, and focus in particular on results from neutron spectroscopy. We outline the underlying principles and review available instrumentation as well as related analysis frameworks.

Dynamic cluster formation determines viscosity and diffusion in dense protein solutions

We develop a detailed description of protein translational and rotational diffusion in concentrated solution on the basis of all-atom molecular dynamics simulations in explicit solvent. Our systems contain up to 540 fully flexible proteins with 3.6 million atoms. In concentrated protein solutions (100 mg/mL and higher), the proteins ubiquitin and lysozyme, as well as the protein domains third IgG-binding domain of protein G and villin headpiece, diffuse not as isolated particles, but as members of transient clusters between which they constantly exchange. A dynamic cluster model nearly quantitatively explains the increase in viscosity and the decrease in protein diffusivity with protein volume fraction, which both exceed the predictions from widely used colloid models. The Stokes-Einstein relations for translational and rotational diffusion remain valid, but the effective hydrodynamic radius grows linearly with protein volume fraction. This increase follows the observed increase in cluster size and explains the more dramatic slowdown of protein rotation compared with translation. Baxter's sticky-sphere model of colloidal suspensions captures the concentration dependence of cluster size, viscosity, and rotational and translational diffusion. The consistency between simulations and experiments for a diverse set of soluble globular proteins indicates that the cluster model applies broadly to concentrated protein solutions, with equilibrium dissociation constants for nonspecific protein-protein binding in the Kd ≈ 10-mM regime.

Consequences of Heterogeneous Crowding on an Enzymatic Reaction: A Residence Time Monte Carlo Approach

Translational diffusion of a free substrate in crowded metabolically active spaces such as cell cytoplasm or mitochondrial matrix is punctuated by collisions and nonspecific interactions with soluble/immobile macromolecules/macrostructures in a variety of shapes/sizes. It is not understood how such disruptions alter enzyme reaction kinetics in such spaces. A novel Monte Carlo (MC) technique, "residence time MC", has been developed to study the kinetics of a simple enzyme-substrate reaction in a crowded milieu using a single immobile enzyme in the midst of diffusing substrates and products. The reaction time lost while the substrate nonspecifically interacts or is transiently trapped with ambient macromolecules is quantified by introducing the residence time "tau". Tau scales with the size of crowding macromolecules but makes the knowledge of their shape redundant. The residence time thus presents a convenient parameter to realistically mimic the sticky surroundings encountered by a diffusing substrate in heterogeneously crowded physiological spaces. Results reveal that for identical substrate concentration and excluded volume, increase in tau significantly diminished enzymatic product yield and reaction rate, slowed down substrate/product diffusion, and prolonged their relaxation times. A smooth transition from the anomalous subdiffusive motion to normal diffusion at long time limits was observed irrespective of the value of tau. The predictions from the model are shown to be in qualitative agreement with in vitro experimental data revealing the rate of alkaline phosphatase-catalyzed hydrolysis of p-nitrophenyl phosphate in the midst of 40/500/2000 kDa dextrans. Our findings from the residence time MC model also attempt to rationalize previously unexplained experimental observations in crowded enzyme kinetics literature. Furthermore, major insights to emerge from this study are the reasons why free diffusion of the substrate in crowded physiological spaces is detrimental to enzyme function. It is argued that organized enzyme clusters such as "metabolon" may perhaps exist to regulate the substrate translocation in such sticky physiological spaces to maintain optimal enzyme function. In summary, this work provides key insights explaining why absence of substrate channeling can dramatically slow down enzyme reaction rate in crowded metabolically active spaces.

Weak Shape Anisotropy Leads to a Nonmonotonic Contribution to Crowding, Impacting Protein Dynamics under Physiologically Relevant Conditions

The effect of a nonspherical particle shape on the dynamics in crowded solutions presents a significant challenge for a comprehensive understanding of interaction and structural relaxation in biological and soft matter. We report that small deviations from a spherical shape induce a nonmonotonic contribution to the crowding effect on the short-time cage diffusion compared with spherical systems, using molecular dynamics simulations with mesoscale hydrodynamics of a multiparticle collision dynamics fluid in semidilute systems with volume fractions smaller than 0.35. We show that the nonmonotonic effect due to anisotropy is caused by the combination of a reduced relative mobility over the entire concentration range and a looser and less homogeneous cage packing of nonspherical particles. Our finding stresses that nonsphericity induces new complexity, which cannot be accounted for in effective sphere models, and is of great interest in applications such as formulations as well as for the fundamental understanding of soft matter in general and crowding effects in living cells in particular.

Nanosecond Tracer Diffusion as a Probe of the Solution Structure and Molecular Mobility of Protein Assemblies: The Case of Ovalbumin

Protein diffusion is not only an important process ensuring biological function but can also be used as a probe to obtain information on structural properties of protein assemblies in liquid solutions. Here, we explore the oligomerization state of ovalbumin at high protein concentrations by means of its short-time self-diffusion. We employ high-resolution incoherent quasielastic neutron scattering to access the self-diffusion on nanosecond timescales, on which interparticle contacts are not altered. Our results indicate that ovalbumin in aqueous (D₂O) solutions occurs in increasingly large assemblies of its monomeric subunits with rising protein concentration. It changes from nearly monomeric toward dimeric and ultimately larger than tetrameric complexes. Simultaneously, we access information on the internal molecular mobility of ovalbumin on the nanometer length scale and compare it with results obtained for bovine serum albumin, immunoglobulin, and β-lactoglobulin.

Hemoglobin diffusion and the dynamics of oxygen capture by red blood cells

Translational diffusion of macromolecules in cell is generally assumed to be anomalous due high macromolecular crowding of the milieu. Red blood cells are a special case of cells filled quasi exclusively (95% of the dry weight of the cell) with an almost spherical protein: hemoglobin. Hemoglobin diffusion has since a long time been recognized as facilitating the rate of oxygen diffusion through a solution. We address in this paper the question on how hemoglobin diffusion in the red blood cells can help the oxygen capture at the cell level and hence to improve oxygen transport. We report a measurement by neutron spin echo spectroscopy of the diffusion of hemoglobin in solutions with increasing protein concentration. We show that hemoglobin diffusion in solution can be described as Brownian motion up to physiological concentration and that hemoglobin diffusion in the red blood cells and in solutions at similar concentration are the same. Finally, using a simple model and the concentration dependence of the diffusion of the protein reported here, we show that hemoglobin concentration observed in human red blood cells ([Formula: see text]330 g.L -1) corresponds to an optimum for oxygen transport for individuals under strong activity.

Modulation of hemoglobin dynamics by an allosteric effector

Hemoglobin (Hb) is an extensively studied paradigm of proteins that alter their function in response to allosteric effectors. Models of its action have been used as prototypes for structure‐function relationships in many proteins, and models for the molecular basis of its function have been deeply studied and extensively argued. Recent reports suggest that dynamics may play an important role in its function. Relatively little is known about the slow, correlated motions of hemoglobin subunits in various structural states because experimental and computational strategies for their characterization are challenging. Allosteric effectors such as inositol hexaphosphate (IHP) bind to both deoxy‐Hb and HbCO, albeit at different sites, leading to a lowered oxygen affinity. The manner in which these effectors impact oxygen binding is unclear and may involve changes in structure, dynamics or both. Here we use neutron spin echo measurements accompanied by wide‐angle X‐ray scattering to show that binding of IHP to HbCO results in an increase in the rate of coordinated motions of Hb subunits relative to one another with little if any change in large scale structure. This increase of large‐scale dynamics seems to be coupled with a decrease in the average magnitude of higher frequency modes of individual residues. These observations indicate that enhanced dynamic motions contribute to the functional changes induced by IHP and suggest that they may be responsible for the lowered oxygen affinity triggered by these effectors.

A Cellular Model of Shear-Induced Hemolysis

A novel model is presented to study red blood cell (RBC) hemolysis at cellular level. Under high shear rates, pores form on RBC membranes through which hemoglobin (Hb) leaks out and increases free Hb content of plasma leading to hemolysis. By coupling lattice Boltzmann and spring connected network models through immersed boundary method, we estimate hemolysis of a single RBC under various shear rates. First, we use adaptive meshing to find local strain distribution and critical sites on RBC membranes, and then we apply underlying molecular dynamics simulations to evaluate damage. Our approach comprises three sub-models: defining criteria of pore formation, calculating pore size, and measuring Hb diffusive flux out of pores. Our damage model uses information of different scales to predict cellular level hemolysis. Results are compared with experimental studies and other models in literature. The developed cellular damage model can be used as a predictive tool for hydrodynamic and hematologic design optimization of blood-wetting medical devices.

Size effects of solvent molecules on the phase behavior and effective interaction of colloidal systems with the bridging attraction

There has been much recent research interest towards understanding the phase behavior of colloidal systems interacting with a bridging attraction, where the small solvent particles and large solute colloidal particles can be reversibly associated with each other. These systems show interesting phase behavior compared to the more widely studied depletion attraction systems. Here, we use Baxter's two-component sticky hard sphere model with a Percus-Yevick closure to solve the Ornstein-Zernike equation and study the size effect on colloidal systems with bridging attractions. The spinodal decomposition regions, percolation transition boundaries and binodal regions are systematically investigated as a function of the relative size of the small solvent and large solute particles as well as the attraction strength between the small and large particles. In the phase space determined by the concentrations of small and large particles, the spinodal and binodal regions form isolated islands. The locations and shapes of the spinodal and binodal regions sensitively depend on the relative size of the small and large particles and the attraction strength between them. The percolation region shrinks by decreasing the size ratio, while the binodal region slightly expands with the decrease of the size ratio. Our results are very important in understanding the phase behavior for a bridging attraction colloidal system, a model system that provides insight into oppositely charged colloidal systems, protein phase behavior, and colloidal gelation mechanisms.

ULTRATHIN SILICON MEMBRANES FOR IMPROVING EXTRACORPOREAL BLOOD THERAPIES

Extracorporeal blood therapies such as hemodialysis and extracorporeal membrane oxygenation supplement or replace organ function by the exchange of molecules between blood and another fluid across a semi-permeable membrane. Traditionally, these membranes are made of polymers with large surface areas and thicknesses on the scale of microns. Therapeutic gas exchange or toxin cleara nce in these devices occurs predominantly by diffusion, a process that is described by an inverse square law relating a distance to the average time a diffusing particle requires to travel that distance. As such, small changes in membrane thickness or other device dimensions can have significant effects on device performance - and large changes can cause dramatic paradigm shifts. In this work, we discuss the application of ultrathin nanoporous silicon membranes (nanomembranes) with thicknesses on the scale of tens of nanometers to diffusion-mediated medical devices. We discuss the theoretical consequences of nanomembrane medical devices for patients, analyzing several notable benefits such as reduced device size (enabling wearability, for instance) and improved clearance specificity. Special attention is paid to computational and analytical models that describe real experimental behavior, and that in doing so provide insights into the relevant parameters governing the devices.

Physical determinants of vesicle mobility and supply at a central synapse

Encoding continuous sensory variables requires sustained synaptic signalling. At several sensory synapses, rapid vesicle supply is achieved via highly mobile vesicles and specialized ribbon structures, but how this is achieved at central synapses without ribbons is unclear. Here we examine vesicle mobility at excitatory cerebellar mossy fibre synapses which sustain transmission over a broad frequency bandwidth. Fluorescent recovery after photobleaching in slices from VGLUT1^Venus knock-in mice reveal 75% of VGLUT1-containing vesicles have a high mobility, comparable to that at ribbon synapses. Experimentally constrained models establish hydrodynamic interactions and vesicle collisions are major determinants of vesicle mobility in crowded presynaptic terminals. Moreover, models incorporating 3D reconstructions of vesicle clouds near active zones (AZs) predict the measured releasable pool size and replenishment rate from the reserve pool. They also show that while vesicle reloading at AZs is not diffusion-limited at the onset of release, diffusion limits vesicle reloading during sustained high-frequency signalling.

DOI:http://dx.doi.org/10.7554/eLife.15133.001

Fast antibody fragment motion: flexible linkers act as entropic spring

A flexible linker region between three fragments allows antibodies to adjust their binding sites to an antigen or receptor. Using Neutron Spin Echo Spectroscopy we observed fragment motion on a timescale of 7 ns with motional amplitudes of about 1 nm relative to each other. The mechanistic complexity of the linker region can be described by a spring model with Brownian motion of the fragments in a harmonic potential. Displacements, timescale, friction and force constant of the underlying dynamics are accessed. The force constant exhibits a similar strength to an entropic spring, with friction of the fragment matching the unbound state. The observed fast motions are fluctuations in pre-existing equilibrium configurations. The Brownian motion of domains in a harmonic potential is the appropriate model to examine functional hinge motions dependent on the structural topology and highlights the role of internal forces and friction to function.

Short-Time Glassy Dynamics in Viscous Protein Solutions with Competing Interactions

The glass transition of colloidal dispersions interacting with both a short-ranged attraction and long-ranged repulsion is studied using highly purified lysozyme solutions. Newtonian liquid behavior is observed at all conditions while measurements of the dynamics in the short-time limit show features typical of glassy colloidal systems at high protein concentrations. This interesting behavior is due to the competition of the attraction and repulsion that produces a heterogeneous microstructure only at intermediate range length scales. The results demonstrate that theories for the macroscopic properties of systems with competing interactions need to include intermediate range order.

Vascular nitric oxide: Beyond eNOS

As the first discovered gaseous signaling molecule, nitric oxide (NO) affects a number of cellular processes, including those involving vascular cells. This brief review summarizes the contribution of NO to the regulation of vascular tone and its sources in the blood vessel wall. NO regulates the degree of contraction of vascular smooth muscle cells mainly by stimulating soluble guanylyl cyclase (sGC) to produce cyclic guanosine monophosphate (cGMP), although cGMP-independent signaling [S-nitrosylation of target proteins, activation of sarco/endoplasmic reticulum calcium ATPase (SERCA) or production of cyclic inosine monophosphate (cIMP)] also can be involved. In the blood vessel wall, NO is produced mainly from l-arginine by the enzyme endothelial nitric oxide synthase (eNOS) but it can also be released non-enzymatically from S-nitrosothiols or from nitrate/nitrite. Dysfunction in the production and/or the bioavailability of NO characterizes endothelial dysfunction, which is associated with cardiovascular diseases such as hypertension and atherosclerosis.

The Multicenter Aerobic Iron Respiratory Chain of Acidithiobacillus ferrooxidans Functions as an Ensemble with a Single Macroscopic Rate Constant

Electron transfer reactions among three prominent colored proteins in intact cells of Acidithiobacillus ferrooxidans were monitored using an integrating cavity absorption meter that permitted the acquisition of accurate absorbance data in suspensions of cells that scattered light. The concentrations of proteins in the periplasmic space were estimated to be 350 and 25 mg/ml for rusticyanin and cytochrome c, respectively; cytochrome a was present as one molecule for every 91 nm(2) in the cytoplasmic membrane. All three proteins were rapidly reduced to the same relative extent when suspensions of live bacteria were mixed with different concentrations of ferrous ions at pH 1.5. The subsequent molecular oxygen-dependent oxidation of the multicenter respiratory chain occurred with a single macroscopic rate constant, regardless of the proteins' in vitro redox potentials or their putative positions in the aerobic iron respiratory chain. The crowded electron transport proteins in the periplasm of the organism constituted an electron conductive medium where the network of protein interactions functioned in a concerted fashion as a single ensemble with a standard reduction potential of 650 mV. The appearance of product ferric ions was correlated with the reduction levels of the periplasmic electron transfer proteins; the limiting first-order catalytic rate constant for aerobic respiration on iron was 7,400 s(-1). The ability to conduct direct spectrophotometric studies under noninvasive physiological conditions represents a new and powerful approach to examine the extent and rates of biological events in situ without disrupting the complexity of the live cellular environment.

Protein-protein interactions in dilute to concentrated solutions: α-chymotrypsinogen in acidic conditions

Protein-protein interactions were investigated for α-chymotrypsinogen by static and dynamic light scattering (SLS and DLS, respectively), as well as small-angle neutron scattering (SANS), as a function of protein and salt concentration at acidic conditions. Net protein-protein interactions were probed via the Kirkwood-Buff integral G22 and the static structure factor S(q) from SLS and SANS data. G22 was obtained by regressing the Rayleigh ratio versus protein concentration with a local Taylor series approach, which does not require one to assume the underlying form or nature of intermolecular interactions. In addition, G22 and S(q) were further analyzed by traditional methods involving fits to effective interaction potentials. Although the fitted model parameters were not always physically realistic, the numerical values for G22 and S(q → 0) were in good agreement from SLS and SANS as a function of protein concentration. In the dilute regime, fitted G22 values agreed with those obtained via the osmotic second virial coefficient B22 and showed that electrostatic interactions are the dominant contribution for colloidal interactions in α-chymotrypsinogen solutions. However, as protein concentration increases, the strength of protein-protein interactions decreases, with a more pronounced decrease at low salt concentrations. The results are consistent with an effective "crowding" or excluded volume contribution to G22 due to the long-ranged electrostatic repulsions that are prominent even at the moderate range of protein concentrations used here (<40 g/L). These apparent crowding effects were confirmed and quantified by assessing the hydrodynamic factor H(q → 0), which is obtained by combining measurements of the collective diffusion coefficient from DLS data with measurements of S(q → 0). H(q → 0) was significantly less than that for a corresponding hard-sphere system and showed that hydrodynamic nonidealities can lead to qualitatively incorrect conclusions regarding B22, G22, and static protein-protein interactions if one uses only DLS to assess protein interactions.

Coarse-grained modeling of protein second osmotic virial coefficients: sterics and short-ranged attractions

A series of coarse-grained models, with different levels of structural resolution, were tested to calculate the steric contributions to protein osmotic second virial coefficients (B(22,S)) for proteins ranging from small single-domain molecules to large multidomain molecules, using the recently developed Mayer sampling method. B(22,S) was compared for different levels of coarse-graining: four-beads-per-amino-acid (4bAA), one-bead-per-amino-acid (1bAA), one-sphere-per-domain (1sD), and one-sphere-per-protein (1sP). Values for the 1bAA and 4bAA models were quantitatively indistinguishable for both spherical and nonspherical proteins, and the agreement with values from all-atom models improved with increasing protein size, making the CG approach attractive for large proteins of biotechnological interest. Interestingly, in the absence of detailed structural information, the hydrodynamic radius (R(h)) along with a simple 1sP approximation provided reasonably accurate values for B(22,S) for both globular and highly asymmetric protein structures, while other 1sP approximations gave poorer agreement; this helps to justify the currently empirical practice of estimating B(22,S) from R(h) for large proteins such as antibodies. The results also indicate that either 1bAA or 4bAA CG models may be good starting points for incorporating short-range attractions. Comparison of gD-crystallin B(22) values including both sterics and short-range attractions shows that 1bAA and 4bAA models give equivalent results when properly scaled to account for differences in the number of surface beads in the two CG descriptions. This provides a basis for future work that will also incorporate long-ranged electrostatic attractions and repulsions.

Mixing normal and anomalous diffusion

In the densely filled biological cells often subdiffusion is observed, where the average squared displacement increases slower than linear with the length of the observation interval. One reason for such subdiffusive behavior is attractive interactions between the diffusing particles that lead to temporary complex formation. Here, we show that such transient binding is not an average state of the particles but that intervals of free diffusion alternate with slower displacement when bound to neighboring particles. The observed macroscopic behavior is then the weighted average of these two contributions. Interestingly, even at very high concentrations, the unbound fraction still exhibits essentially normal diffusion.

A method for computing association rate constants of atomistically represented proteins under macromolecular crowding

In cellular environments, two protein molecules on their way to form a specific complex encounter many bystander macromolecules. The latter molecules, or crowders, affect both the energetics of the interaction between the test molecules and the dynamics of their relative motion. In earlier work (Zhou and Szabo 1991 J. Chem. Phys. 95 5948-52), it has been shown that, in modeling the association kinetics of the test molecules, the presence of crowders can be accounted for by their energetic and dynamic effects. The recent development of the transient-complex theory for protein association in dilute solutions makes it possible to easily incorporate the energetic and dynamic effects of crowders. The transient complex refers to a late on-pathway intermediate, in which the two protein molecules have near-native relative separation and orientation, but have yet to form the many short-range specific interactions of the native complex. The transient-complex theory predicts the association rate constant as k(a) = k(a0)exp(-ΔG*(el)/k(B)T), where k(a0) is the 'basal' rate constant for reaching the transient complex by unbiased diffusion, and the Boltzmann factors captures the influence of long-range electrostatic interactions between the protein molecules. Crowders slow down the diffusion, therefore reducing the basal rate constant (to k(ac0)), and induce an effective interaction energy ΔG(c). We show that the latter interaction energy for atomistic proteins in the presence of spherical crowders is 'long'-ranged, allowing the association rate constant under crowding to be computed as k(ac) = k(ac0)exp[-(ΔG*(el) + ΔG*(c))/k(B)T]. Applications demonstrate that this computational method allows for realistic modeling of protein association kinetics under crowding.

Atomic detail brownian dynamics simulations of concentrated protein solutions with a mean field treatment of hydrodynamic interactions

High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. In this paper, we describe the implementation of mean field models of translational and rotational hydrodynamic interactions into an atomically detailed many-protein brownian dynamics simulation method. Concentrated solutions (30-40% volume fraction) of myoglobin, hemoglobin A, and sickle cell hemoglobin S were simulated, and static structure factors, oligomer formation, and translational and rotational self-diffusion coefficients were computed. Good agreement of computed properties with available experimental data was obtained. The results show the importance of both solvent mediated interactions and weak protein-protein interactions for accurately describing the dynamics and the association properties of concentrated protein solutions. Specifically, they show a qualitative difference in the translational and rotational dynamics of the systems studied. Although the translational diffusion coefficient is controlled by macromolecular shape and hydrodynamic interactions, the rotational diffusion coefficient is affected by macromolecular shape, direct intermolecular interactions, and both translational and rotational hydrodynamic interactions.

Light-controlled protein dynamics observed with neutron spin echo measurements

A photoresponsive surfactant has been used as a means to control protein structure and dynamics with light illumination. This cationic azobenzene surfactant, azoTAB, which undergoes a reversible photoisomerization upon exposure to the appropriate wavelength of light, adopts a relatively hydrophobic, trans structure under visible light illumination and a relatively hydrophilic cis structure under UV light illumination. Small-angle neutron scattering (SANS) and neutron spin echo (NSE) spectroscopy were used to measure the tertiary structure and internal dynamics of lysozyme in the presence of the photosurfactant, respectively. The SANS-based in vitro structures indicate that under visible light the photosurfactant induces partial unfolding that principally occurs away from the active site near the hinge region connecting the α and β domains. Upon UV exposure, however, the protein refolds to a nativelike structure. At the same time, enhanced internal dynamics of lysozyme were detected with the surfactant in the trans form through NSE measurements of the Q-dependent effective diffusion coefficient (D(eff)) of the protein. In contrast, the D(eff) values of lysozyme in the presence of cis azoTAB largely agree with the rigid-body calculation as well as those measured for pure lysozyme, suggesting that the native protein is dormant on the nanosecond time and nanometer length scales. Lysozyme internal motions were modeled by assuming a protein of two (α and β domains) or three (α and β domains and the hinge region) domains connects by either soft linkers or rigid, freely rotating bonds. Protein dynamics were also tracked with Fourier transform infrared spectroscopy through hydrogen-deuterium exchange kinetics, which further demonstrated enhanced protein flexibility induced by the trans form of the surfactant relative to the native protein. Ensemble-averaged intramolecular fluorescent resonance energy transfer measurements similarly demonstrated the enhanced dynamics of lysozyme with the trans form of the photosurfactant. Previous results have shown a significant increase in protein activity in the presence of azoTAB in the trans conformation. Combined, these results provide insight into a unique light-based method of controlling protein structure, dynamics, and function and strongly support the relevance of large domain motions for the activity of proteins.

Protein self-diffusion in crowded solutions

Macromolecular crowding in biological media is an essential factor for cellular function. The interplay of intermolecular interactions at multiple time and length scales governs a fine-tuned system of reaction and transport processes, including particularly protein diffusion as a limiting or driving factor. Using quasielastic neutron backscattering, we probe the protein self-diffusion in crowded aqueous solutions of bovine serum albumin on nanosecond time and nanometer length scales employing the same protein as crowding agent. The measured diffusion coefficient D(ϕ) strongly decreases with increasing protein volume fraction ϕ explored within 7% ≤ ϕ ≤ 30%. With an ellipsoidal protein model and an analytical framework involving colloid diffusion theory, we separate the rotational D(r)(ϕ) and translational D(t)(ϕ) contributions to D(ϕ). The resulting D(t)(ϕ) is described by short-time self-diffusion of effective spheres. Protein self-diffusion at biological volume fractions is found to be slowed down to 20% of the dilute limit solely due to hydrodynamic interactions.

Self-diffusion of biomolecules in solution

A simple soft-core model potential is proposed to discuss the self-diffusion of biomolecules in solution. Extensive Brownian-dynamics simulations are performed to obtain the long-time self-diffusion coefficient. Then the simulation results are compared with the experimental data from a unified point of view recently obtained for suspensions of hard spheres. Thus, it is shown that the proposed potential can qualitatively well describe the experimental data.