Lattice Protein Research Articles

A First Look at Lattice Effects in Coarse-Grained Protein Models via Wang-Landau Simulations

In order to study the effects of lattice constraints on coarse-grained protein models, we apply Wang-Landau sampling to the continuum analogue of the hydrophobic-polar (HP) lattice protein model. The continuum version is inspired by the AB polymer model but incorporates potentials chosen specifically to mimic those of the lattice case. Because of their relative simplicity, both the lattice and continuum models offer significant computational advantage over all-atom simulations, but the impact of the additional lattice constraint on generic folding behavior is unknown. In this preliminary study, we compare and contrast thermodynamics during the folding process of the continuum model to the original HP lattice protein model for sequences mapped from Crambin, a 46 amino acid plant protein. We find that the folding process for both of these coarse-grained models is quite similar, with major structural transitions occurring at almost exactly the same temperatures.

Crambin Homologues in the H0P Lattice Model

To compare folding behavior among lattice proteins which have similar corresponding structures in nature, Crambin homologues are tested in the semi-flexible H0P lattice model using replica-exchange Wang-Landau sampling. Our simulation shows that, at low temperature, these lattice homologues have two common signals in their specific heat curves, implying similarity in the thermodynamic behaviors; while the structural behaviors are more diverse, showing the different stability of their ground state structures at very low temperature. The ground state structures of different homologues can also vary dramatically.

Nemaline myopathies: a current view

Nemaline myopathies are a heterogenous group of congenital myopathies caused by de novo, dominantly or recessively inherited mutations in at least twelve genes. The genes encoding skeletal α-actin (ACTA1) and nebulin (NEB) are the commonest genetic cause. Most patients have congenital onset characterized by muscle weakness and hypotonia, but the spectrum of clinical phenotypes is broad, ranging from severe neonatal presentations to onset of a milder disorder in childhood. Most patients with adult onset have an autoimmune-related myopathy with a progressive course. The wide application of massively parallel sequencing methods is increasing the number of known causative genes and broadening the range of clinical phenotypes. Nemaline myopathies are identified by the presence of structures that are rod-like or ovoid in shape with electron microscopy, and with light microscopy stain red with the modified Gömöri trichrome technique. These rods or nemaline bodies are derived from Z lines (also known as Z discs or Z disks) and have a similar lattice structure and protein content. Their shape in patients with mutations in KLHL40 and LMOD3 is distinctive and can be useful for diagnosis. The number and distribution of nemaline bodies varies between fibres and different muscles but does not correlate with severity or prognosis. Additional pathological features such as caps, cores and fibre type disproportion are associated with the same genes as those known to cause the presence of rods. Animal models are advancing the understanding of the effects of various mutations in different genes and paving the way for the development of therapies, which at present only manage symptoms and are aimed at maintaining muscle strength, joint mobility, ambulation, respiration and independence in the activities of daily living.

Learning protein constitutive motifs from sequence data.

Statistical analysis of evolutionary-related protein sequences provides information about their structure, function, and history. We show that Restricted Boltzmann Machines (RBM), designed to learn complex high-dimensional data and their statistical features, can efficiently model protein families from sequence information. We here apply RBM to 20 protein families, and present detailed results for two short protein domains (Kunitz and WW), one long chaperone protein (Hsp70), and synthetic lattice proteins for benchmarking. The features inferred by the RBM are biologically interpretable: they are related to structure (residue-residue tertiary contacts, extended secondary motifs (α-helixes and β-sheets) and intrinsically disordered regions), to function (activity and ligand specificity), or to phylogenetic identity. In addition, we use RBM to design new protein sequences with putative properties by composing and 'turning up' or 'turning down' the different modes at will. Our work therefore shows that RBM are versatile and practical tools that can be used to unveil and exploit the genotype-phenotype relationship for protein families.

Studying the Folding Behavior of a 3D Lattice Protein under Oscillatory Conditions

By spontaneously and reliably folding from a primary amino acid sequence into a highly specific native geometry with bioactive functionalities, the natively-folded protein plays a significant role in fundamental biological processes. Protein folding is governed by the interactions between residues and between residues and the environment. The structural stability and bio-functionality of proteins depend on physiological environmental factors, such as temperature, acidity, crowding, and ionic strength. In addition, the local cellular environment is highly dynamic -- both spatially and temporally heterogeneous. In this work, we employed a 3D lattice protein model to investigate the changes to the equilibrium folded state properties and to the kinetics of folding pathways for small proteins that fold amidst ongoing temperature oscillations.

Simulating the Folding Trajectories of Lattice Proteins within an Oscillatory Environment

Simulating the Folding Trajectories of Lattice Proteins within an Oscillatory Environment

Simulating the Folding States of Lattice Proteins within an Oscillatory Environment

Simulating the Folding States of Lattice Proteins within an Oscillatory Environment

On-Chip Hardware Accelerator for Automated Diagnosis Through Human–Machine Interactions in Healthcare Delivery

The automated diagnosis helps us better understand the complex landscape of diseases, leading to more effective, early and reliable medical diagnosis and therapy. The human–machine interactions in healthcare delivery relying on automated cyber-physical systems (ACPSs) play an important role in the automated diagnosis. Currently, the multicore accelerator used for ACPS has utilized the network-on-chip (NoC) for personalized healthcare. However, the discrete cores based on NoC are affected by limited computation speed, since the data have to pass through an electrical interconnect. In this paper, we propose a novel optical NoC (ONoC) solution of designing discrete cores to quickly understand biomarkers for early detecting abnormal pathophysiology, such as the deviation from the protein’s native state. We analyze the performance of our ONoC-based ACPS accelerator for personalized healthcare by virtue of the tested proteins widely adopted in the lattice protein model. Our mathematical analysis and simulation results demonstrate that: 1) the chip area becomes smaller than a traditional design, which makes the personalized healthcare product more convenient; 2) the computation speed is promoted, resulting in the rapid understanding of biomarkers; and 3) we improve the data transmission reliability through accurately capturing the photonic effect so that desirable human–machine interactions can be guaranteed. Note to Practitioners —We design an on-chip hardware accelerator for automated diagnosis and personalized healthcare by predicting biological protein folding. The simulation results based on the lattice protein model can well guide the practitioners to design a more convenient and reliable product quickly detecting the biomarker, such as the deviation from the protein’s native state.

Elucidating thermal behavior, native contacts, and folding funnels of simple lattice proteins using replica exchange Wang-Landau sampling.

We studied the folding behavior of two coarse-grained, lattice models, the HP (hydrophobic-polar) model and the semi-flexible H0P model, whose 124 monomer long sequences were derived from the protein Ribonuclease A. Taking advantage of advanced parallel computing techniques, we applied replica exchange Wang-Landau sampling and calculated the density of states over the models entire energy ranges to high accuracy. We then determined both energetic and structural quantities in order to elucidate the folding behavior of each model completely. As a result of sufficiently long sequences and model complexity, yet computational accessibility, we were able to depict distinct free energy folding funnels for both models. In particular, we found that the HP model folds in a single-step process with a very highly degenerate native state and relatively flat low temperature folding funnel minimum. By contrast, the semi-flexible H0P model folds via a multi-step process and the native state is almost four orders of magnitude less degenerate than that for the HP model. In addition, for the H0P model, the bottom of the free energy folding funnel remains rough, even at low temperatures.

The role of chain-stiffness in lattice protein models: A replica-exchange Wang-Landau study.

Using Monte Carlo simulations, we investigate simple, physically motivated extensions to the hydrophobic-polar lattice protein model for the small (46 amino acid) protein Crambin. We use two-dimensional replica-exchange Wang-Landau sampling to study the effects of a bond angle stiffness parameter on the folding and uncover a new step in the collapse process for particular values of this stiffness parameter. A physical interpretation of the folding is developed by analysis of changes in structural quantities, and the free energy landscape is explored. For these special values of stiffness, we find non-degenerate ground states, a property that is consistent with behavior of real proteins, and we use these unique ground states to elucidate the formation of native contacts during the folding process. Through this analysis, we conclude that chain-stiffness is particularly influential in the low energy, low temperature regime of the folding process once the lattice protein has partially collapsed.

Fusion to Tetrahymena thermophila granule lattice protein 1 confers solubility to sexual stage malaria antigens in Escherichia coli

A transmission-blocking vaccine targeting the sexual stages of Plasmodium species could play a key role in eradicating malaria. Multiple studies have identified the P. falciparum proteins Pfs25 and Pfs48/45 as prime targets for transmission-blocking vaccines. Although significant advances have been made in recombinant expression of these antigens, they remain difficult to produce at large scale and lack strong immunogenicity as subunit antigens. We linked a self-assembling protein, granule lattice protein 1 (Grl1p), from the ciliated protozoan, Tetrahymena thermophila, to regions of the ectodomains of either Pfs25 or Pfs48/45. We found that resulting protein chimera could be produced in E. coli as nanoparticles that could be readily purified in soluble form. When produced in the E. coli SHuffle strain, fusion to Grl1p dramatically increased solubility of target antigens while at the same time directing the formation of particles with diameters centering on 38 and 25 nm depending on the antigen. In a number of instances, co-expression with chaperone proteins and induction at a lower temperature further increased expression and solubility. Based on Western blotting and ELISA analysis, Pfs25 and Pfs48/45 retained their transmission-blocking epitopes within E. coli-derived particles, and the particles themselves elicited strong antibody responses in rabbits when given with an aluminum-based adjuvant. Antibodies against Pfs25-containing nanoparticles blocked parasite transmission in standard membrane-feeding assays. In conclusion, fusion to Grl1p can act as a solubility enhancer for proteins with limited solubility while retaining correct folding, which may be useful for applications such as the production of vaccines and other biologics.

Non-deterministic genotype-phenotype maps of biological self-assembly(a)(a)Contribution to the Focus Issue Evolutionary Modeling and Experimental Evolution edited by José Cuesta, Joachim Krug and Susanna Manrubia.

In recent years large-scale studies of different genotype-phenotype (GP) maps, including those of RNA secondary structure, lattice proteins, and self-assembling Polyominoes, have revealed that these maps share structural properties. Such properties include skewed distributions of genotypes per phenotype, negative correlations between genotypic evolvability and robustness, positive correlations between phenotypic evolvability and robustness, and the fact that a majority of phenotypes can be reached from any genotype in just a few mutations. Traditionally this research has focused on deterministic GP maps, meaning that a single sequence maps to a single outcome. Here, by contrast, we consider non-deterministic GP maps, in which a single sequence can map to multiple outcomes. Most GP maps already contain such sequences, but these are typically classified as a single, undesirable phenotype for the reason that biological processes typically rely on robust transformation of sequences into biological structures and functions. For the same reason, however, non-deterministic phenotypes play an important role in diseases, and a deeper understanding of non-deterministic GP maps may therefore inform the study of their evolution. By redefining deterministic and non-deterministic Polyomino self-assembly phenotypes in terms of the pattern of possible interactions rather than the final structure we are able to calculate GP map properties for the non-deterministic part of the map, and find that they match those found in deterministic maps.

The characteristics of molten globule states and folding pathways strongly depend on the sequence of a protein

ABSTRACTThe majority of proteins perform their cellular function after folding into a specific and stable native structure. Additionally, for many proteins less compact ‘molten globule’ states have been observed. Current experimental observations show that the molten globule state can show varying degrees of compactness and solvent accessibility; the underlying molecular cause for this variation is not well understood. While the specificity of protein folding can be studied using protein lattice models, current design procedures for these models tend to generate sequences without molten globule-like behaviour. Here we alter the design process so the distance between the molten globule ensemble and the native structure can be steered; this allows us to design protein sequences with a wide range of folding pathways, and sequences with well-defined heat-induced molten globules. Simulating these sequences we find that (1) molten globule states are compact, but have less specific configurations compared to the folded state, (2) the nature of the molten globule state is highly sequence dependent, (3) both two-state and multi-state folding proteins may show heat-induced molten globule states, as observed in heat capacity curves. The varying nature of the molten globules and typical heat capacity curves associated with the transitions closely resemble experimental observations.

Influence of substrate pattern on the adsorption of HP lattice proteins

With the highly simplified hydrophobic-polar model representation of a protein, we can study essential qualitative physics without an unnecessarily large computational overhead. Using Wang-Landau sampling in conjunction with a set of efficient Monte Carlo trial moves, we studied the adsorption of short HP lattice proteins on various simple patterned substrates and in particular for checkered patterned surfaces. A set of single-site mutated HP proteins is used to investigate the role of hydrophobicity of a protein chain and surface pattern for substrates with various pattern cell sizes relative to the protein’s native configuration. For most cases, we found that the adsorption transition occurs at a lower temperature, while the hydrophobic core formation is less affected. The flattening procedure after the HP protein is adsorbed is more sensitive to the change in surface patterns and single-site mutations. These observations stay valid for both strongly and weakly attractive surfaces.

Catalytic activation of β-arrestin by GPCRs.

β-arrestins are critical regulator and transducer proteins for G protein-coupled receptors (GPCRs). Cellular β-arrestin function is presently thought to require stable and stoichiometric GPCR/β-arrestin scaffold complex formation driven by the phosphorylated GPCR tail. We demonstrate a distinct and additional mechanism that does not require stable GPCR/β-arrestin scaffolding or the GPCR tail. Instead, it is activated by transient engagement of the GPCR core that destabilizes a conserved inter-domain charge network in β-arrestin. This promotes capture of β-arrestin at the plasma membrane and accumulation in clathrin-coated endocytic structures (CCSs) after GPCR dissociation, requiring a series of β-arrestin interactions with membrane phosphoinositides and CCS lattice proteins. β-arrestin clustering in CCSs without its upstream activating GPCR is associated with a β-arrestin-dependent component of the cellular ERK (Extracellular signal-regulated kinase) response. These results delineate a discrete mechanism of cellular β-arrestin function that is activated catalytically by GPCRs.

Effects of Stiffness on Low Energy States in a Lattice Protein Model for Crambin

Many studies inspired by the HP lattice protein model have helped to confirm the importance of the hydrophobic “driving force” during folding. Unfortunately, the high level of coarse-graining inherent to this model leads to significant limitations; results from proteins studied under the framework of the HP model fail to reproduce many, sometimes significant, details of the folding process, and the obtained ground states are usually highly degenerate. We propose simple modifications to the original HP model, with the goal of reducing degeneracy and gaining insight into how other interaction parameters influence the folding, while retaining the computational simplicity of lattice models. Namely, we introduce a “neutral” monomer (0) to further divide the hydrophobicity scale and an energetic penalty for “bends” in the protein to account for rigidity. Using replica-exchange Wang-Landau (REWL) sampling and suitable Monte Carlo trial moves, we obtain a unique (non-degenerate) ground state for the new lattice mapping of Crambin (a small, 46 amino acid plant protein), and investigate the effects of stiffness on the folding and the low energy structures.

Grl1 Protein is a Candidate K Antigen in Tetrahymena thermophila

In Tetrahymena, K antigens associate only with mature basal bodies and are expected to play important roles in the morphogenesis and function of the membrane skeleton around basal bodies, but these proteins have not been identified and their functions are unknown. Commercially available anti-human Rho GDP-dissociation inhibitor α (RhoGDIα) antibody (sc-33201) was accidentally found to show very similar immunofluorescence staining patterns to those of anti-K antigen antibodies, such as 424A8 and 10D12 mouse monoclonal antibodies, in Tetrahymena. A 40kDa protein recognized by this antibody was partially purified and identified as granule lattice protein 1 (Grl1p) by matrix-assisted laser desorption/ionization-tandem time-of-flight mass spectrometry. In immunoblotting experiments this antibody was suggested to recognize endogenous Grl1p. The three-dimensional structure of proGrl1p protein predicted by I-TASSER was similar to a spectrin family protein. Grl1 may be a K antigen and a spectrin-like protein in Tetrahymena.

Model Selection Using BICePs: A Bayesian Approach for Force Field Validation and Parameterization.

The Bayesian Inference of Conformational Populations (BICePs) algorithm reconciles theoretical predictions of conformational state populations with sparse and/or noisy experimental measurements. Among its key advantages is its ability to perform objective model selection through a quantity we call the BICePs score, which reflects the integrated posterior evidence in favor of a given model, computed through free energy estimation methods. Here, we explore how the BICePs score can be used for force field validation and parametrization. Using a 2D lattice protein as a toy model, we demonstrate that BICePs is able to select the correct value of an interaction energy parameter given ensemble-averaged experimental distance measurements. We show that if conformational states are sufficiently fine-grained, the results are robust to experimental noise and measurement sparsity. Using these insights, we apply BICePs to perform force field evaluations for all-atom simulations of designed β-hairpin peptides against experimental NMR chemical shift measurements. These tests suggest that BICePs scores can be used for model selection in the context of all-atom simulations. We expect this approach to be particularly useful for the computational foldamer design as a tool for improving general-purpose force fields given sparse experimental measurements.

Proteins at the air-water interface in a lattice model

We construct a lattice protein version of the hydrophobic-polar model to study the effects of the air-water interface on the protein and on an interfacial layer formed through aggregation of many proteins. The basic unit of the model is a 14-mer that is known to have a unique ground state in three dimensions. The equilibrium and kinetic properties of the systems with and without the interface are studied through a Monte Carlo process. We find that the proteins at high dilution can be pinned and depinned many times from the air-water interface. When pinned, the proteins undergo deformation. The staying time depends on the strength of the coupling to the interface. For dense protein systems, we observe glassy effects. Thus, the lattice model yields results which are similar to those obtained through molecular dynamics in off-lattice models. In addition, we study dynamical effects induced by local temperature gradients in protein films.

Molecular Ensembles Shape Evolutionary Trajectories

Evolutionary prediction is of deep practical and philosophical importance. One avenue for such a prediction would be to measure the fitness effects of all mutations to a protein, and then use this information to predict evolution. We attempted such a prediction for the simple case of evolving increased thermodynamic stability in a simple protein lattice model. Surprisingly, we were unable to predict evolutionary trajectories, even given complete knowledge of the effects of all mutations to the ancestral protein. This is a direct consequence of the ensemble of similar structures populated by proteins. The effect of a mutation depends on the relative probabilities of conformations in the ensemble, which in turn depend on the exact amino acid sequence of the protein. Accumulating substitutions alter the relative probabilities of conformations, thereby changing the effects of future mutations. This manifests itself as subtle, but pervasive, multi-way interactions between mutations (high-order epistasis). As mutations accumulate, uncertainty in the predicted effect of each mutation accumulates and undermines prediction. We then developed computational and statistical tools to look for evidence of this high-order epistasis in experimentally determined genotype-fitness maps. We find that high-order epistasis is ubiquitous. This work reveals that evolutionary unpredictability arises—even for fixed environments and under strong natural selection—as a direct consequence of the thermodynamic ensemble populated by proteins.