Excluded volume as a determinant of macromolecular structure and reactivity

The effect of excluded volume on the thermodynamic activity of globular macromolecules and macromolecular complexes in solution is studied in the hard-particle approximation. Activity coefficients are calculated as a function of the fraction of total volume occupied by macromolecules using relations obtained from scaled particle and lattice models. Significant and readily observable effects are predicted to occur as the fraction of volume occupied by globular macromolecules increases, including the following: (i) Compact quasi-spherical macromolecular conformations become increasingly energetically favored over extended anisometric conformations. (ii) Self- and heteroassociation processes are enhanced, particularly those leading to the formation of compact quasi-spherical aggregates. (iii) Depending upon the details of the reaction mechanism, the rate of an enzyme-catalyzed reaction may monotonically decrease, go through a maximum, or exhibit more complex behavior. A given degree of volume occupancy by larger macromolecules is predicted to have less effect on the structure and self-association of smaller macromolecules than the same degree of volume occupancy by smaller macromolecules has on the structure and self-association of larger macromolecules.     

Cooperativity in macromolecular assembly

The thermodynamic principle of cooperativity is used to drive the formation of specific macromolecular complexes during the assembly of a macromolecular machine. Understanding cooperativity provides insight into the mechanisms that govern assembly and disassembly of multicomponent complexes. Our understanding of assembly mechanisms is lagging considerably behind our understanding of the structure and function of these complexes. A significant challenge remains in tackling the thermodynamics and kinetics of the intermolecular interactions required for all cellular functions.     

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.     

Velocity of linear crystallization of ice in macromolecular systems

The velocity of ice crystallization in gelled systems was compared with that in solutions of similar macromolecular materials. Neither the constituting material nor the dimensions of the tubes in which the measurements were made influenced the results. The velocity of linear crystallization of ice was slowed in macromolecular solutions and gels, and this decrease was not associated with changes in dynamic or thermodynamic properties of water. It was probably the consequence of a mechanical effect of the macromolecules directly on ice crystal growth.     

Growth and disorder of macromolecular crystals: insights from atomic force microscopy and X-ray diffraction studies

The growth processes and defect structures of protein and virus crystals have been studied in situ by atomic force microscopy (AFM), X-ray diffraction topography, and high-resolution reciprocal space scanning. Molecular mechanisms of macromolecular crystallization were visualized and fundamental kinetic and thermodynamic parameters, which govern the crystallization process of a number of macromolecular crystals, have been determined. High-resolution AFM imaging of crystal surfaces provides information on the packing of macromolecules within the unit cell and on the structure of large macromolecular assemblies. X-ray diffraction techniques provide a bulk probe with poorer spatial resolution but excellent sensitivity to mosaicity and strain. Defect structures and disorder created in macromolecular crystals during growth, seeding, and post-growth treatments including flash cooling were characterized and their impacts on the diffraction properties of macromolecular crystals have been analyzed. The diverse and dramatic effects of impurities on growth and defect formation have also been studied. Practical implications of these fundamental insights into the improvement of macromolecular crystallization protocols are discussed.     

Macromolecular crowding and its role as intracellular signalling of cell volume regulation.

Macromolecular crowding has been proposed as a mechanism by means of which a cell can sense relatively small changes in volume or, more accurately, the concentration of intracellular solutes. According to the macromolecular theory, the kinetics and equilibria of enzymes can be greatly influenced by small changes in the concentration of ambient, inert macromolecules. A 10% change in the concentration of intracellular proteins can lead to changes of up to a factor of ten in the thermodynamic activity of putative molecular regulatory species, and consequently, the extent to which such regulator(s) may bind to and activate membrane-associated ion transporters. The aim of this review is to examine the concept of macromolecular crowding and how it profoundly affects macromolecular association in an intact cell with particular emphasis on its implication as a sensor and a mechanism through which cell volume is regulated.     

Quantitative considerations of the consequences of an interplay between ligand binding and reversible adsorption of a macromolecular solute

Explicit expressions are derived which determine the equilibrium composition of mixtures comprising a multivalent, insoluble matrix, a multivalent, macromolecular solute (acceptor) and a univalent ligand. With three-reactant mixtures of this type a range of combinations of interactions is possible wherein the ligand interacts with either the acceptor or the matrix, in either event perturbing the acceptor-matrix equilibria. Theory encompassing this range of possibilities is written in terms of a single site-binding constant for each type of interaction to account, in general terms, for both multiple binding and crosslinking effects. These explicit thermodynamic relationships are discussed, with the use of reported findings on several biological systems, in two frameworks. First, it is established that the theory is applicable to the quantitative interpretation of affinity chromatography experiments designed to elucidate the thermodynamic interaction parameters governing the various types of interacting system. Second, it is emphasized that the relationships are also relevant to metabolite-induced changes in the subcellular distribution of macromolecular species.     

HYDROMIC: prediction of hydrodynamic properties of rigid macromolecular structures obtained from electron microscopy images

We have developed a procedure for the prediction of hydrodynamic coefficients and other solution properties of macromolecules and macromolecular complexes whose volumes have been generated from electron microscopy images. Starting from the structural files generated in the three-dimensional reconstructions of such molecules, it is possible to construct a hydrodynamic model for which the solution properties can be calculated. We have written a computer program, HYDROMIC, that implements all the stages of the calculation. The use of this procedure is illustrated with a calculation of the solution properties of the volume of the cytosolic chaperonin CCT, obtained from cryoelectron microscopy images.     

Hydrodynamics of macromolecular complexes. II. Rotation

We have used the modified Oseen hydrodynamic interaction tensor along with iterative numerical solution of the coupled hydrodynamic interaction equations to calculate the rotational diffusion coefficients of macromolecular complexes composed of nonidentical spherical subunits. For the one structure, a prolate ellipsoid of revolution, for which exact solutions are available, a subunit model with the same length and volume gives asymptotic agreement with the Perrin equations. Other structures considered include plane polygonal rings, lollipops, and dumbbells.     

Effects of macromolecular crowding on the inhibition of virus assembly and virus-cell receptor recognition

Biological fluids contain a very high total concentration of macromolecules that leads to volume exclusion by one molecule to another. Theory and experiment have shown that this condition, termed macromolecular crowding, can have significant effects on molecular recognition. However, the influence of molecular crowding on recognition events involving virus particles, and their inhibition by antiviral compounds, is virtually unexplored. Among these processes, capsid self-assembly during viral morphogenesis and capsid-cell receptor recognition during virus entry into cells are receiving increasing attention as targets for the development of new antiviral drugs. In this study, we have analyzed the effect of macromolecular crowding on the inhibition of these two processes by peptides. Macromolecular crowding led to a significant reduction in the inhibitory activity of: 1), a capsid-binding peptide and a small capsid protein domain that interfere with assembly of the human immunodeficiency virus capsid, and 2), a RGD-containing peptide able to block the interaction between foot-and-mouth disease virus and receptor molecules on the host cell membrane (in this case, the effect was dependent on the conditions used). The results, discussed in the light of macromolecular crowding theory, are relevant for a quantitative understanding of molecular recognition processes during virus infection and its inhibition.     

Size-dependent studies of macromolecular crowding on the thermodynamic stability,structure and functional activity of proteins: in vitro and in silico approaches

BackgroundThe environment inside cells in which proteins fold and function are quite different from that of the dilute buffer solutions often used during in vitro experiments. The presence of large amounts of macromolecules of varying shapes, sizes and compositions makes the intracellular milieu extremely crowded.Scope of reviewThe overall concentration of macromolecules ranges from 50 to 400 g l^− 1, and they occupy 10–40% of the total cellular volume. These differences in solvent conditions and the level of crowdedness resulting in excluded volume effects can have significant consequences on proteins' biophysical properties. A question that arises is: how important is it to examine the roles of shape, size and composition of macromolecular crowders in altering the biological properties of proteins? This review article aims at focusing, gathering and summarizing all of the research investigations done by means of in vitro and in silico approaches taking into account the size-dependent influence of the crowders on proteins' properties.Major conclusionsAltogether, the internal architecture of macromolecular crowding environment including size, shape and concentration of crowders, appears to be playing an extremely important role in causing changes in the biological processes. Most often the small sized crowders have been found more effective crowding agents. However, thermodynamic stability, structure and functional activity of proteins have been governed by volume exclusion as well as soft (chemical) interactions.General significanceThe article provides an understanding of importance of internal architecture of the cellular environment in altering the biophysical properties of proteins.     

On the hydrodynamic analysis of macromolecular conformation

Hydrodynamics provides a powerful complementary role to the traditional "high resolution" techniques for the investigation of macromolecular conformation, especially in dilute solution, conditions which are generally inaccessible to other structural techniques. This paper describes the state of art of hydrodynamic representations for macromolecular conformation, in terms of (1) simple but straightforward ellipsoid of revolution modelling; (2) general triaxial ellipsoid modelling; (3) hydrodynamic bead modelling; (4) the ability, especially for polydisperse macromolecular systems, to distinguish between various conformation types; (5) analysis of macromolecular flexibility.     

X-ray solution scattering (SAXS) combined with crystallography and computation: defining accurate macromolecular structures, conformations and assemblies in solution

Crystallography supplies unparalleled detail on structural information critical for mechanistic analyses; however, it is restricted to describing low energy conformations of macromolecules within crystal lattices. Small angle X-ray scattering (SAXS) offers complementary information about macromolecular folding, unfolding, aggregation, extended conformations, flexibly linked domains, shape, conformation, and assembly state in solution, albeit at the lower resolution range of about 50 A to 10 A resolution, but without the size limitations inherent in NMR and electron microscopy studies. Together these techniques can allow multi-scale modeling to create complete and accurate images of macromolecules for modeling allosteric mechanisms, supramolecular complexes, and dynamic molecular machines acting in diverse processes ranging from eukaryotic DNA replication, recombination and repair to microbial membrane secretion and assembly systems. This review addresses both theoretical and practical concepts, concerns and considerations for using these techniques in conjunction with computational methods to productively combine solution scattering data with high-resolution structures. Detailed aspects of SAXS experimental results are considered with a focus on data interpretation tools suitable to model protein and nucleic acid macromolecular structures, including membrane protein, RNA, DNA, and protein-nucleic acid complexes. The methods discussed provide the basis to examine molecular interactions in solution and to study macromolecular flexibility and conformational changes that have become increasingly relevant for accurate understanding, simulation, and prediction of mechanisms in structural cell biology and nanotechnology.     

Stability of macromolecular complexes

Macromolecular interactions are crucial in numerous biologic processes, yet few general principles are available that establish firm expectations for the strength of these interactions or the expected contribution of specific forces. The simplest principle would be a monotonic increase in interactions as the size of the interface grows. The exact relationship might be linear or nonlinear depending on the nature of the forces involved. Simple "linear-free energy" relationships based on atomic properties have been well documented, for example, additivity for the interaction of small molecules with solvent, and, recently, have been explored for ligand-receptor interactions. Horton and Lewis propose such additivity based on buried surface area for protein-protein complexes. We investigated macromolecular interactions and found that the highest-affinity complexes do not fulfill this simple expectation. Instead, binding free energies of the tightest macromolecular complexes are roughly constant, independent of interface size, with the notable exception of DNA duplexes. By comparing these results to an earlier study of protein-ligand interactions we find that: (1) The maximum affinity is approximately 1.5 kcal/mol per nonhydrogen atom or 120 cal/mol A(2) of buried surface area, comparable to results of our earlier work; (2) the lack of an increase in affinity with interface size is likely due to nonthermodynamic factors, such as functional and evolutionary constraints rather than some fundamental physical limitation. The implication of these results have some importance for molecular design because they suggest that: (1) The stability of any given complex can be increased significantly if desired; (2) small molecule inhibitors of macromolecular interactions are feasible; and (3) different functional classes of protein-protein complexes exhibit differences in maximal stability, perhaps in response to differing evolutionary pressures. These results are consistent with the widespread observation that proteins have not evolved to maximize thermodynamic stability, but are only marginally stable.     

Induction of 3T3 cell division at the monolayer stage : Early changes in macromolecular processes

We have previously demonstrated that 3T3 cells at the monolayer stage can be induced to divide by brief treatment with a variety of proteases. We have now used this system to investigate the macromolecular changes occurring in 3T3 cells induced to divide in this manner. Immediately after pronase treatment, 3T3 cells become agglutinable with concanavalin A. This is rapidly followed in order by a decrease in cyclic AMP concentration within the cell, and an increase in RNA synthesis and uridine transport. The increases in RNA synthesis and uridine transport are dependent on concomitant protein synthesis. Specific protein synthesis follows 1 h after protease treatment, with DNA synthesis occurring 24 h after treatment and mitosis 30 h after treatment. This work suggests that following alteration of the surface membrane a variety of intercellular macromolecular processes occur which eventually culminate in DNA synthesis and cell division. Such a series of events may occur during each cell cycle in non-confluent 3T3 cells.     

Analysis of sedimentation equilibrium distributions reflecting nonideal macromolecular associations

A rigorous statistical-mechanical approach is adopted to derive general quantitative expressions that allow for the effects of thermodynamic nonideality in equilibrium measurements reflecting interaction between dissimilar macromolecular reactants. An analytical procedure based on these expressions is then formulated for obtaining global estimates of equilibrium constants and the corresponding reference thermodynamic activities of the free reactants in each of several sedimentation equilibrium experiments. The method is demonstrated by application to results from an ultracentrifugal study of an electrostatic interaction between ovalbumin and cytochrome c (Winzor, D. J., M. P. Jacobsen, and P. R. Wills. 1998. Biochemistry. 37:2226-2233). It is demonstrated that reliable estimates of relevant thermodynamic parameters are extracted from the data through statistical analysis by means of a simple nonlinear fitting procedure.     

Contractile elements in the regulation of macromolecular permeability

The leakage of macromolecules from the vasculature to the interstitium is greatly accentuated by mediators of edema such as histamine and bradykinin. The mechanism for this effect is not well delineated although many agents that affect smooth muscle tone may also affect macromolecular leakage. Leakage occurs primarily from the small venules. The demonstration that mediators of edema produce interendothelial gaps in the venules as well as changes in the shape of the endothelial nuclei has led to the hypothesis that a contraction of a vascular wall component may be responsible for the observed leakage of macromolecules. This component does not appear to be the vascular smooth muscle itself. Two other elements of the vascular wall, the endothelium and the pericytes, have been shown to contain many of the same elements of the contractile machinery present in smooth muscle. Most recent studies have presumed that endothelial cell contraction is responsible for the formation of the interendothelial gaps through which the macromolecules move. However, endothelial contraction has been difficult to demonstrate experimentally. Alternatively, inasmuch as pericytic processes can end near endothelial junctions and there is an abundance of fibronectin between the pericytes and the endothelium, it may be a pericytic contraction that causes the interendothelial gap formation.     

Effects of macromolecular crowding agents on protein folding in vitro and in silico

Proteins fold and function inside cells which are environments very different from that of dilute buffer solutions most often used in traditional experiments. The crowded milieu results in excluded-volume effects, increased bulk viscosity and amplified chances for inter-molecular interactions. These environmental factors have not been accounted for in most mechanistic studies of protein folding executed during the last decades. The question thus arises as to how these effects—present when polypeptides normally fold in vivo—modulate protein biophysics. To address excluded volume effects, we use synthetic macromolecular crowding agents, which take up significant volume but do not interact with proteins, in combination with strategically selected proteins and a range of equilibrium and time-resolved biophysical (spectroscopic and computational) methods. In this review, we describe key observations on macromolecular crowding effects on protein stability, folding and structure drawn from combined in vitro and in silico studies. As expected based on Minton’s early predictions, many proteins (apoflavodoxin, VlsE, cytochrome c, and S16) became more thermodynamically stable (magnitude depends inversely on protein stability in buffer) and, unexpectedly, for apoflavodoxin and VlsE, the folded states changed both secondary structure content and, for VlsE, overall shape in the presence of macromolecular crowding. For apoflavodoxin and cytochrome c, which have complex kinetic folding mechanisms, excluded volume effects made the folding energy landscapes smoother (i.e., less misfolding and/or kinetic heterogeneity) than in buffer.