Diffusion of α-Chymotrypsin in Solution-Crowded Media. A Fluorescence Recovery after Photobleaching Study

Dynamics of Single-Chain Nanoparticles under Crowding: A Neutron Spin Echo Study

We present a neutron spin echo (NSE) investigation to examine the impact of macromolecular crowding on the dynamics of single-chain nanoparticles (SCNPs), serving as synthetic models for biomacromolecules with flexibility and internal degrees of freedom, such as intrinsically disordered proteins (IDPs). In particular, we studied the dynamics of a medium-size poly(methyl methacrylate) (PMMA)-based SCNP (33 kDa) in solutions with low- (10 kDa) and high- (100 kDa) molecular weight analogous deuterated PMMA linear crowders. The dynamic structure factors of the SCNPs in dilute solution show certain degrees of freedom, yet the analysis in terms of the Zimm model reveals high internal friction that effectively stiffens the chain-a phenomenon also observed for IDPs. Under crowding conditions, the internal dynamics remains essentially unchanged, but the center-of-mass diffusion slows down. The effective viscosity felt by the SCNPs at the timescales probed by NSE is lower than the macroscopic viscosity of the crowder solution, and it does not depend significantly on the molecular weight.

Enabling High Activation of Glucose-6-Phosphate Dehydrogenase Activity Through Liquid Condensate Formation and Compression

Droplet formation via liquid-liquid phase separation is thought to be involved in the regulation of various biological processes, including enzymatic reactions. We investigated a glycolytic enzymatic reaction, the conversion of glucose-6-phosphate to 6-phospho-D-glucono-1,5-lactone with concomitant reduction of NADP+ to NADPH both in the absence and presence of dynamically controlled liquid droplet formation. Here, the nucleotide serves as substrate as well as the scaffold required for the formation of liquid droplets. To further expand the process parameter space, temperature and pressure dependent measurements were performed. Incorporation of the reactants in the liquid droplet phase led to a boost in enzymatic activity, which was most pronounced at medium-high pressures. The crowded environment of the droplet phase induced a marked increase of the affinity of the enzyme and substrate. An increase in turnover number in the droplet phase at high pressure contributed to a further strong increase in catalytic efficiency. Enzyme systems that are dynamically coupled to liquid condensate formation may be the key to deciphering many biochemical reactions. Expanding the process parameter space by adjusting temperature and pressure conditions can be a means to further increase the efficiency of industrial enzyme utilization and help uncover regulatory mechanisms adopted by extremophiles.

Experimentally Probing the Effect of Confinement Geometry on Lipid Diffusion

The lateral mobility of molecules within the cell membrane is ultimately governed by the local environment of the membrane. Confined regions induced by membrane structures, such as protein aggregates or the actin meshwork, occur over a wide range of length scales and can impede or steer the diffusion of membrane components. However, a detailed picture of the origins and nature of these confinement effects remains elusive. Here, we prepare model lipid systems on substrates patterned with confined domains of varying geometries constructed with different materials to explore the influences of physical boundary conditions and specific molecular interactions on diffusion. We demonstrate a platform that is capable of significantly altering and steering the long-range diffusion of lipids by using simple oxide deposition approaches, enabling us to systematically explore how confinement size and shape impact diffusion over multiple length scales. While we find that a "boundary condition" description of the system captures underlying trends in some cases, we are also able to directly compare our systems to analytical models, revealing the unexpected breakdown of several approximate solutions. Our results highlight the importance of considering the length scale dependence when discussing properties such as diffusion.

Unusual Aspects of Charge Regulation in Flexible Weak Polyelectrolytes

This article reviews the state of the art of the studies on charge regulation (CR) effects in flexible weak polyelectrolytes (FWPE). The characteristic of FWPE is the strong coupling of ionization and conformational degrees of freedom. After introducing the necessary fundamental concepts, some unconventional aspects of the the physical chemistry of FWPE are discussed. These aspects are: (i) the extension of statistical mechanics techniques to include ionization equilibria and, in particular, the use of the recently proposed Site Binding-Rotational Isomeric State (SBRIS) model, which allows the calculation of ionization and conformational properties on the same foot; (ii) the recent progresses in the inclusion of proton equilibria in computer simulations; (iii) the possibility of mechanically induced CR in the stretching of FWPE; (iv) the non-trivial adsorption of FWPE on ionized surfaces with the same charge sign as the PE (the so-called "wrong side" of the isoelectric point); (v) the influence of macromolecular crowding on CR.

Biomolecular Condensates Regulate Enzymatic Activity under a Crowded Milieu: Synchronization of Liquid-Liquid Phase Separation and Enzymatic Transformation

Cellular crowding plays a key role in regulating the enzymatic reactivity in physiological conditions, which is challenging to realize in the dilute phase. Enzymes drive a wide range of complex metabolic reactions with high efficiency and selectivity under extremely heterogeneous and crowded cellular environments. However, the molecular interpretation behind the enhanced enzymatic reactivity under a crowded milieu is poorly understood. Herein, using the horseradish peroxidase (HRP) and glucose oxidase (GOx) cascade pair, we demonstrate for the first time that macromolecular crowding induces liquid-liquid phase separation (LLPS) via the formation of liquid-like condensates/droplets and thereby increases the intrinsic catalytic efficiencies of HRP and GOx. Both these enzymes undergo crowding induced homotypic LLPS via enthalpically driven multivalent electrostatic as well as hydrophobic interactions. Using a set of kinetic and microscopic experiments, we show that precise synchronization of spontaneous LLPS and enzymatic transformations is key to realize the enhanced enzymatic activity under the crowded environments. Our findings reveal an unprecedented enhancement (91- to 205-fold) in the catalytic efficiency (k_cat/K_m) of HRP at pH 4.0 within the droplet phase relative to that in the bulk aqueous phase in the presence of different crowders. In addition, we have shown that other enzymes also undergo spontaneous LLPS under macromolecular crowding, signifying the generality of this phenomenon under the crowded environments. More importantly, coalescence driven highly regulated GOx/HRP cascade reactions within the fused droplets have been demonstrated with enhanced activity and specificity under the crowded environments. The present discovery highlights the active role of membraneless condensates in regulating the enzymatic efficacy for complex metabolic reactions under the crowded cellular environments and may find significant importance in the field of biocatalysis.

Impact of Inert Crowders on Host-Guest Recognition Process

Biological environments typically contain high concentrations (300-400 mg/mL) of different macromolecules at volume fractions as large as 30%-40%. Biomolecular recognition processes, a ubiquitous biological phenomena, occurring in such crowded heterogeneous media would differ significantly compared to the dilute buffer solutions. Here we quantify the potential impact of inert crowders on prototypical host-guest recognition process by explicit-solvent molecular dynamics (MD) simulations in atomic resolution. We demonstrate that the crowders, when smaller in size, would facilitate the binding process of the guest molecule by decreasing the free energy barrier for binding via excluded volume effect and desolvation of the host receptor. However, the extent of crowder-induced stabilization of a host-guest complex is found to be significantly higher when the guest molecule is sterically constricted to approach the host along a centrosymmetric direction, compared to its unrestricted, freely diffusive movement. A kinetic analysis of the recognition process reveals that the origin of a relatively stronger crowder impact during constricted movement of guest molecule lies in the relatively enhanced residence time of the guest inside the host by crowders. Together, our results suggest that the extent of impact of crowding on recognition processes would be contingent upon the presence or absence of constriction on ligand movement.

Effect of Molecular Crowding on Complexation of Metal Ions and 8-Quinolinol-5-Sulfonic Acid

The effect of molecular crowding on macromolecular reactions has been revealed by many researchers. In this study, we investigate the complexation of metal ions (Zn, Co, and Cd) with 8-quinolinol-5-sulfonic acid as a model of small-molecular reactions in molecular crowding. The complexation constants for 1:1, 1:2, and total complexation in the presence of polyethylene glycol (PEG, a molecular crowding reagent) are evaluated based on the increase in the reactant activity by volume exclusion and the decrease in the water activity due to the change in osmotic pressure. All complexation constants are enhanced by increasing the concentration of PEG. Its mechanisms differ for 1:1, 1:2, and total complexation. The 1:1 complexation is promoted only by the influence of the water activity, while the reactant and water activities influence the increase in the 1:2 complexation constant. Increasing the molecular weight of PEG further increases the complexation constants, as dehydration of the complex is promoted by a higher hydration number of PEG. Because this study gives the fundamental knowledge for the protein-metal interaction, in which solvation is an important factor, in molecular crowding, it provides new insights into molecular crowding studies and should attract the attention of a broad spectrum of biochemistry researchers.

Tracer diffusion in crowded solutions of sticky polymers

Macromolecular diffusion in strongly confined geometries and crowded environments is still to a large extent an open subject in soft matter physics and biology. In this paper, we employ large-scale Langevin dynamics simulations to investigate how the diffusion of a tracer is influenced by the combined action of excluded-volume and weak attractive crowder-tracer interactions. We consider two species of tracers, standard hard-core particles described by the Weeks-Chandler-Andersen (WCA) repulsive potential and core-softened (CS) particles, which model, e.g., globular proteins, charged colloids, and nanoparticles covered by polymeric brushes. These systems are characterized by the presence of two length scales in the interaction and can show waterlike anomalies in their diffusion, stemming from the inherent competition between different length scales. Here we report a comprehensive study of both diffusion and structure of these two tracer species in an environment crowded by quenched configurations of polymers at increasing density. We analyze in detail how the tracer-polymer affinity and the system density affect transport as compared to the emergence of specific static spatial correlations. In particular, we find that, while hardly any differences emerge in the diffusion properties of WCA and CS particles, the propensity to develop structural order for large crowding is strongly frustrated for CS particles. Surprisingly, for large enough affinity for the crowding matrix, the diffusion coefficient of WCA tracers display a nonmonotonic trend as their density is increased when compared to the zero affinity scenario. This waterlike anomaly turns out to be even larger than what observed for CS particle and appears to be rooted in a similar competition between excluded-volume and affinity effects.

Molecular transport in systems containing binding obstacles

We studied the movement of particles in crowded environments by means of extensive Monte Carlo simulations. The dynamic lattice liquid model was employed for this purpose. It is based on the cooperative movement concept and allows the study of systems at high densities. The cooperative model of molecular transport is assumed: the motion of all moving particles is highly correlated. The model is supposed to mimic lateral motion in a membrane and therefore the system is two-dimensional with moving objects and traps placed on a triangular lattice. In our study the interaction (binding) of traps with moving particles was assumed. The conditions in which subdiffusive motion appeared in the system were analysed. The influence of the strength of binding on the dynamic percolation threshold was also shown. The differences in the dynamics compared to systems with impenetrable obstacles and with systems without correlation in motion were presented and discussed. It was shown that in the case of correlated motion the influence of deep traps is similar to that of impenetrable obstacles. If the traps are shallow a recovery to normal diffusion was observed for longer time periods.

A general phenomenological relation for the subdiffusive exponent of anomalous diffusion in disordered media

This work numerically investigates the diffusion of finite inert tracer particles in different types of fixed gels. The mean square displacement (MSD) of the tracers reveals a transition to subdiffusive motion MSD ∼ tα as soon as the accessible volume fraction p in the gel decreases from unity. Individual tracer dynamics reveals two types of particles in the gels: mobile tracers cross the system through percolating pores following subdiffusive dynamics MSDmob ∼ tαmob, while a fraction ptrap(p) of the particles remain trapped in finite pores. Below the void percolation threshold p < pc all the particles get trapped and α → 0. By separately studying both populations we find a simple phenomenological law for the mobile tracers αmob(p) ≈ a ln p + c where c ≈ 1 and a ∼ 0.2 depends on the gel type. On the other hand, a cluster-analysis of the gel accessible volume reveals a power law for the trapping probability ptrap ∼ (p/pc)-γ, with γ ≃ 2.9. This yields a prediction for the ensemble averaged subdiffusion exponent α = αmob(1 - ptrap). Our predictions are successfully validated against the different gels studied here and against numerical and experimental results in the literature (silica gels, polyacrylamide gels, flexible F-actin networks and in different random obstacles). Notably, the parameter a ∼ 0.2 presents small differences amongst all these cases, indicating the robustness of the proposed relation.

Macromolecular crowding effects in flexible polymer solutions

Biological environments are often “crowded” due to high concentrations (300–400[Formula: see text]g/L) of macromolecules. Computational modeling approaches like Molecular Dynamics (MD), rigid-body Brownian Dynamics and Monte Carlo simulations have recently emerged, which allow to study the effects macromolecular crowding at a microscopic level and to provide complementary information to experiments. Here, we use a recently introduced multiple-conformation Monte Carlo (mcMC) approach in order to study the influence of intermolecular interactions on the structural equilibrium of flexible polyethylene glycol (PEG) polymers under self-crowding conditions. The large conformational space accessible to PEG polymers allows us to evaluate the general applicability of the mcMC approach, which describes the intramolecular degrees of freedom by a finite-size ensemble of discrete conformations. Despite the simplicity of the approach, we show that influences of intermolecular interactions on the intramolecular free energy surface can be described qualitatively using mcMC. By varying the magnitude of distinct terms in the intermolecular potential, we can further study the compensating effects of repulsive and nonspecific attractive intermolecular interactions, which favor compact and extended polymer states, respectively. We use our simulation results to derive an analytical model that describes the effects of intermolecular interactions on the stability of PEG polymer conformations as a function of the radius of gyration and the corresponding solvent accessible surface. We use this model to confirm the role of molecular surfaces for attractive interactions that can counteract excluded volume effects. Extrapolation of the model further allows for the analysis of scenarios that are not easily accessible to direct simulations as described here.

Macromolecular diffusion in crowded media beyond the hard-sphere model

The effect of macromolecular crowding on diffusion beyond the hard-core sphere model is studied. A new coarse-grained model is presented, the Chain Entanglement Softened Potential (CESP) model, which takes into account the macromolecular flexibility and chain entanglement. The CESP model uses a shoulder-shaped interaction potential that is implemented in the Brownian Dynamics (BD) computations. The interaction potential contains only one parameter associated with the chain entanglement energetic cost (Ur). The hydrodynamic interactions are included in the BD computations via Tokuyama mean-field equations. The model is used to analyze the diffusion of a streptavidin protein among different sized dextran obstacles. For this system, Ur is obtained by fitting the streptavidin experimental long-time diffusion coefficient Dlongversus the macromolecular concentration for D50 (indicating their molecular weight in kg mol-1) dextran obstacles. The obtained Dlong values show better quantitative agreement with experiments than those obtained with hard-core spheres. Moreover, once parametrized, the CESP model is also able to quantitatively predict Dlong and the anomalous exponent (α) for streptavidin diffusion among D10, D400 and D700 dextran obstacles. Dlong, the short-time diffusion coefficient (Dshort) and α are obtained from the BD simulations by using a new empirical expression, able to describe the full temporal evolution of the diffusion coefficient.

Quantitative Characterization of the Membrane Dynamics of Newly Delivered TGF-β Receptors by Single-Molecule Imaging

The dynamics and stoichiometry of receptors newly delivered on the plasma membrane play a vital role in cell signal transduction, yet knowledge of this process is limited because of the lack of suitable analytical methods. Here we developed a new strategy that combines single-molecule imaging (SMI) and fluorescence recovery after photobleaching (FRAP), named FRAP-SMI, to monitor and quantify individual newly delivered and inserted transmembrane receptors on plasma membranes of living cells. Transforming-growth-factor-β type II receptor (TβRII), a typical serine/threoninekinase receptor, was studied with this method. We first eliminated the fluorescence signals from the pre-existing EGFP-labeled TβRII molecules on the plasma membrane, and then we recorded the individual newly appeared TβRII-GFP by total-internal-reflection fluorescence imaging. The fluorescence-intensity distributions, photobleaching steps, and diffusion rates of the single TβRII-GFP molecules were analyzed. We reported, for the first time, that TβRII was transported to the plasma membrane mainly in the monomeric form in both resting and TGF-β1stimulated cells. This strongly supported our former discovery that TβRII could exist as a monomer on the cell membrane. We also found that ligand stimulation resulted in enhanced delivery rates and prolonged membrane-association times for the TβRII molecules. On the basis of these observations, we proposed a mechanism of TGF-β1-induced TβRII dimerization for receptor activation. Our method provides a useful tool for the real-time quantification of the spatial arrangement, mobility, and oligomerization of cell-surface proteins in living cells, thus providing a better understanding of cell signaling.

Transition from double to single diffusive behavior with increase in polymer concentration for oppositely charged guest - host systems of green fluorescent protein diffusing inside poly-l-lysine solutions

The effect of crowding, background and probe charges and chain flexibility on probe dynamics of Green Fluorescent Protein in polyelectrolyte solutions of poly-l-lysine was investigated using Fluorescence Recovery After Photobleaching (FRAP). An interesting double diffusive behavior in FRAP recovery curve was observed at low polymer concentration resulting in two relaxation modes, which disappears with rise in polymer concentration. The fast relaxation mode attributes to diffusion of free protein molecules alone, where as slow mode is credited to polymer adsorbed protein molecules. Absence of double diffusive behavior at higher polymer concentration is argued in terms of varying host chain conformation and the only relaxation mode present is due to movement of free probes alone rather than that of adsorbed proteins. We noticed only a marginal decrease in diffusion coefficient with rise in salt concentration and the trend is reversed when variation in sample viscosity with salt is taken into account. In addition a small but systematic decrease in diffusion coefficient is seen with increase in magnitude of probe charge. Comparison of results with ideal Stoke - Einstein relation brings out the importance of polyelectrolyte effect and indicates ∼200 - fold positive deviations from predicted value for both variation in ionic strength and solution pH.

Simulation of Molecular Transport in Systems Containing Mobile Obstacles

In this paper, we investigate the movement of molecules in crowded environments with obstacles undergoing Brownian motion by means of extensive Monte Carlo simulations. Our investigations were performed using the dynamic lattice liquid model, which was based on the cooperative movement concept and allowed to mimic systems at high densities where the motion of all elements (obstacles as well as moving particles) were highly correlated. The crowded environments are modeled on a two-dimensional triangular lattice containing obstacles (particles whose mobility was significantly reduced) moving by a Brownian motion. The subdiffusive motion of both elements in the system was analyzed. It was shown that the percolation transition does not exist in such systems in spite of the cooperative character of the particles' motion. The reduction of the obstacle mobility leads to the longer caging of liquid particles by mobile obstacles.

Effects of Macromolecular Crowding on Alcohol Dehydrogenase Activity Are Substrate-Dependent

Enzymes operate in a densely packed cellular environment that rarely matches the dilute conditions under which they are studied. To better understand the ramifications of this crowding, the Michaelis-Menten kinetics of yeast alcohol dehydrogenase (YADH) were monitored spectrophotometrically in the presence of high concentrations of dextran. Crowding decreased the maximal rate of the reaction by 40% for assays with ethanol, the primary substrate of YADH. This observation was attributed to slowed release of the reduced β-nicotinamide adenine dinucleotide product, which is rate-limiting. In contrast, when larger alcohols were used as the YADH substrate, the rate-limiting step becomes hydride transfer and crowding instead increased the maximal rate of the reaction by 20-40%. This work reveals the importance of considering enzyme mechanism when evaluating the ways in which crowding can alter kinetics.

Diffusion NMR studies of macromolecular complex formation, crowding and confinement in soft materials

Label-free methods to obtain hydrodynamic size from diffusion measurements are desirable in environments that contain multiple macromolecular species at a high total concentration: one example is the crowded cellular environment. In complex, multi-species macromolecular environments - in this article, we feature aqueous systems involving polymers, surfactants and proteins - the link between dynamics and size is harder to unpack due to macromolecular crowding and confinement. In this review, we demonstrate that the pulsed-field gradient NMR technique, with its spectral separation of different chemical components, is ideal for studying the dynamics of the entire system simultaneously and without labelling, in a wide range of systems. The simultaneous measurement of the dynamics of multiple components allows for internal consistency checks and enables quantitative statements about the link between macromolecular dynamics, size, complex formation and crowding in soft materials.

Fluorescence recovery after photobleaching in material and life sciences: putting theory into practice

Fluorescence recovery after photobleaching (FRAP) is a versatile tool for determining diffusion and interaction/binding properties in biological and material sciences. An understanding of the mechanisms controlling the diffusion requires a deep understanding of structure–interaction–diffusion relationships. In cell biology, for instance, this applies to the movement of proteins and lipids in the plasma membrane, cytoplasm and nucleus. In industrial applications related to pharmaceutics, foods, textiles, hygiene products and cosmetics, the diffusion of solutes and solvent molecules contributes strongly to the properties and functionality of the final product. All these systems are heterogeneous, and accurate quantification of the mass transport processes at the local level is therefore essential to the understanding of the properties of soft (bio)materials. FRAP is a commonly used fluorescence microscopy-based technique to determine local molecular transport at the micrometer scale. A brief high-intensity laser pulse is locally applied to the sample, causing substantial photobleaching of the fluorescent molecules within the illuminated area. This causes a local concentration gradient of fluorescent molecules, leading to diffusional influx of intact fluorophores from the local surroundings into the bleached area. Quantitative information on the molecular transport can be extracted from the time evolution of the fluorescence recovery in the bleached area using a suitable model. A multitude of FRAP models has been developed over the years, each based on specific assumptions. This makes it challenging for the non-specialist to decide which model is best suited for a particular application. Furthermore, there are many subtleties in performing accurate FRAP experiments. For these reasons, this review aims to provide an extensive tutorial covering the essential theoretical and practical aspects so as to enable accurate quantitative FRAP experiments for molecular transport measurements in soft (bio)materials.

Nonmonotonic diffusion of particles among larger attractive crowding spheres

We study the diffusive motion of particles among fixed spherical crowders. The diffusers interact with the crowders through a combination of a hard-core repulsion and a short-range attraction. The long-time effective diffusion coefficient of the diffusers is found to depend nonmonotonically on the strength of their attraction to the crowders. That is, for a given concentration of crowders, a weak attraction to the crowders enhances diffusion. We show that this counterintuitive fact can be understood in terms of the mesoscopic excess chemical potential landscape experienced by the diffuser. The roughness of this excess chemical potential landscape quantitatively captures the nonmonotonic dependence of the diffusion rate on the strength of crowder-diffuser attraction; thus, it is a purely static predictor of dynamic behavior. The mesoscopic view given here provides a unified explanation for enhanced diffusion effects that have been found in various systems of technological and biological interest.

Macromolecular crowding effect upon in vitro enzyme kinetics: mixed activation-diffusion control of the oxidation of NADH by pyruvate catalyzed by lactate dehydrogenase

Enzyme kinetics studies have been usually designed as dilute solution experiments, which differ substantially from in vivo conditions. However, cell cytosol is crowded with a high concentration of molecules having different shapes and sizes. The consequences of such crowding in enzymatic reactions remain unclear. The aim of the present study is to understand the effect of macromolecular crowding produced by dextran of different sizes and at diverse concentrations in the well-known reaction of oxidation of NADH by pyruvate catalyzed by L-lactate dehydrogenase (LDH). Our results indicate that the reaction rate is determined by both the occupied volume and the relative size of dextran obstacles with respect to the enzyme present in the reaction. Moreover, we analyzed the influence of macromolecular crowding on the Michaelis-Menten constants, vmax and Km. The obtained results show that only high concentrations and large sizes of dextran reduce both constants suggesting a mixed activation-diffusion control of this enzymatic reaction due to the dextran crowding action. From our knowledge, this is the first experimental study that depicts mixed activation-diffusion control in an enzymatic reaction due to the effect of crowding.

Bioactive hydrogels demonstrate mediated release of a chromophore by chymotrypsin

A model system, α-chymotrypsin (Cht) (a protease) and a cleavable peptide-chromogen (pro-drug) covalently incorporated into a hydrogel, was investigated to understand the mechanisms of covalent loading and release by enzymatic cleavage in bio-responsive delivery systems. Using EDC and Sulfo-NHS, terminal carboxyl groups of N-succinyl-Ala-Ala-Pro-Phe p-nitroanilide, a cleavable chromogen, were conjugated to primary amines of a hydrated poly(HEMA)-based hydrogel. Hydrogel disks were incubated in buffered Cht causing enzyme-mediated cleavage of the peptide and concomitant release of the chromophore for monitoring. To investigate substrate loading and the effects of hydrogel morphology on the system, the concentration of the amino groups (5, 10, 20, and 30 mol%) and the cross-linked density (1, 5, 7, 9 and 12 mol%) were independently varied. Loading-Release Efficiency of the chromogen was shown to exhibit a positive relation to increasing amino groups (AEMA). The release rates demonstrated a negative relation to increasing cross-linked density attributed to decreasing void fractions and increasing tortuosities. The diffusion coefficient of Cht, D(0,Cht), was determined to be 6.9±0.5×10(-7)cm(2)s(-1), and the range of D(eff) of Cht for 1 to 12 mol% TEGDA was determined to be 6.9×10(-8) to 0.1×10(-8)cm(2)s(-1). We show how these parameters may be optimized and used to achieve programmed release rates in engineered bio-responsive systems.

New insights into diffusion in 3D crowded media by Monte Carlo simulations: effect of size, mobility and spatial distribution of obstacles

Particle diffusion in crowded media was studied through Monte Carlo simulations in 3D obstructed lattices. Three particular aspects affecting the diffusion, not extensively treated in a three-dimensional geometry, were analysed: the relative particle-obstacle size, the relative particle-obstacle mobility and the way of having the obstacles distributed in the simulation space (randomly or uniformly). The results are interpreted in terms of the parameters that characterize the time dependence of the diffusion coefficient: the anomalous diffusion exponent (α), the crossover time from anomalous to normal diffusion regimes (τ) and the long time diffusion coefficient (D*). Simulation results indicate that there are a more anomalous diffusion (smaller α) and a lower long time diffusion coefficient (D*) when obstacle concentration increases, and that, for a given total excluded volume and immobile obstacles, the anomalous diffusion effect is less important for bigger size obstacles. However, for the case of mobile obstacles, this size effect is inverted yielding values that are in qualitatively good agreement with in vitro experiments of protein diffusion in crowded media. These results underline that the pattern of the spatial partitioning of the obstacle excluded volume is a factor to be considered together with the value of the excluded volume itself.

Diffusion in crowded biological environments: applications of Brownian dynamics

Biochemical reactions in living systems occur in complex, heterogeneous media with total concentrations of macromolecules in the range of 50 - 400 mgml. Molecular species occupy a significant fraction of the immersing medium, up to 40% of volume. Such complex and volume-occupied environments are generally termed 'crowded' and/or 'confined'. In crowded conditions non-specific interactions between macromolecules may hinder diffusion - a major process determining metabolism, transport, and signaling. Also, the crowded media can alter, both qualitatively and quantitatively, the reactions in vivo in comparison with their in vitro counterparts. This review focuses on recent developments in particle-based Brownian dynamics algorithms, their applications to model diffusive transport in crowded systems, and their abilities to reproduce and predict the behavior of macromolecules under in vivo conditions.