The previously developed particle mesh Ewald method is reformulated in terms of efficient B‐spline interpolation of the structure factors This reformulation allows a natural extension of the method to potentials of the form 1/rp with p≥1 Furthermore, efficient calculation of the virial tensor follows Use of B‐splines in place of Lagrange interpolation leads to analytic gradients as well as a significant improvement in the accuracy We demonstrate that arbitrary accuracy can be achieved, independent of system size N, at a cost that scales as N log(N) For biomolecular systems with many thousands of atoms this method permits the use of Ewald summation at a computational cost comparable to that of a simple truncation method of 10 A or less

A smooth particle mesh Ewald method

NAMD is a parallel molecular dynamics code designed for high-performance simulation of large biomolecular systems. NAMD scales to hundreds of processors on high-end parallel platforms, as well as tens of processors on low-cost commodity clusters, and also runs on individual desktop and laptop computers. NAMD works with AMBER and CHARMM potential functions, parameters, and file formats. This article, directed to novices as well as experts, first introduces concepts and methods used in the NAMD program, describing the classical molecular dynamics force field, equations of motion, and integration methods along with the efficient electrostatics evaluation algorithms employed and temperature and pressure controls used. Features for steering the simulation across barriers and for calculating both alchemical and conformational free energy differences are presented. The motivations for and a roadmap to the internal design of NAMD, implemented in C++ and based on Charm++ parallel objects, are outlined. The factors affecting the serial and parallel performance of a simulation are discussed. Finally, typical NAMD use is illustrated with representative applications to a small, a medium, and a large biomolecular system, highlighting particular features of NAMD, for example, the Tcl scripting language. The article also provides a list of the key features of NAMD and discusses the benefits of combining NAMD with the molecular graphics/sequence analysis software VMD and the grid computing/collaboratory software BioCoRE. NAMD is distributed free of charge with source code at www.ks.uiuc.edu.

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Scalable molecular dynamics with NAMD

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Scalable Molecular Dynamics with NAMD

While the quality of the current CHARMM22/CMAP additive force field for proteins has been demonstrated in a large number of applications, limitations in the model with respect to the equilibrium between the sampling of helical and extended conformations in folding simulations have been noted. To overcome this, as well as make other improvements in the model, we present a combination of refinements that should result in enhanced accuracy in simulations of proteins. The common (non Gly, Pro) backbone CMAP potential has been refined against experimental solution NMR data for weakly structured peptides, resulting in a rebalancing of the energies of the α-helix and extended regions of the Ramachandran map, correcting the α-helical bias of CHARMM22/CMAP. The Gly and Pro CMAPs have been refitted to more accurate quantum-mechanical energy surfaces. Side-chain torsion parameters have been optimized by fitting to backbone-dependent quantum-mechanical energy surfaces, followed by additional empirical optimization targeting NMR scalar couplings for unfolded proteins. A comprehensive validation of the revised force field was then performed against data not used to guide parametrization: (i) comparison of simulations of eight proteins in their crystal environments with crystal structures; (ii) comparison with backbone scalar couplings for weakly structured peptides; (iii) comparison with NMR residual dipolar couplings and scalar couplings for both backbone and side-chains in folded proteins; (iv) equilibrium folding of mini-proteins. The results indicate that the revised CHARMM 36 parameters represent an improved model for the modeling and simulation studies of proteins, including studies of protein folding, assembly and functionally relevant conformational changes.

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Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ(1) and χ(2) dihedral angles.

By removing the fastest degrees of freedom, constraints allow for an increase of the time step in molecular simulations. In the last decade parallel simulations have become commonplace. However, up till now efficient parallel constraint algorithms have not been used with domain decomposition. In this paper the parallel linear constraint solver (P-LINCS) is presented, which allows the constraining of all bonds in macromolecules. Additionally the energy conservation properties of (P-)LINCS are assessed in view of improvements in the accuracy of uncoupled angle constraints and integration in single precision.

P-LINCS: A Parallel Linear Constraint Solver for Molecular Simulation

We describe how the true statistical error on an average of correlated data can be obtained with ease and efficiency by a renormalization group method. The method is illustrated with numerical and analytical examples, having finite as well as infinite range correlations.

Error estimates on averages of correlated data

In this article, a recently proposed method called the particle mesh Ewald (PME) method for computing the long ranged Coulomb interactions in for example molecular dynamics simulations is studied. The PME method has a complexity O(N log N), where N is the total number of charges. This complexity should in particular be compared with the complexity O(N3/2) for the well known Ewald method and O(N) for the rather new (but already famous) fast multipole method (FMM). However, these complexities say nothing about which method is fastest at some finite N. The purpose of this article is thus to study the PME method and compare its efficiency with the Ewald method and the fast multipole method. To enable this, a theoretical estimate for the accuracy of the PME method as function of its truncation parameters is derived. It is shown that this estimate is very precise by comparing it with results obtained from molecular dynamics simulations of a molten NaCl. Based on this estimate and very careful time experiments, ...

Accuracy and efficiency of the particle mesh Ewald method

Current supercomputers and the impending availability of large scale parallel machines makes possible the study by molecular dynamics of a number of fundamental problems in condensed matter science hitherto beyond our scope because of the enormous computing time involved. This is because a realistic model of such systems contains one or two orders of magnitude more particles than the systems studied to date. Moreover, the intermolecular forces between these particles will usually include contributions from distributions of permanent electric charges, so that the usual assumption of short-ranged forces cannot be made. We give a list of typical problems in this class and attack the problem of improving the performance of molecular dynamics algorithms to take advantage of these new architectures. We use the Jacobi theta function transformation to derive rapidly computable forms for the energy of and forces between large assemblies of N particles interacting in periodic boundary conditions as the sum of real ...

An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles

The need for open model-based robot controllers becomes more and more important with the increasing quality of autonomous joint motion planners and the increasing amount of applications for these. An important item in a model-based controller is a precise dynamical model of the robot. Such a model is designed in terms of various inertial and friction parameters that must be either measured directly or determined experimentally. In this paper, we present a new method for determining parameters of a dynamical robot model based on experiments. We compare the method with existing methods both theoretically and experimentally, and show that we achieved some improvements in the parameter values by using the new method. The experiments were carried out on the two first links of a seven-axis Mitsubishi PA-10 robot.

A new method for estimating parameters of a dynamic robot model

Study Type – Diagnostic (exploratory cohort)



Level of Evidence 2a



What's known on the subject? and What does the study add?



Staging of patients with prostate cancer is the cornerstone of treatment. However, after curative intended therapy a high portion of patients relapse with local and/or distant recurrence. Therefore, one may question whether surgical lymph node dissection (LND) is sufficiently reliable for staging of these patients.



Several imaging methods for primary LN staging of patients with prostate cancer have been tested. Acceptable detection rates have not been achieved by CT or MRI or for that matter with PET/CT using the most common tracer fluoromethylcholine (FCH). Other more recent metabolic tracers like acetate and choline seem to be more sensitive for assessment of LNs in both primary staging and re-staging. However, previous studies were small. Therefore, we assessed the value of [18F]FCH PET/CT for primary LN staging in a prospective study of a larger sample and with a ‘blinded’ review. After a study period of 3 years and >200 included patients, we concluded that [18F]FCH PET/CT did not reach an optimal detection rate compared with LND, and, therefore, it cannot replace this procedure. However, we did detect several bone metastases with [18F]FCH PET/CT that the normal bone scans had missed, and this might be worth pursuing.



OBJECTIVES

• 
To assess the value of [18F]fluoromethylcholine (FCH) positron emission tomography/computed tomography (PET/CT) for lymph node (LN) staging of prostate cancer.

• 
To evaluate if FCH PET/CT can replace LN dissection (LND) for LN staging of prostate cancer, as about one-third of patients with prostate cancer who receive intended curative therapy will have recurrence, one reason being undetected LN involvement.





PATIENTS AND METHODS

• 
From January 2008 to December 2010, 210 intermediate- or high-risk patients had a FCH PET/CT scan before regional LND.

• 
After dissection, the result of histological examination of the LNs (gold standard) was compared with the result of FCH PET/CT obtained by ‘blinded review’.

• 
Sensitivity, specificity, positive (PPV), and negative predictive values (NPV) of FCH PET/CT were measured for detection of LNe metastases.





RESULTS

• 
Of the 210 patients, 76 (36.2%) were in the intermediate-risk group and 134 (63.8%) were in the high-risk group. A medium (range) of 5 (1–28) LNs were removed per patient.

• 
Histological examination of removed LNs showed metastases in 41 patients. Sensitivity, specificity, PPV, and NPV of FCH PET/CT for patient-based LN staging were 73.2%, 87.6%, 58.8% and 93.1%, respectively.

• 
Corresponding values for LN-based analyses were 56.2%, 94.0%, 40.2%, and 96.8%, respectively.

• 
The mean diameter of the true positive LN metastases was significantly larger than that of the false negative LNs (10.3 vs 4.6 mm; P < 0.001).

• 
In addition, FCH PET/CT detected a high focal bone uptake, consistent with bone metastases, in 18 patients, 12 of which had histologically benign LNs.





CONCLUSIONS

• 
Due to a relatively low sensitivity and a correspondingly rather low PPV, FCH PET/CT is not ideal for primary LN staging in patients with prostate cancer.

• 
However, FCH PET/CT does convey important additional information otherwise not recognised, especially for bone metastases.

[18F]fluoromethylcholine (FCH) positron emission tomography/computed tomography (PET/CT) for lymph node staging of prostate cancer: a prospective study of 210 patients

Henrik Gordon Petersen

Papers

Error estimates on averages of correlated data

Accuracy and efficiency of the particle mesh Ewald method

An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles

A new method for estimating parameters of a dynamic robot model

[18F]fluoromethylcholine (FCH) positron emission tomography/computed tomography (PET/CT) for lymph node staging of prostate cancer: a prospective study of 210 patients