A rough-cut capacity planning model with overlapping

In the early phases of projects, capacity planning is performed to assess the feasibility of the project in terms of delivery date, resource usage and cost. This tactical approach relies on an aggregated representation of tasks in work packages. At this level, aggressive project duration objectives are achieved by adopting work package overlapping policies that affect both workload and resource usage. In this article, we propose a mixed-time MILP model for project capacity planning with different possibilities for overlapping levels between work packages. In the model, the planning time horizon is divided into time buckets used to evaluate resource usage, while starting and ending times for work packages are continuous. The model was tested on a benchmark of 5 sets of 450 theoretical instances each. More than half of the tested instances were solved to optimality within 500 s. Results also show that, while overlapping is more beneficial for accelerating project delivery times, it can still have a positive impact on project cost by allowing a better distribution of workload. Finally, overlapping options seem to have less influence on the performance of the model than project slack or number of work packages

A rough-cut capacity planning model with overlapping

In the early phases of projects, capacity planning is performed to assess the feasibility of the project in terms of delivery date, resource usage and cost. This tactical approach relies on an aggregated representation of tasks in work packages. At this level, aggressive project duration objectives are achieved by adopting work package overlapping policies that affect both workload and resource usage. In this article, we propose a mixed-time MILP model for project capacity planning with different possibilities for overlapping levels between work packages. In the model, the planning time horizon is divided into time buckets used to evaluate resource usage, while starting and ending times for work packages are continuous. The model was tested on a benchmark of 5 sets of 450 theoretical instances each. More than half of the tested instances were solved to optimality within 500 s. Results also show that, while overlapping is more beneficial for accelerating project delivery times, it can still have a positive impact on project cost by allowing a better distribution of workload. Finally, overlapping options seem to have less influence on the performance of the model than project slack or number of work packages

Conformational Exchange Processes in Biological Systems: Detection by Solid-State NMR

International audienceWe review recent advances in methodologies to study microseconds-to-milliseconds exchange processes in biological molecules using magic-angle spinning solid-state nuclear magnetic resonance (MAS ssNMR) spectroscopy. The particularities of MAS ssNMR, as compared to solution-state NMR, are elucidated using numerical simulations and experimental data. These simulations reveal the potential of MAS NMR to provide detailed insight into short-lived conformations of biological molecules. Recent studies of conformational exchange dynamics in microcrystalline ubiquitin are discussed

Protein folding on the ribosome studied using NMR spectroscopy

NMR spectroscopy is a powerful tool for the investigation of protein folding and misfolding, providing a characterization of molecular structure, dynamics and exchange processes, across a very wide range of timescales and with near atomic resolution. In recent years NMR methods have also been developed to study protein folding as it might occur within the cell, in a de novo manner, by observing the folding of nascent polypeptides in the process of emerging from the ribosome during synthesis. Despite the 2.3 MDa molecular weight of the bacterial 70S ribosome, many nascent polypeptides, and some ribosomal proteins, have sufficient local flexibility that sharp resonances may be observed in solution-state NMR spectra. In providing information on dynamic regions of the structure, NMR spectroscopy is therefore highly complementary to alternative methods such as X-ray crystallography and cryo-electron microscopy, which have successfully characterized the rigid core of the ribosome particle. However, the low working concentrations and limited sample stability associated with ribosome-nascent chain complexes means that such studies still present significant technical challenges to the NMR spectroscopist. This review will discuss the progress that has been made in this area, surveying all NMR studies that have been published to date, and with a particular focus on strategies for improving experimental sensitivity

Structural Biology by NMR: Structure, Dynamics, and Interactions

The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time-scales from picoseconds to seconds. Nuclear Magnetic Resonance (NMR) spectroscopy has emerged as the method of choice for studying both protein structure and dynamics in solution. Typically, NMR experiments are sensitive both to structural features and to dynamics, and hence the measured data contain information on both. Despite major progress in both experimental approaches and computational methods, obtaining a consistent view of structure and dynamics from experimental NMR data remains a challenge. Molecular dynamics simulations have emerged as an indispensable tool in the analysis of NMR data

Long-Range Intra-Protein Communication Can Be Transmitted by Correlated Side-Chain Fluctuations Alone

Allosteric regulation is a key component of cellular communication, but the way in which information is passed from one site to another within a folded protein is not often clear. While backbone motions have long been considered essential for long-range information conveyance, side-chain motions have rarely been considered. In this work, we demonstrate their potential utility using Monte Carlo sampling of side-chain torsional angles on a fixed backbone to quantify correlations amongst side-chain inter-rotameric motions. Results indicate that long-range correlations of side-chain fluctuations can arise independently from several different types of interactions: steric repulsions, implicit solvent interactions, or hydrogen bonding and salt-bridge interactions. These robust correlations persist across the entire protein (up to 60 Å in the case of calmodulin) and can propagate long-range changes in side-chain variability in response to single residue perturbations

Modeling Conformational Ensembles of Slow Functional Motions in Pin1-WW

Protein-protein interactions are often mediated by flexible loops that experience conformational dynamics on the microsecond to millisecond time scales. NMR relaxation studies can map these dynamics. However, defining the network of inter-converting conformers that underlie the relaxation data remains generally challenging. Here, we combine NMR relaxation experiments with simulation to visualize networks of inter-converting conformers. We demonstrate our approach with the apo Pin1-WW domain, for which NMR has revealed conformational dynamics of a flexible loop in the millisecond range. We sample and cluster the free energy landscape using Markov State Models (MSM) with major and minor exchange states with high correlation with the NMR relaxation data and low NOE violations. These MSM are hierarchical ensembles of slowly interconverting, metastable macrostates and rapidly interconverting microstates. We found a low population state that consists primarily of holo-like conformations and is a “hub” visited by most pathways between macrostates. These results suggest that conformational equilibria between holo-like and alternative conformers pre-exist in the intrinsic dynamics of apo Pin1-WW. Analysis using MutInf, a mutual information method for quantifying correlated motions, reveals that WW dynamics not only play a role in substrate recognition, but also may help couple the substrate binding site on the WW domain to the one on the catalytic domain. Our work represents an important step towards building networks of inter-converting conformational states and is generally applicable

Accessing ns–μs side chain dynamics in ubiquitin with methyl RDCs

This study presents the first application of the model-free analysis (MFA) (Meiler in J Am Chem Soc 123:6098–6107, 2001; Lakomek in J Biomol NMR 34:101–115, 2006) to methyl group RDCs measured in 13 different alignment media in order to describe their supra-τc dynamics in ubiquitin. Our results indicate that methyl groups vary from rigid to very mobile with good correlation to residue type, distance to backbone and solvent exposure, and that considerable additional dynamics are effective at rates slower than the correlation time τc. In fact, the average amplitude of motion expressed in terms of order parameters S2 associated with the supra-τc window brings evidence to the existence of fluctuations contributing as much additional mobility as those already present in the faster ps-ns time scale measured from relaxation data. Comparison to previous results on ubiquitin demonstrates that the RDC-derived order parameters are dominated both by rotameric interconversions and faster libration-type motions around equilibrium positions. They match best with those derived from a combined J-coupling and residual dipolar coupling approach (Chou in J Am Chem Soc 125:8959–8966, 2003) taking backbone motion into account. In order to appreciate the dynamic scale of side chains over the entire protein, the methyl group order parameters are compared to existing dynamic ensembles of ubiquitin. Of those recently published, the broadest one, namely the EROS ensemble (Lange in Science 320:1471–1475, 2008), fits the collection of methyl group order parameters presented here best. Last, we used the MFA-derived averaged spherical harmonics to perform highly-parameterized rotameric searches of the side chains conformation and find expanded rotamer distributions with excellent fit to our data. These rotamer distributions suggest the presence of concerted motions along the side chains