### abstract ###
Many protein functions can be directly linked to conformational changes.
Inside cells, the equilibria and transition rates between different conformations may be affected by macromolecular crowding.
We have recently developed a new approach for modeling crowding effects, which enables an atomistic representation of test proteins.
Here this approach is applied to study how crowding affects the equilibria and transition rates between open and closed conformations of seven proteins: yeast protein disulfide isomerase, adenylate kinase, orotidine phosphate decarboxylase, Trp repressor, hemoglobin, DNA -glucosyltransferase, and Ap 4A hydrolase.
For each protein, molecular dynamics simulations of the open and closed states are separately run.
Representative open and closed conformations are then used to calculate the crowding-induced changes in chemical potential for the two states.
The difference in chemical-potential change between the two states finally predicts the effects of crowding on the population ratio of the two states.
Crowding is found to reduce the open population to various extents.
In the presence of crowders with a 15 radius and occupying 35 percent of volume, the open-to-closed population ratios of yPDI, AdK, ODCase and TrpR are reduced by 79 percent, 78 percent, 62 percent and 55 percent, respectively.
The reductions for the remaining three proteins are 20 44 percent.
As expected, the four proteins experiencing the stronger crowding effects are those with larger conformational changes between open and closed states.
Larger proteins also tend to experience stronger crowding effects than smaller ones e.g., comparing yPDI and TrpR.
The potentials of mean force along the open-closed reaction coordinate of apo and ligand-bound ODCase are altered by crowding, suggesting that transition rates are also affected.
These quantitative results and qualitative trends will serve as valuable guides for expected crowding effects on protein conformation changes inside cells.
### introduction ###
It is increasingly recognized that protein dynamics serves the critical link between structure and function CITATION CITATION.
An important manifestation of protein dynamics is the sampling of alternative conformations.
These conformational changes can be triggered by substrate binding CITATION and post-translational modifications such as phosphorylation CITATION.
Increasingly, structures of the same proteins at different functional states are becoming available.
These structures provide atomistic details of conformational changes.
For example, adenylate kinase, an enzyme that catalyzes the phosphoryl transfer from ATP to AMP, undergoes a significant conformational transition, from an open conformation in the apo form and to a closed conformation in the ligand-bound form CITATION CITATION.
The main differences between these two conformations occur in the ATP- and AMP-binding domains, with the CORE domain relatively rigid.
Other examples with well-characterized conformational transitions include proteins responsible for signal transduction across cell membranes CITATION CITATION and ion channels CITATION .
Biophysical characterizations of protein conformational changes have mostly been carried out under dilute conditions.
However, the environments where proteins perform their biological functions, i.e., extracellular space, cell membrane, and cytoplasm, are crowded with macromolecules.
For example, the cytoplasm of Escherichia coli contains about 300 400 g/l of macromolecules CITATION, which are estimated to occupy over 30 percent of the total volume.
In cell membranes, membrane proteins occupy a similar level of the total surface area CITATION.
How the crowded cellular environments affect the equilibria and transition rates between different conformations of proteins is still poorly understood.
Qualitatively, one expects that macromolecular crowding will significantly modify the energy landscapes of conformational changes, favoring more compact structures over more open ones CITATION.
Such effects of crowding have been scrutinized experimentally.
Molecular dynamics simulations have also been carried out to investigate the energy landscapes of a number of proteins under crowding, in the context of either conformational change CITATION or folding-unfolding transition CITATION CITATION.
To speed up conformational sampling, the proteins in these studies were represented at a coarse-grained level.
Recently we have developed an approach CITATION, CITATION, referred to as postprocessing, which opens the door to atomistic modeling of proteins under crowding.
In this approach, the motions of a test protein are simulated in the absence of crowders.
Conformations from this simulation are then used to calculate the change in chemical potential if they are transferred to a crowded solution.
The dependence of the change in chemical potential on reaction coordinates then captures the influence of crowding on the energy landscape.
The postprocessing approach has been applied to study effects of crowding on protein folding and binding stability CITATION, CITATION, CITATION and on the open-closed equilibrium of the HIV-1 protease dimer CITATION.
In the latter application it has been shown that the postprocessing approach yields results identical to those obtained from direct simulations of the protein in the presence of crowders CITATION, CITATION .
Here we apply the postprocessing approach to investigate the impact of macromolecular crowding on the open-closed equilibria of seven proteins: AdK CITATION, CITATION, yeast protein disulfide isomerase CITATION, CITATION, orotidine phosphate decarboxylase CITATION, Trp repressor CITATION, hemoglobin CITATION, DNA -glucosyltransferase CITATION, and Ap 4A hydrolase CITATION, CITATION.
The biological functions and subcellular locations of these proteins are listed in Table 1.
We find crowding to reduce the open-to-closed population ratios to various extents; the potentials of mean force along the open-closed reaction coordinate of apo and ligand-bound ODCase, and hence the transition rates, are similarly affected.
The biological implications of these results are discussed below.
