How can biochemical reactions within cells differ from those in test tubes?

In vivo anomalous diffusion and weak ergodicity breaking of lipid granules

Combining extensive single particle tracking microscopy data of endogenous lipid granules in living fission yeast cells with analytical results we show evidence for anomalous diffusion and weak ergodicity breaking. Namely we demonstrate that at short times the granules perform subdiffusion according to the laws of continuous time random walk theory. The associated violation of ergodicity leads to a characteristic turnover between two scaling regimes of the time averaged mean squared displacement. At longer times the granule motion is consistent with fractional Brownian motion.

Crowding effects on protein association: effect of interactions between crowding agents

The cell cytoplasm is a dense environment where the presence of inert cosolutes can significantly alter the rates of protein folding and protein association reactions. Most theoretical studies focus on hard sphere crowding agents and quantify the effect of excluded volume on reaction rates. In this work the effect of interactions between the crowding agents on the thermodynamics of protein association is studied using computer simulation. Three cases are considered, where the crowding agents are (i) hard spheres, (ii) hard spheres with additional attractive or repulsive interactions, and (iii) chains of hard spheres. Reactants and products of the protein association are modeled as hard spheres. Although crowding effects are sensitive to the shape of the reaction product, in most cases the excess free energy difference between the product and reactants (nonideality factor) is insensitive to the interactions between crowding agents, due to a cancellation of effects. The simulations therefore suggest that the hard sphere model of crowding agents has a surprisingly large regime of validity and should be sufficient for a qualitative understanding of the thermodynamics of crowding effects when the interactions of associating proteins with crowding agents other than excluded volume interactions are not significant.

Attractive protein-polymer interactions markedly alter the effect of macromolecular crowding on protein association equilibria

The dependence of the fluorescence of catalase upon the concentration of added superoxide dismutase (SOD) indicates that SOD binds to saturable sites on catalase. The affinity of SOD for these sites varies with temperature, and with the concentration of each of three nominally inert polymeric additives--dextran 70, Ficoll 70, and polyethylene glycol 2000. At room temperature (25.0 degrees C) and higher, the addition of high concentrations of polymer is found to significantly enhance the affinity of SOD for catalase, but with decreasing temperature the enhancing effect of polymer addition diminishes, and at 8.0 degrees C, addition of polymer has little or no effect on the affinity of SOD for catalase. The results presented here provide the first experimental evidence for the existence of competition between a repulsive excluded volume interaction between protein and polymer, which tends to enhance association of dilute protein, and an attractive interaction between protein and polymer, which tends to inhibit protein association. The net effect of high concentrations of polymer upon protein associations depends upon the relative strength of these two types of interactions at the temperature of measurement, and may vary significantly between different proteins and/or polymers.

The intranuclear environment

Many of the chapters in this volume are concerned with processes or structures inside the nucleus, and it is relevant to consider the properties of their environment, or rather of the multiple different and specific environments that must exist in local regions of the highly heterogeneous intranuclear space. Relatively little is known about the fundamental physical properties of these environments, and theoretical treatments of phenomena in such concentrated mixtures of charged macromolecules are complex and as yet poorly developed. Some of the phenomena that occur at the molecular level are unexpected and counterintuitive for biologists, although well known to colloid and polymer scientists; for example, the existence of short-range attractive forces between macromolecules or structures with like charges. As a background for the chapters that follow, we consider here some of the particular features of intranuclear environments, how they may influence processes and structures in the nucleus, and their implications for working with nuclei.

Approaches for targeting mitochondria in cancer therapy

The recognition of the role that mitochondria play in human health and disease is evidenced by the emergence in recent decades of a whole new field of "Mitochondrial Medicine". Molecules located on or inside mitochondria are considered prime pharmacological targets and a wide range of efforts are underway to exploit these targets to develop targeted therapies for various diseases including cancer. However the concept of targeting, while seemingly simple in theory, has multiple subtly different practical approaches. The focus of this article is to highlight these differences in the context of a discussion on the current status of various mitochondria-targeted approaches to cancer therapy.

FRAP and kinetic modeling in the analysis of nuclear protein dynamics: what do we really know?

The binding of nuclear proteins to chromatin in live cells has been analyzed by kinetic modeling procedures applied to experimental data from fluorescence recovery after photobleaching (FRAP). The kinetic models have yielded a number of important biological predictions about transcription, but concerns have arisen about the accuracy of these predictions. First, different studies using different kinetic models have arrived at very different predictions for the same or similar proteins. Second, some of these divergent predictions have been shown to arise from technical issues rather than biological differences. For confidence and accuracy, gold standards for the measurement of in vivo binding must be established by extensive cross validation using both different experimental methods and different kinetic modeling procedures.

Quantifying the effects of elastic collisions and non-covalent binding on glutamate receptor trafficking in the post-synaptic density

One mechanism of information storage in neurons is believed to be determined by the strength of synaptic contacts. The strength of an excitatory synapse is partially due to the concentration of a particular type of ionotropic glutamate receptor (AMPAR) in the post-synaptic density (PSD). AMPAR concentration in the PSD has to be plastic, to allow the storage of new memories; but it also has to be stable to preserve important information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which AMPAR can enter, leave and remain in the synapse are unclear. We used Monte Carlo simulations to determine the influence of PSD structure and activity in maintaining homeostatic concentrations of AMPARs in the synapse. We found that, the high concentration and excluded volume caused by PSD molecules result in molecular crowding. Diffusion of AMPAR in the PSD under such conditions is anomalous. Anomalous diffusion of AMPAR results in retention of these receptors inside the PSD for periods ranging from minutes to several hours in the absence of strong binding of receptors to PSD molecules. Trapping of receptors in the PSD by crowding effects was very sensitive to the concentration of PSD molecules, showing a switch-like behavior for retention of receptors. Non-covalent binding of AMPAR to anchored PSD molecules allowed the synapse to become well-mixed, resulting in normal diffusion of AMPAR. Binding also allowed the exchange of receptors in and out of the PSD. We propose that molecular crowding is an important biophysical mechanism to maintain homeostatic synaptic concentrations of AMPARs in the PSD without the need of energetically expensive biochemical reactions. In this context, binding of AMPAR with PSD molecules could collaborate with crowding to maintain synaptic homeostasis but could also allow synaptic plasticity by increasing the exchange of these receptors with the surrounding extra-synaptic membrane.

One of the most accepted theories of information storage in neurons is that it is partially localized in the strength of synaptic contacts. Evidence suggests that at the cellular level, in combination with other cellular mechanisms, this is implemented by increasing or decreasing the concentration of a particular type of membrane molecules. Two opposing mechanisms have to coexist in synapses to allow them to store information. On one hand, synapses have to be flexible, to allow the storage of new memories. On the other hand, synapses have to be stable to preserve previously learned information. Although much is known about the molecular identity of synapses, the biophysical mechanisms by which molecules can enter, leave and remain in the synapse are unclear. Our modeling work uses fundamental biophysical principles to quantify the effects of molecular collisions and biochemical reactions. Our results show that molecular collisions alone, between the diffusing proteins with anchored molecules in the synapse, can replicate known experimental results. Molecular collision in combination with biochemical binding can be fundamental biophysical principles used by synapses for the formation and preservation of memories.

Regulation of protein function: crystal packing interfaces and conformational dimerization

The accepted view of interprotein electron transport involves molecules diffusing between donor and acceptor redox sites. An emerging alternative hypothesis is that efficient long-range electron transport can be achieved through proteins arranged in supramolecular assemblies. In this study, we have investigated the crystal packing interfaces in three crystal forms of plastocyanin, an integral component of the photosynthetic electron transport chain, and discuss their potential relevance to in vivo supramolecular assemblies. Symmetry-related protein chains within these crystals have Cu-Cu separations of <25 A, a distance that readily supports electron transfer. In one structure, the plastocyanin molecule exists in two forms in which a backbone displacement coupled with side chain rearrangements enables the modulation of protein-protein interfaces.

Concentration-dependent effect of fibrinogen on IgG-specific antigen binding and phagocytosis

In this paper, we aim to characterize fibrinogen-IgG interactions, and explore how fibrinogen alters IgG-mediated phagocytosis. Using enzyme-linked binding assays, we found that fibrinogen binding to IgG is optimized for surfaces coated with high levels of IgG. Using a similar method, we have shown that for an antigen unable to specifically bind fibrinogen, fibrinogen enhances binding of antibodies towards that antigen. For binding of IgG antibodies to cells expressing Fc receptors, we found a bimodal binding response, where low levels of fibrinogen enhance binding of antibody to Fc receptors and high levels reduce it. This corresponds to a bimodal effect on phagocytosis of IgG-coated particles, which is inhibited in the presence of excess IgG during coating of the particles with antibodies and fibrinogen. We conclude that fibrinogen can modulate phagocytosis of IgG-coated particles in vitro by changing IgG binding behavior, and that high fibrinogen levels could negatively affect phagocytosis.

Molecular crowding affects diffusion and binding of nuclear proteins in heterochromatin and reveals the fractal organization of chromatin

The nucleus of eukaryotes is organized into functional compartments, the two most prominent being heterochromatin and nucleoli. These structures are highly enriched in DNA, proteins or RNA, and thus thought to be crowded. In vitro, molecular crowding induces volume exclusion, hinders diffusion and enhances association, but whether these effects are relevant in vivo remains unclear. Here, we establish that volume exclusion and diffusive hindrance occur in dense nuclear compartments by probing the diffusive behaviour of inert fluorescent tracers in living cells. We also demonstrate that chromatin-interacting proteins remain transiently trapped in heterochromatin due to crowding induced enhanced affinity. The kinetic signatures of these crowding consequences allow us to derive a fractal model of chromatin organization, which explains why the dynamics of soluble nuclear proteins are affected independently of their size. This model further shows that the fractal architecture differs between heterochromatin and euchromatin, and predicts that chromatin proteins use different target-search strategies in the two compartments. We propose that fractal crowding is a fundamental principle of nuclear organization, particularly of heterochromatin maintenance.

Hybridization kinetics is different inside cells

It is generally expected that the kinetics of reactions inside living cells differs from the situation in bulk solutions. Macromolecular crowding and specific binding interactions could change the diffusion properties and the availability of free molecules. Their impact on reaction kinetics in the relevant context of living cells is still elusive, mainly because the difficulty of capturing fast kinetics in vivo. This article shows spatially resolved measurements of DNA hybridization kinetics in single living cells. HeLa cells were transfected with a FRET-labeled dsDNA probe by lipofection. We characterized the hybridization reaction kinetics with a kinetic range of 10 micros to 1 s by a combination of laser-driven temperature oscillations and stroboscopic fluorescence imaging. The time constant of the hybridization depended on DNA concentration within individual cells and between cells. A quantitative analysis of the concentration dependence revealed several-fold accelerated kinetics as compared with free solution for a 16-bp probe and decelerated kinetics for a 12-bp probe. We did not find significant effects of crowding agents on the hybridization kinetics in vitro. Our results suggest that the reaction rates in vivo are specifically modulated by binding interactions for the two probes, possibly triggered by their different lengths. In general, the presented imaging modality of temperature oscillation optical lock-in microscopy allows to probe biomolecular interactions in different cell compartments in living cells for systems biology.

A nonprocessive class V myosin drives cargo processively when a kinesin- related protein is a passenger

During secretory events, kinesin transports cargo along microtubules and then shifts control to myosin V for delivery on actin filaments to the cell membrane [1]. When kinesin and myosin V are present on the same cargo, kinesin interacts electrostatically with actin to enhance myosin V-based transport in vitro [2]. The relevance of this observation within the cell was questioned. In budding yeast, overexpression of a kinesin-family protein (Smy1p) suppressed a transport defect in a strain with a mutant class V myosin (Myo2p) [3]. We postulate that this is a cellular manifestation of the in vitro observation. We demonstrate that Smy1p binds electrostatically to actin bundles. Although a single Myo2p cannot transport cargo along actin bundles, addition of Smy1p causes the complex to undergo long-range, continuous movement. We propose that the kinesin-family protein acts as a tether that prevents cargo dissociation from actin, allowing the myosin to take many steps before dissociating. We demonstrate that both the tether and the motor reside on moving secretory vesicles in yeast cells, a necessary feature for this mechanism to apply in vivo. The presence of both kinesin and myosin on the same cargo may be a general mechanism to enhance cellular transport in yeast and higher organisms.

Investigating the robustness of the classical enzyme kinetic equations in small intracellular compartments

Background

Classical descriptions of enzyme kinetics ignore the physical nature of the intracellular environment. Main implicit assumptions behind such approaches are that reactions occur in compartment volumes which are large enough so that molecular discreteness can be ignored and that molecular transport occurs via diffusion. Though these conditions are frequently met in laboratory conditions, they are not characteristic of the intracellular environment, which is compartmentalized at the micron and submicron scales and in which active means of transport play a significant role.

Results

Starting from a master equation description of enzyme reaction kinetics and assuming metabolic steady-state conditions, we derive novel mesoscopic rate equations which take into account (i) the intrinsic molecular noise due to the low copy number of molecules in intracellular compartments (ii) the physical nature of the substrate transport process, i.e. diffusion or vesicle-mediated transport. These equations replace the conventional macroscopic and deterministic equations in the context of intracellular kinetics. The latter are recovered in the limit of infinite compartment volumes. We find that deviations from the predictions of classical kinetics are pronounced (hundreds of percent in the estimate for the reaction velocity) for enzyme reactions occurring in compartments which are smaller than approximately 200 nm, for the case of substrate transport to the compartment being mediated principally by vesicle or granule transport and in the presence of competitive enzyme inhibitors.

Conclusion

The derived mesoscopic rate equations describe subcellular enzyme reaction kinetics, taking into account, for the first time, the simultaneous influence of both intrinsic noise and the mode of transport. They clearly show the range of applicability of the conventional deterministic equation models, namely intracellular conditions compatible with diffusive transport and simple enzyme mechanisms in several hundred nanometre-sized compartments. An active transport mechanism coupled with large intrinsic noise in enzyme concentrations is shown to lead to huge deviations from the predictions of deterministic models. This has implications for the common approach of modeling large intracellular reaction networks using ordinary differential equations and also for the calculation of the effective dosage of competitive inhibitor drugs.

Parameter effects on binding chemistry in crowded media using a two-dimensional stochastic off-lattice model

The intracellular environment imposes a variety of constraints on biochemical reaction systems that can substantially change reaction rates and equilibria relative to an ideal solution-based environment. One of the most notable features of the intracellular environment is its dense macromolecular crowding, which, among many other effects, tends to strongly enhance binding and assembly reactions. Despite extensive study of biochemistry in crowded media, it remains extremely difficult to predict how crowding will quantitatively affect any given reaction system due to the dependence of the crowding effect on numerous assumptions about the reactants and crowding agents involved. We previously developed a two dimensional stochastic off-lattice model of binding reactions based on the Green's function reaction dynamics method in order to create a versatile simulation environment in which one can explore interactions among many parameters of a crowded assembly system. In the present work, we examine interactions among several critical parameters for a model dimerization system: the total concentration of reactants and inert particles, the binding probability upon a collision between two reactant monomers, the mean time of dissociation reactions, and the diffusion coefficient of the system. Applying regression models to equilibrium constants across parameter ranges shows that the effect of the total concentration is approximately captured by a low-order nonlinear polynomial model, while the other three parameter effects are each accurately captured by a linear model. Furthermore, validation on tests with multi-parameter variations reveals that the effects of these parameters are separable from one another over a broad range of variation in all four parameters. The simulation work suggests that predictive models of crowding effects can accommodate a wider variety of parameter variations than prior theoretical models have so far achieved.

Analysis of reaction-diffusion systems with anomalous subdiffusion

Reaction-diffusion equations are the cornerstone of modeling biochemical systems with spatial gradients, which are relevant to biological processes such as signal transduction. Implicit in the formulation of these equations is the assumption of Fick's law, which states that the local diffusive flux of species i is proportional to its concentration gradient; however, in the context of complex fluids such as cytoplasm and cell membranes, the use of Fick's law is based on empiricism, whereas evidence has been mounting that such media foster anomalous subdiffusion (with mean-squared displacement increasing less than linearly with time) over certain length scales. Particularly when modeling diffusion-controlled reactions and other systems where the spatial domain is considered semi-infinite, assuming Fickian diffusion might not be appropriate. In this article, two simple, conceptually extreme models of anomalous subdiffusion are used in the framework of Green's functions to demonstrate the solution of four reaction-diffusion problems that are well known in the biophysical context of signal transduction: fluorescence recovery after photobleaching, the Smolochowski limit for diffusion-controlled reactions in solution, the spatial range of a diffusing molecule with finite lifetime, and the collision coupling mechanism of diffusion-controlled reactions in two dimensions. In each case, there are only subtle differences between the two subdiffusion models, suggesting how measurements of mean-squared displacement versus time might generally inform models of reactive systems with partial diffusion control.

Crowded cell-like environment accelerates the nucleation step of amyloidogenic protein misfolding

To understand the role of a crowded physiological environment in the pathogenesis of neurodegenerative diseases, we report the following. 1) The formation of fibrous aggregates of the human Tau fragment Tau-(244-441), when hyperphosphorylated by glycogen synthase kinase-3beta, is dramatically facilitated by the addition of crowding agents. 2) Fibril formation of nonphosphorylated Tau-(244-441) is only promoted moderately by macromolecular crowding. 3) Macromolecular crowding dramatically accelerates amyloid formation by human prion protein. A sigmoidal equation has been used to fit these kinetic data, including published data of human alpha-synuclein, yielding lag times and apparent rate constants for the growth of fibrils for these amyloidogenic proteins. These biochemical data indicate that crowded cell-like environments significantly accelerate the nucleation step of fibril formation of human Tau fragment/human prion protein/human alpha-synuclein (a significant decrease in the lag time). These results can in principle be predicted based on some known data concerning protein concentration effects on fibril formation both in vitro and in vivo. Furthermore, macromolecular crowding causes human prion protein to form short fibrils and nonfibrillar particles with lower conformational stability and higher protease resistance activity, compared with those formed in dilute solutions. Our data demonstrate that a crowded physiological environment could play an important role in the pathogenesis of neurodegenerative diseases by accelerating amyloidogenic protein misfolding and inducing human prion fibril fragmentation, which is considered to be an essential step in prion replication.

Interrelationship of steric stabilization and self-crowding of a glycosylated protein

In the eukaryotic cell, protein glycosylation takes place in the crowded environment of the endoplasmatic reticulum. With the purpose of elucidating the impact of high concentration on the interactions of glycoproteins, we have conducted a series of small-angle x-ray scattering experiments on the heavily glycosylated enzyme Peniophora lycii phytase (Phy) and its deglycosylated counterpart (dgPhy). The small-angle x-ray scattering data were analyzed using an individual numerical form factor for each of the two glycoforms combined with two structure factors, a hard sphere and a screened coulomb potential structure factor, respectively, as determined by ab initio analysis. Based on this data analysis, three main conclusions could be drawn. First, at comparable protein concentrations (mg/ml), the relative excluded volume of Phy was approximately 75% higher than that of dgPhy, showing that the glycans significantly increase excluded-volume interactions. Second, the relative excluded volume of dgPhy increased with concentration, as expected; however, the opposite effect was observed for Phy, where the relative excluded volume decreased in response to increasing protein concentration. Third, a clear difference in the effect of salinity on the excluded-volume interactions was observed between the two glycol forms. Although the relative excluded volume of dgPhy decreased with increasing ionic strength, the relative excluded volume of Phy was basically insensitive to increased salinity. We suggest that protrusion forces from the glycans contribute to steric stabilization of the protein, and that glycosylation helps to sustain repulsive electrostatic interactions under crowded conditions. In combination, this aids in stabilizing high concentrations of glycosylated proteins.

Quantitative assignment of reaction directionality in constraint-based models of metabolism: application to Escherichia coli

Constraint-based modeling is an approach for quantitative prediction of net reaction flux in genome-scale biochemical networks. In vivo, the second law of thermodynamics requires that net macroscopic flux be forward, when the transformed reaction Gibbs energy is negative. We calculate the latter by using (i) group contribution estimates of metabolite species Gibbs energy, combined with (ii) experimentally measured equilibrium constants. In an application to a genome-scale stoichiometric model of Escherichia coli metabolism, iAF1260, we demonstrate that quantitative prediction of reaction directionality is increased in scope and accuracy by integration of both data sources, transformed appropriately to in vivo pH, temperature and ionic strength. Comparison of quantitative versus qualitative assignment of reaction directionality in iAF1260, assuming an accommodating reactant concentration range of 0.02-20mM, revealed that quantitative assignment leads to a low false positive, but high false negative, prediction of effectively irreversible reactions. The latter is partly due to the uncertainty associated with group contribution estimates. We also uncovered evidence that the high intracellular concentration of glutamate in E. coli may be essential to direct otherwise thermodynamically unfavorable essential reactions, such as the leucine transaminase reaction, in an anabolic direction.

Investigating the effects of molecular crowding on Ca2+ diffusion using a particle-based simulation model

Calcium ions (Ca(2+)) are an important second messenger in eucaryotic cells. They are involved in numerous physiological processes which are triggered by calcium signals in the form of local release events, temporal oscillations, or reaction-diffusion waves. The diffusive spread of calcium signals in the cytosol is strongly affected by calcium-binding proteins (buffers). In addition, the cytosol contains a large number of inert molecules and molecular structures which make it a crowded environment. Here, we investigate the effects of such excluded volumes on calcium diffusion in the presence of different kinds of buffers. We find that the contributions in slowing down Ca(2+) diffusion coming from buffering and molecular crowding are not additive, i.e., the reduction in Ca(2+) diffusivity due to crowding and buffering together is not the sum of each single contribution. In the presence of Ca(2+) gradients and high affinity mobile buffers the effective diffusion coefficient of Ca(2+) can be reduced by up to 60% in highly crowded environments. This suggests that molecular crowding may significantly affect the shape of Ca(2+) microdomains and wave propagation in cell types with high excluded volume fractions.

Elucidating the origin of anomalous diffusion in crowded fluids

Anomalous diffusion in crowded fluids, e.g., in the cytoplasm of living cells, is a frequent phenomenon. So far, however, the associated stochastic process, i.e., the propagator of the random walk, has not been uncovered. Here we show by means of fluorescence correlation spectroscopy and simulations that the properties of crowding-induced subdiffusion are consistent with the predictions for fractional Brownian motion or obstructed (percolationlike) diffusion, both of which have stationary increments. In contrast, our experimental results cannot be explained by a continuous time random walk with its distinct non-Gaussian propagator.

Elucidating anomalous protein diffusion in living cells with fluorescence correlation spectroscopy-facts and pitfalls

Anomalous protein diffusion has been frequently observed in intracellular fluids and on membranes of living cells. Indeed, a large variety of specimen, from bacteriae to mammalian cells, and several non-invasive measurement techniques, e.g. fluorescence correlation spectroscopy, have revealed that the mean square displacement (MSD) of proteins in vivo is often characterized by an anomalous power-law increase mean value of tau(t)(2) mean value of ~ t(alpha) with 0.5 < alpha </= 0.8. Here, we review these results with a particular focus on fluorescence correlation spectroscopy, and we report on possible causes of variations of the anomaly degree alpha. Moreover, we highlight generic consequences of anomalous diffusion that are likely to play an important role in the cellular context.

Entropic flows, crowding effects, and stability of asymmetric proteins

The study of the excluded-volume effects on protein stability and reactions or the stability of colloidal suspensions is an active area of research. Using hard-disk collisional dynamics we investigate whether the presence of a crowding agent can induce a shape change from a nonspherical molecule to a spherical one. We show the averaged density profiles and velocity field of hard-disk crowders with an interior noncircular convex shape as a boundary condition. The density profile is not axially symmetric, consistent with other hard-potential experiments with asymmetry. However, more interestingly, the averaged velocity field was found to have a nonzero curl, implying a region of vorticity without a thermal gradient, advective field, or other motivating potential. To explain the occurrence of the vortices, a theoretical model is provided based on angular momentum of hard disks at contact. All these results, as well as difference in pressure along the axes, support the fact that as the packing fraction of the crowder rises, increasing force is exerted on an asymmetric molecule toward a symmetric one.

Lattice model of diffusion-limited bimolecular chemical reactions in confined environments

We study the effect of confinement on diffusion-limited bimolecular reactions within a lattice model where a small number of reactants diffuse among a much larger number of inert particles. When the number of inert particles is held constant, the rate of the reaction is slow for small reaction volumes due to limited mobility from crowding and for large reaction volumes due to the reduced concentration of the reactants. The reaction rate proceeds fastest at an intermediate confinement corresponding to a volume fraction near 50%. We generalize the model to off-lattice systems with hydrodynamic coupling and predict that the optimal reaction rate for monodisperse colloidal systems occurs when the volume fraction is approximately 19%. Finally, we discuss the implications of our model for bimolecular reactions inside cells and the dynamics of confined polymers.

Biomechanics: cell research and applications for the next decade

With the recent revolution in Molecular Biology and the deciphering of the Human Genome, understanding of the building blocks that comprise living systems has advanced rapidly. We have yet to understand, however, how the physical forces that animate life affect the synthesis, folding, assembly, and function of these molecular building blocks. We are equally uncertain as to how these building blocks interact dynamically to create coupled regulatory networks from which integrative biological behaviors emerge. Here we review recent advances in the field of biomechanics at the cellular and molecular levels, and set forth challenges confronting the field. Living systems work and move as multi-molecular collectives, and in order to understand key aspects of health and disease we must first be able to explain how physical forces and mechanical structures contribute to the active material properties of living cells and tissues, as well as how these forces impact information processing and cellular decision making. Such insights will no doubt inform basic biology and rational engineering of effective new approaches to clinical therapy.

Solute effects on spin labels at an aqueous-exposed site in the flap region of HIV-1 protease

The effects of solutes on spin-label mobility and protein conformation have been investigated with X-band continuous-wave and pulsed electron paramagnetic resonance (EPR) spectroscopy for spin labels attached to an aqueous-exposed site in the beta-hairpin flap region of HIV-1 protease. Specifically, we examined the effects of glycerol, sucrose, PEG3000, and Ficoll400 for four commonly used nitroxide spin labels and found that the largest perturbations to the EPR line shapes occur for solutions containing PEG3000 and glycerol. From comparisons of the spectral line shapes and distance distribution profiles of spin-labeled HIV-1 protease with and without inhibitor, it was concluded that solutes such as glycerol and PEG3000 alter the line shapes of the spin label in the beta-hairpin flaps of HIV-1 PR by modulation of spin-label mobility through changes in preferential interactions with the solutes. It is noteworthy that the high osmolality of the 40% glycerol solution did not alter the conformation of the flaps as determined from pulsed EPR distance measurements.

Effect of macromolecular crowding on reaction rates: a computational and theoretical study

The effect of macromolecular crowding on the rates of association reactions are investigated using theory and computer simulations. Reactants and crowding agents are both hard spheres, and when two reactants collide they form product with a reaction probability, p(rxn). A value of p(rxn) < 1 crudely mimics the fact that proteins must be oriented properly for an association reaction to occur. The simulations show that the dependence of the reaction rate on the volume fraction of crowding agents varies with the reaction probability. For reaction probabilities close to unity where most of encounters between reactants lead to a reaction, the reaction rate always decreases as the volume fraction of crowding agents is increased due to the reduced diffusion coefficient of reactants. On the other hand, for very small reaction probabilities where, in most of encounters, the reaction does not occur, the reaction rate increases with the volume fraction of crowding agents--in this case, due to the increase probability of a recollision. The Smoluchowski theory refined with the radiation boundary condition and the radial distribution function at contact is in quantitative agreement with simulations for the reaction rate constant and allows the quantitative analysis of both effects separately.

Control of translation initiation: a model-based analysis from limited experimental data

We have built a detailed kinetic model of translation initiation in yeast and have used a novel approach to determine the flux controlling steps based on limited experimental data. An efficient parameter estimation method was adapted in order to fit the most uncertain parameters (rate constants) to in vivo measurements in yeast. However, it was found that there were many other sets of plausible parameter values that also gave a good fit of the model to the data. We therefore used random sampling of this uncertain parameter space to generate a large number of diverse fitted parameter sets. A compact characterization of these parameter sets was provided by considering flux control. In particular, we suggest that the rate of translation initiation is most strongly influenced by one of two reactions: either the guanine nucleotide exchange reaction involving initiation factors eIF2 and eIF2B or the assembly of the multifactor complex from its constituent protein/tRNA containing complexes. It is hoped that the approach presented in this paper will add to our understanding of translation initiation pathway and can be used to identify key system-level properties of other biochemical processes.

A method for direct measurement of protein stability in vivo

The stability of proteins is tuned by evolution to enable them to perform their cellular functions for the success of an organism. Yet, most of the arsenal of biophysical techniques at our disposal to characterize the thermodynamic stability of proteins is limited to in vitro samples. We describe an approach that we have developed to observe a protein directly in a cell and to monitor a fluorescence signal that reports the unfolding transition of the protein, yielding quantitatively interpretable stability data in vivo. The method is based on incorporation of structurally nonperturbing, specific binding motifs for a bis-arsenical fluorescein derivative in sites that result in dye fluorescence differences between the folded and unfolded states of the protein under study. This fluorescence labeling approach makes possible the determination of thermodynamic stability by direct urea titration in Escherichia coli cells. The specific case study we describe was carried out on the predominantly beta-sheet intracellular lipid-binding protein, cellular retinoic acid-binding protein (CRABP), expressed in E. coli.

The effects of macromolecular crowding on the mechanical stability of protein molecules

Macromolecular crowding, a common phenomenon in the cellular environments, can significantly affect the thermodynamic and kinetic properties of proteins. A single-molecule method based on atomic force microscopy (AFM) was used to investigate the effects of macromolecular crowding on the forces required to unfold individual protein molecules. It was found that the mechanical stability of ubiquitin molecules was enhanced by macromolecular crowding from added dextran molecules. The average unfolding force increased from 210 pN in the absence of dextran to 234 pN in the presence of 300 g/L dextran at a pulling speed of 0.25 microm/sec. A theoretical model, accounting for the effects of macromolecular crowding on the native and transition states of the protein molecule by applying the scaled-particle theory, was used to quantitatively explain the crowding-induced increase in the unfolding force. The experimental results and interpretation presented could have wide implications for the many proteins that experience mechanical stresses and perform mechanical functions in the crowded environment of the cell.

Automated measurement of the static light scattering of macromolecular solutions over a broad range of concentrations

A method and apparatus for automated measurement of the concentration dependence of static light scattering of protein solutions over a broad range of concentrations is described. The gradient of protein concentrations is created by successive dilutions of an initially concentrated solution contained within the scattering measurement cell, which is maintained at constant total volume. The method is validated by measurement of the concentration dependence of light scattering of bovine serum albumin, ovalbumin, and ovomucoid at concentrations up to 130 g/L. The experimentally obtained concentration dependence of scattering obtained from all three proteins is quantitatively consistent with the assumption that no significant self-association occurs over the measured range of concentrations.

Impact of limited solvent capacity on metabolic rate, enzyme activities, and metabolite concentrations of S. cerevisiae glycolysis

The cell's cytoplasm is crowded by its various molecular components, resulting in a limited solvent capacity for the allocation of new proteins, thus constraining various cellular processes such as metabolism. Here we study the impact of the limited solvent capacity constraint on the metabolic rate, enzyme activities, and metabolite concentrations using a computational model of Saccharomyces cerevisiae glycolysis as a case study. We show that given the limited solvent capacity constraint, the optimal enzyme activities and the metabolite concentrations necessary to achieve a maximum rate of glycolysis are in agreement with their experimentally measured values. Furthermore, the predicted maximum glycolytic rate determined by the solvent capacity constraint is close to that measured in vivo. These results indicate that the limited solvent capacity is a relevant constraint acting on S. cerevisiae at physiological growth conditions, and that a full kinetic model together with the limited solvent capacity constraint can be used to predict both metabolite concentrations and enzyme activities in vivo.

The concentration of enzymes and metabolites is continuously adjusted in order to achieve specific metabolic demands. It is highly likely that during evolution global metabolic regulation has evolved such as to achieve a given metabolic demand with an optimal use of intracellular resources. However, the size of enzymes and intermediate metabolites is dramatically different. Enzymes are macromolecules that occupy a relatively large amount of space within a cell's crowded cytoplasm, while metabolites are much smaller. This implies that metabolite concentrations are likely to be adjusted to minimize the overall “enzymatic cost” (in terms of space cost). In this work, we explore this hypothesis using Saccharomyces cerevisiae glycolysis as a case study. Our results indicate that metabolite concentrations attain optimal values, minimizing the intracellular space occupied by metabolic enzymes. And, at these optimal concentrations, glycolysis achieves the maximum rate given the intracellular volume fraction occupied by glycolysis enzymes. Taken together with previous studies for Escherichia coli, our results indicate that macromolecular crowding is a general constraint on cell metabolism.

Exploring the interfacial structure of protein adsorbates and the kinetics of protein adsorption: an in situ high-energy X-ray reflectivity study

The high energy X-ray reflectivity technique has been applied to study the interfacial structure of protein adsorbates and protein adsorption kinetics in situ. For this purpose, the adsorption of lysozyme at the hydrophilic silica-water interface has been chosen as a model system. The structure of adsorbed lysozyme layers was probed for various aqueous solution conditions. The effect of solution pH and lysozyme concentration on the interfacial structure was measured. Monolayer formation was observed for all cases except for the highest concentration. The adsorbed protein layers consist of adsorbed lysozyme molecules with side-on or end-on orientation. By means of time-dependent X-ray reflectivity scans, the time-evolution of adsorbed proteins was monitored as well. The results of this study demonstrate the capabilities of in situ X-ray reflectivity experiments on protein adsorbates. The great advantages of this method are the broad wave vector range available and the high time resolution.

Macromolecular crowding and size effects on probe microviscosity

Development of biologically relevant crowding solutions necessitates improved understanding of how the relative size and density of mobile obstacles affect probe diffusion. Both the crowding density and relative size of each co-solute in a mixture will contribute to the measured microviscosity as assessed by altered translational mobility. Using multiphoton fluorescent correlation spectroscopy, this study addresses how excluded volume of dextran polymers from 10 to 500 kDa affect microviscosity quantified by measurements of calmodulin labeled with green fluorescent protein as the diffusing probe. Autocorrelation functions were fit using both a multiple-component model with maximum entropy method (MEMFCS) and an anomalous model. Anomalous diffusion was not detected, but fits of the data with the multiple-component model revealed separable modes of diffusion. When the dominant mode of diffusion from the MEMFCS analysis was used, we observed that increased excluded volume slows probe mobility as a simple exponential with crowder concentration. This behavior can be modeled with a single parameter, beta, which depends on the dextran size composition. Two additional modes of diffusion were observed using MEMFCS and were interpreted as unique microviscosities. The fast mode corresponded to unhindered free diffusion as in buffer, whereas the slower agreed well with the bulk viscosity. At 10% crowder concentration, one finds a microviscosity approximately three times that of water, which mimics that reported for intracellular viscosity.

Stochastic off-lattice modeling of molecular self-assembly in crowded environments by Green's function reaction dynamics

The environment inside a living cell is dramatically different from that found in in vitro models, presenting a problem for computational models of biochemistry that are only beginning to capture these differences. This deviation between idealized in vitro models and more realistic intracellular conditions is particularly problematic for models of molecular self-assembly, but also specifically hard to address because the large sizes and long assembly times of biological self-assembly systems force the use of highly simplified models. We have developed a prototype of a molecular self-assembly simulator based on the Green's function reaction dynamics (GFRD) model to achieve more realistic models of assembly in the crowded conditions of the cell without unduly sacrificing tractability. We tested the model on a simple representation of dimer assembly in a two-dimensional space. Our simulations verify that the model is computationally efficient, provides a realistic quantitative model of reaction kinetics in uncrowded conditions, and exhibits expected excluded volume effects under conditions of high crowding. This work confirms the effectiveness of the GFRD technique for more realistic coarse-grained modeling of self-assembly in crowded conditions and helps lay the groundwork for exploring the effects of in vivo crowding on more complex assembly systems.

Binding of calcium ions to Ras promotes Ras guanine nucleotide exchange under emulated physiological conditions

Both Ras protein and calcium play significant roles in various cellular processes via complex signaling transduction networks. However, it is not well understood whether and how Ca(2+) can directly regulate Ras function. Here we demonstrate by isothermal titration calorimetry that Ca(2+) directly binds to the H-Ras.GDP.Mg(2+) complex with moderate affinity at the first binding site followed by two weak binding events. The results from limited proteinase degradation show that Ca(2+) protects the fragments of H-Ras from being further degraded by trypsin and by proteinase K. HPLC studies together with fluorescence spectroscopic measurements indicate that binding of Ca(2+) to the H-Ras.GDP.Mg(2+) complex remarkably promotes guanine nucleotide exchange on H-Ras under emulated physiological Ca(2+) concentration conditions. Addition of high concentrations of either of two macromolecular crowding agents, Ficoll 70 and dextran 70, dramatically enhances H-Ras guanine nucleotide exchange extent in the presence of Ca(2+) at emulated physiological concentrations, and the nucleotide exchange extent increases significantly with the concentrations of crowding agents. Together, these results indicate that binding of calcium ions to H-Ras remarkably promotes H-Ras guanine nucleotide exchange under emulated physiological conditions. We thus propose that Ca(2+) may activate Ras signaling pathway by interaction with Ras, providing clues to understand the role of calcium in regulating Ras function in physiological environments.

Building the cell: design principles of cellular architecture

The astounding structural complexity of a cell arises from the action of a relatively small number of genes, raising the question of how this complexity is achieved. Self-organizing processes combined with simple physical constraints seem to have key roles in controlling organelle size, number, shape and position, and these factors then combine to produce the overall cell architecture. By examining how these parameters are controlled in specific cell biological examples we can identify a handful of simple design principles that seem to underlie cellular architecture and assembly.

Macromolecular crowding and its potential impact on nuclear function

It is well established, that biochemical reactions are dependent on pH, ionic strength, temperature and the concentration of reactants. However, the steric repulsion among bulky components of biological systems also affect biochemical behavior: The 'excluded volume effect of macromolecular crowding' drives bulky components into structurally compact organizations, increases their thermodynamic activities and slows down diffusion. The very special composition of the cell nucleus, which is packed with high-molecular chromatin, ribonucleo-particles and associated proteins, suggests that crowding-effects are part of nuclear functionality. Realizing that many nuclear processes, notably gene transcription, hnRNA splicing and DNA replication, use macromolecular machines, and taking into account that macromolecular crowding provides a cooperative momentum for the assembly of macromolecular complexes, we here elaborate why macromolecular crowding may be functionally important in supporting the statistical significance of nuclear activities.

The cell biology of DNA methylation in mammals

In this review, we will provide a brief reminder of epigenetic phenomena in general, and DNA methylation in particular. We will then underline the characteristics of the in vivo organization of the genome that limit the applicability of in vitro results. We will use several examples to point out the connections between DNA methylation and nuclear architecture. Finally, we will outline some of the hopes and challenges for future research in the field. The study of DNA methylation, its effectors, and its roles, illustrates the complementarity of in vitro approaches and cell biology.