Thermal Effects in Stretching of Go-Like Models of Titin and Secondary Structures

The effect of temperature on mechanical unfolding of proteins is studied using a Go-like model with a realistic contact map and Lennard-Jones contact interactions. The behavior of the I27 domain of titin and its serial repeats is contrasted to that of simple secondary structures. In all cases, thermal fluctuations accelerate the unraveling process, decreasing the unfolding force nearly linearly at low temperatures. However, differ-ences in bonding geometry lead to different sensitiv-ity to temperature and different changes in the unfolding pattern. Due to its special native-state geometry, titin is much more thermally and elasti-cally stable than the secondary structures. At low temperatures, serial repeats of titin show a parallel unfolding of all domains to an intermediate state, followed by serial unfolding of the domains. At high temperatures, all domains unfold simultaneously, and the unfolding distance decreases monotonically with the contact order, that is, the sequence dis-tance between the amino acids that form the native contact. Proteins 2004;56:285-297.

The giant molecule titin is one of the prime objects of mechanical studies of single biological molecules, because of its role in controlling the degree of extension and elasticity of smooth, skeletal, and cardiac muscles.^1-5 Titin is known to consist of many ( 300) globular domains,which are connected in series. The domains are of similar structure but different homology. The first domain to have its native conformation determined was the 27th immunoglobulin domain of the I band of titin, I27, which has the structure of a -sandwich.⁶ The structures of a growing number of other domains have been determined,^7-10 many of which contain short -helix regions in addition to-sheets. Stretching studies of both natural and engineered titin have been accomplished by a variety of techniques.^11-20 All reveal sawtooth patterns in the force (F)-tip displacement (d) curves that are consistent with a predominantly serial unraveling of domains.^13,21 The rea-son is that the bonds that require the largest force to break rupture near the start of the unraveling process of each domain.

All-atom simulations of a single I27 domain in water have reproduced many experimental properties and have helped to interpret them. For example, the bonds that require the largest force to break have been identified as 6 hydrogen bonds,^22,23 and the structure of an intermediate state that forms during unfolding has been identified.²⁴ However, these studies are limited to very high velocities and cannot easily address the behavior of multiple do-mains. In addition, their computational expense makes it difficult to explore generic features of unfolding in a wide range of proteins, in order to develop a more global theoretical understanding.

Coarse-grained Go-like models^25,26 that only use structural information about proteins are able to capture many of their properties with minimal computational effort. In recent articles, we have contrasted the folding and mechani cal unfolding behavior of typical secondary structures,²⁷ and then of a titin domain and its tandem repeats,²¹ as modeled by a Go-like system.^25,26 The focus of these studies was on establishing scenarios of unfolding, as determined by the order of bond breaking, and investigating their relationship to contact formation during thermal folding. In general, there is no correlation, because of the crucial role the geometry of loading plays in unfolding. Our previous mechanical unfolding studies were effectively done at zero temperature in order to minimize fluctuations and rate dependence. The purpose of this article is to investigate the effects of thermal fluctuations on unfolding of proteins. While temperature cannot be varied dramatically in an aqueous environment, the effective strength of thermal fluctuations can be varied experimentally through changes in solute concentrations. This does not yet appear to have been done systematically, but we find it can produce marked changes in unfolding scenarios. We begin by considering two simple secondarystructures:-helices and -sheets. Then single domains and multiple repeats of titin are studied. Thermal fluctuations aid unfolding in all cases, decreasing both the unfolding force and the extension at unfolding. At low temperatures, the rate of these changes and their effect on the unfolding pattern depend strongly on the geometry of the protein. In some cases, the stiffness of the mechanical device can also be important. However, at high tempera-tures, the unfolding scenarios become universal, and the force can be described by an entropic, worm-like chain model.^28,29

The remainder of the article is organized as follows: The next section discusses the Go-like model that we use and the details of our molecular dynamics simulations. The following section examines the behavior of secondary structures and titin. Changes induced by coupling many domains and varying velocity are discussed for titin. The final section presents a summary and conclusions.

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