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Exploring the Effects of Hydrogen Bonding and Hydrophobic Chemical Physics 307 (2004) 187–199 www.elsevier.com/locate/chemphys Exploring the effects of hydrogen bonding and hydrophobic interactions on the foldability and cooperativity of helical proteins using a simplified atomic model Michael Knott, Hue Sun Chan * Protein Engineering Network of Centres of Excellence (PENCE), Department of Biochemistry, 1 Kings College Circle, University of Toronto, Toronto, Ont., Canada M5S 1A8 Department of Medical Genetics and Microbiology, Faculty of Medicine, University of Toronto, Toronto, Ont., Canada M5S 1A8 Received 16 February 2004; accepted 3 June 2004 Available online 6 July 2004 Abstract Using a simplified atomic model, we perform Langevin dynamics simulations of polypeptide chains designed to fold to one-, two- and three-helix native conformations. The impact of the relative strengths of the hydrophobic and hydrogen bonding interactions on folding is investigated. Provided that the two interactions are appropriately balanced, a simple potential function allows the chains to fold to their respective target native structures, which are essentially lowest-energy conformations. However, if the hydrophobic interaction is too strong, helix formation is preempted by hydrophobic collapse into compact conformations with little helical content. While the transition from denatured to compact non-native conformations is not cooperative, the transition between native (helical) and denatured states exhibits certain cooperative features. The degree of apparent cooperativity increases with the length of the polypeptide; but it falls far short of that observed experimentally for small, single-domain ‘‘two-state’’ proteins. Even for the three-helix bundle, the present model interaction scheme leads to a distribution of energy which is not bimodal, although a heat capacity peak associated with thermal unfolding is observed. This finding suggests that models with simple pairwise additive in- teraction schemes, involving hydrophobic interactions and hydrogen bonding, can mimic the folding of small helical proteins, but that such models are insufficient to produce high degrees of folding cooperativity. Certain features of our model are reminiscent of a recent scenario proposed for downhill folding. Their ramifications are discussed. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Calorimetry; Langevin dynamics; Two-state cooperativity; Helical proteins; Radius of gyration; Heat capacity 1. Introduction thermodynamic (calorimetric) cooperativity and of folding/unfolding kinetic cooperativity. Thermodynamic Polymer chain models are indispensable tools for the cooperativity of protein folding refers to an apparent understanding of protein folding. In particular, it has two-state behaviour deduced from differential scanning become clear that we can gain considerable insight into calorimetry and other measurements. This property protein energetics by rigorously evaluating the ability of implies that a given protein’s conformational distribu- explicit-chain, self-contained polymer models to repro- tion (distribution in enthalpy or energy in the case of duce generic experimental properties of proteins. A calorimetry) is well separated into two populations – prime example of such a property is cooperativity: many native and denatured – at the folding/unfolding transi- small single-domain proteins exhibit a high degree of tion midpoint, with very low (though not non-existent) intermediate conformational population in between. * Corresponding author. Tel: +1-416-978-2697; fax: +1-416-978- Kinetic cooperativity of protein folding refers to a 8548. protein’s apparent two-state folding and unfolding re- E-mail address: [email protected] (H.S. Chan). laxation as characterised by a linear chevron plot. 0301-0104/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2004.06.014 188 M. Knott, H.S. Chan / Chemical Physics 307 (2004) 187–199 Comparison of the behaviours of several representative all proteins. Recent years have witnessed tremendous models has shown that kinetic cooperativity is corre- progress in atomic simulation of peptide and protein lated with a high degree of thermodynamic cooperativity folding. There have been all-atom simulations with ex- [1]. plicit treatment of the aqueous solvent [17–21], implicit- Because of their computational tractability, contin- solvent investigations [22–27], and critical comparisons uum (off-lattice) Go models [2–5] have been instru- of different approaches (see, e.g., [28,29]). Some of these mental in elucidating the folding behaviour of real efforts have been facilitated by massive distributed proteins. However, as is the case for their lattice coun- computing [24,27]. The most impressive advances have terparts [6–8], common continuum Go models – at least involved the simulation of small peptides and ‘‘mini- those tested so far – fail to reproduce the linear chevron proteins’’, with several notable cases of successful in plots that are observed in real ‘‘two-state’’ proteins [1,4], silico folding to stable conformations that essentially because kinetic trapping in these models – though not coincide with known native structures (e.g., serious – becomes non-negligible under mildly native [18,19,23,27], see also the recent review [30] and refer- conditions [8]. ences therein). Kinetic trapping in these models arises from stable Traditionally, the main emphasis of many all-atom compact non-native conformations, which have inter- molecular dynamics studies has been on molecular mediate energies between the native and fully unfolded structures rather than on energetics [20,31]. This is be- values and thus are associated with attenuated thermo- cause the complexity of these models has often pre- dynamic cooperativity. A possible reason for the insuf- cluded the extensive conformational sampling that ficiently high cooperativity of the common Go models is statistical mechanical considerations require. Recently, that their interaction schemes are essentially pairwise however, simulations have begun to overcome this additive: recent investigations indicate that many-body problem. Reversible folding and unfolding have been interactions [9,10] are probably necessary for a high le- achieved in all-atom explicit-solvent simulations of vel of cooperativity quantitatively similar to that ob- small peptides, allowing thermodynamic issues to be served in some real, small, single-domain proteins. addressed [30,32]. Indeed, it has been demonstrated, using native-centric There are multiple approaches to the level of detail lattice constructs, that a many-body local–non-local incorporated in a simulation model. All-atom simula- coupling mechanism [1,10] can lead to enhanced coop- tion is perhaps the only approach that could, in princi- erativity as well as to a strong correlation between ple, predict the details of the folding process of a given contact order and folding rate, reminiscent of the cor- protein. However, we wish to address the question of relation that is observed experimentally [11]. This sug- cooperativity, and it is currently still problematic to use gests that a similar local–non-local cooperative all-atom explicit-solvent models to address the folding mechanism may be at play in certain classes of real thermodynamics of proteins with 50 or more residues. proteins (see also [12]). This is because explicit-solvent simulations of proteins This line of investigation highlights our limited un- of such sizes have yet to obtain a single continuous derstanding of protein energetics: it shows that highly folding trajectory from an open conformation to the cooperative behaviour is non-trivial. A protein chain native structure. In all-atom implicit-solvent models, on model that purports to incorporate simple, intuitive the other hand, the lowest-energy conformations in the intrachain interactions will not inevitably be highly model often do not correspond to the known native cooperative. structures [24,25]. On the other hand, it is equally important to recog- With this background, a complementary approach, nise that not all natural proteins are highly cooperative. very much in the traditional spirit of physics, is to use In view of recent advances in protein science, it is rea- simplified continuum chain representations that are sonable to expect that a broad range of polymer be- reasonably geometrically accurate and that capture the haviours can be exploited by Nature for biological desired aspects of the real system [33,34]. It is unlikely function. It has been pointed out [1] that polymer that this approach could ever predict the full behaviour models with somewhat reduced cooperativity (certain of a specific protein, but by allowing us to make changes Go models, for example) can be appropriate for proteins to a relatively small input of information, and to eval- with chevron rollovers [8]. And polymer models with uate their effects on the results, it enables us to gain a even much diminished cooperativity would be applica- general theoretical understanding of the process [35–38]. ble to the study of downhill folding [13–16]. In accordance with this perspective, the overall goals of Although Go-like native-centric constructs are useful our effort to employ simplified models to address protein for making conceptual advances [2–4], a fundamental folding cooperativity are the following. (i) To delineate physical understanding of protein folding ultimately the strengths and weaknesses of simplified, implicit- requires an atomistic approach based on general,
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