Protein-ligand binding free energy estimation using molecular mechanics and continuum electrostatics. Application to HIV-1 protease inhibitors.

A method is proposed for the estimation of absolute binding free energy of interaction between proteins and ligands. Conformational sampling of the protein-ligand complex is performed by molecular dynamics (MD) in vacuo and the solvent effect is calculated a posteriori by solving the Poisson or the Poisson-Boltzmann equation for selected frames of the trajectory. The binding free energy is written as a linear combination of the buried surface upon complexation, SASbur, the electrostatic interaction energy between the ligand and the protein, Eelec, and the difference of the solvation free energies of the complex and the isolated ligand and protein, deltaGsolv. The method uses the buried surface upon complexation to account for the non-polar contribution to the binding free energy because it is less sensitive to the details of the structure than the van der Waals interaction energy. The parameters of the method are developed for a training set of 16 HIV-1 protease-inhibitor complexes of known 3D structure. A correlation coefficient of 0.91 was obtained with an unsigned mean error of 0.8 kcal/mol. When applied to a set of 25 HIV-1 protease-inhibitor complexes of unknown 3D structures, the method provides a satisfactory correlation between the calculated binding free energy and the experimental pIC5o without reparametrization.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Changes in running mechanics and spring-mass behaviour during a 5-km time trial.

Research into the biomechanical manifestation of fatigue during exhaustive runs is increasingly popular but additional understanding of the adaptation of the spring-mass behaviour during the course of strenuous, self-paced exercises continues to be a challenge in order to develop optimized training and injury prevention programs. This study investigated continuous changes in running mechanics and spring-mass behaviour during a 5-km run. 12 competitive triathletes performed a 5-km running time trial (mean performance: ̴17 min 30 s) on a 200 m indoor track. Vertical and anterior-posterior ground reaction forces were measured every 200 m by a 5-m long force platform system, and used to determine spring-mass model characteristics. After a fast start, running velocity progressively decreased (- 11.6%; P<0.001) in the middle part of the race before an end spurt in the final 400-600 m. Stride length (- 7.4%; P<0.001) and frequency (- 4.1%; P=0.001) decreased over the 25 laps, while contact time (+ 8.9%; P<0.001) and total stride duration (+ 4.1%; P<0.001) progressively lengthened. Peak vertical forces (- 2.0%; P<0.01) and leg compression (- 4.3%; P<0.05), but not centre of mass vertical displacement (+ 3.2%; P>0.05), decreased with time. As a result, vertical stiffness decreased (- 6.0%; P<0.001) during the run, whereas leg stiffness changes were not significant (+ 1.3%; P>0.05). Spring-mass behaviour progressively changes during a 5-km time trial towards deteriorated vertical stiffness, which alters impact and force production characteristics.

Influence of the world's most challenging mountain ultra-marathon on energy cost and running mechanics

PURPOSE: To examine the effects of the world's most challenging mountain ultra-marathon (Tor des Géants(®) 2012) on the energy cost of three types of locomotion (cycling, level and uphill running) and running kinematics. METHODS: Before (pre-) and immediately after (post-) the competition, a group of ten male experienced ultra-marathon runners performed in random order three submaximal 4-min exercise trials: cycling at a power of 1.5 W kg(-1) body mass; level running at 9 km h(-1) and uphill running at 6 km h(-1) at an inclination of +15 % on a motorized treadmill. Two video cameras recorded running mechanics at different sampling rates. RESULTS: Between pre- and post-, the uphill-running energy cost decreased by 13.8 % (P = 0.004); no change was noted in the energy cost of level running or cycling (NS). There was an increase in contact time (+10.3 %, P = 0.019) and duty factor (+8.1 %, P = 0.001) and a decrease in swing time (-6.4 %, P = 0.008) in the uphill-running condition. CONCLUSION: After this extreme mountain ultra-marathon, the subjects modified only their uphill-running patterns for a more economical step mechanics.

Outcome of unilateral ankle arthrodesis and total ankle replacement in terms of bilateral gait mechanics.

Previous studies assessed the outcome of ankle arthrodesis (AA) and total ankle replacement (TAR) surgeries; however, the extent of postoperative recovery towards bilateral gait mechanics (BGM) is unknown. We evaluated the outcome of the two surgeries at least 2 years post rehabilitation, focusing on BGM. 36 participants, including 12 AA patients, 12 TAR patients, and 12 controls were included. Gait assessment over 50 m distance was performed utilizing pressure insoles and 3D inertial sensors, following which an intraindividual comparison was performed. Most spatiotemporal and kinematic parameters in the TAR group were indicative of good gait symmetry, while the AA group presented significant differences. Plantar pressure symmetry among the AA group was also significantly distorted. Abnormality in biomechanical behavior of the AA unoperated, contralateral foot was observed. In summary, our results indicate an altered BGM in AA patients, whereas a relatively fully recovered BGM is observed in TAR patients, despite the quantitative differences in several parameters when compared to a healthy population. Our study supports a biomechanical assessment and rehabilitation of both operated and unoperated sides after major surgeries for ankle osteoarthrosis.

Tuning the design procedures for laser processed microwave mechanics

This research has been focused at the development of a tuned systematic design methodology, which gives the best performance in a computer aided environment and utilises a cross-technological approach, specially tested with and for laser processed microwave mechanics. A tuned design process scheme is also presented. Because of the currently large production volumes of microwave and radio frequency mechanics even slight improvements of design methodologies or manufacturing technologies would give reasonable possibilities for cost reduction. The typical number of required iteration cycles could be reduced to one fifth of normal. The research area dealing with the methodologies is divided firstly into a function-oriented, a performance-oriented or a manufacturability-oriented product design. Alternatively various approaches can be developed for a customer-oriented, a quality-oriented, a cost-oriented or an organisation-oriented design. However, the real need for improvements is between these two extremes. This means that the effective methodology for the designers should not be too limited (like in the performance-oriented design) or too general (like in the organisation-oriented design), but it should, include the context of the design environment. This is the area where the current research is focused. To test the developed tuned design methodology for laser processing (TDMLP) and the tuned optimising algorithm for laser processing (TOLP), seven different industrial product applications for microwave mechanics have been designed, CAD-modelled and manufactured by using laser in small production series. To verify that the performance of these products meets the required level and to ensure the objectiveness ofthe results extensive laboratory tests were used for all designed prototypes. As an example a Ku-band horn antenna can be laser processed from steel in 2 minutes at the same time obtaining a comparable electrical performance of classical aluminium units or the residual resistance of a laser joint in steel could be limited to 72 milliohmia.

Moment Operators of Observables in Quantum Mechanics, with Applications to Quantization and Homodyne Detection

The questions studied in this thesis are centered around the moment operators of a quantum observable, the latter being represented by a normalized positive operator measure. The moment operators of an observable are physically relevant, in the sense that these operators give, as averages, the moments of the outcome statistics for the measurement of the observable. The main questions under consideration in this work arise from the fact that, unlike a projection valued observable of the von Neumann formulation, a general positive operator measure cannot be characterized by its first moment operator. The possibility of characterizing certain observables by also involving higher moment operators is investigated and utilized in three different cases: a characterization of projection valued measures among all the observables is given, a quantization scheme for unbounded classical variables using translation covariant phase space operator measures is presented, and, finally, a mathematically rigorous description is obtained for the measurements of rotated quadratures and phase space observables via the high amplitude limit in the balanced homodyne and eight-port homodyne detectors, respectively. In addition, the structure of the covariant phase space operator measures, which is essential for the above quantization, is analyzed in detail in the context of a (not necessarily unimodular) locally compact group as the phase space.

Statistical mechanics of multi-edge networks

Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There are, however, subtle yet important considerations to be made regarding the nature of the weights used in this generalization. Weights can be either continuous or discrete magnitudes, and in the latter case, they can additionally have undistinguishable or distinguishable nature. This fact has not been addressed in the literature insofar and has deep implications on the network statistics. In this work we face this problem introducing multiedge networks as graphs where multiple (distinguishable) connections between nodes are considered. We develop a statistical mechanics framework where it is possible to get information about the most relevant observables given a large spectrum of linear and nonlinear constraints including those depending both on the number of multiedges per link and their binary projection. The latter case is particularly interesting as we show that binary projections can be understood from multiedge processes. The implications of these results are important as many real-agent-based problems mapped onto graphs require this treatment for a proper characterization of their collective behavior.

Energetics and mechanics of walking in patients with chronic low back pain and healthy matched controls.

PURPOSE: Walking in patients with chronic low back pain (cLBP) is characterized by motor control adaptations as a protective strategy against further injury or pain. The purpose of this study was to compare the preferred walking speed, the biomechanical and the energetic parameters of walking at different speeds between patients with cLBP and healthy men individually matched for age, body mass and height. METHODS: Energy cost of walking was assessed with a breath-by-breath gas analyser; mechanical and spatiotemporal parameters of walking were computed using two inertial sensors equipped with a triaxial accelerometer and gyroscope and compared in 13 men with cLBP and 13 control men (CTR) during treadmill walking at standard (0.83, 1.11, 1.38, 1.67 m s(-1)) and preferred (PWS) speeds. Low back pain intensity (visual analogue scale, cLBP only) and perceived exertion (Borg scale) were assessed at each walking speed. RESULTS: PWS was slower in cLBP [1.17 (SD = 0.13) m s(-1)] than in CTR group [1.33 (SD = 0.11) m s(-1); P = 0.002]. No significant difference was observed between groups in mechanical work (P ≥ 0.44), spatiotemporal parameters (P ≥ 0.16) and energy cost of walking (P ≥ 0.36). At the end of the treadmill protocol, perceived exertion was significantly higher in cLBP [11.7 (SD = 2.4)] than in CTR group [9.9 (SD = 1.1); P = 0.01]. Pain intensity did not significantly increase over time (P = 0.21). CONCLUSIONS: These results do not support the hypothesis of a less efficient walking pattern in patients with cLBP and imply that high walking speeds are well tolerated by patients with moderately disabling cLBP.

New insight in the relationship between regional patterns of knee cartilage thickness, osteoarthritis disease severity, and gait mechanics.

To test if the relationship between knee kinetics during walking and regional patterns of cartilage thickness is influenced by disease severity we tested the following hypotheses in a cross-sectional study of medial compartment osteoarthritis (OA) subjects: (1) the peak knee flexion (KFM) and adduction moments (KAM) during walking are associated with regional cartilage thickness and medial-to-lateral cartilage thickness ratios, and (2) the associations between knee moments and cartilage thickness data are dependent on disease severity. Seventy individuals with medial compartment knee OA were studied. Gait analysis was used to determine the knee moments and cartilage thickness was measured from magnetic resonance imaging. Multiple linear regression analyses tested for associations between cartilage thickness and knee kinetics. Medial cartilage thickness and medial-to-lateral cartilage thickness ratios were lower in subjects with greater KAM for specific regions of the femoral condyle and tibial plateau with no associations for KFM in patients of all disease severities. When separated by severity, the association between KAM and cartilage thickness was found only in patients with more severe OA, and KFM was significantly associated with cartilage thickness only for the less severe OA subjects for specific tibial plateau regions. The results support the idea that the KAM is larger in patients with more severe disease and the KFM has greater influence early in the disease process, which may lessen as pain increases with disease severity. Each component influences different regions of cartilage. Thus the relative contributions of both KAM and KFM should be considered when evaluating gait mechanics and the influence of any intervention for knee OA.

Comparison of Four Sections for Analyzing Running Mechanics Alterations During Repeated Treadmill Sprints.

We compared different approaches to analyze running mechanics alterations during repeated treadmill sprints. Thirteen active male athletes performed five 5-second sprints with 25 seconds of recovery on an instrumented treadmill. This approach allowed continuous measurement of running kinetics/kinematics and calculation of vertical and leg stiffness variables that were subsequently averaged over 3 distinct sections of the 5-second sprint (steps 2-5, 7-10, and 12-15) and for all steps (steps 2-15). Independently from the analyzed section, propulsive power and step frequency decreased with fatigue, while contact time and step length increased (P < .05). Except for step frequency, all mechanical variables varied (P < .05) across sprint sections. The only parameters that highly depend on running velocity (propulsive power and vertical stiffness) showed a significant interaction (P < .05) between the analyzed sections, with smaller magnitude of fatigue-induced change observed for steps 2-5. Considering all steps or only a few steps during early, middle, or late phases of 5-second sprints provides similar mechanical outcomes during repeated treadmill sprinting, although acceleration induces noticeable differences between the sections studied. Furthermore, quantifying mechanical alterations from the early acceleration phase may not be readily detectable, and is not recommended.

Imprecise measurements in quantum mechanics

In this thesis the structure and properties of imprecise quantum measurements are investigated. The starting point for this investigation is the representation of a quantum observable as a normalized positive operator measure. A general framework to describe measurement inaccuracy is presented. Requirements for accurate measurements are discussed, and the relation of inaccuracy to some optimality criteria is studied. A characterization of covariant observables is given in the case when they are imprecise versions of a sharp observable. Also the properties of such observables are studied. The case of position and momentum observables is studied. All position and momentum observables are characterized, and the joint positionmomentum measurements are discussed.