Abstract
A protein at equilibrium is commonly thought of as a fully relaxed structure, with the intra-molecular interactions showing fluctuations around their energy minimum. In contrast, here we find direct evidence for a protein as a molecular tensegrity structure, comprising a balance of tensed and compressed interactions, a concept that has been put forward for macroscopic structures. We quantified the distribution of inter-residue prestress in ubiquitin and immunoglobulin from all-atom molecular dynamics simulations. The network of highly fluctuating yet significant inter-residue forces in proteins is a consequence of the intrinsic frustration of a protein when sampling its rugged energy landscape. In beta sheets, this balance of forces is found to compress the intra-strand hydrogen bonds. We estimate that the observed magnitude of this pre-compression is enough to induce significant changes in the hydrogen bond lifetimes; thus, prestress, which can be as high as a few 100 pN, can be considered a key factor in determining the unfolding kinetics and pathway of proteins under force. Strong pre-tension in certain salt bridges on the other hand is connected to the thermodynamic stability of ubiquitin. Effective force profiles between some side-chains reveal the signature of multiple, distinct conformational states, and such static disorder could be one factor explaining the growing body of experiments revealing non-exponential unfolding kinetics of proteins. The design of prestress distributions in engineering proteins promises to be a new tool for tailoring the mechanical properties of made-to-order nanomaterials.
Highlights
The principle of ‘minimal frustration’ [1,2] underlies the thermodynamic picture of protein folding
A tensegrity structure is one composed of members that are permanently under either tension or compression, and the balance of these tensile and compressive forces provides the structure with its mechanical stability
Using Molecular Dynamics simulations of the protein ubiquitin, we measure the network of pairwise forces connecting the amino acid residues and show that this network does have the character of a tensegrity structure
Summary
The principle of ‘minimal frustration’ [1,2] underlies the thermodynamic picture of protein folding. Even in the simplest crystals, the equilibrium state is one that minimises the energy of the structure as a whole, not every atom-atom interaction individually; global constraints prevent every pairwise interactions from being perfectly satisfied This is even more the case for proteins, in which the topological contraints of the backbone peptide bonds further restrict the freedom of individual atoms to individually satisfy every interaction. The concept of biomolecular tensegrity has come under focus very recently in the work of Shih, Ingber, and co-workers, who have designed and synthesised prestressed DNA structures [5]; it has been invoked in a novel method for interpreting free energy profiles inferred from the forced unfolding of single biomolecules [6] In contrast to this tensegrity picture, classic coarse-grained models of proteins, which have been used extensively to study protein folding and dynamics, typically neglect prestress. Especially in research areas that rely on these coarse-grained approaches, the consequences of prestress for folding and dynamics have not been well explored
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