Trinh Xuan Hoang

Geometry and symmetry presculpt the free-energy landscape of proteins

We present a simple physical model that demonstrates that the native-state folds of proteins can emerge on the basis of considerations of geometry and symmetry. We show that the inherent anisotropy of a chain molecule, the geometrical and energetic constraints placed by the hydrogen bonds and sterics, and hydrophobicity are sufficient to yield a free-energy landscape with broad minima even for a homopolymer. These minima correspond to marginally compact structures comprising the menu of folds that proteins choose from to house their native states in. Our results provide a general framework for understanding the common characteristics of globular proteins.

Universality Classes in Folding Times of Proteins

Molecular dynamics simulations in simplified models allow one to study the scaling properties of folding times for many proteins together under a controlled setting. We consider three variants of the Go models with different contact potentials and demonstrate scaling described by power laws and no correlation with the relative contact order parameter. We demonstrate existence of at least three kinetic universality classes that are correlated with the types of structure: the alpha-, alpha-beta-, and beta- proteins have the scaling exponents of approximately 1.7, 2.5, and 3.2, respectively. The three classes merge into one when the contact range is truncated at a reasonable value. We elucidate the role of the potential associated with the chirality of a protein.

Sequencing of folding events in Go-type proteins

We have studied folding mechanisms of three small globular proteins: crambin, chymotrypsin inhibitor 2 (CI2), and the fyn Src Homology 3 domain (SH3) which are modeled by a Go-type Hamiltonian with the Lennard-Jones interactions. It is shown that folding is dominated by a well-defined sequencing of events as determined by establishment of particular contacts. The order of events depends primarily on the geometry of the native state. Variations in temperature, coupling strengths, and viscosity affect the sequencing scenarios to a rather small extent. The sequencing is strongly correlated with the distance of the contacting amino acids along the sequence. Thus α helices get established first. Crambin is found to behave like a single-route folder, whereas in CI2 and SH3 the folding trajectories are more diversified. The folding scenarios for CI2 and SH3 are consistent with experimental studies of their transition states.

Molecular dynamics of folding of secondary structures in Go-type models of proteins

We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic amino acid–amino acid potential is Lennard–Jones for the native contacts and a soft repulsion for the non-native contacts. The interactions are chosen to make the target secondary structure be the native state of the system. We provide a thorough equilibrium and kinetic characterization of the sequences through the molecular dynamics simulations with the Langevin noise. Models with the steric constraints are found to be better folders and to be more stable, especially in the case of the β structures. Phononic spectra for vibrations around the native states have low frequency gaps that correlate with the thermodynamic stability. Folding of the secondary structures proceeds through a well-defined sequence of events. For instance, α helices fold from the ends first. The closer to the native state, the faster establishment of the contacts. Increas...

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, differences in bonding geometry lead to different sensitivity to temperature and different changes in the unfolding pattern. Due to its special native‐state geometry, titin is much more thermally and elastically 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 distance between the amino acids that form the native contact. Proteins 2004.

Folding and stretching in a Go‐like model of titin

Mechanical stretching of the I27 domain of titin and of its double and triple repeats are studied through molecular dynamics simulations of a Go‐like model with Lennard‐Jones contact interactions. We provide a thorough characterization of the system and correlate the sequencing of the folding and unraveling events with each other and with the contact order. The roles of cantilever stiffness and pulling rate are studied. Unraveling of tandem titin structures has a serial nature. The force‐displacement curves in this coarse‐grained model are similar to those obtained through all atom calculations. Proteins 2002;49:114–124.

Thermal folding and mechanical unfolding pathways of protein secondary structures.

Mechanical stretching of secondary structures is studied through molecular dynamics simulations of a Go‐like model. Force versus displacement curves are studied as a function of the stiffness and velocity of the pulling device. The succession of stretching events, as measured by the order in which contacts are ruptured, is compared to the sequencing of events during thermal folding and unfolding. Opposite cross‐correlations are found for an α‐helix and a β‐hairpin structure. In a tandem of two α‐helices, the two constituent helices unravel nearly simultaneously. A simple condition for simultaneous versus sequential unraveling of repeat units is presented. Proteins 2002;49:104–113.

Scaling of Folding Properties in Simple Models of Proteins

Scaling of folding properties of proteins is studied in a toy system — the lattice Go model with various two- and three-dimensional geometries of the maximally compact native states. Characteristic folding times grow as power laws with the system size. The corresponding exponents are not universal. Scaling of the thermodynamic stability also indicates size-related deterioration of the folding properties.

Unified perspective on proteins: a physics approach.

We study a physical system which, while devoid of the complexity one usually associates with proteins, nevertheless displays a remarkable array of proteinlike properties. The constructive hypothesis that this striking resemblance is not accidental not only leads to a unified framework for understanding protein folding, amyloid formation, and protein interactions but also has implications for natural selection.

Energy landscapes, supergraphs, and "folding funnels" in spin systems.

Dynamical connectivity graphs, which describe dynamical transition rates between local energy minima of a system, can be displayed against the background of a disconnectivity graph which represents the energy landscape of the system. The resulting supergraph describes both dynamics and statics of the system in a unified coarse-grained sense. We give examples of the supergraphs for several two-dimensional spin and protein-related systems. We demonstrate that disordered ferromagnets have supergraphs akin to those of model proteins whereas spin glasses behave like random sequences of amino acids that fold badly.