Yang-Lee zeros and the helix-coil transition in a continuum model of polyalanine

We calculate the Yang-Lee zeros for characteristic temperatures of the helix-coil transition in a continuum model of polyalanine. The distribution of these zeros differs from predictions of the Zimm-Bragg theory and supports recent claims that polyalanine exhibits a true phase transition. New estimates for critical exponents are presented and the relation of our results to the Lee-Yang theorem is discussed.Comment: 15 pages and 5 figure

Numerical comparison of two approaches for the study of phase transitions in small systems

We compare two recently proposed methods for the characterization of phase transitions in small systems. The validity and usefulness of these approaches are studied for the case of the q=4 and q=5 Potts model, i.e. systems where a thermodynamic limit and exact results exist. Guided by this analysis we discuss then the helix-coil transition in polyalanine, an example of structural transitions in biological molecules.Comment: 16 pages and 7 figure

Structure and mechanism of maximum stability of isolated alpha-helical protein domains at a critical length scale

The stability of alpha helices is important in protein folding, bioinspired materials design, and controls many biological properties under physiological and disease conditions. Here we show that a naturally favored alpha helix length of 9 to 17 amino acids exists at which the propensity towards the formation of this secondary structure is maximized. We use a combination of thermodynamical analysis, well-tempered metadynamics molecular simulation and statistical analyses of experimental alpha helix length distributions and find that the favored alpha helix length is caused by a competition between alpha helix folding, unfolding into a random coil and formation of higher-order tertiary structures. The theoretical result is suggested to be used to explain the statistical distribution of the length of alpha helices observed in natural protein structures. Our study provides mechanistic insight into fundamental controlling parameters in alpha helix structure formation and potentially other biopolymers or synthetic materials. The result advances our fundamental understanding of size effects in the stability of protein structures and may enable the design of de novo alpha-helical protein materials.United States. Air Force Office of Scientific Research. Young Investigator ProgramNational Science Foundation (U.S.)Multidisciplinary University Research Initiative (MURI

Structure and stability of helices in square-well homopolymers

Recently, it has been demonstrated [Magee et al., Phys. Rev. Lett. 96, 207802 (2006)] that isolated, square-well homopolymers can spontaneously break chiral symmetry and freeze into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics, combined with an optimized parallel tempering scheme, to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of the polymer govern the details of the helix structure. The width of the square well (proportional to lambda) is found to control the radius of the helix, which decreases with increasing well width until the polymer forms a coiled sphere for sufficiently large wells. The helices are found to be stable for only a window of molecular weights. If the polymer is too short, the helix will not form. If the polymer is too long, the helix is no longer the minimum energy structure, and other folded structures will form. The size of this window is governed by the chain stiffness, which in this model is a function of the ratio of the monomer size to the bond length. Outside this window, the polymer still freezes into a locked structure at low temperature, however, unless the chain is sufficiently stiff, this structure will not be unique and is similar to a glassy state.Comment: Submitted to Physical Review

Effect of Surface Curvature and Chemistry on Protein Stability, Adsorption and Aggregation

Enzyme immobilization has been of great industrial importance because of its use in various applications like bio-fuel cells, bio-sensors, drug delivery and bio-catalytic films. Although research on enzyme immobilization dates back to the 1970's, it has been only in the past decade that scientists have started to address the problems involved systematically. Most of the previous works on enzyme immobilization have been retrospective in nature i.e enzymes were immobilized on widely used substrates without a compatibility study between the enzyme and the substrate. Consequently, most of the enzymes lost their activity upon immobilization onto these substrates due to many governing factors like protein-surface and inter-protein interactions. These interactions also play a major role biologically in cell signaling, cell adhesion and inter-protein interactions specifically is believed to be the major cause for neurodegenerative diseases like Alzheimer's and Parkinson's disease. Therefore understanding the role of these forces on proteins is the need of the hour. In my current research, I have mainly focused on two factors a) Surface Curvature b) Surface Chemistry as both of these play a pivotal role in influencing the activity of the enzymes upon immobilization. I study the effect of these factors computationally using a stochastic method known as Monte Carlo simulations. My research work carried out in the frame work of a Hydrophobic-Polar (HP) lattice model for the protein shows that immobilizing enzymes inside moderately hydrophilic or hydrophobic pores results in an enhancement of the enzymatic activity compared to that in the bulk. Our results also indicate that there is an optimal value of surface curvature and hydrophobicity/hydrophilicity where this enhancement of enzymatic activity is highest. Further, our results also show that immobilization of enzymes inside hydrophobic pores of optimal sizes are most effective in mitigating protein-aggregation. These results provide us a rationale to understand the role of chaperonins in protein folding and disaggregation. Our results indicate that strong protein-surface interactions and confinement inducement stability inside pores makes it best suitable for enzyme immobilization

Minimal model for the secondary structures and conformational conversions in proteins

Better understanding of protein folding process can provide physical insights on the function of proteins and makes it possible to benefit from genetic information accumulated so far. Protein folding process normally takes place in less than seconds but even seconds are beyond reach of current computational power for simulations on a system of all-atom detail. Hence, to model and explore protein folding process it is crucial to construct a proper model that can adequately describe the physical process and mechanism for the relevant time scale. We discuss the reduced off-lattice model that can express α-helix and β-hairpin conformations defined solely by a given sequence in order to investigate a protein folding mechanism of conformations such as a β-hairpin and also to investigate conformational conversions in proteins. The first two chapters introduce and review essential concepts in protein folding modelling physical interaction in proteins, various simple models, and also review computational methods, in particular, the Metropolis Monte Carlo method, its dynamic interpretation and thermodynamic Monte Carlo algorithms. Chapter 3 describes the minimalist model that represents both α-helix and β-sheet conformations using simple potentials. The native conformation can be specified by the sequence without particular conformational biases to a reference state. In Chapter 4, the model is used to investigate the folding mechanism of β-hairpins exhaustively using the dynamic Monte Carlo and a thermodynamic Monte Carlo method an effcient combination of the multicanonical Monte Carlo and the weighted histogram analysis method. We show that the major folding pathways and folding rate depend on the location of a hydrophobic. The conformational conversions between α-helix and β-sheet conformations are examined in Chapter 5 and 6. First, the conformational conversion due to mutation in a non-hydrophobic system and then the conformational conversion due to mutation with a hydrophobic pair at a different position at various temperatures are examined

Development of crystallographic methods for phasing highly modulated macromolecular structures

[eng] Pathologies that result in highly modulated intensities in macromolecular crystal structures pose a challenge for structure solution. To address this issue two studies have been performed: a theoretical study of one of these pathologies, translational non- crystallographic symmetry (tNCS), and a practical study of paradigms of highly modulated macromolecular structures, coiled-coils. tNCS is a structural situation in which multiple, independent copies of a molecular assembly are found in similar orientations in the crystallographic asymmetric unit. Structure solution is problematic because the intensity modulations caused by tNCS cause the intensity distribution to differ from a Wilson distribution. If the tNCS is properly detected and characterized, expected intensity factors for each reflection that model the modulations observed in the data can be refined against a likelihood function to account for the statistical effects of tNCS. In this study, a curated database of 80482 protein structures from the PDB was analysed to investigate how tNCS manifests in the Patterson function. These studies informed the algorithm for detection of tNCS, which includes a method for detecting the tNCS order in any commensurate modulation. In the context of automated structure solution pipelines, the algorithm generates a ranked list of possible tNCS associations in the asymmetric unit, which can be explored to efficiently maximize the probability of structure solution. Coiled-coils are ubiquitous protein folding motifs present in a wide range of proteins that consist of two or more α-helices wrapped around each other to form a supercoil. Despite the apparent simplicity of their architecture, solution by molecular replacement is challenging due to the helical irregularities found in these domains, tendency to form fibers, large dimensions in their typically anisometric asymmetric units, low-resolution and anisotropic diffraction. In addition, the internal symmetry of the helices and their alignment in preferential directions gives rise to systematic overlap of Patterson vectors, a Patterson map that indicates tNCS is present, and intensity modulations similar to those in true tNCS. In this study, we have explored fragment phasing on a pool of 150 coiled-coils with ARCIMBOLDO_LITE, an ab initio phasing approach that combines fragment location with Phaser and density modification and autotracing with SHELXE. The results have been used to identify limits and bottlenecks in coiled-coil phasing that have been addressed in a specific mode for solving coiled-coils, allowing the solution of 95% of the test set and four previously unknown structures, and extending the resolution limit from 2.5 Å to 3.0 Å