Long-range electron exchange measured in proteins by quenching of tryptophan phosphorescence.

Ten proteins that span a wide range of phosphorescence lifetimes were examined for sensitivity to quenching by four agents of disparate chemical nature. The results show that quenching efficiency is relatively independent of the quencher and is highly correlated with depth of burial of the phosphorescent tryptophan. The bimolecular quenching rate constants (kq) measured for the different proteins, spanning 5 orders of magnitude in kq, are found to decrease exponentially with the distance (r) of the tryptophan in angstroms from the protein surface--i.e., kq = Aexp(-r/rho), where A contains a geometrical factor dependent on tryptophan burial and surface geometry [corrected]. Theoretical analysis shows that this behavior can be expected for an electron-exchange reaction between the buried tryptophans and quenchers in solution in the rapid diffusion limit. Therefore, the results obtained provide evidence for an exponential dependence of electron-transfer rate on distance in a protein environment and evaluate the distance parameter, rho, for electron transfer through the general protein matrix at 1.0 A. For a unimolecular donor-acceptor pair with ket = koexp(-r/rho), ko approximately 10(9) sec-1.     

Highly sensitive biological and chemical sensors based on reversible fluorescence quenching in a conjugated polymer.

The fluorescence of a polyanionic conjugated polymer can be quenched by extremely low concentrations of cationic electron acceptors in aqueous solutions. We report a greater than million-fold amplification of the sensitivity to fluorescence quenching compared with corresponding "molecular excited states." Using a combination of steady-state and ultrafast spectroscopy, we have established that the dramatic quenching results from weak complex formation [polymer(-)/quencher(+)], followed by ultrafast electron transfer from excitations on the entire polymer chain to the quencher, with a time constant of 650 fs. Because of the weak complex formation, the quenching can be selectively reversed by using a quencher-recognition diad. We have constructed such a diad and demonstrate that the fluorescence is fully recovered on binding between the recognition site and a specific analyte protein. In both solutions and thin films, this reversible fluorescence quenching provides the basis for a new class of highly sensitive biological and chemical sensors.     

Solute diffusion is hindered in the mitochondrial matrix

Intracellular chemical reactions generally constitute reaction-diffusion systems located inside nanostructured compartments like the cytosol, nucleus, endoplasmic reticulum, Golgi, and mitochondrion. Understanding the properties of such systems requires quantitative information about solute diffusion. Here we present a novel approach that allows determination of the solvent-dependent solute diffusion constant (D(solvent)) inside cell compartments with an experimentally quantifiable nanostructure. In essence, our method consists of the matching of synthetic fluorescence recovery after photobleaching (FRAP) curves, generated by a mathematical model with a realistic nanostructure, and experimental FRAP data. As a proof of principle, we assessed D(solvent) of a monomeric fluorescent protein (AcGFP1) and its tandem fusion (AcGFP1(2)) in the mitochondrial matrix of HEK293 cells. Our results demonstrate that diffusion of both proteins is substantially slowed by barriers in the mitochondrial matrix (cristae), suggesting that cells can control the dynamics of biochemical reactions in this compartment by modifying its nanostructure.     

Kinetic Constants Determined from Membrane Transport Measurements: Carbonic Anhydrase Activity at High Concentrations

Facilitated diffusion rates can be used to determine kinetic constants for rapid reactions occurring within membranes and thin fluid layers. We have applied this technique to the study of the reversible CO(2) hydration reactions catalyzed by carbonic anhydrase (EC 4.2.1.1; carbonate hydro-lyase). The experimental method entails the diffusion of tracer (14)CO(2) through Millipore filter membranes impregnated with aqueous bicarbonate solutions containing various concentrations of dissolved enzyme. A mathematical model of the simultaneous diffusion/reaction transport process is analyzed to predict the effective diffusion rate in terms of the relevant kinetic parameters. The solution to the mathematical model can be transformed to yield straight-line relations analogous to Lineweaver-Burk plots. The pseudo-first-order enzymatic rate constant for the hydration reaction can be determined from the slope or intercept of a plot of this straight-line relationship. Rate constants were accurately measured at high enzyme concentrations for reactions having half-times under a millisecond. The rate constants agree well with other reported kinetic constants for carbonic anhydrase, and the known pH-activity dependence and bicarbonate inhibition are quantitatively demonstrated. The specific activity is constant up to 4.0 mg/ml, which is believed to be the highest concentration at which the activity has been measured. The membrane transport technique has general applicability for other rapid reaction systems.     

Kinetics of protein-protein association explained by Brownian dynamics computer simulation.

Protein-protein bond formations, such as antibody-antigen complexation or aggregation of protein monomers into dimers and larger aggregates, occur with bimolecular rate constants on the order of 10(6) M-1.s-1, which is only 3 orders of magnitude slower than the diffusion-limited Smoluchowski rate. However, since the protein-protein bond requires rotational alignment to within a few angstroms of tolerance, purely geometric estimates would suggest that the observed rates might be 6 orders of magnitude below the Smoluchowski rate. Previous theoretical treatments have not been solved for the highly specific docking criteria of protein-protein association--the entire subunit interface must be aligned within 2 A of the correct position. Several studies have suggested that diffusion alone could not produce the rapid association kinetics and have postulated "lengthy collisions" and/or the operation of electrostatic or hydrophobic steering forces to accelerate the association. In the present study, the Brownian dynamics simulation method is used to compute the rate of association of neutral spherical model proteins with the stated docking criteria. The Brownian simulation predicts a rate of 2 x 10(6) M-1.s-1 for this generic protein-protein association, a rate that is 2000 times faster than that predicted by the simplest geometric calculation and is essentially equal to the rates observed for protein-protein association in aqueous solution. This high rate is obtained by simple diffusive processes and does not require any attractive or steering forces beyond those achieved for a partially formed bond. The rate enhancement is attributed to a diffusive entrapment effect, in which a protein pair surrounded and trapped by water undergoes multiple collisions with rotational reorientation during each encounter.     

Distinct roles of the photosystem II protein PsbS and zeaxanthin in the regulation of light harvesting in plants revealed by fluorescence lifetime snapshots

The photosystem II (PSII) protein PsbS and the enzyme violaxanthin deepoxidase (VDE) are known to influence the dynamics of energy-dependent quenching (qE), the component of nonphotochemical quenching (NPQ) that allows plants to respond to fast fluctuations in light intensity. Although the absence of PsbS and VDE has been shown to change the amount of quenching, there have not been any measurements that can detect whether the presence of these proteins alters the type of quenching that occurs. The chlorophyll fluorescence lifetime probes the excited-state chlorophyll relaxation dynamics and can be used to determine the amount of quenching as well as whether two different genotypes with the same amount of NPQ have similar dynamics of excited-state chlorophyll relaxation. We measured the fluorescence lifetimes on whole leaves of Arabidopsis thaliana throughout the induction and relaxation of NPQ for wild type and the qE mutants, npq4, which lacks PsbS; npq1, which lacks VDE and cannot convert violaxanthin to zeaxanthin; and npq1 npq4, which lacks both VDE and PsbS. These measurements show that although PsbS changes the amount of quenching and the rate at which quenching turns on, it does not affect the relaxation dynamics of excited chlorophyll during quenching. In addition, the data suggest that PsbS responds not only to ΔpH but also to the Δψ across the thylakoid membrane. In contrast, the presence of VDE, which is necessary for the accumulation of zeaxanthin, affects the excited-state chlorophyll relaxation dynamics.Plants regulate light harvesting by photosystem II (PSII) in response to changes in light intensity. One way that plants are able to regulate light harvesting is through turning on and off mechanisms that dissipate excess energy. This energy dissipation is assessed via nonphotochemical quenching (NPQ) measurements of chlorophyll fluorescence. Energy-dependent quenching (qE) is the NPQ process with the fastest kinetics. It turns on and off in seconds to minutes, allowing plants to respond to rapid fluctuations in light intensity, which is thought to reduce photodamage (1, 2).Illumination causes the formation of gradients of electrical potential (Δψ) and of proton concentration (ΔpH) across the thylakoid membrane. Although it has been suggested that Δψ may play a role in qE (3), only ΔpH is thought to trigger different proteins and enzymes to induce qE (4). The major known factors involved in induction of qE are the enzyme violaxanthin deepoxidase (VDE) (5) and the PSII protein PsbS (6). The mutant npq1, which lacks VDE and cannot convert violaxanthin to zeaxanthin, has a phenotype with lower qE compared with the wild type (7). Transient absorption measurements suggest that zeaxanthin may quench excited chlorophyll (8). The npq4 mutant, which lacks PsbS, shows no rapidly reversible quenching of chlorophyll fluorescence, suggesting that PsbS is required for qE in vivo (6). PsbS is pH sensitive (9) but is not thought to bind pigments, and thus is likely not the site of quenching (10). It has therefore been hypothesized that PsbS plays an indirect role in quenching, perhaps facilitating a rearrangement of proteins within the grana (11–13). In this paper, we examine the fluorescence lifetime of chlorophyll throughout the induction and relaxation of quenching in intact leaves with and without PsbS and zeaxanthin to examine whether PsbS and zeaxanthin change the type of quenching that occurs in plants.The amount and dynamics of qE are generally measured by changes in the chlorophyll fluorescence yield. One limitation of the chlorophyll fluorescence yield is that it can only inform on the amount of quenching, not on excited-state chlorophyll relaxation dynamics, which reflect how chlorophyll is quenched. Despite this issue, the amount of quenching is commonly used as a proxy for the type of quenching by separating components of quenching based on kinetics, mutants, and the effects of chemical inhibitors. By artificially increasing ΔpH in isolated chloroplasts from npq4, Johnson and Ruban (14, 15) have been able to increase the amount of quenching in npq4 plants to levels observed in wild type plants, suggesting that PsbS may catalyze qE. One potential complication with these studies is that the use of the chemical mediators of cyclic electron transport often necessitates studying isolated chloroplasts rather than intact leaves. In addition, the observation of equivalent amounts of quenching still does not prove that the type of quenching in npq4 is the same as in wild type.In contrast with fluorescence yield measurements, fluorescence lifetime measurements can be used to determine whether the relaxation dynamics of excited chlorophyll are modified by different mutations, informing on the role of a protein or molecule during quenching. The relaxation dynamics of excited chlorophyll during NPQ depends on many variables, including the distance to a quencher, the interactions between the orbitals of chlorophyll and the quencher, and the number of quenchers (16). The shape of the fluorescence lifetime decay curve can be used to determine whether two samples have similar excited chlorophyll relaxation dynamics. Our results show that, although the presence of PsbS does not alter excited chlorophyll relaxation dynamics, the absence of VDE does. These measurements are performed in intact leaves without any chemical treatments, and the data strongly suggest that PsbS plays a catalytic role in vivo.     

Diffusion-limited contact formation in unfolded cytochrome c: estimating the maximum rate of protein folding.

How fast can a protein fold? The rate of polypeptide collapse to a compact state sets an upper limit to the rate of folding. Collapse may in turn be limited by the rate of intrachain diffusion. To address this question, we have determined the rate at which two regions of an unfolded protein are brought into contact by diffusion. Our nanosecond-resolved spectroscopy shows that under strongly denaturing conditions, regions of unfolded cytochrome separated by approximately 50 residues diffuse together in 35-40 microseconds. This result leads to an estimate of approximately (1 microsecond)-1 as the upper limit for the rate of protein folding.     

Mobility in geometrically confined membranes

Lipid and protein lateral mobility is essential for biological function. Our theoretical understanding of this mobility can be traced to the seminal work of Saffman and Delbrück, who predicted a logarithmic dependence of the protein diffusion coefficient (i) on the inverse of the size of the protein and (ii) on the “membrane size” for membranes of finite size [Saffman P, Delbrück M (1975) Proc Natl Acad Sci USA 72:3111—3113]. Although the experimental proof of the first prediction is a matter of debate, the second has not previously been thought to be experimentally accessible. Here, we construct just such a geometrically confined membrane by forming lipid bilayer nanotubes of controlled radii connected to giant liposomes. We followed the diffusion of individual molecules in the tubular membrane using single particle tracking of quantum dots coupled to lipids or voltage-gated potassium channels KvAP, while changing the membrane tube radius from approximately 250 to 10 nm. We found that both lipid and protein diffusion was slower in tubular membranes with smaller radii. The protein diffusion coefficient decreased as much as 5-fold compared to diffusion on the effectively flat membrane of the giant liposomes. Both lipid and protein diffusion data are consistent with the predictions of a hydrodynamic theory that extends the work of Saffman and Delbrück to cylindrical geometries. This study therefore provides strong experimental support for the ubiquitous Saffman–Delbrück theory and elucidates the role of membrane geometry and size in regulating lateral diffusion.Cell membrane fluidity is crucial for living cells. Lateral transport and mixing take molecular components from where they are delivered onto the membrane to where they are needed. Diffusion is thought to be the primary mechanism for this transport and is therefore central to a variety of fundamental biomolecular processes (1) including signaling, transport, and self-assembly (2). Whether the changes in molecular mobility alone can provide a regulatory pathway in cellular processes is one of the recurring questions in membrane biophysics. It is well established that the protein lateral mobility depends on membrane fluidity and on the size of the diffusing species and can be further modified by molecular crowding (3–5) as well as interactions with membrane microdomains (6) and the cytoskeleton (6, 7). Our aim is to study experimentally how membrane geometry and, in particular, membrane area confinement can affect the diffusion of lipids and membrane proteins. We will do this by studying tracer diffusion on membrane tubes, rather than in the more usual membrane geometry of nearly planar sheets (large-radius vesicles).In this paper, we restrict our attention to membrane diffusion in perfectly mixed, single fluid phase membranes so as to study the role of membrane geometry on diffusion, without needing to consider additional contributions from membrane phase or molecular ordering. Although curvature of a membrane can lead to changes in membrane thickness or ordering, these effects can be neglected when the smallest radius of curvature for the surface, R (in our case the radius of the cylindrical membrane tether), is much larger than the membrane thickness, h (8). Recent theoretical work has suggested that membrane geometry should influence diffusion in a particular way (9), with the diffusion constant of tracer particles becoming smaller as the radius of a membrane tube is reduced. The area of membrane (per unit length) in a tube should affect the local diffusion constant because the movement of any particle embedded in the membrane creates a shear gradient that is proportional to the particle velocity and inversely related to the tube size. When, for instance, the particle moves along the tube axis, the membrane on the opposite side to the particle actually flows in the opposite direction, and here R_tube is the relevant length over which the shear gradient extends (10). According to the fluctuation dissipation theorem (11), the larger force/velocity ratio corresponds to a smaller mobility and hence a reduced diffusion constant.These arguments can be rigorously formalized. The first papers on the subject by Saffman and Delbrück (12, 13) are seminal. These authors analyzed the low Reynolds number hydrodynamics of an embedded disk diffusing in a quasi two-dimensional membrane. Later refinements include analyzing the effect of flows in a surrounding fluid (13, 14). Saffman and Delbrück predicted that the diffusion constant on a membrane of finite area should depend logarithmically on the ratio of the size of the membrane (frame) to the radius of the diffusant particle r. Experimental verification of this important prediction was, for many years, elusive. Very recently, experimental evidence for the logarithmic dependence on the size of the diffusant particle r has been reported (5), although some debate remains (15, 16). No possible experimental test of the corresponding logarithmic dependence on the size of the membrane frame has previously been identified. We report on just such a test in the present work. Daniels and Turner (9) have shown that for membranes in a tubular geometry, which we study here, the role of effective membrane (frame) size R_memb introduced by Saffman and Delbrück is played by the radius of the membrane tube R_tube and not, for example, by its length. More recently, Henle and Levine (10) have presented a comprehensive analysis of the membrane flows and particle mobilities in spherical and tubular membranes; their solution for longitudinal mobility in the limit of thin tubes coincides with the logarithmic dependence obtained by Daniels and Turner.In the present work we report on measurements of tracer diffusion on membrane tubes with carefully controlled radii. These tubes were pulled from giant unilamellar vesicles (GUVs) by combining micropipette aspiration and optical trapping (17, 18). Diffusion of lipid and membrane proteins was measured by single particle tracking (SPT) of quantum dots (QDs) linked either to lipids or proteins detected with a fast and sensitive camera (19). Our primary results are that membrane geometry can significantly affect tracer diffusion and that this is consistent with a logarithmic dependence on the tube radius R_tube. This therefore represents experimental verification of the corresponding predictions of Saffmann and Delbrück.     

Lateral diffusion of membrane lipids and proteins during the cell cycle of neuroblastoma cells.

The fluorescence photobleaching recovery method has been used to determine the lateral mobilities of membrane lipids and proteins during the cell cycle of synchronized C1300 mouse neuroblastoma cells (clone Neuro-2A). As probes for lipid mobility, 3,3'-dioctadecylindocarbocyanine iodide and a fluorescein-labeled analog of ganglioside GM1 were used. Membrane proteins were labeled with rhodamine-labeled rabbit antibodies against mouse E14 cells. For both lipid probes the diffusion coefficients reach a minimum in mitosis, increase 2- to 3-fold during G1, remain constant at maximal values during S, and decrease again shortly before mitosis. Membrane proteins also exhibit minimum diffusion coefficients in mitosis, followed by a similar rise in G1. However, as cells proceed through S and G2, the lateral mobility of the membrane proteins gradually decreases. It is argued that lipid mobility is controlled by the fluidity of the membrane lipid matrix whereas protein mobility is governed also by other constraints.     

Configuration-dependent diffusion can shift the kinetic transition state and barrier height of protein folding

We show that diffusion can play an important role in protein-folding kinetics. We explicitly calculate the diffusion coefficient of protein folding in a lattice model. We found that diffusion typically is configuration- or reaction coordinate-dependent. The diffusion coefficient is found to be decreasing with respect to the progression of folding toward the native state, which is caused by the collapse to a compact state constraining the configurational space for exploration. The configuration- or position-dependent diffusion coefficient has a significant contribution to the kinetics in addition to the thermodynamic free-energy barrier. It effectively changes (increases in this case) the kinetic barrier height as well as the position of the corresponding transition state and therefore modifies the folding kinetic rates as well as the kinetic routes. The resulting folding time, by considering both kinetic diffusion and the thermodynamic folding free-energy profile, thus is slower than the estimation from the thermodynamic free-energy barrier with constant diffusion but is consistent with the results from kinetic simulations. The configuration- or coordinate-dependent diffusion is especially important with respect to fast folding, when there is a small or no free-energy barrier and kinetics is controlled by diffusion. Including the configurational dependence will challenge the transition state theory of protein folding. The classical transition state theory will have to be modified to be consistent. The more detailed folding mechanistic studies involving phi value analysis based on the classical transition state theory also will have to be modified quantitatively.     

The effect of retinol on Ito cell proliferation in vitro

Hepatic sinusoidal fat-storing Ito cells are felt to represent the primary storage site for hepatic vitamin A and may be important collagen-producing effector cells during hepatic fibrogenesis. The cirrhotic liver generally has a decreased vitamin A content with increased numbers of "transitional" myofibroblasts adjacent to developing fibrous bands. It has been suggested that Ito cells "transform" into these myofibroblasts. The in vivo loss of Ito cell vitamin A can be simulated in vitro as Ito cells spontaneously lose their vitamin A lipid droplets during primary culture. The current study evaluated Ito cell proliferation in vitro with respect to vitamin A content and the extracellular collagen matrix. The cells were grown on a Type I or Type IV collagen matrix to simulate the types of collagens presumed to be present in the space of Disse. Initially it was observed that freshly isolated Ito cells begin to proliferate several days after isolation coincident with the decline of the vitamin A lipid droplets and a decrease in cellular retinyl palmitate. The proliferation rate for passaged Ito cells was similar on either matrix (on Type I collagen: T 1/2 = 2.2 +/- 1.1 days, n = 16; on Type IV collagen: T 1/2 = 3.3 +/- 1.4 days, n = 4; p less than 0.11). This proliferation rate remained constant through Cell Generation 16 and was similar to the rate for primary Ito cells in culture. To evaluate the possibility that primary Ito cell proliferation is causally related to the loss of vitamin A, Ito cells were re-exposed to an increased concentration of retinol in vitro.(ABSTRACT TRUNCATED AT 250 WORDS)     

Rotational diffusion affects the dynamical self-assembly pathways of patchy particles

Predicting the self-assembly kinetics of particles with anisotropic interactions, such as colloidal patchy particles or proteins with multiple binding sites, is important for the design of novel high-tech materials, as well as for understanding biological systems, e.g., viruses or regulatory networks. Often stochastic in nature, such self-assembly processes are fundamentally governed by rotational and translational diffusion. Whereas the rotational diffusion constant of particles is usually considered to be coupled to the translational diffusion via the Stokes–Einstein relation, in the past decade it has become clear that they can be independently altered by molecular crowding agents or via external fields. Because virus capsids naturally assemble in crowded environments such as the cell cytoplasm but also in aqueous solution in vitro, it is important to investigate how varying the rotational diffusion with respect to transitional diffusion alters the kinetic pathways of self-assembly. Kinetic trapping in malformed or intermediate structures often impedes a direct simulation approach of a kinetic network by dramatically slowing down the relaxation to the designed ground state. However, using recently developed path-sampling techniques, we can sample and analyze the entire self-assembly kinetic network of simple patchy particle systems. For assembly of a designed cluster of patchy particles we find that changing the rotational diffusion does not change the equilibrium constants, but significantly affects the dynamical pathways, and enhances (suppresses) the overall relaxation process and the yield of the target structure, by avoiding (encountering) frustrated states. Besides insight, this finding provides a design principle for improved control of nanoparticle self-assembly.In nature, self-assembled complex structures and networks often provide function. Prime examples are virus capsids, where capsomer proteins with specific interaction sites self-assemble into various structures, such as icosahedrons and dodecahedrons. Protein complexes can spontaneously form in the living cell, e.g., in signal transduction networks. Self-assembly of small designed building blocks can provide novel (bio)materials with desired properties. Such building blocks can consist of proteins, synthetic polypeptides, but also of colloidal particles. Particularly, the advent of novel synthesis routes for colloidal particles with a valence, so-called “patchy particles” opened up avenues for designing colloidal superstructures. Numerous experimental, theoretical, and numerical studies have enabled understanding of the phase behavior of these particles, predicting not only interesting building blocks for new functional materials, but also demonstrating new physics (1–5). Design principles for colloidal superstructures can predict which structure is the most thermodynamically favorable state (6). However, the fact that kinetics often trumps thermodynamics can hamper such design of colloidal superstructures. Strong directional binding and slow dissociation (7) can kinetically trap patchy-particle systems in a malformed state, rendering it unable to reach the designed equilibrium (ground) state. Controlling the self-assembly of colloidal particles thus requires understanding how the system evolves toward equilibrium, which is dictated by the kinetic network spanning all the states in which the system can occur. Several studies have demonstrated that the assembly toward the final ground state is affected by changing the interaction between patchy particles (8, 9), which affects both the thermodynamics and kinetics of the system. In contrast, here we study how the pathways change upon changing the dynamics only. Colloidal dynamics is often stochastic, and well described by overdamped Langevin (Brownian) dynamics (10). The rotational and translational diffusion constants of anisotropic particles are under standard conditions coupled via the Stokes–Einstein relation. However, in environments with high molecular crowding or in external fields the Stokes–Einstein relation is not necessarily valid anymore (11–13). Depending on the molecular crowder, the ratio between the rotational and translation diffusion constant can go up or down. Whereas crowding agents can in principle also change the binding equilibrium constants, this effect is expected to be weak if the specific interactions are sufficiently strong. Moreover, through the use of external fields, e.g., magnetic or electric, rotational motion could be controlled to a much further extent (14). In this work we investigate how varying the ratio of translational versus rotational diffusion constant influences the equilibrium kinetic network for small self-assembled clusters of colloidal patchy particles and how it could affect the design of self-assembling biological or artificial functional building blocks. Such particles provide a simple model for self-assembly of protein complexes such as in viruses or signal-transduction networks. Understanding and prediction of the colloidal self-assembly mechanisms requires the rates and pathways for all possible dissociation and association events in the kinetic network. However, on the timescale of the dynamics of the microscopic particles, binding and certainly dissociation processes are usually rare events due to high free-energy barriers caused by strong directional binding. As straightforward dynamical simulation is extremely inefficient, we used the Single Replica Transition Interface Sampling (SRTIS) algorithm to collect all possible (un)binding trajectory ensembles relevant to the patchy colloid assembly (15).Surprisingly, even for the dimerization of a one-patch particle we already find an effect of the rotation on the formation dynamics. Next, we investigate a dimerization of two-patch particles, which exhibits an intermediate state and multiple pathways of formation. However, the effect of the rotation becomes truly important if metastable intermediates are possible, such as in tetrahedron formation of a three-patch particle. Here we find that varying rotational diffusion favors one pathway over the other, without changing the equilibrium constants. Finally, we investigate the entire nine-state kinetic network of a tetrahedron cluster, and show that a change in the rotational diffusion shifts the preferred self-assembly pathways significantly. Whereas for low rotational diffusion the overall rate of tetrahedron formation decreases, frustrated states are avoided, leading to significantly less kinetic trapping.In principle, this effect results in a better yield of the designed ground state, and in less kinetic trapping. Whereas in our examples the intermediate states are not truly kinetic traps, we envision that for more complex target structures, e.g., virus capsids, which compete against disordered aggregates, the price paid for slowing down the dynamics is outweighed by a preference for the correct self-assembly route and leads to higher relative yields. Experiments on protein complex formation and colloidal assembly should be able to test this prediction, for instance by searching for nonmonotonous behavior upon dilution of the crowding environment. Including the interplay between rotational and translational diffusion in the self-assembly design of new supracolloidal structures opens up new opportunities for improved control of bottom-up synthesis of functional materials. Controlling the dynamics could also lead to a design principle for functional materials where the target structure is not necessarily the thermodynamic ground state. Besides crowding agents, such control could be exerted on the rotational motion of the particles via external fields, such as in ref. 14. Moreover, this work helps in understanding how rotational diffusion influences self-assembly processes in naturally occurring crowded environments such as the cell. As it has been established that a crowded protein environment can decrease the ratio of rotational diffusion over the translation diffusion up to more than a factor of 3 (13), our simulations provide (an additional) explanation why protein complex assembly does not suffer more from kinetic trapping as one would naively expect.     

Effect of rotation on the diffusion-controlled rate of ligand-protein association.

The rate of binding a fairly large ligand molecule to a protein is reduced below the usual diffusion-controlled rate by the requirement of a certain rotational orientation. A simple, approximate treatment of this effect is given for special cases of spherical and ellipsoidal ligands. As the center of an ellipsoidal ligand approaches a protein surface, there is an effective repulsive potential between ligand and surface owning to restricted rotation of the ligand. The frequency factor kT/h of the Eyring rate theory is replaced in these reactions involving diffusion in solution by D/Rlambda, where D = diffusion coefficient of ligand, lambda = thermal deBroglie wavelength of ligand, and R = "capture" distance around the binding site on the protein.     

Direct observation of ultrafast folding and denatured state dynamics in single protein molecules

Single-molecule fluorescence resonance energy transfer (smFRET) experiments are extremely useful in studying protein folding but are generally limited to time scales of greater than ≈100 μs and distances greater than ≈2 nm. We used single-molecule fluorescence quenching by photoinduced electron transfer, detecting short-range events, in combination with fluorescence correlation spectroscopy (PET-FCS) to investigate folding dynamics of the small binding domain BBL with nanosecond time resolution. The kinetics of folding appeared as a 10-μs decay in the autocorrelation function, resulting from stochastic fluctuations between denatured and native conformations of individual molecules. The observed rate constants were probe independent and in excellent agreement with values derived from conventional temperature-jump (T-jump) measurements. A submicrosecond relaxation was detected in PET-FCS data that reported on the kinetics of intrachain contact formation within the thermally denatured state. We engineered a mutant of BBL that was denatured under the reaction conditions that favored folding of the parent wild type (“D_phys”). D_phys had the same kinetic signature as the thermally denatured state and revealed segmental diffusion with a time constant of intrachain contact formation of 500 ns. This time constant was more than 10 times faster than folding and in the range estimated to be the “speed limit” of folding. D_phys exhibited significant deviations from a random coil. The solvent viscosity and temperature dependence of intrachain diffusion showed that chain motions were slaved by the presence of intramolecular interactions. PET-FCS in combination with protein engineering is a powerful approach to study the early events and mechanism of ultrafast protein folding.     

Dynamics, structure, and function are coupled in the mitochondrial matrix.

The coupling between molecular diffusion and the structure and function of the rat liver mitochondrial matrix was explored using fluorescence anisotropy techniques and electron microscopy. The results confirm that matrix ultrastructure and the concentration of matrix protein are influenced by the respiratory state of mitochondria and the osmolarity of the external medium. At physiological osmolarity, a fluorescent metabolite-sized probe was found to diffuse slowly in the mitochondrial matrix but not to be completely immobile. In addition, significant differences in diffusion rates were found to exist between different mitochondrial respiratory states, with the slowest diffusion occurring in states with the highest matrix protein concentration. These data support the concept of a matrix structure in which diffusion is considerably hindered due to limited probe-accessible water and further suggest that volume-dependent regulation of matrix protein packing may modulate metabolite diffusion and, in turn, mitochondrial metabolism.     

Extremely slow intramolecular diffusion in unfolded protein L

A crucial parameter in many theories of protein folding is the rate of diffusion over the energy landscape. Using a microfluidic mixer we have observed the rate of intramolecular diffusion within the unfolded B1 domain of protein L before it folds. The diffusion-limited rate of intramolecular contact is about 20 times slower than the rate in 6 M GdnHCl, and because in these conditions the protein is also more compact, the intramolecular diffusion coefficient decreases 100–500 times. The dramatic slowdown in diffusion occurs within the 250 μs mixing time of the mixer, and there appears to be no further evolution of this rate before reaching the transition state of folding. We show that observed folding rates are well predicted by a Kramers model with a denaturant-dependent diffusion coefficient and speculate that this diffusion coefficient is a significant contribution to the observed rate of folding.     

Diffusion frequency factors in some simple examples of transition-state rate theory.

In the Eyring rate theory, the rate constant is expressed as a product of a frequency factor (kT/h) and a quotient of partition functions. Continuing an earlier paper, it is shown here by means of simple examples that the Eyring formalism may be extended to include diffusion-controlled processes if a new frequency factor, D/Rlambda, is substituted for kT/h, where D = diffusion coefficient, lambda = thermal de Broglie wavelength, and R = a characteristic distance that depends on the particular case. The Eyring formalism is also applicable in hybrid cases, intermediate between diffusion (D/Rlambda) and dynamics (kT/h). Because these modified frequency factors are not "universal" (as kT/h is), their main use (other than conceptual) would appear to be in cases in which one considers a simple model (with calculable frequency factor) together with a related more complicated model. In the latter case, as an approximation, one would combine the "simple" frequency factor with the "complicated" quotient of partition functions in order to obtain the desired rate constant. Examples are given.     

Precipitation during Quenching in 2A97 Aluminum Alloy and the Influences from Grain Structure

The quench-induced precipitation and subsequent aging response in 2A97 aluminum alloy was investigated based on the systematic microstructure characterization. Specifically, the influence on precipitation from grain structure was examined. The results indicated the evident influence from the cooling rate of the quenching process. Precipitation of T₁ and δ′ phase can hardly occur in the specimen exposed to water quenching while become noticeable in the case of air cooling. The yield strength of 2A97-T6 alloy de-graded by 234 MPa along with a comparable elongation when water quenching was replaced by air cooling. Sub-grains exhibited a much higher sensitivity to the precipitation during quenching. The presence of dislocations in sub-grains promoted the quench-induced precipitation by acting as nucleation sites and enhancing the diffusion of the solute. A quenching rate of 3 °C/s is tolerable for recrystallized grains in 2A97 Al alloy but is inadequate for sub-grains to inhibit precipitation. The study fosters the feasibility of alleviating quench-induced precipitation through cultivating the recrystallization structure in highly alloyed Al–Cu–Li alloys.