Combining Optimal Control Theory and Molecular Dynamics for Protein Folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the atoms. In turn, MD simulation provides an all-atom conformation whose positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization - MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages

Interplay between hydrophobic cluster and loop propensity in beta-hairpin formation: A mechanistic study

We investigated the structural determinants of the stability of a designed P-hairpin containing a natural hydrophobic cluster from the protein GB1 and a D-Pro-Gly turn forming sequence. The results of our simulations shed light on the factors leading to an ordered secondary structure in a model peptide: in particular, the importance of the so-called diagonal interactions in forming a stable hydrophobic nucleus in the beta-hairpin, together with the more obvious lateral interactions, is examined. With the use of long timescale MD simulations in explicit water, we show the role of diagonal interactions in driving the peptide to the correct folded structure (formation of the hydrophobic core with Trp 2, Tyr 4, and Phe 9 in the first stages of refolding) and in keeping it in the ensemble of folded conformations. The combination of the stabilizing effects of the D-Pro-Gly turn sequence and of the hydrophobic nucleus formation thus favors the attainment of an ordered secondary structure compatible with the one determined experimentally. Moreover, our data underline the importance of the juxtapositions of the side chains of amino acids not directly facing each other in the three-dimensional structure. The combination of these interactions forces the peptide to sample a nonrandom portion of the conformational space, as can be seen in the rapid collapse to an ordered structure in the refolding simulation, and shows that the unfolded state can be closely correlated to the folded ensemble of structures, at least in the case of small model peptides

Folding and mis-folding of peptides and proteins: Insights from molecular simulations

In this paper, the main achievements and problems of the application of all-atom molecular simulations, with particular attention for Molecular Dynamics (MD), will be critically reviewed. Starting from unfolding simulations, through biased simulations, which require a knowledge of the native state conformation, to folding studies based on the simple knowledge of the protein (or peptide) sequence, the strengths and weaknesses of theoretical approaches to the study of folding and their matching with experimental observations will be discussed. Finally, we will give a critical outlook on the possible developments of this field in the near future

Sequence dependence of amyloid fibril formation: Insights from molecular dynamics simulations

The clarification of the physico-chemical determinants underlying amyloid deposition is critical for our understanding of misfolding diseases. With this purpose we have performed a systematic all-atom molecular dynamics (MD) study of a series of single point mutants of the de novo designed amyloidogenic peptide STVIIE. Sixteen different 50 ns long simulations using explicit solvent have been carried out starting from four different conformations of a polymeric six-stranded beta-sheet. The simulations have provided evidence for the influence of a small number of site-specific hydrophobic interactions on the packing and stabilization of nascent aggregates, as well as the interplay between side-chain interactions and the net charge of the molecule on the strand arrangement of polymeric beta-sheets. This MD analysis has also shed light into the origin of the position dependence on mutation of beta-sheet polymerization that was found experimentally for this model system. Our results suggest that MD can be applied to detect critical positions for beta-sheet aggregation within a given amyloiclogenic stretch. Studies similar to the one presented here can guide site-directed mutations or the design of drugs that specifically disrupt the key stabilizing interactions of beta-sheet aggregates. (c) 2005 Published by Elsevier Ltd

Structure-activity relationships of linear and cyclic peptides containing the NGR tumor-homing motif

Cyclic and linear peptides containing the Asn-Gly-Arg (NGR) motif have proven useful for delivering various anti-tumor compounds and viral particles to tumor vessels. We have investigated the role of cyclic constraints on the structure and tumor-homing properties of NGR peptides using tumor necrosis factor-alpha (TNF) derivatives containing disulfide-bridged (CNGRC-TNF) and linear (GNGRG-TNF) NGR domains. Experiments carried out in animal models showed that both GNGRG and CNGRC can target TNF to tumors. However, the antitumor activity of CNGRC-TNF was > 10-fold higher than that of GNGRG-TNF. Molecular dynamic simulation of cyclic CNGRC showed the presence of a bend geometry involving residues Gly(3)-Arg(4). Molecular dynamic simulation of the same peptide without disulfide constraints showed that the most populated and thermodynamically favored configuration is characterized by the presence of a beta-turn involving residues Gly(3)-Arg(4) and hydrogen bonding interactions between the backbone atoms of Asn(2) and Cys(5). These results suggest that the NGR motif has a strong propensity to form beta-turn in linear peptides and may explain the finding that GNGRG peptide can target TNF to tumors, albeit to a lower extent than CNGRC. The disulfide bridge constraint is critical for stabilizing the bent conformation and for increasing the tumor targeting efficiency

Protein folding simulations: combining coarse-grained models and all-atom molecular dynamics

The investigation of protein folding and its ramifications in biological contexts is at the heart of molecular biology. Theoretical and computational studies provide a steadily growing contribution to the understanding of factors driving a given polypeptide sequence into the native state. Simplified coarse-grained protein models have proven very useful to gain insights into the general thermodynamic and kinetic features of the folding process. On the other hand, allatom simulations allowto follow, with microscopic detail, the delicate interplay of the various chemical interactions leading to the formation of the native or intermediate states. In this paper we will discuss different computational strategies employed to tackle the protein folding problem, based on the use of either coarse-grained or all-atom protein descriptions. Finallywewill discuss a recent approach that allows to extend the reach of ordinary folding simulations by using a simplified description of protein structures and energy functional in conjunction with all-atom molecular dynamics

Opportunities for improvement on current nuclear cardiology practices and radiation exposure in Latin America: Findings from the 65-country IAEA Nuclear Cardiology Protocols cross-sectional Study (INCAPS)

Background: Comparison of Latin American (LA) nuclear cardiology (NC) practice with that in the rest of the world (RoW) will identify areas for improvement and lead to educational activities to reduce radiation exposure from NC. Methods and Results: INCAPS collected data on all SPECT and PET procedures performed during a single week in March-April 2013 in 36 laboratories in 10 LA countries (n = 1139), and 272 laboratories in 55 countries in RoW (n = 6772). Eight “best practices” were identified a priori and a radiation-related Quality Index (QI) was devised indicating the number used. Mean radiation effective dose (ED) in LA was higher than in RoW (11.8 vs 9.1 mSv, p < 0.001). Within a populous country like Brazil, a wide variation in laboratory mean ED was found, ranging from 8.4 to 17.8 mSv. Only 11% of LA laboratories achieved median ED <9 mSv, compared to 32% in RoW (p < 0.001). QIs ranged from 2 in a laboratory in Mexico to 7 in a laboratory in Cuba. Three major opportunities to reduce ED for LA patients were identified: (1) more laboratories could implement stress-only imaging, (2) camera-based methods of ED reduction, including prone imaging, could be more frequently used, and (3) injected activity of 99mTc could be adjusted reflecting patient weight/habitus. Conclusions: On average, radiation dose from NC is higher in LA compared to RoW, with median laboratory ED <9 mSv achieved only one third as frequently as in RoW. Opportunities to reduce radiation exposure in LA have been identified and guideline-based recommendations made to optimize protocols and adhere to the “as low as reasonably achievable” (ALARA) principle

Impact of age on the selection of nuclear cardiology stress protocols: The INCAPS (IAEA nuclear cardiology protocols) study

Background: There is growing concern about radiation exposure from nuclear myocardial perfusion imaging (MPI), particularly among younger patients who are more prone to develop untoward effects of ionizing radiation, and hence US and European professional society guidelines recommend age as a consideration in weighing radiation risk from MPI. We aimed to determine how patient radiation doses from MPI vary across age groups in a large contemporary international cohort. Methods: Data were collected as part of a global cross-sectional study of centers performing MPI coordinated by the International Atomic Energy Agency (IAEA). Sites provided information on each MPI study completed during a single week in March–April 2013. We compared across age groups laboratory adherence to pre-specified radiation-related best practices, radiation effective dose (ED; a whole-body measure reflecting the amount of radiation to each organ and its relative sensitivity to radiation's deleterious effects), and the proportion of patients with ED ≤ 9 mSv, a target level specified in guidelines. Results: Among 7911 patients undergoing MPI in 308 laboratories in 65 countries, mean ED was 10.0 ± 4.5 mSv with slightly higher exposure among younger age groups (trend p value < 0.001). There was no difference in the proportion of patients with ED ≤ 9 mSv across age groups, or in adherence to best practices based on the median age of patients in a laboratory. Conclusions: In contemporary nuclear cardiology practice, the age of the patient appears not to impact protocol selection and radiation dose, contrary to professional society guidelines

Nuclear cardiology practice and associated radiation doses in Europe: results of the IAEA Nuclear Cardiology Protocols Study (INCAPS) for the 27 European countries

PURPOSE: Nuclear cardiology is widely used to diagnose coronary artery disease and to guide patient management, but data on current practices, radiation dose-related best practices, and radiation doses are scarce. To address these issues, the IAEA conducted a worldwide study of nuclear cardiology practice. We present the European subanalysis. METHODS: In March 2013, the IAEA invited laboratories across the world to document all SPECT and PET studies performed in one week. The data included age, gender, weight, radiopharmaceuticals, injected activities, camera type, positioning, hardware and software. Radiation effective dose was calculated for each patient. A quality score was defined for each laboratory as the number followed of eight predefined best practices with a bearing on radiation exposure (range of quality score 0 - 8). The participating European countries were assigned to regions (North, East, South, and West). Comparisons were performed between the four European regions and between Europe and the rest-of-the-world (RoW). RESULTS: Data on 2,381 European patients undergoing nuclear cardiology procedures in 102 laboratories in 27 countries were collected. A cardiac SPECT study was performed in 97.9 % of the patients, and a PET study in 2.1 %. The average effective dose of SPECT was 8.0 ± 3.4 mSv (RoW 11.4 ± 4.3 mSv; P < 0.001) and of PET was 2.6 ± 1.5 mSv (RoW 3.8 ± 2.5 mSv; P < 0.001). The mean effective doses of SPECT and PET differed between European regions (P < 0.001 and P = 0.002, respectively). The mean quality score was 6.2 ± 1.2, which was higher than the RoW score (5.0 ± 1.1; P < 0.001). Adherence to best practices did not differ significantly among the European regions (range 6 to 6.4; P = 0.73). Of the best practices, stress-only imaging and weight-adjusted dosing were the least commonly used. CONCLUSION: In Europe, the mean effective dose from nuclear cardiology is lower and the average quality score is higher than in the RoW. There is regional variation in effective dose in relation to the best practice quality score. A possible reason for the differences between Europe and the RoW could be the safety culture fostered by actions under the Euratom directives and the implementation of diagnostic reference levels. Stress-only imaging and weight-adjusted activity might be targets for optimization of European nuclear cardiology practice

Current worldwide nuclear cardiology practices and radiation exposure: results from the 65 country IAEA Nuclear Cardiology Protocols Cross-Sectional Study (INCAPS)

AIMS: To characterize patient radiation doses from nuclear myocardial perfusion imaging (MPI) and the use of radiation-optimizing 'best practices' worldwide, and to evaluate the relationship between laboratory use of best practices and patient radiation dose. METHODS AND RESULTS: We conducted an observational cross-sectional study of protocols used for all 7911 MPI studies performed in 308 nuclear cardiology laboratories in 65 countries for a single week in March-April 2013. Eight 'best practices' relating to radiation exposure were identified a priori by an expert committee, and a radiation-related quality index (QI) devised indicating the number of best practices used by a laboratory. Patient radiation effective dose (ED) ranged between 0.8 and 35.6 mSv (median 10.0 mSv). Average laboratory ED ranged from 2.2 to 24.4 mSv (median 10.4 mSv); only 91 (30%) laboratories achieved the median ED ≤ 9 mSv recommended by guidelines. Laboratory QIs ranged from 2 to 8 (median 5). Both ED and QI differed significantly between laboratories, countries, and world regions. The lowest median ED (8.0 mSv), in Europe, coincided with high best-practice adherence (mean laboratory QI 6.2). The highest doses (median 12.1 mSv) and low QI (4.9) occurred in Latin America. In hierarchical regression modelling, patients undergoing MPI at laboratories following more 'best practices' had lower EDs. CONCLUSION: Marked worldwide variation exists in radiation safety practices pertaining to MPI, with targeted EDs currently achieved in a minority of laboratories. The significant relationship between best-practice implementation and lower doses indicates numerous opportunities to reduce radiation exposure from MPI globally