The protein folding transition state: Insights from kinetics and thermodynamics

We perform extensive lattice Monte Carlo simulations of protein folding to construct and compare the equilibrium and the kinetic transition state ensembles of a model protein that folds to the native state with two-state kinetics. The kinetic definition of the transition state is based on the folding probability analysis method, and therefore on the selection of conformations with 0.4<Pfold<0.6, while for the equilibrium characterization we consider conformations for which the evaluated values of several reaction coordinates correspond to the maximum of the free energy measured as a function of those reaction coordinates. Our results reveal a high degree of structural similarity between the ensembles determined by the two methods. However, the folding probability distribution of the conformations belonging to our definition of the equilibrium transition state (0.2<Pfold<0.8) is broader than that displayed by the kinetic transition state

Cooperativity and the origins of rapid, single-exponential kinetics in protein folding

The folding of naturally occurring, single domain proteins is usually well-described as a simple, single exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers we find that, even under conditions where the folding energy landscape is relatively optimized (designed sequences folding at their temperature of maximum folding rate), the folding of protein-like heteropolymers is accelerated when their thermodynamic cooperativity enhanced by enhancing the non-additivity of their energy potentials. At lower temperatures, where kinetic traps presumably play a more significant role in defining folding rates, we observe still greater cooperativity-induced acceleration. Consistent with these observations, we find that the folding kinetics of our computational models more closely approximate single-exponential behavior as their cooperativity approaches optimal levels. These observations suggest that the rapid folding of naturally occurring proteins is, at least in part, consequences of their remarkably cooperative folding

Interview with Mike Kosterlitz

In the summer of 2018, Professor Michael Kosterlitz visited Portugal as a plenary speaker of the FÍSICA2018 conference organised by the Portuguese Physical Society (SPF) and by the University of Beira Interior. FÍSICA 2018 comprised two meetings: the 28th Iberian Meeting for Physics Teaching, and the 21st National Conference of Physics, a biannual event that brings together researchers from all areas of Physics working in Portugal

How determinant is N-terminal to C-terminal coupling for protein folding?

This work investigates the role of N- to C- termini coupling in the folding transition of small, single domain proteins via extensive Monte Carlo simulations of both lattice and off-lattice models. The reported results provide compelling evidence that the existence of native interactions between the terminal regions of the polypeptide chain (i.e. termini coupling) is a major determinant of the height of the free energy barrier that separates the folded from the denatured state in a two-state folding transition, therefore being a critical modulator of protein folding rates and thermodynamic cooperativity. We further report that termini interactions are able to substantially modify the kinetic behavior dictated by the full set of native interactions. Indeed, a native structure of high contact order with ‘‘switched-off’’ termini-interactions actually folds faster than its circular permutant of lowest CO

Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding

The chaperonin complex GroEL–GroES is able to accelerate the folding process of knotted proteins considerably. However, the folding mechanism inside the chaperonin cage is elusive. Here we use a combination of lattice and off-lattice Monte Carlo simulations of simple Go models to study the effect of physical confinement and local flexibility on the folding process of protein model systems embedding a trefoil knot in their native structure. This study predicts that steric confinement plays a specific role in the folding of knotted proteins by increasing the knotting probability for very high degrees of confinement. This effect is observed for protein MJ0366 even above the melting temperature for confinement sizes compatible with the size of the GroEL/GroES chaperonin cage. An enhanced local flexibility produces the same qualitative effects on the folding process. In particular, we observe that knotting probability increases up to 40% in the transition state of protein MJ0366 when flexibility is enhanced. This is underlined by a structural change in the transition state, which becomes devoid of helical content. No relation between the knotting mechanism and flexibility was found in the context of the off-lattice model adopted in this work

Topology in soft and biological matter

International audienceThe last years have witnessed remarkable advances in our understanding of the emergence and consequences of topological constraints in biological and soft matter. Examples are abundant in relation to (bio)polymeric systems and range from the characterization of knots in single polymers and proteins to that of whole chromosomes and polymer melts. At the same time, considerable advances have been made in the description of the interplay between topological and physical properties in complex fluids, with the development of techniques that now allow researchers to control the formation of and interaction between defects in diverse classes of liquid crystals. Thanks to technological progress and the integration of experiments with increasingly sophisticated numerical simulations, topological biological and soft matter is a vibrant area of research attracting scientists from a broad range of disciplines. However, owing to the high degree of specialization of modern science, many results have remained confined to their own particular fields, with different jargon making it difficult for researchers to share ideas and work together towards a comprehensive view of the diverse phenomena at play. Compelled by these motivations, here we present a comprehensive overview of topological effects in systems ranging from DNA and genome organization to entangled proteins, polymeric materials, liquid crystals, and theoretical physics, with the intention of reducing the barriers between different fields of soft matter and biophysics. Particular care has been taken in providing a coherent formal introduction to the topological properties of polymers and of continuum materials and in highlighting the underlying common aspects concerning the emergence, characterization, and effects of topological objects in different systems. The second half of the review is dedicated to the presentation of the latest results in selected problems, specifically, the effects of topological constraints on the viscoelastic properties of polymeric materials; their relation with genome organization; a discussion on the emergence and possible effects of knots and other entanglements in proteins; the emergence and effects of topological defects and solitons in complex fluids. This review is dedicated to the memory of Marek Cieplak