Evolved Minimal Frustration in Multifunctional Biomolecules

Protein folding is often viewed in terms of a funneled potential or free energy landscape. A variety of experiments now indicate the existence of multifunnel landscapes, associated with multifunctional biomolecules. Here, we present evidence that these systems have evolved to exhibit the minimal number of funnels required to fulfill their cellular functions, suggesting an extension to the principle of minimum frustration. We find that minimal disruptive mutations result in additional funnels, and the associated structural ensembles become more diverse. The same trends are observed in an atomic cluster. These observations suggest guidelines for rational design of engineered multifunctional biomolecules

Energy Landscapes for the Aggregation of Aβ_17–42

The aggregation of the Aβ peptide (Aβ_1–42) to form fibrils is a key feature of Alzheimer’s disease. The mechanism is thought to be a nucleation stage followed by an elongation process. The elongation stage involves the consecutive addition of monomers to one end of the growing fibril. The aggregation process proceeds in a stop-and-go fashion and may involve off-pathway aggregates, complicating experimental and computational studies. Here we present exploration of a well-defined region in the free and potential energy landscapes for the Aβ_17–42 pentamer. We find that the ideal aggregation process agrees with the previously reported dock-lock mechanism. We also analyze a large number of additional stable structures located on the multifunnel energy landscape, which constitute kinetic traps. The key contributors to the formation of such traps are misaligned strong interactions, for example the stacking of F19 and F20, as well as entropic contributions. Our results suggest that folding templates for aggregation are a necessity and that aggregation studies could employ such species to obtain a more detailed description of the process

Kinetics of Molecular Diffusion and Self-Assembly: Glycine on Cu{110}

Nanofabrication and the growth of self-assembled monolayers (SAM) of organic molecules are increasingly important in various industries, including microelectronics and health care. Glycine adsorbed on Cu{110} provides a good model with a rich phenomenological space to explore and understand the self-assembly of more complex amino acids. Our focus is on (a) the dynamics exhibited by glycine molecules already adsorbed on Cu{110} when diffusing on the metal surface and (b) the chemical kinetics of how these molecules form clusters, networks, and islands. The stochastic discrete event algorithm we employ can be viewed as a multiscale approach, based on density functional energies and transition barriers. The method extends from the femtosecond time-scale of molecular rotations to the nano- and microsecond range of molecular self-assembly. Hydrogen-bonds and van der Waals forces play a crucial role in pattern formation. Investigations of chemical kinetics show that enantiopure, homochiral islands are an intermediate step during the formation process of larger stable racemic, heterochiral islands, especially when two islands merge. At lower temperature, defects stabilize mainly homochiral clusters and prevent the molecules from synchronizing their footprint orientation, in contrast to higher temperature. On the way, we solve the long-standing puzzle of how the pseudocentered (3 × 2) enantiopure clusters can have glide plane symmetry. We end with a comparison to similar amino acids, such as alanine and proline. The results provide insight into mechanisms for fine-tuning the self-organization of organic molecules on metal surfaces

Evolution of the Potential Energy Landscape with Static Pulling Force for Two Model Proteins

The energy landscape is analyzed for off-lattice bead models of protein L and protein G as a function of a static pulling force. Two different pairs of attachment points (pulling directions) are compared in each case, namely, residues 1/56 and 10/32. For the terminal residue pulling direction 1/56, the distinct global minimum structures are all extended, aside from the compact geometry that correlates with zero force. The helical turns finally disappear at the highest pulling forces considered. For the 10/32 pulling direction, the changes are more complicated, with a variety of competing arrangements for beads outside the region where the force is directly applied. These alternatives produce frustrated energy landscapes, with low-lying minima separated by high barriers. The calculated folding pathways in the absence of force are in good agreement with previous work. The N-terminal hairpin folds first for protein L and the C-terminal hairpin for protein G, which exhibits an intermediate. However, for a relatively low static force, where the global minimum retains its structure, the folding mechanisms change, sometimes dramatically, depending on the protein and the attachment points. The scaling relations predicted by catastrophe theory are found to hold in the limit of short path lengths

Clusters of Coarse-Grained Water Molecules

Global optimization for molecular clusters can be significantly more difficult than for atomic clusters because of the coupling between orientational and translational degrees of freedom. A coarse-grained representation of the potential can reduce the complexity of this problem, while retaining the essential features of the intermolecular interactions. In this study, we use a basin-hopping algorithm to locate putative global minima for clusters of coarse-grained water molecules modeled using a monatomic water potential for cluster sizes 3 ≤ <i>N</i> ≤ 55. We characterize these structures and identify structural trends using ideas from graph theory. The agreement with atomistic results and experiment is rather patchy, which we attribute to the tetrahedral bias in the three-body potential that results in too few nearest neighbor contacts and premature emergence of bulk-like structure. In spite of this issue, the results offer further useful insight into the relationship between the structure of clusters and bulk phases, and the mathematical form of a widely used model potential

Conformational Energy Landscape of the Ritonavir Molecule

Conformational polymorphism of ritonavir, a well-known pharmaceutical drug, is intricately linked to its efficacy in the treatment of acquired immunodeficiency syndrome (AIDS). Polymorphic transition from the crystalline form I to form II leads to the loss of bioactivity. The constituent ritonavir molecules adopt a trans configuration about the carbamate torsion angle in the form I crystal, and a cis configuration in the form II crystal. Investigating the energetics and mechanistic features of conformational transitions at the single molecule level is a key step toward decoding the complex features of the solid state polymorphism. In this work, we employ the energy landscape framework to investigate the conformational transitions of an isolated ritonavir molecule. The landscape is explored using discrete path sampling (DPS) and visualized in terms of disconnectivity graphs. We identify two distinct funnels corresponding to the two molecular forms that are identified by crystallography. The two regions can be reliably distinguished using the carbamate torsion angle, and the corresponding interconversion rates are predicted to follow Arrhenius behavior. The results provide mechanistic insight into pathways for cis ↔ trans interconversion at the molecular level and may also help in elucidating the polymorphic transitions in the crystal state

Energy Landscapes, Folding Mechanisms, and Kinetics of RNA Tetraloop Hairpins

RNA hairpins play a pivotal role in a diverse range of cellular functions, and are integral components of ribozymes, mRNA, and riboswitches. However, the mechanistic and kinetic details of RNA hairpin folding, which are key determinants of most of its biological functions, are poorly understood. In this work, we use the discrete path sampling (DPS) approach to explore the energy landscapes of two RNA tetraloop hairpins, and provide insights into their folding mechanisms and kinetics in atomistic detail. Our results show that the potential energy landscapes have a distinct funnel-like bias toward the folded hairpin state, consistent with efficient structure-seeking properties. Mechanistic and kinetic information is analyzed in terms of kinetic transition networks. We find microsecond folding times, consistent with temperature jump experiments, for hairpin folding initiated from relatively compact unfolded states. This process is essentially driven by an initial collapse, followed by rapid zippering of the helix stem in the final phase. Much lower folding rates are predicted when the folding is initiated from extended chains, which undergo longer excursions on the energy landscape before nucleation events can occur. Our work therefore explains recent experiments and coarse-grained simulations, where the folding kinetics exhibit precisely this dependency on the initial conditions

A Local Rigid Body Framework for Global Optimization of Biomolecules

We present a local rigid body framework for simulations of biomolecules. In this framework, arbritrary sets of atoms may be treated as rigid bodies. Such groupings reduce the number of degrees of freedom, which can result in a significant reduction of computational time. As benchmarks, we consider global optimization for the tryptophan zipper (trpzip 1, 1LE0; using the CHARMM force field) and chignolin (1UAO; using the AMBER force field). We use a basin-hopping algorithm to find the global minima and compute the mean first encounter time from random starting configurations with and without the local rigid body framework. Minimal groupings are used, where only peptide bonds, termini, and side chain rings are considered rigid. Finding the global minimum is 4.2 and 2.5 times faster, respectively, for trpzip 1 and chignolin, within the local rigid body framework. We further compare <i>O</i>(10⁵) low-lying local minima to the fully relaxed unconstrained representation for trpzip 1 at different levels of rigidification. The resulting Pearson correlation coefficients, and thus the apparent intrinsic rigidity of the various groups, appear in the following order: side chain rings > termini > trigonal planar centers ≥ peptide bonds ≫ side chains. This approach is likely to be even more beneficial for structure prediction in larger biomolecules

What Makes Telomeres Unique?

Telomeres are repetitive nucleotide sequences, which are essential for protecting the termini of chromosomes. Thousands of such repetitions are necessary to maintain the stability of the whole chromosome. Several similar repeated telomeric sequences have been found in different species, but why has nature chosen them? What features do telomeres have in common? In this article, we study the physical properties of human-like (TTAGGG), plant (TTTAGG), insect (TTAGG), and Candida guilermondi (GGTGTAC) telomeres in comparison with seven control, nontelomeric sequences. We used steered molecular dynamics with the nucleic acid united residue (NARES) coarse-grained force field, which we compared with the all-atom AMBER14 force field and experimental data. Our results reveal important features in all of the telomeric sequences, including their exceptionally high mechanical resistance and stability to untangling and stretching, compared to those of nontelomeric sequences. We find that the additional stability of the telomeres comes from their ability to form triplex structures and wrap around loose chains of linear DNA by regrabbing the chain. We find that, with slower pulling speed, regrabbing and triplex formation is more frequent. We also found that some of the sequences can form triplexes experimentally, such as TTTTTCCCC, and can mimic telomeric properties

A Local Rigid Body Framework for Global Optimization of Biomolecules

We present a local rigid body framework for simulations of biomolecules. In this framework, arbritrary sets of atoms may be treated as rigid bodies. Such groupings reduce the number of degrees of freedom, which can result in a significant reduction of computational time. As benchmarks, we consider global optimization for the tryptophan zipper (trpzip 1, 1LE0; using the CHARMM force field) and chignolin (1UAO; using the AMBER force field). We use a basin-hopping algorithm to find the global minima and compute the mean first encounter time from random starting configurations with and without the local rigid body framework. Minimal groupings are used, where only peptide bonds, termini, and side chain rings are considered rigid. Finding the global minimum is 4.2 and 2.5 times faster, respectively, for trpzip 1 and chignolin, within the local rigid body framework. We further compare <i>O</i>(10⁵) low-lying local minima to the fully relaxed unconstrained representation for trpzip 1 at different levels of rigidification. The resulting Pearson correlation coefficients, and thus the apparent intrinsic rigidity of the various groups, appear in the following order: side chain rings > termini > trigonal planar centers ≥ peptide bonds ≫ side chains. This approach is likely to be even more beneficial for structure prediction in larger biomolecules