Effects of Flexibility in Coarse-Grained Models for Bovine Serum Albumin and Immunoglobulin G

We construct a coarse-grained, structure-based, low-resolution, 6-bead flexible model of bovine serum albumin (BSA, PDB: 4F5S), which is a popular example of a globular protein in biophysical research. The model is obtained via direct Boltzmann inversion using all-atom simulations of a single molecule, and its particular form is selected from a large pool of 6-bead coarse-grained models using two suitable metrics that quantify the agreement in the distribution of collective coordinates between all-atom and coarse-grained Brownian dynamics simulations of solutions in the dilute limit. For immunoglobulin G (IgG), a similar structure-based 12-bead model has been introduced in the literature [Chaudhri et al., J. Phys. Chem. B 116, 8045 (2012)] and is employed here to compare findings for the compact BSA molecule and the more anisotropic IgG molecule. We define several modified coarse-grained models of BSA and IgG, which differ in their internal constraints and thus account for a variation of flexibility. We study denser solutions of the coarse-grained models with purely repulsive molecules (achievable by suitable salt conditions) and address the effect of packing and flexibility on dynamic and static behavior. Translational and rotational self-diffusivity is enhanced for more elastic models. Finally, we discuss a number of effective sphere sizes for the BSA molecule, which can be defined from its static and dynamic properties. Here, it is found that the effective sphere diameters lie between 4.9 and 6.1 nm, corresponding to a relative spread of about ±10% around a mean of 5.5 nm

Self-assembly in patchy proteins: From transient networks to attractive glasses

Dynamic properties of crowded protein solutions are difficult to predict and control. This for example considerably limits our ability to create stable and injectable formulations of proteins or peptides at high concentrations. Another physiologically relevant case is presbyopia, or age-related farsightedness, where the pathological stiffening of the eye lens can be related to a liquid-solid transition of the protein mixtures inside the eye lens cells1. It is thus essential to achieve a quantitative understanding of the link between the molecular structure of the proteins and the interactions between them, and how these interactions influence the stability, dynamics and flow properties of the solutions as a function of their concentration. Here we show how we can use a combination of advanced characterization techniques1-4 such as neutron spin echo, small-angle scattering, 3D cross correlation light scattering and microrheology, combined with state-of-the-art computer simulations to assess and predict interparticle interactions and their impact on the dynamics and flow behavior of crowded protein solutions. We particularly point out the enormous influence of weak attractive interactions known to exist between many globular proteins, and demonstrate the dramatic effect of an interaction potential anisotropy such as attractive patches4 and shape anisotropy on the dynamic properties. [1] G. Foffi, G. Savin, S. Bucciarelli, N. Dorsaz, G. Thurston, A. Stradner, P. Schurtenberger; A Hard Sphere-Like Glass Transition in Eye Lens Alpha Crystallin Solutions ; Proc. Natl. Acad. Sci. U. S. A., 111, 16748-16753 (2014). [2] F. Cardinaux, E. Zaccarelli, A. Stradner, S. Bucciarelli, B. Farago, S. Egelhaaf, F. Sciortino, P. Schurtenberger; Cluster-driven dynamical arrest in concentrated lysozyme solutions J. Phys. Chem. B, 115, 7227 (2011). [3] S. Bucciarelli, L. Casal-Dujat, C. De Michele, F. Sciortino, J. Dhont, J. Bergenholtz, B. Farago, P. Schurtenberger, and A. Stradner; Unusual Dynamics of Concentration Fluctuations in Solutions of Weakly Attractive Globular Proteins ; The Journal of Physical Chemistry Letters, 6, 4470-4474 (2015). [4] S. Bucciarelli, J. S. Myung, B. Farago, S. Das, G. A. Viegenthart, O. Holderer, R. G. Winkler, P. Schurtenberger, G. Gompper, and A. Stradner; Dramatic Influence of Attractions on Short-Time Protein Diffusion under Crowded Conditions ; Science Advances, 2, e1601432 (2016)

Protein cluster formation in aqueous solution in the presence of multivalent metal ions -a light scattering study

The formation of protein clusters as precursors for crystallization and phase separation is of fundamental and practical interest in protein science. Using multivalent ions, the strengths of both long-range Coulomb repulsion and short-range attraction can be tuned in protein solutions, representing a wellcontrolled model system to study static and dynamic properties of clustering during the transition from a charge-stabilized to an aggregate regime. Here, we study compressibility, diffusion, and size of solutes by means of static (SLS) and dynamic light scattering (DLS) in solutions of bovine serum albumin (BSA) and YCl 3 . For this and comparable systems, an increasing screening and ultimately inversion of the protein surface charge induce a rich phase behavior including reentrant condensation, liquid-liquid phase separation and crystallization, which puts the cluster formation in the context of precursor formation and nucleation of liquid and crystalline phases. We find that, approaching the turbid aggregate regime with increasing salt concentration c s , the diffusion coefficients decrease and the scattered intensity increases by orders of magnitude, evidencing increasing correlation lengths likely associated with clustering. The combination of static and dynamic observations suggests the formation of BSA clusters with a size on the order of 100 nm. The global thermodynamic state seems to be stable over at least several hours. Surprisingly, results on collective diffusion and inverse compressibility from different protein concentrations can be rescaled into master curves as a function of c s /c*, where c* is the critical salt concentration of the transition to the turbid aggregate regime

Viscosity and Diffusion: Crowding and Salt Effects in Protein Solutions

We report on a joint experimental-theoretical study of collective diffusion in, and static shear viscosity of solutions of bovine serum albumin (BSA) proteins, focusing on the dependence on protein and salt concentration. Data obtained from dynamic light scattering and rheometric measurements are compared to theoretical calculations based on an analytically treatable spheroid model of BSA with isotropic screened Coulomb plus hard-sphere interactions. The only input to the dynamics calculations is the static structure factor obtained from a consistent theoretical fit to a concentration series of small-angle X-ray scattering (SAXS) data. This fit is based on an integral equation scheme that combines high accuracy with low computational cost. All experimentally probed dynamic and static properties are reproduced theoretically with an at least semi-quantitative accuracy. For lower protein concentration and low salinity, both theory and experiment show a maximum in the reduced viscosity, caused by the electrostatic repulsion of proteins. The validity range of a generalized Stokes-Einstein (GSE) relation connecting viscosity, collective diffusion coefficient, and osmotic compressibility, proposed by Kholodenko and Douglas [PRE 51, 1081 (1995)] is examined. Significant violation of the GSE relation is found, both in experimental data and in theoretical models, in semi-dilute systems at physiological salinity, and under low-salt conditions for arbitrary protein concentrations

Soft matter roadmap

Soft materials are usually defined as materials made of mesoscopic entities, often self-organised, sensitive to thermal fluctuations and to weak perturbations. Archetypal examples are colloids, polymers, amphiphiles, liquid crystals, foams. The importance of soft materials in everyday commodity products, as well as in technological applications, is enormous, and controlling or improving their properties is the focus of many efforts. From a fundamental perspective, the possibility of manipulating soft material properties, by tuning interactions between constituents and by applying external perturbations, gives rise to an almost unlimited variety in physical properties. Together with the relative ease to observe and characterise them, this renders soft matter systems powerful model systems to investigate statistical physics phenomena, many of them relevant as well to hard condensed matter systems. Understanding the emerging properties from mesoscale constituents still poses enormous challenges, which have stimulated a wealth of new experimental approaches, including the synthesis of new systems with, e.g. tailored self-assembling properties, or novel experimental techniques in imaging, scattering or rheology. Theoretical and numerical methods, and coarse-grained models, have become central to predict physical properties of soft materials, while computational approaches that also use machine learning tools are playing a progressively major role in many investigations. This Roadmap intends to give a broad overview of recent and possible future activities in the field of soft materials, with experts covering various developments and challenges in material synthesis and characterisation, instrumental, simulation and theoretical methods as well as general concepts

Effekte von Salzen auf das Phasenverhalten von Proteinlösungen

The addition of salts to protein solutions affects both the protein interaction and the related phase behavior, invoking the question how the protein--ion interaction can induce these effects. For salts without specific protein--ion interactions, the DLVO theory for solubility and the formation of the electrostatic double-layer represents the basic picture. The interaction of ions with the protein surface, however, can be affected by several effects such as specific binding sites or water-mediated features. In a first step, protein solutions with different salts along the Hofmeister series are investigated. Protein interactions are characterized by small-angle scattering and can be successfully described with a model of effective spheres if hydration and non-spherical shape are accounted for. Colloid-like modeling of proteins is employed in several studies throughout the thesis, and opportunities as well as limitations of the modeling approaches are discussed. In the main part of the thesis, phenomena in protein solutions induced by multivalent cations are studied. As the basic phenomenon, an inversion of the protein net charge and a related reentrant condensation---i.e.~stable solutions at low and high cation concentrations, condensation at intermediate cation concentrations---has been observed in earlier studies. In this thesis, the influence of different cations as well as the effect of additional monovalent salt on the reentrant condensation is investigated. Metal salts with strong pH effects due to hydrolysis narrow the condensed regime considerably. Additional monovalent salt increases both transition concentrations of the reentrant condensation. These effects are described successfully by a coarse-grained model accounting for the interplay of ion binding, charge regulation and pH effects due to hydrolysis. The reentrant phase behavior is attributed to the competition of an ion-induced attraction and the reentrant charge stabilization through the charge inversion. Exploring the reentrant phase diagram in greater detail, a liquid--liquid phase separation (LLPS) is observed in a closed area within the condensed regime. The phase boundaries as well as the protein interactions measured by small-angle scattering are interpreted consistently with a colloidal picture of a metastable LLPS with two control parameters. Close to the dilute phase boundary, crystal growth is found, whereas amorphous aggregates are formed in the dense coexisting phase. The protein crystallization from the dilute phase is studied in more detail, and a two-step nucleation pathway via cluster precursor is suggested and evidenced by real-time SAXS measurements. The rich phase diagram of protein solutions with multivalent cations is described by a model of particles with ion-activated attractive patches in a very natural and conceptually understandable way. The patches represent binding sites for the cations and, once a cation is bound, act as attractive patches caused by ion bridging. The LLPS, the reentrant condensation, and cluster formation are reproduced with excellent qualitative and reasonable quantitative agreement. Furthermore, the crystallization pathways are rationalized by the percolated and potentially arrested structures in the dense coexisting phase.Das Phasenverhalten von Proteinlösungen sowie die Wechselwirkungen zwischen Proteinen werden durch die Hinzugabe von Salzen beeinflusst. Der Mechanismus der salzinduzierten Effekte ist dabei wichtiger Bestandteil des theoretischen Verstöndnisses sowie Grundlage für biotechnologische Anwendungen in Proteinlösungen. Das grundlegende Bild für Salze ohne spezifische Wechselwirkung mit den Proteinen beinhaltet die DLVO-Theorie und die verbundene elektrochemische Doppelschicht. Im Allgemeinen kann die Wechselwirkung zwischen Proteinoberfläche und Ionen sehr spezifisch sein, wie z.B. bei Bindestellen für Ionen. Als einen ersten vorbereitenden Schritt werden Proteinlösungen mit Salzen entlang der Hofmeister-Reihe untersucht. Die Protein-Interaktionen werden mit Kleinwinkelstreuung charakterisiert und lassen sich mit einem Modell von effektiven Kugeln beschreiben, wenn Hydratisationseffekte und die nicht-sphärische Form der Proteine adäquat berücksichtigt werden. Das Resultat, dass eine kolloidartige Modellierung für Proteine möglich ist, wird durch die Invarianz der Konformation der untersuchten Proteine unter verschiedenen Salzbedingungen unterstützt. Der Hauptteil der Arbeit untersucht Phänomene in Proteinlösungen, die von mehrwertigen Kationen induziert werden. Als allen anderen Phänomenen zugrundeliegend wurde schon in vorherigen Studien eine Umkehr der Proteinladung beobachtet, sowie eine damit verbundene „Reentrant Condensation“, also eine klare und stabilisierte Lösung bei kleinen und groß en Salzkonzentrationen, während die Proteinlösung bei mittleren Salzkonzentrationen ausfällt oder phasensepariert. In dieser Arbeit wurde der Einfluss verschiedener Kationen und zusätzlichen einwertigen Salzes auf die „Reentrant Condensation“ untersucht. Während Metallsalze mit starken pH-Effekten aus der Salzhydrolyse das Kondensationsregime deutlich verkleinern, verschiebt zusätzliches einwertiges Salz das Kondensationsregime zu höheren Salzkonzentrationen. Die Ladungsinversion wird erfolgreich mit einem Modell beschrieben, das das Wechselspiel von Ionenbindung, Ladungsregulation und pH-Effekten berücksichtigt. Das Phasenverhalten kann dem Zusammenwirken von einer ioneninduzierten Anziehung und einer Ladungsstabilisation, die durch die Ladungsumkehr in ihrer Stärke variiert, zugeschrieben werden. Interessanterweise wird in einem Bereich der Kondensation eine Flüssig-Flüssig-Phasenkoexistenz beobachtet. Die Proteininteraktionen werden mit Kleinwinkelstreuung vermessen und stimmen mit Erwartungen der Kolloidtheorie überein. Nahe der niedrig konzentrierten Phasengrenze wird Kristallisation beobachtet, während die hoch konzentrierte Proteinphase amorphe Aggregate ausbildet. Proteinkristallisation in der dünneren Phase wird detaillierter diskutiert und führt zu der Vermutung, dass eine zweistufige Nukleation über einen Oligomer-Zwischenschritt auftritt. Hinweise auf diesen Prozess werden aus Echtzeit-Kleinwinkelstreuung gewonnen. Abschließ end wird das vielfältige Phasenverhalten der Proteinlösungen mit einem Modell von Kugeln mit ionenaktivierten attraktiven Oberflächenregionen beschrieben. Diese Regionen entsprechen dabei Bindestellen für Kationen und modellieren die attraktive Wechselwirkung zwischen Proteinen durch Ionenbrückenbildung, wenn genau ein Kation gebunden ist. Mit diesem Modell können sowohl die Flüssig-Flüssig-Phasenkoexistenz als auch die „Reentrant Condensation“ und Oligomerbildung beschrieben werden. Weiterhin lassen sich die beobachteten Kristallisationsprozesse verstehen, indem berücksichtigt wird, dass die hochkonzentrierte Proteinphase durch viele Ionenbrücken eventuell kinetisch daran gehindert wird, sich zu einem Kristall umzuordnen

A generalized mean-squared displacement from inelastic fixed window scans of incoherent neutron scattering as a model-free indicator of anomalous diffusion confinement

Elastic fixed window scans of incoherent neutron scattering are an established and frequently employed method to study dynamical changes, usually over a broad temperature range or during a process such as a conformational change in the sample. In particular, the apparent mean-squared displacement can be extracted via a model-free analysis based on a solid physical interpretation as an effective amplitude of molecular motions. Here, we provide a new account of elastic and inelastic fixed window scans, defining a generalized mean-squared displacement for all fixed energy transfers. We show that this generalized mean-squared displacement in principle contains all information on the real mean-square displacement accessible in the instrumental time window. The derived formula provides a clear understanding of the effects of instrumental resolution on the apparent mean-squared displacement. Finally, we show that the generalized mean-square displacement can be used as a model-free indicator on confinement effects within the instrumental time window