proteins STRUCTURE O FUNCTION O BIOINFORMATICS Analyzing the effect of homogeneous frustration in protein folding Vin  ıcius G. Contessoto, 1† Debora T. Lima, 1† Ronaldo J. Oliveira, 1,2 Aline T. Bruni, 3 Jorge Chahine, 1 and Vitor B. P. Leite 1 * 1 Departamento de F  ısica, Instituto de Bioci ^ encias, Letras e Ci ^ encias Exatas, Universidade Estadual Paulista, Sao Jos e do Rio Preto, S~ ao Paulo 15054-000, Brazil 2 Laborat orio Nacional de Ci ^ encia e Tecnologia do Bioetanol, Campinas, S~ ao Paulo 13083-970, Brazil 3 Departamento de Qu  ımica, Faculdade de Filosofia, Ci ^ encias e Letras de Ribeir~ ao Preto, Universidade de S~ ao Paulo, S~ ao Paulo, Brazil ABSTRACT The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustra- tion. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration crite- rion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a C a structure-based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 pro- teins are completely characterized as a function of increasing level of energetic frustration. We observed two well-separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non-native contact interactions in different folding scenarios. These findings strongly correlate with the protein free- energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for exper- imentalists to predict the limits of improvements in real proteins. Proteins 2013; 81:1727–1737. V C 2013 Wiley Periodicals, Inc. Key words: structure-based model; multivariate analysis; molecular dynamics; C-alpha model. INTRODUCTION The protein folding problem is an important challenge in the understanding of biomolecular mechanisms. In the late 1960s, Levinthal 1 raised the question of how many configurational states a typical protein accesses before it dynamically reaches its lowest energy-folded state. In the last decades, based on the energy landscape theory and on the concept of folding funnels, the apparent Levinthal folding paradox has been solved. 2–6 The energy land- scape has been revealed to be a robust framework in the qualitative and quantitative protein-folding studies in the- oretical 7–9 as well as experimental 10–13 works. In addi- tion, protein folding has been investigated using different computational models to predict rates and stability to correlate with experimentalists. 8,14,15 According to the theory, protein folding is described as the diffusion of an ensemble of partially folded structures through which a protein passes on its way to the native state. 16–18 The overall landscape resembles a funnel with some roughness, reflecting transient traps in local energy minima. 19 The folded native state is associ- ated with the global energy minimum of the system. 20 To be kinetically foldable, the funnel must have a steep enough slope to be able to overcome local traps, leading Additional Supporting Information may be found in the online version of this article. Grant sponsor: Fundac ¸~ ao de Amparo  a Pesquisa do Estado de S~ ao Paulo (FAPESP); Conselho Nacional de Desenvolvimento Cient  ıfico e Tecnol ogico (CNPq); Coordenac¸~ ao de Aperfeic ¸oamento de Pessoal de N  ıvel Superior (CAPES). † Vinicius G. Contessoto and Debora T. Lima contributed equally to this work. *Correspondence to: Departamento de F  ısica Instituto de Bioci ^ encias, Letras e Ci^ encias Exatas Universidade Estadual Paulista Sao Jose do Rio Preto, S~ ao Paulo 15054-000, Brazil. E-mail:vleite@sjrp.unesp.br Received 26 September 2012; Revised 13 March 2013; Accepted 18 March 2013 Published online 23 April 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/prot.24309 V V C 2013 WILEY PERIODICALS, INC. PROTEINS 1727