Automatic procedure for using models of proteins in molecular replacement

In a crystallography experiment, a crystal is irradiated with X-rays whose diffracted waves are collected and measured. The reconstruction of the structure of the molecule in the crystal requires knowledge of the phase of the diffracted waves, information that is lost in the passage from the three-dimensional structure of the molecule to its diffraction pattern. It can be recovered using experimental methods such as heavy-atom isomorphous replacement and anomalous scattering or by molecular replacement, which relies on the availability of an atomic model of the target structure. This can be the structure of the target protein itself, if a previous structure determination is available, or a computational model or, in some cases, the structure of a homologous protein. It is not straightforward to predict beforehand whether or not a computational model will work in a molecular replacement experiment, although some rules of thumb exist. The consensus is that even minor differences in the quality of the model, which are rather difficult to estimate a priori, can have a significant effect on the outcome of the procedure. We describe here a method for quickly assessing whether a protein structure can be solved by molecular replacement. The procedure consists in submitting the sequence of the target protein to a selected list of freely available structure prediction servers, cluster the resulting models, select the representative structures of each cluster and use them as search models in an automatic phasing procedure. We tested the procedure using the structure factors of newly released proteins of known structure downloaded from the Protein Data Bank as soon as they were made available. Using our automatic procedure we were able to obtain an interpretable electron density map in more than half the cases.     

Accurate molecular classification of cancer using simple rules

Background

One intractable problem with using microarray data analysis for cancer classification is how to reduce the extremely high-dimensionality gene feature data to remove the effects of noise. Feature selection is often used to address this problem by selecting informative genes from among thousands or tens of thousands of genes. However, most of the existing methods of microarray-based cancer classification utilize too many genes to achieve accurate classification, which often hampers the interpretability of the models. For a better understanding of the classification results, it is desirable to develop simpler rule-based models with as few marker genes as possible.

Methods

We screened a small number of informative single genes and gene pairs on the basis of their depended degrees proposed in rough sets. Applying the decision rules induced by the selected genes or gene pairs, we constructed cancer classifiers. We tested the efficacy of the classifiers by leave-one-out cross-validation (LOOCV) of training sets and classification of independent test sets.

Results

We applied our methods to five cancerous gene expression datasets: leukemia (acute lymphoblastic leukemia [ALL] vs. acute myeloid leukemia [AML]), lung cancer, prostate cancer, breast cancer, and leukemia (ALL vs. mixed-lineage leukemia [MLL] vs. AML). Accurate classification outcomes were obtained by utilizing just one or two genes. Some genes that correlated closely with the pathogenesis of relevant cancers were identified. In terms of both classification performance and algorithm simplicity, our approach outperformed or at least matched existing methods.

Conclusion

In cancerous gene expression datasets, a small number of genes, even one or two if selected correctly, is capable of achieving an ideal cancer classification effect. This finding also means that very simple rules may perform well for cancerous class prediction.     

Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models.

The emergence of antibiotic resistance in a wide variety of important pathogens of humans presents a worldwide threat to public health. This paper describes recent work on the use of mathematical models of the emergence and spread of resistance bacteria, on scales ranging from within the patient, in hospitals and within communities of people. Model development starts within the treated patient, and pharmacokinetic and pharmacodynamic principles are melded within a framework that mirrors the interaction between bacterial population growth, drug treatment and the immunological responses targeted at the pathogen. The model helps identify areas in which more precise information is needed, particularly in the context of how drugs influence pathogen birth and death rates (pharmacodynamics). The next area addressed is the spread of multiply drug-resistant bacteria in hospital settings. Models of the transmission dynamics of the pathogen provide a framework for assessing the relative merits of different forms of intervention, and provide criteria for control or eradication. The model is applied to the spread of vancomycin-resistant enterococci in an intensive care setting. This model framework is generalized to consider the spread of resistant organisms between hospitals. The model framework allows for heterogeneity in hospital size and highlights the importance of large hospitals in the maintenance of resistant organisms within a defined country. The spread of methicillin resistant Staphylococcus aureus (MRSA) in England and Wales provides a template for model construction and analysis. The final section addresses the emergence and spread of resistant organisms in communities of people and the dependence on the intensity of selection as measured by the volume or rate of drug use. Model output is fitted to data for Finland and Iceland and conclusions drawn concerning the key factors determining the rate of spread and decay once drug pressure is relaxed.     

Understanding cisplatin resistance using cellular models

Many mechanisms of cisplatin resistance have been proposed from studies of cellular models of resistance including changes in cellular drug accumulation, detoxification of the drug, inhibition of apoptosis and repair of the DNA adducts. A series of resistant models were developed from CCRF-CEM leukaemia cells with increasing doses of cisplatin from 100 ng/ml. This produced increasing resistance up to 7-fold with a treatment dose of 1.6 microg/ml. Cisplatin resistance in these cells correlated with increases in the antioxidant glutathione, yet treatment with buthionine sulphoximine, an inhibitor of glutathione synthesis, had no effect on resistance, suggesting that the increase in glutathione was not directly involved in cisplatin resistance. Two models were developed from H69 SCLC cells, H69-CP and H69CIS200 using 100 ng/ml or 200 ng/ml cisplatin respectively. Both cell models were 2-4 fold resistant to cisplatin, and have decreased expression of p21 which may increase the cell's ability to progress through the cell cycle in the presence of DNA damage. Both the H69-CP and H69CIS200 cells showed no decrease in cellular cisplatin accumulation. However, the H69-CP cells have increased levels of cellular glutathione and are cross resistant to radiation whereas the H69CIS200 cells have neither of these changes. This suggests that increases in glutathione may contribute to cross-resistance to other drugs and radiation, but not directly to cisplatin resistance. There are multiple resistance mechanisms induced by cisplatin treatment, even in the same cell type. How then should cisplatin-resistant cancers be treated? Cisplatin-resistant cell lines are often more sensitive to another chemotherapeutic drug paclitaxel (H69CIS200), or are able to be sensitized to cisplatin with paclitaxel pre-treatment (H69-CP). The understanding of this sensitization by paclitaxel using cell models of cisplatin resistance will lead to improvements in the clinical treatment of cisplatin resistant tumours.     

Mechanical unfolding of a beta-hairpin using molecular dynamics

Single-molecule mechanical unfolding experiments have the potential to provide insights into the details of protein folding pathways. To investigate the relationship between force-extension unfolding curves and microscopic events, we performed molecular dynamics simulations of the mechanical unfolding of the C-terminal hairpin of protein G. We have studied the dependence of the unfolding pathway on pulling speed, cantilever stiffness, and attachment points. Under conditions that generate low forces, the unfolding trajectory mimics the untethered, thermally accessible pathway previously proposed based on high-temperature studies. In this stepwise pathway, complete breakdown of backbone hydrogen bonds precedes dissociation of the hydrophobic cluster. Under more extreme conditions, the cluster and hydrogen bonds break simultaneously. Transitions between folding intermediates can be identified in our simulations as features of the calculated force-extension curves.     

Dynamics of proteins in crystals: comparison of experiment with simple models

The dynamic behavior of proteins in crystals is examined by comparing theory and experiments. The Gaussian network model (GNM) and a simplified version of the crystallographic translation libration screw (TLS) model are used to calculate mean square fluctuations of C(alpha) atoms for a set of 113 proteins whose structures have been determined by x-ray crystallography. Correlation coefficients between the theoretical estimations and experiment are calculated and compared. The GNM method gives better correlation with experimental data than the rigid-body libration model and has the added benefit of being able to calculate correlations between the fluctuations of pairs of atoms. By incorporating the effect of neighboring molecules in the crystal the correlation is further improved.     

Testing macro-evolutionary models using incomplete molecular phylogenies.

Phylogenies reconstructed from gene sequences can be used to investigate the tempo and mode of species diversification. Here we develop and use new statistical methods to infer past patterns of speciation and extinction from molecular phylogenies. Specifically, we test the null hypothesis that per-lineage speciation and extinction rates have remained constant through time. Rejection of this hypothesis may provide evidence for evolutionary events such as adaptive radiations or key adaptations. In contrast to previous approaches, our methods are robust to incomplete taxon sampling and are conservative with respect to extinction. Using simulation we investigate, first, the adverse effects of failing to take incomplete sampling into account and, second, the power and reliability of our tests. When applied to published phylogenies our tests suggest that, in some cases, speciation rates have decreased through time.     

Prediction of nuclear proteins using SVM and HMM models

Background  

The nucleus, a highly organized organelle, plays important role in cellular homeostasis. The nuclear proteins are crucial for chromosomal maintenance/segregation, gene expression, RNA processing/export, and many other processes. Several methods have been developed for predicting the nuclear proteins in the past. The aim of the present study is to develop a new method for predicting nuclear proteins with higher accuracy.     

Mechanical stresses in carotid plaques using MRI-based fluid-structure interaction models

Risk assessment in patients with carotid atherosclerosis relies on the degree of luminal stenosis. Incorporating morphological information on plaque composition obtained noninvasively through the use of magnetic resonance imaging (MRI) could include other variables besides the degree of stenosis into carotid plaque risk assessment. Knowledge of the morphologic composition of the plaque allows determination of mechanic stresses exerted on the protective fibrous cap, which may be of importance in the assessment of plaque vulnerability. Based on image processing of transverse MRI scans, longitudinal 2D fluid-structure interaction (FSI) simulations of carotid atherosclerotic plaques were performed facilitating in-vivo estimation of longitudinal internal fibrous cap stresses. The FSI simulation combined finite element analysis (FEA) with computational fluid dynamics (CFD) simulations of blood-flow variables. Preliminary results from two symptomatic patients revealed longitudinal stress levels (max. 254.1 and 143.2 kPa) approaching established criteria for plaque rupture at known predilection sites of plaque rupture. Determination of longitudinal fibrous cap stresses may prove useful in assessing plaque vulnerability and improve risk stratification in patients with carotid atherosclerosis.     

Analysis of ligand binding to proteins using molecular dynamics simulations

This work aims to explore theoretically the molecular mechanisms of ligand binding to proteins through the use of molecular dynamics simulations. The binding of sodium dodecyl sulfate (SDS) to cobra cardio toxin A3 (CTX A3) and thiourea (TOU) to lysozyme have been chosen as the two model systems. Data acquisitions were made by Gromacs software. To begin with, the collisions of ligand molecules with every residue of CTX A3 and lysozyme were evaluated. With this information in hand, the average numbers of collisions with each residue was defined and then assessed. Next, a measure of the affinity of a residue, P_i, referred to as conformational factor, toward a ligand molecule was established. Based on the results provided, all site-making residues for CTX A3 and lysozyme were identified. The results are in good agreement with the experimental data. Finally, based on this method, all site-making residues of bovine carbonic anhydrase (BCA) toward the SDS ligand were predicted.     

Nonlinear processes in seagrass colonisation explained by simple clonal growth rules

The development of single clones of the seagrass Cymodocea nodosa was analysed using a growth model based on the formation of structures limited by diffusive aggregation. The model implemented the measured clonal growth rules (i.e. rhizome elongation and branching rates, branching angle, and spacer length between consecutive shoots) and shoot mortality rate for C. nodosa at Alfacs Bay (Spain). The simulated patches increased their size nonlinearly with time displaying two different domains of growth. Young patches showed a rapid increase with time of the length of rhizome network and the number of living shoots, which depended on rhizome branching rate, and increased the radial patch size (R_g) algebraically with the number of living shoots as R_g ∝ N_s^1/Df, being D_f the fractal dimension of the patch structure. Patches older than 4 years increased the production of rhizome network and the number of living shoots much more slowly, while their radial patch size behaved as R_g ∝ N_s^0.5 resulting from an internal patch compactation. Moreover, the linear growth rate of the simulated patches changed up to 30 fold during patch development, increasing with increasing patch size until patches reached an intermediate size. The modelled patch development was found to closely reproduce the observed patch structure for the species at the Alfacs Bay (Spain). Hence, the growth of C. nodosa patches initially proceeds with a growth mode controlled by the branching pattern (branching frequency and angle) of the species, producing sparse and elongated patches. Once patches exceed 4–5 years of age and contained >500 shoots, becoming dense and circular, they shifts to a growth model typical of compact structures. These results explain previously unaccounted evidence of the emergence of nonlinear patch growth from simple clonal growth rules, and highlight the importance of branching frequency and angles as critical determinants of the space occupation rate of seagrasses and probably other clonal plants.     

Reduced point charge models of proteins: assessment based on molecular dynamics simulations

A reduced point charge distribution is used to model Ubiquitin and two complexes, Vps27 UIM-1–Ubiquitin and Barnase–Barstar. It is designed from local extrema in charge density distributions obtained from the Poisson equation applied to smoothed molecular electrostatic potentials. A variant distribution is built by locating point charges on atoms. Various charge fitting conditions are selected, i.e. from either electrostatic Amber99 (Assisted Model Building with Energy Refinement) Coulomb potential or forces, considering reference grid points located within various distances from the protein atoms, with or without separate treatment of main and side chain charges. The program GROMACS (Groningen Machine for Chemical Simulations) is used to generate Amber99SB molecular dynamics (MD) trajectories of the solvated proteins modelled using the various reduced point charge models (RPCMs) so obtained. Point charges that are not located on atoms are considered as virtual sites. Some RPCMs lead to stable MD trajectories. They, however, involve a partial loss in the protein secondary structure and lead to a less-structured solute solvation shell. The model built by fitting charges on Coulomb forces calculated at grid points ranging between 1.4 and 2.0 times the van der Waals radius of the atoms, with a separate treatment of main chain and side chain charges, appears to best approximate all-atom MD trajectories.     

Assessing the lethality of ship strikes on whales using simple biophysical models

Studies of ship strikes on whales often focus on large vessels (>20 m), with attention to their speeds and the resulting risk of lethality. Smaller coastal vessels also co-occur with whales, resulting in collisions that merit study. To cast light on injuries caused by vessels of all sizes, we used knowledge of right whale anatomy and Newtonian mechanics to construct simple models that predict the mechanical stresses experienced by whales during collisions. By comparing our predictions with published models and with data from ship strikes on various whale species, we developed a model for lethal injury as a function of several vessel and whale properties, finding that collisions that create stresses in excess of 0.241 MPa were likely to cause lethal injuries to large whales. Furthermore, this model has revealed that (1) vessels of all sizes can yield stresses higher than this critical level, and (2) large vessels produce stresses much larger than this even when travelling at reduced speeds (i.e., 10 knots). The model is fast enough to power an interactive GUI-based tool (in R) and flexible enough to simulate strikes by vessels of different masses and speeds upon whales of different species, sizes, and physical conditions.     

Neutral evolution of Protein-protein interactions: a computational study using simple models

Background  

Protein-protein interactions are central to cellular organization, and must have appeared at an early stage of evolution. To understand better their role, we consider a simple model of protein evolution and determine the effect of an explicit selection for Protein-protein interactions.     

Analysing the origin of long-range interactions in proteins using lattice models

Background  

Long-range communication is very common in proteins but the physical basis of this phenomenon remains unclear. In order to gain insight into this problem, we decided to explore whether long-range interactions exist in lattice models of proteins. Lattice models of proteins have proven to capture some of the basic properties of real proteins and, thus, can be used for elucidating general principles of protein stability and folding.     

Building self-avoiding lattice models of proteins using a self-consistent field optimization

We present an algorithm to build self-avoiding lattice models of chain molecules with low RMS deviation from their actual 3D structures. To find the optimal coordinates for the lattice chain model, we minimize a function that consists of three terms: (1) the sum of squared deviations of link coordinates on a lattice from their off-lattice values, (2) the sum of “short-range” terms, penalizing violation of chain connectivity, and (3) the sum of “long-range” repulsive terms, penalizing chain self-intersections. We treat this function as a chain molecule “energy” and minimize it using self-consistent field (SCF) theory to represent the pairwise link repulsions as 3D fields acting on the links. The statistical mechanics of chain molecules enables computation of the chain distribution in this field on the lattice. The field is refined by iteration to become self-consistent with the chain distribution, then dynamic programming is used to find the optimal lattice model as the “lowest-energy” chain pathway in this SCF. We have tested the method on one of the coarsest (and most difficult) lattices used for model building on proteins of all structural types and show that the method is adequate for building self-avoiding models of proteins with low RMS deviations from the actual structures. © 1996 Wiley-Liss, Inc.