Generalized concentration dependence of globular protein self-diffusion coefficients in aqueous solutions

Translational Diffusion and Self-Association of an Intrinsically Disordered Protein κ-Casein Using NMR with Ultra-High Pulsed-Field Gradient and Time-Resolved FRET

Much attention has been given to studying the translational diffusion of globular proteins, whereas the translational diffusion of intrinsically disordered proteins (IDPs) is less studied. In this study, we investigate the translational diffusion and how it is affected by the self-association of an IDP, κ-casein, using pulsed-field gradient nuclear magnetic resonance and time-resolved Förster resonance energy transfer. Using the analysis of the shape of diffusion attenuation and the concentration dependence of κ-casein diffusion coefficients and intermolecular interactions, we demonstrate that κ-casein exhibits continuous self-association. When the volume fraction of κ-casein is below 0.08, we observe that κ-casein self-association results in a macroscopic phase separation upon storage at 4 °C. At κ-casein volume fractions above 0.08, self-association leads to the formation of labile gel-like networks without subsequent macroscopic phase separation. Unlike α-casein, which shows a strong concentration dependence and extensive gel-like network formation, only one-third of κ-casein molecules participate in the gel network at a time, resulting in a more dynamic and less extensive structure. These findings highlight the unique association properties of κ-casein, contributing to a better understanding of its behavior under various conditions and its potential role in casein micelle formation.

Elastin-Like Peptide as a Model for Disordered Proteins: Diffusion Behaviour in Self-Crowding Conditions

Despite the current high interest, there is limited information on diffusion data for intrinsically disordered proteins (IDPs). This study investigates the effect of crowding on the diffusion behaviour of an elastin-like peptide (ELP), by combined pulse field gradient (PFG) and static field gradient (SFG) NMR techniques. We interpret our findings in terms of highly dynamic chain assemblies with weak interactions, resulting in ELP diffusion that is primarily governed by the viscous flow of the solvent. The diffusion behaviour of the peptide appears to resemble that of globular proteins rather than flexible linear polymers over a wide concentration range.

Protein translational diffusion as a way to detect intermolecular interactions

In this work, we analyze the information on the protein intermolecular interactions obtained from macromolecular diffusion. We have shown that the most hopeful results are given by our approach based on analysis of protein translational self-diffusion and collective diffusion obtained by dynamic light scattering and pulsed-field gradient NMR (PFG NMR) spectroscopy with the help of Vink's approach to analyze diffusion motion of particles by frictional formalism of non-equilibrium thermodynamics and the usage of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of colloid particles interactions in electrolyte solutions. Early we have shown that integration of Vink's theory with DLVO provides a reliable basis for uniform interpreting of PFG NMR and DLS experiments on concentration dependence of diffusion coefficients. Basic details of theoretical and mathematical procedures and a broad analysis of experimental attestation of proposed conception on proteins of various structural form, size, and shape are presented. In the present review, the main capabilities of our approach obtain the details of intermolecular interactions of proteins with different shapes, internal structures, and mass. The universality of Vink's approach is experimentally shown, which gives the appropriate description of experimental results for proteins of complicated structure and shape.

Effects of Homogeneous and Heterogeneous Crowding on Translational Diffusion of Rigid Bovine Serum Albumin and Disordered Alfa-Casein

Intracellular environment includes proteins, sugars, and nucleic acids interacting in restricted media. In the cytoplasm, the excluded volume effect takes up to 40% of the volume available for occupation by macromolecules. In this work, we tested several approaches modeling crowded solutions for protein diffusion. We experimentally showed how the protein diffusion deviates from conventional Brownian motion in artificial conditions modeling the alteration of medium viscosity and rigid spatial obstacles. The studied tracer proteins were globular bovine serum albumin and intrinsically disordered α-casein. Using the pulsed field gradient NMR, we investigated the translational diffusion of protein probes of different structures in homogeneous (glycerol) and heterogeneous (PEG 300/PEG 6000/PEG 40,000) solutions as a function of crowder concentration. Our results showed fundamentally different effects of homogeneous and heterogeneous crowded environments on protein self-diffusion. In addition, the applied "tracer on lattice" model showed that smaller crowding obstacles (PEG 300 and PEG 6000) create a dense net of restrictions noticeably hindering diffusing protein probes, whereas the large-sized PEG 40,000 creates a "less restricted" environment for the diffusive motion of protein molecules.

Optimized OPEP Force Field for Simulation of Crowded Protein Solutions

Macromolecular crowding has profound effects on the mobility of proteins, with strong implications on the rates of intracellular processes. To describe the dynamics of crowded environments, detailed molecular models are needed, capturing the structures and interactions arising in the crowded system. In this work, we present OPEPv7, which is a coarse-grained force field at amino-acid resolution, suited for rigid-body simulations of the structure and dynamics of crowded solutions formed by globular proteins. Using the OPEP protein model as a starting point, we have refined the intermolecular interactions to match the experimentally observed dynamical slowdown caused by crowding. The resulting force field successfully reproduces the diffusion slowdown in homogeneous and heterogeneous protein solutions at different crowding conditions. Coupled with the lattice Boltzmann technique, it allows the study of dynamical phenomena in protein assemblies and opens the way for the in silico rheology of protein solutions.

Interaction of Hyaluronan Acid with Some Proteins in Aqueous Solution as Studied by NMR

According to actual literature data, hyaluronic acid (HA) that is presented in the extracellular matrix can interact with proteins and thereby affect several important functions of the cell membrane. The purpose of this work was to reveal the features of the interaction of HA with proteins using the PFG NMR method by sampling two systems: aqueous solutions of HA with bovine serum albumin (BSA) and aqueous solutions of HA with hen egg-white lysozyme (HEWL). It was found that the presence of BSA in the HA aqueous solution initiates a certain additional mechanism; as a result, the population of HA molecules in the gel structure increases to almost 100%. At the same time, for an aqueous solution of HA/HEWL, even in the range of low (0.01-0.2%) HEWL contents, strong signs of degradation (depolymerization) of some HA macromolecules were observed such that they lost the ability to form a gel. Moreover, lysozyme molecules form a strong complex with degraded HA molecules and lose their enzymatic function. Thus, the presence of HA molecules in the intercellular matrix, as well as in the state associated with the surface of the cell membrane, can, in addition to the known ones, perform one more important function: the function of protecting the cell membrane from the destructive action of lysozymes. The obtained results are important for understanding the mechanism and features of the interaction of extracellular matrix glycosaminoglycan with cell membrane proteins.

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.

Effect of Protein–Protein Interactions on Translational Diffusion of Spheroidal Proteins

One of the commonly accepted approaches to estimate protein–protein interactions (PPI) in aqueous solutions is the analysis of their translational diffusion. The present review article observes a phenomenological approach to analyze PPI effects via concentration dependencies of self- and collective translational diffusion coefficient for several spheroidal proteins derived from the pulsed field gradient NMR (PFG NMR) and dynamic light scattering (DLS), respectively. These proteins are rigid globular α-chymotrypsin (ChTr) and human serum albumin (HSA), and partly disordered α-casein (α-CN) and β-lactoglobulin (β-Lg). The PPI analysis enabled us to reveal the dominance of intermolecular repulsion at low ionic strength of solution (0.003–0.01 M) for all studied proteins. The increase in the ionic strength to 0.1–1.0 M leads to the screening of protein charges, resulting in the decrease of the protein electrostatic potential. The increase of the van der Waals potential for ChTr and α-CN characterizes their propensity towards unstable weak attractive interactions. The decrease of van der Waals interactions for β-Lg is probably associated with the formation of stable oligomers by this protein. The PPI, estimated with the help of interaction potential and idealized spherical molecular geometry, are in good agreement with experimental data.

Molecular and Ionic Diffusion in Ion Exchange Membranes and Biological Systems (Cells and Proteins) Studied by NMR

The results of NMR, and especially pulsed field gradient NMR (PFG NMR) investigations, are summarized. Pulsed field gradient NMR technique makes it possible to investigate directly the partial self-diffusion processes in spatial scales from tenth micron to millimeters. Modern NMR spectrometer diffusive units enable to measure self-diffusion coefficients from 10-13 m2/s to 10-8 m2/s in different materials on 1 H, 2 H, 7 Li, 13 C, 19 F, 23 Na, 31 P, 133 Cs nuclei. PFG NMR became the method of choice for reveals of transport mechanism in polymeric electrolytes for lithium batteries and fuel cells. Second wide field of application this technique is the exchange processes and lateral diffusion in biological cells as well as molecular association of proteins. In this case a permeability, cell size, and associate lifetime could be estimated. The authors have presented the review of their research carried out in Karpov Institute of Physical Chemistry, Moscow, Russia; Institute of Problems of Chemical Physics RAS, Chernogolovka, Russia; Kazan Federal University, Kazan, Russia; Korea University, Seoul, South Korea; Yokohama National University, Yokohama, Japan. The results of water molecule and Li+, Na+, Cs+ cation self-diffusion in Nafion membranes and membranes based on sulfonated polystyrene, water (and water soluble) fullerene derivative permeability in RBC, casein molecule association have being discussed.

Hydrophobicity, amphilicity, and flexibility: Relation between molecular protein properties and the macroscopic effects of surface activity

Their surface activity enables proteins to form and stabilize foam, which can be used for in situ product separation or foam fractionation. Thus, it would be highly desirable to predict the surface activity of proteins based on their molecular properties like hydrophobicity, amphilicity, or structure on primary, secondary, and tertiary level. Ionic strength and pH were adjusted to gain maximum surface activity. The surface activity decreased in the order α lactalbumin > β‑lactoglobulin > trypsinogen > papain. For the theoretical analysis, the database was extended by including 2 hydrophobins into the investigation, since they are known to exhibit an outstanding surface activity. No relation to the macroscopic behavior was found considering the hydrophobicity. I.e., the non-hydrophobins did not differ significantly from each other, and from the hydrophobins, one was significantly hydrophobic, and the other was significantly hydrophilic. Also, no relations were found considering the amphilicity of the secondary structure elements. However, taking into account the tertiary protein structure, it was found that for most of the proteins investigated, the presence of non-buried amphiphilic secondary structure elements in combination with a certain amount of flexibility correlates with the surface activity.

The self-diffusion of polymethylsilsesquioxane (PMSSO) dendrimers in diluted solutions and melts

Recently developed non-functional derivatives of polymethylsilsesquioxane (PMSSO) dendrimers of the first to fifth generation were characterized by 1H, 13C and 29Si NMR spectroscopy. The self-diffusion and NMR relaxation of PMSSO dendrimers in dilute solutions of toluene and melts were investigated in a wide temperature range (-50-80 °C). The hydrodynamic radii of dendrimers were determined from the self-diffusion coefficients measured in diluted solutions according to the Stokes-Einstein equation. The hydrodynamic radius of PMSSO dendrimers as a function of molecular mass follows a power law with the scaling exponent of 0.32 ± 0.02 in the investigated temperature range. The temperature dependences of the self-diffusion coefficients of dendrimers were described by the Arrhenius-type equation. The activation energies of self-diffusion of dendrimers in diluted toluene solutions are identical for different generations while the dependence of activation energy for dendrimers in melts shows a maximum for the third generation (G3) dendrimer. Taking into account the absence of specific interactions in PMSSO dendrimer melts the observed behavior was ascribed to the manifestation of interpenetration of dendrimer molecules. For low generations (G1 and G2) the short length of the branches does not considerably affect the translational diffusion while for higher generations (G4 and G5) the densification of the structure prevents significant interpenetration.

Translational diffusion of unfolded and intrinsically disordered proteins

Translational (or self-diffusion) coefficient in dilute solution is inversely proportional to the size of a diffusing molecule, and hence self-diffusion coefficient measurements have been applied to determine the effective hydrodynamic radii for a range of native and nonnative protein conformations. In particular, translational diffusion coefficient measurements are useful to estimate the hydrodynamic radius of natively (or intrinsically) disordered proteins in solution, and, thereby, probe the compactness of a protein as well as its change when environmental parameters such as temperature, solution pH, or protein concentration are varied. The situation becomes more complicated in concentrated solutions. In this review, we discuss the translational diffusion of disordered proteins in dilute and crowded solutions, focusing primarily on the information provided by pulsed-field gradient NMR technique, and draw analogies to well-structured globular proteins and synthetic polymers.

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.

The Investigation of Protein Diffusion via H-Cell Microfluidics

In this study, we developed a microfluidics method, using a so-called H-cell microfluidics device, for the determination of protein diffusion coefficients at different concentrations, pHs, ionic strengths, and solvent viscosities. Protein transfer takes place in the H-cell channels between two laminarly flowing streams with each containing a different initial protein concentration. The protein diffusion coefficients are calculated based on the measured protein mass transfer, the channel dimensions, and the contact time between the two streams. The diffusion rates of lysozyme, cytochrome c, myoglobin, ovalbumin, bovine serum albumin, and etanercept were investigated. The accuracy of the presented methodology was demonstrated by comparing the measured diffusion coefficients with literature values measured under similar solvent conditions using other techniques. At low pH and ionic strength, the measured lysozyme diffusion coefficient increased with the protein concentration gradient, suggesting stronger and more frequent intermolecular interactions. At comparable concentration gradients, the measured lysozyme diffusion coefficient decreased drastically as a function of increasing ionic strength (from zero onwards) and increasing medium viscosity. Additionally, a particle tracing numerical simulation was performed to achieve a better understanding of the macromolecular displacement in the H-cell microchannels. It was found that particle transfer between the two channels tends to speed up at low ionic strength and high concentration gradient. This confirms the corresponding experimental observation of protein diffusion measured via the H-cell microfluidics.

How Important Is Protein Diffusion in Prokaryotes?

That diffusion is important for the proper functioning of cells is without question. The extent to which the diffusion coefficient is important is explored here for prokaryotic cells. We discuss the principles of diffusion focusing on diffusion-limited reactions, summarize the known values for diffusion coefficients in prokaryotes and in in vitro model systems, and explain a number of cases where diffusion coefficients are either limiting for reaction rates or necessary for the existence of phenomena. We suggest a number of areas that need further study including expanding the range of organism growth temperatures, direct measurements of diffusion limitation, expanding the range of cell sizes, diffusion limitation for membrane proteins, and taking into account cellular context when assessing the possibility of diffusion limitation.

Effect of Intrinsic Disorder and Self-Association on the Translational Diffusion of Proteins: The Case of α-Casein

Translational diffusion is the major mode of macromolecular transport in leaving organisms, and therefore it is vital to many biological and biotechnological processes. Although translational diffusion of proteins has received considerable theoretical and experimental scrutiny, much of that attention has been directed toward the description of globular proteins. The translational diffusion of intrinsically disordered proteins (IDPs), however, is much less studied. Here, we use a pulsed-gradient nuclear magnetic resonance technique (PFG NMR) to investigate the translational diffusion of a disordered protein in a wide range of concentrations using α-casein that belongs to the class of natively disordered proteins as an example.

Theoretical and Experimental Investigation of the Translational Diffusion of Proteins in the Vicinity of Temperature-Induced Unfolding Transition

Translational diffusion is the most fundamental form of transport in chemical and biological systems. The diffusion coefficient is highly sensitive to changes in the size of the diffusing species; hence, it provides important information on the variety of macromolecular processes, such as self-assembly or folding-unfolding. Here, we investigate the behavior of the diffusion coefficient of a macromolecule in the vicinity of heat-induced transition from folded to unfolded state. We derive the equation that describes the diffusion coefficient of the macromolecule in the vicinity of the transition and use it to fit the experimental data from pulsed-field-gradient nuclear magnetic resonance (PFG NMR) experiments acquired for two globular proteins, lysozyme and RNase A, undergoing temperature-induced unfolding. A very good qualitative agreement between the theoretically derived diffusion coefficient and experimental data is observed.

Hofmeister Anion Effects on Protein Adsorption at an Air-Water Interface

Hofmeister anion effects on adsorption kinetics of the positively charged lysozyme (pH < pI) at an air-water interface were studied by surface tension measurements and time-resolved X-ray reflectometry. In the salt-free solution, the protein adsorption rate increases with decreasing the net positive charge of lysozyme. When salt ions are dissolved in water, the protein adsorption rate drastically increases, and the rate is following an inverse Hoffmeister series (Br(-) > Cl(-) > F(-)). This is the result of the strongly polarized halide anion Br(-) being attracted to the adsorbed protein layer due to strong interaction with local electric field, while weakly polarized anion F(-) having no ability to penetrate the protein layer. In X-ray reflection studies, we observed that the lysozyme molecules initially adsorbed on the air-water interface have a flat unfolded structure as previously reported in the salt-free solution. In contrast, in the concentrated salt solutions, the lysozyme molecules begin to refold during adsorption. This protein refolding as a result of protein-protein rearrangements may be a precursor phenomenon of crystallization. The refolding is most significant for Cl(-), which is a good crystallization agent, whereas it is less observed for the strongly hydrated F(-). It is widely known in the bulk state that kosmotropic anions tend to precipitate proteins but at the same time stabilize proteins against denaturing. On the other hand, at the air-water interface where adsorbed proteins usually unfold, we observed chaotropic anions strongly bound to proteins that reduce electrostatic repulsion between protein molecules, and subsequently they induce protein refolding whereas the kosmotropic anions do not.

NMR-detected brownian dynamics of αB-crystallin over a wide range of concentrations

Knowledge about the global translational and rotational motion of proteins under crowded conditions is highly relevant for understanding the function of proteins in vivo. This holds in particular for human αB-crystallin, which is strongly crowded in vivo and inter alia responsible for preventing cataracts. Quantitative information on translational and rotational diffusion is not readily available, and we here demonstrate an approach that combines pulsed-field-gradient NMR for translational diffusion and proton T1ρ/T2 relaxation-time measurements for rotational diffusion, thus overcoming obstacles encountered in previous studies. The relaxation times measured at variable temperature provide a quantitative measure of the correlation function of protein tumbling, which cannot be approximated by a single exponential, because two components are needed for a minimal and adequate description of the data. We find that at high protein concentrations, rotational diffusion is decoupled from translational diffusion, the latter following the macroscopic viscosity change almost quantitatively, resembling the behavior of spherical colloids. Analysis of data reported in the literature shows that well-packed globular proteins follow a scaling relation between the hydrodynamic radius and the molar mass, Rh ∼ M(1/d), with a fractal dimension of d ∼ 2.5 rather than 3. Despite its oligomeric nature, Rh of αB-crystallin as derived from both NMR methods is found to be fully consistent with this relation.

Contribution of rotational diffusivity towards the transport of antigens in heterogeneous immunosensors

Quantification of rotational diffusivities of biomarkers and their contribution to the overall transport using time resolved fluorescence anisotropy method would enable higher capture efficiency in heterogeneous immunosensors.

Coating formation during drying of β-lactoglobulin: gradual and sudden changes

The drying dynamics of protein coatings is of importance for many applications. The main focus of research so far was to investigate macroscopic properties of protein coatings, leaving drying dynamics virtually unexplored. A unique combination of techniques is used to monitor drying of a coating containing the protein β-lactoglobulin. The techniques used cover both macroscopic and microscopic aspects of the drying process. For all water fractions amenable to diffusing wave spectroscopy analysis (xw > 0.2 w/w), the tracer particles diffuse in the coating as in a Newtonian viscous medium. Magnetic resonance imaging shows both protein and water are distributed homogeneously over the coating during drying, up to water fractions above 0.2 w/w. When drying continues to lower water fractions, sudden transitions in drying behavior are observed by both dynamic vapor sorption and IR spectroscopy, which we suggest are due to changes in molecular interactions caused by dehydration of the protein backbone.

The folding of the specific DNA recognition subdomain of the sleeping beauty transposase is temperature-dependent and is required for its binding to the transposon DNA

The reaction of DNA transposition begins when the transposase enzyme binds to the transposon DNA. Sleeping Beauty is a member of the mariner family of DNA transposons. Although it is an important tool in genetic applications and has been adapted for human gene therapy, its molecular mechanism remains obscure. Here, we show that only the folded conformation of the specific DNA recognition subdomain of the Sleeping Beauty transposase, the PAI subdomain, binds to the transposon DNA. Furthermore, we show that the PAI subdomain is well folded at low temperatures, but the presence of unfolded conformation gradually increases at temperatures above 15°C, suggesting that the choice of temperature may be important for the optimal transposase activity. Overall, the results provide a molecular-level insight into the DNA recognition by the Sleeping Beauty transposase.

Length-scale dependent transport properties of colloidal and protein solutions for prediction of crystal nucleation rates

We propose a scaling equation describing transport properties (diffusion and viscosity) in the solutions of colloidal particles. We apply the equation to 23 different systems including colloids and proteins differing in size (range of diameters: 4 nm to 1 μm), and volume fractions (10(-3)-0.56). In solutions under study colloids/proteins interact via steric, hydrodynamic, van der Waals and/or electrostatic interactions. We implement contribution of those interactions into the scaling law. Finally we use our scaling law together with the literature values of the barrier for nucleation to predict crystal nucleation rates of hard-sphere like colloids. The resulting crystal nucleation rates agree with existing experimental data.

A model of cell biological signaling predicts a phase transition of signaling and provides mathematical formulae

A biological signal is transmitted by interactions between signaling molecules in the cell. To date, there have been extensive studies regarding signaling pathways using numerical simulation of kinetic equations that are based on equations of continuity and Fick’s law. To obtain a mathematical formulation of cell signaling, we propose a stability kinetic model of cell biological signaling of a simple two-parameter model based on the kinetics of the diffusion-limiting step. In the present model, the signaling is regulated by the binding of a cofactor, such as ATP. Non-linearity of the kinetics is given by the diffusion fluctuation in the interaction between signaling molecules, which is different from previous works that hypothesized autocatalytic reactions. Numerical simulations showed the presence of a critical concentration of the cofactor beyond which the cell signaling molecule concentration is altered in a chaos-like oscillation with frequency, which is similar to a discontinuous phase transition in physics. Notably, we found that the frequency is given by the logarithm function of the difference of the outside cofactor concentration from the critical concentration. This implies that the outside alteration of the cofactor concentration is transformed into the oscillatory alteration of cell inner signaling. Further, mathematical stability kinetic analysis predicted a discontinuous dynamic phase transition in the critical state at which the cofactor concentration is equivalent to the critical concentration. In conclusion, the present model illustrates a unique feature of cell signaling, and the stability analysis may provide an analytical framework of the cell signaling system and a novel formulation of biological signaling.

Confining ss-DNA/carbon nanotube complexes in ordered droplets

In 1/1 mass ratio mixtures made of single strand DNA and single-walled carbon nanotubes lyotropic nematic phases are formed. The process is assisted by segregative phase separation procedures. The liquid crystalline order occurring therein was confirmed by optical polarizing microscopy and zero-shear rheology. The resulting nematic droplets were dispersed in protein or cationic surfactant solutions, under appropriate pH and/or ionic strength conditions. The components of the hosting fluid(s) rapidly adsorb onto the droplets, form a permanent peel on their surface, and confine them. The peel resists osmotic gradients and has significant stability. The distribution of the species in the droplet and in the peel was determined by SEM. Data indicate that the peel contains protein or surfactant, depending on the titrant, when the core is rich in DNA and nanotubes. According to electron microscopy, nematic order in the droplets is partly retained.

The shape of protein crowders is a major determinant of protein diffusion

As a model for understanding how molecular crowding influences diffusion and transport of proteins in cellular environments, we combined experimental and theoretical approaches to study the diffusion of proteins in highly concentrated protein solutions. Bovine serum albumin and γ-Globulin were chosen as molecular crowders and as tracers. These two proteins are representatives of the main types of plasma protein and have different shapes and sizes. Solutions consisting of one or both proteins were studied. The self-diffusion coefficients of the fluorescently labeled tracer proteins were measured by means of fluorescence correlation spectroscopy at a total protein concentration of up to 400 g/L. γ-Globulin is found to have a stronger influence as a crowder on the tracer self-diffusion coefficient than Bovine serum albumin. Brownian dynamics simulations show that the excluded volume and the shape of the crowding protein have a significantly stronger influence on translational and rotational diffusion coefficients, as well as transient oligomerization, than hydrodynamic or direct interactions. Anomalous subdiffusion, which is not observed at the experimental fluorescence correlation spectroscopy timescales (>100 μs), appears only at very short timescales (<1 μs) in the simulations due to steric effects of the proteins. We envision that the combined experimental and computational approach employed here can be developed to unravel the different biophysical contributions to protein motion and interaction in cellular environments by systematically varying protein properties such as molecular weight, size, shape, and electrostatic interactions.

Kidney branching morphogenesis under the control of a ligand-receptor-based Turing mechanism

The main signalling proteins that control early kidney branching have been defined. Yet the underlying mechanism is still elusive. We have previously shown that a Schnakenberg-type Turing mechanism can recapitulate the branching and protein expression patterns in wild-type and mutant lungs, but it is unclear whether this mechanism would extend to other branched organs that are regulated by other proteins. Here, we show that the glial cell line-derived neurotrophic factor-RET regulatory interaction gives rise to a Schnakenberg-type Turing model that reproduces the observed budding of the ureteric bud from the Wolffian duct, its invasion into the mesenchyme and the observed branching pattern. The model also recapitulates all relevant protein expression patterns in wild-type and mutant mice. The lung and kidney models are both based on a particular receptor-ligand interaction and require (1) cooperative binding of ligand and receptor, (2) a lower diffusion coefficient for the receptor than for the ligand and (3) an increase in the receptor concentration in response to receptor-ligand binding (by enhanced transcription, more recycling or similar). These conditions are met also by other receptor-ligand systems. We propose that ligand-receptor-based Turing patterns represent a general mechanism to control branching morphogenesis and other developmental processes.

Characteristic size for onset of coffee-ring effect in evaporating lysozyme-water solution droplets

Liquid droplets containing suspended particles deposited on a solid surface often form a ring-like structure due to the redistribution of solute during evaporation, a phenomenon known as the "coffee ring effect". The complex patterns left on the substrate after evaporation are characteristic of the nature of the solute and the particle transport mechanisms. In this study, the morphological evolution and conditions for coffee ring formation for simplified model biological solutions of DI water and lysozyme are examined by AFM and optical microscopy. Lysozyme is a globular protein found in high concentration, for example, in human tears and saliva. The drop diameters studied are very small, ranging from 1 to 50 μm. In this size range, protein motion and the resulting dried residue morphology are highly influenced by the decreased evaporation time of the drop. In this work, we consider the effect of droplet size and concentration on the morphology of the deposited drop as well as the minimal conditions for coffee ring formation in this system. Two distinct deposit types are observed: a simple cap-shaped deposit for drops with small diameters and a ring-like deposit at larger diameters. Ring formation occurs at a critical diameter, which depends systematically on initial lysozyme concentration.

Branch mode selection during early lung development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modes.

Most organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching. While the branching sequence is identical in mice of identical genetic background it differs between mouse strains. This suggests that the positioning of branch points and the type of branching sensitively depends on information encoded in the genome. Encoding every branching point independently in the genome would require a large number of genes, and it is more likely that a recursive, self-organized process exists that determines the patterning. While many regulatory molecules have been identified an integrated understanding of the regulatory network (program) is missing. Based on available experimental data we have developed a model for lung branching. The model correctly predicts branching phenotypes in mutants and suggests that also the growth speed of the lung tip can affect the positioning and type of the next branching event.

Self-diffusion in a hyaluronic acid-albumin-water system as studied by NMR

Hyaluronic acid (HA) is an anionic biopolymer that is present in many tissues and can be involved in cancerous neoformations. HA can form complexes with proteins (particularly, serum albumin) in the body. However, HA structures and processes involving HA have not been extensively studied by NMR because the molecule's rigid structure makes these studies problematic. In the current work, self-diffusion of HA and bovine serum albumin (BSA), and water in solutions was measured by (1)H pulsed field gradient NMR (PFG NMR) with a focus on the HA-BSA-D2O systems at various concentrations of BSA and HA. It was shown that in the presence of even a small amount of HA, the self-diffusion coefficient (SDC) of BSA decreases. To explain this fact, three hypotheses were proposed and analyzed. The first one was based on the effect of slowing down of water mobility in the presence of HA. The second hypothesis suggested an effect of mechanical collisions of BSA with HA molecules. The third hypothesized that BSA and HA molecules form a complex where BSA molecules reduced in mobility. It was shown that the third mechanism is the most likely. The state of the BSA molecules in the BSA-HA-D2O system corresponds to a 'fast exchange' condition from the NMR point of view: BSA molecules reside in the 'free' and 'bound' (with HA) states for much shorter time than the diffusion time of the PFG NMR experiment, 7 ms. The fractions of 'bound' BSA molecules in the BSA-HA complex were estimated.

Integrated multifunctional microfluidics for automated proteome analyses

Proteomics is a challenging field for realizing totally integrated microfluidic systems for complete proteome processing due to several considerations, including the sheer number of different protein types that exist within most proteomes, the large dynamic range associated with these various protein types, and the diverse chemical nature of the proteins comprising a typical proteome. For example, the human proteome is estimated to have >10(6) different components with a dynamic range of >10(10). The typical processing pipeline for proteomics involves the following steps: (1) selection and/or extraction of the particular proteins to be analyzed; (2) multidimensional separation; (3) proteolytic digestion of the protein sample; and (4) mass spectral identification of either intact proteins (top-down proteomics) or peptide fragments generated from proteolytic digestions (bottom-up proteomics). Although a number of intriguing microfluidic devices have been designed, fabricated and evaluated for carrying out the individual processing steps listed above, work toward building fully integrated microfluidic systems for protein analysis has yet to be realized. In this chapter, information will be provided on the nature of proteomic analysis in terms of the challenges associated with the sample type and the microfluidic devices that have been tested to carry out individual processing steps. These include devices such as those for multidimensional electrophoretic separations, solid-phase enzymatic digestions, and solid-phase extractions, all of which have used microfluidics as the functional platform for their implementation. This will be followed by an in-depth review of microfluidic systems, which are defined as units possessing two or more devices assembled into autonomous systems for proteome processing. In addition, information will be provided on the challenges involved in integrating processing steps into a functional system and the approaches adopted for device integration. In this chapter, we will focus exclusively on the front-end processing microfluidic devices and systems for proteome processing, and not on the interface technology of these platforms to mass spectrometry due to the extensive reviews that already exist on these types of interfaces.

Development of an efficient on-chip digestion system for protein analysis using MALDI-TOF MS

A solid-phase trypsin microreactor was constructed and operated with electrokinetically-driven flow for the digestion of proteins and coupled off-line with MALDI-TOF MS. The bioreactor was fabricated from poly(methyl methacrylate), PMMA, by hot embossing using a mold master prepared by micro-milling. The solid-phase bioreactor consisted of a 4 cm long, 200 microm wide, and 50 microm deep microfluidic channel that was populated with an array of 50 microm diameter micropost structures with a 50 microm inter-post spacing. The bioreactor was prepared by covalently attaching the proteolytic enzyme, trypsin, to the UV-modified surface of the PMMA microstructures using the appropriate coupling reagents. The performance of the system was evaluated using a set of proteins. The bioreactor provided efficient digestion of cytochrome c at a field strength of 375 V/cm, producing a reaction time of approximately 20 s to produce 97% sequence coverage for protein identification. Bovine serum albumin (BSA), phosphorylase b, and beta-casein were also assessed and the sequence coverages were 46, 63, and 79%, respectively, using the same reactor residence time. Furthermore, Escherichia coli was used as a model to demonstrate the feasibility of fingerprint analysis for intact cells using this solid-phase bioreactor.

Microfluidic chips for mass spectrometry-based proteomics

Microfluidic devices coupled to mass spectrometers have emerged as excellent tools for solving the complex analytical challenges associated with the field of proteomics. Current proteome identification procedures are accomplished through a series of steps that require many hours of labor-intensive work. Microfluidics can play an important role in proteomic sample preparation steps prior to mass spectral identification such as sample cleanup, digestion, and separations due to its ability to handle small sample quantities with the potential for high-throughput parallel analysis. To utilize microfluidic devices for proteomic analysis, an efficient interface between the microchip and the mass spectrometer is required. This tutorial provides an overview of the technologies and applications of microfluidic chips coupled to mass spectrometry for proteome analysis. Various approaches for combining microfluidic devices with electrospray ionization (ESI) and matrix-assisted laser desorption/ionization (MALDI) are summarized and applications of chip-based separations and digestion technologies to proteomic analysis are presented.

Cytoplasmic protein mobility in osmotically stressed Escherichia coli

Facile diffusion of globular proteins within a cytoplasm that is dense with biopolymers is essential to normal cellular biochemical activity and growth. Remarkably, Escherichia coli grows in minimal medium over a wide range of external osmolalities (0.03 to 1.8 osmol). The mean cytoplasmic biopolymer volume fraction ((phi)) for such adapted cells ranges from 0.16 at 0.10 osmol to 0.36 at 1.45 osmol. For cells grown at 0.28 osmol, a similar phi range is obtained by plasmolysis (sudden osmotic upshift) using NaCl or sucrose as the external osmolyte, after which the only available cellular response is passive loss of cytoplasmic water. Here we measure the effective axial diffusion coefficient of green fluorescent protein (D(GFP)) in the cytoplasm of E. coli cells as a function of (phi) for both plasmolyzed and adapted cells. For plasmolyzed cells, the median D(GFP) (D(GFP)(m)) decreases by a factor of 70 as (phi) increases from 0.16 to 0.33. In sharp contrast, for adapted cells, D(GFP)(m) decreases only by a factor of 2.1 as (phi) increases from 0.16 to 0.36. Clearly, GFP diffusion is not determined by (phi) alone. By comparison with quantitative models, we show that the data cannot be explained by crowding theory. We suggest possible underlying causes of this surprising effect and further experiments that will help choose among competing hypotheses. Recovery of the ability of proteins to diffuse in the cytoplasm after plasmolysis may well be a key determinant of the time scale of the recovery of growth.

Development of an automated digestion and droplet deposition microfluidic chip for MALDI-TOF MS

An automated proteolytic digestion bioreactor and droplet deposition system was constructed with a plastic microfluidic device for off-line interfacing to matrix assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). The microfluidic chips were fabricated in poly(methyl methacrylate) (PMMA), using a micromilling machine and incorporated a bioreactor, which was 100 microm wide, 100 microm deep, and possessed a 4 cm effective channel length (400 nL volume). The chip was operated by pressure-driven flow and mounted on a robotic fraction collector system. The PMMA bioreactor contained surface immobilized trypsin, which was covalently attached to the UV-modified PMMA surface using coupling reagents N-(3-dimethylaminopropyl)-N'-ethylcarbodiimide hydrochloride (EDC) and hydroxysulfosuccinimide (sulfo-NHS). The digested peptides were mixed with a MALDI matrix on-chip and deposited as discrete spots on MALDI targets. The bioreactor provided efficient digestion of a test protein, cytochrome c, at a flow rate of 1 microL/min, producing a reaction time of approximately 24 s to give adequate sequence coverage for protein identification. Other proteins were also evaluated using this solid-phase bioreactor. The efficiency of digestion was evaluated by monitoring the sequence coverage, which was 64%, 35%, 58%, and 47% for cytochrome c, bovine serum albumin (BSA), myoglobin, and phosphorylase b, respectively.

Toward realistic modeling of dynamic processes in cell signaling: quantification of macromolecular crowding effects

One of the major factors distinguishing molecular processes in vivo from biochemical experiments in vitro is the effect of the environment produced by macromolecular crowding in the cell. To achieve a realistic modeling of processes in the living cell based on biochemical data, it becomes necessary, therefore, to consider such effects. We describe a protocol based on Brownian dynamics simulation to characterize and quantify the effect of various forms of crowding on diffusion and bimolecular association in a simple model of interacting hard spheres. We show that by combining the elastic collision method for hard spheres and the mean field approach for hydrodynamic interaction (HI), our simulations capture the correct dynamics of a monodisperse system. The contributions from excluded volume effect and HI to the crowding effect are thus quantified. The dependence of the results on size distribution of each component in the system is illustrated, and the approach is applied as well to the crowding effect on electrostatic-driven association in both neutral and charged environments; values for effective diffusion constants and association rates are obtained for the specific conditions. The results from our simulation approach can be used to improve the modeling of cell signaling processes without additional computational burdens.

Merozoite surface protein 2 of Plasmodium falciparum: expression, structure, dynamics, and fibril formation of the conserved N-terminal domain

Merozoite surface protein 2 (MSP2) is a GPI-anchored protein on the surface of the merozoite stage of the malaria parasite Plasmodium falciparum. It is largely disordered in solution, but has a propensity to form amyloid-like fibrils under physiological conditions. The N-terminal conserved region (MSP2(1-25)) is part of the protease-resistant core of these fibrils. To investigate the structure and dynamics of this region, its ability to form fibrils, and the role of individual residues in these properties, we have developed a bacterial expression system that yields > or =10 mg of unlabeled or (15)N-labeled peptide per litre of culture. Two recombinant versions of MSP2(1-25), wild-type and a Y7A/Y16A mutant, have been produced. Detailed conformational analysis of the wild-type peptide and backbone (15)N relaxation data indicated that it contains beta-turn and nascent helical structures in the central and C-terminal regions. Residues 6-21 represent the most ordered region of the structure, although there is some flexibility around residues 8 and 9. The 10-residue sequence (MSP2(7-16)) (with two Tyr residues) was predicted to have a higher propensity for beta-aggregation than the 8-mer sequence (MSP2(8-15)), but there was no significant difference in conformation between MSP2(1-25) and [Y7A,Y16A]MSP2(1-25) and the rate of fibril formation was only slightly slower in the mutant. The peptide expression system described here will facilitate further mutational analyses to define the roles of individual residues in transient structural elements and fibril formation, and thus contribute to the further development of MSP2 as a malaria vaccine candidate.

Dynamics of the SPRY domain-containing SOCS box protein 2: flexibility of key functional loops

The SPRY domain was identified originally as a sequence repeat in the dual-specificity kinase splA and ryanodine receptors and subsequently found in many other distinct proteins, including more than 70 encoded in the human genome. It is a subdomain of the B30.2/SPRY domain and is believed to function as a protein-protein interaction module. Three-dimensional structures of several B30.2/SPRY domain-containing proteins have been reported recently: murine SSB-2 in solution by NMR spectroscopy, a Drosophila SSB (GUSTAVUS), and human PRYSPRY protein by X-ray crystallography. The three structures share a core of two antiparallel beta-sheets for the B30.2/SPRY domain but show differences located mainly at one end of the beta-sandwich. Analysis of SSB-2 residues required for interactions with its intracellular ligands has provided insights into B30.2/SPRY binding specificity and identified loop residues critical for the function of this domain. We have investigated the backbone dynamics of SSB-2 by means of Modelfree analysis of its backbone (15)N relaxation parameters and carried out coarse-grained dynamics simulation of B30.2/SPRY domain-containing proteins using normal mode analysis. Translational self-diffusion coefficients of SSB-2 measured using pulsed field gradient NMR were used to confirm the monomeric state of SSB-2 in solution. These results, together with previously reported amide exchange data, highlight the underlying flexibility of the loop regions of B30.2/SPRY domain-containing proteins that have been shown to be important for protein-protein interactions. The underlying flexibility of certain regions of the B30.2/SPRY domain-containing proteins may also contribute to some apparent structural differences observed between GUSTAVUS or PRYSPRY and SSB-2.

Intermolecular Interaction of Myoglobin with Water Molecules along the pH Denaturation Curve

A method of diffusion coefficient (D) measurement for proteins based on the pulsed laser-induced transient grating method using a photosensitive cross-linker was applied to the characterization of the pH denaturation process of holo- and apo-myoglobin (Mb) from the viewpoint of protein-water interaction. It was found that the pH denaturation curve monitored by D agrees quite well with that determined by the circular dichroism intensity for holo-Mb. This fact indicates that the changes in intermolecular interaction and the alpha-helix content occur simultaneously during the unfolding process. However, the pH dependence of D for apo-Mb was different from that of alpha-helix content. This different behavior can be explained in terms of the different denaturation steps for the secondary structure and the hydrogen bonding network of the intermediate species around pH 4; i.e., this intermediate is partially unfolded, but the hydrogen bonding network is dominantly an intramolecular one. Taking previously reported properties of this species into account, we conclude that water molecules are trapped in the hydrophobic core of the apo-Mb pH 4 intermediate. This fact suggests that the kinetic intermediate state of the protein folding process is a swollen state without water molecular exchange with the bulk phase.

Optimization of Diffusion-Filtered NMR Experiments for Selective Suppression of Residual Nondeuterated Solvent and Water Signals from 1H NMR Spectra of Organic Compounds

Interpretation of 1H NMR spectra of organic compounds is sometimes hampered by the presence of strong peaks arising from residual nondeuterated solvent and water that obscure compound signals. Classical solvent suppression techniques such as presaturation or those based on pulsed field gradients are not effective in this regard because they also remove the compound resonances that overlap with the solvent signal being suppressed. Here, we propose an alternative scheme by using an optimized NMR diffusion filter that eliminates the nondesired peaks while retaining the signals of interest. This strategy has proved to be useful in three common deuterated solvents, namely, CDCl3, DMSO-d6, and CD3OD, resulting in clean spectra with no interference from solvent or water peaks.