Force Matching Research Articles

A comparison of three DFT exchange-correlation functionals and two basis sets for the prediction of the conformation distribution of hydrated polyglycine.

The performance of three density functional theory (DFT) exchange-correlation functionals, namely, Perdew-Burke-Ernzerhof (PBE), BP86, and B3LYP, in predicting conformational distributions of a hydrated glycine peptide is tested with two different basis sets in the framework of adaptive force matching (AFM). The conformational distributions yielded the free energy profiles of the DFT functional and basis set combinations. Unlike traditional validations of potential energy and structural parameters, our approach allows the free energy of DFT to be validated. When compared to experimental distributions, the def2-TZVP basis set provides better agreement than a slightly trimmed aug-cc-pVDZ basis set. B3LYP is shown to be better than BP86 and PBE. The glycine model fitted against B3LYP-D3(BJ) with the def2-TZVP basis set is the most accurate and named the AFM2021 model for glycine. The AFM2021 glycine model provides better agreement with experimental J-coupling constants than C36m and ff14SB, although the margin is very small when compared to C36m. Our previously published alanine model is also refitted with the slightly simplified AFM2021 energy expression. This work shows good promise of AFM for developing force fields for a range of proteinogenic peptides using only DFT as reference.

Impairments in grip and pinch force accuracy and steadiness in people with osteoarthritis of the hand: A case-control comparison

BackgroundSymptomatic hand osteoarthritis (OA) is severely disabling condition. Limited evidence has focused on force control measures in this population. ObjectivesIt was the aim of the present study to determine whether force matching accuracy and steadiness are impaired in people with hand OA. In addition, the relationship between force control measures (accuracy and steadiness) and measures of hand function and pain in people with symptomatic hand OA was explored. DesignCase-control study. MethodSixty-two participants with symptomatic hand OA and 26 healthy pain-free controls undertook an isometric grip and pinch force matching task at 50 % of their maximum voluntary contraction. Average pain hand pain was recorded. In addition, the Disability of the Arm Shoulder and Hand Questionnaire (DASH), and the Functional Index of Hand Osteoarthritis were collected. ResultsGrip force-matching accuracy and steadiness were significantly impaired in the hand OA group compared to controls (P < 0.05). Pinch force-matching error was greater in people with hand OA (P < 0.05), however, pinch force steadiness was not different between groups. There was a learning effect in people with hand OA, with resolution of force matching impairments with task repetition. A small positive correlation was identified between grip force control and the DASH. No association was found between other measures of force control and self-reported measures of function or pain. ConclusionsPeople with hand OA presented with greater impairments in measures of submaximal force control. These were correlated with self-reported hand function but not pain. Future studies may wish to examine whether objective measures of functional performance are related to force-matching error and steadiness.

Performing Molecular Dynamics Simulations and Computing Hydration Free Energies on the B3LYP-D3(BJ) Potential Energy Surface with Adaptive Force Matching: A Benchmark Study with Seven Alcohols and One Amine.

The potential energy surfaces at the B3LYP-D3(BJ) level for eight solutes in dilute aqueous solutions were mapped into simple pairwise additive force field expressions using the adaptive force matching (AFM) method. The quality of the fits was validated by computing the hydration free energy (HFE), enthalpy of hydration, and diffusion constant for each solute. By force matching B3LYP-D3(BJ), the predictions from the models agree with the closest experimental HFE and enthalpy of hydration within chemical accuracy. The diffusion constants from the models are also in good agreement with experimental references. The good agreement provides confidence on the quality of B3LYP-D3(BJ) in producing potential energy surfaces for thermodynamic property calculations through AFM for the molecules studied. Accurate computational predictions could potentially provide validations to experimental measurements in cases where experimental measurements from different sources do not agree.

Reaction Path-Force Matching in Collective Variables: Determining Ab Initio QM/MM Free Energy Profiles by Fitting Mean Force.

First-principles determination of free energy profiles for condensed-phase chemical reactions is hampered by the daunting costs associated with configurational sampling on ab initio quantum mechanical/molecular mechanical (AI/MM) potential energy surfaces. Here, we report a new method that enables efficient AI/MM free energy simulations through mean force fitting. In this method, a free energy path in collective variables (CVs) is first determined on an efficient reactive aiding potential. Based on the configurations sampled along the free energy path, correcting forces to reproduce the AI/MM forces on the CVs are determined through force matching. The AI/MM free energy profile is then predicted from simulations on the aiding potential in conjunction with the correcting forces. Such cycles of correction-prediction are repeated until convergence is established. As the instantaneous forces on the CVs sampled in equilibrium ensembles along the free energy path are fitted, this procedure faithfully restores the target free energy profile by reproducing the free energy mean forces. Due to its close connection with the reaction path-force matching (RP-FM) framework recently introduced by us, we designate the new method as RP-FM in collective variables (RP-FM-CV). We demonstrate the effectiveness of this method on a type-II solution-phase SN2 reaction, NH3 + CH3Cl (the Menshutkin reaction), simulated with an explicit water solvent. To obtain the AI/MM free energy profiles, we employed the semiempirical AM1/MM Hamiltonian as the base level for determining the string minimum free energy pathway, along which the free energy mean forces are fitted to various target AI/MM levels using the Hartree-Fock (HF) theory, density functional theory (DFT), and the second-order Møller-Plesset perturbation (MP2) theory as the AI method. The forces on the bond-breaking and bond-forming CVs at both the base and target levels are obtained by force transformation from Cartesian to redundant internal coordinates under the Wilson B-matrix formalism, where the linearized FM is facilitated by the use of spline functions. For the Menshutkin reaction tested, our FM treatment greatly reduces the deviations on the CV forces, originally in the range of 12-33 to ∼2 kcal/mol/Å. Comparisons with the experimental and benchmark AI/MM results, tests of the new method under a variety of simulation protocols, and analyses of the solute-solvent radial distribution functions suggest that RP-FM-CV can be used as an efficient, accurate, and robust method for simulating solution-phase chemical reactions.

Effect of elbow joint angles on electromyographic activity versus force relationships of synergistic muscles of the triceps brachii.

The electromyographic (EMG) activity and force relationship, i.e. EMG-force relationship, is a valuable indicator of the degree of the neuromuscular activation during isometric force production. However, there is minimal information available regarding the EMG-force relationship of individual triceps brachii (TB) muscles at different elbow joint angles. This study aimed to compare the EMG-force relationships of the medial (TB-Med), lateral (TB-Lat), and long heads (TB-Long) of the TB. 7 men and 10 women performed force matching isometric tasks at 20%, 40%, 60%, and 80%maximum voluntary contraction (MVC) at 60°, 90°, and 120° of extension. During the submaximal force matching tasks, the surface EMG signals of the TB-Med, TB-Lat, and TB-Long were recorded and calculated the root mean square (RMS). RMS of each force level were then normalized by RMS at 100%MVC. For the TB-Med, ultrasonography was used to determine the superficial region of the muscle that faced the skin surface to minimize cross-talk. The joint angle was monitored using an electrogoniometer. The elbow extension force, elbow joint angle, and surface EMG signals were simultaneously sampled at 2 kHz and stored on a personal computer. The RMS did not significantly differ between the three muscles, except between the TB-Med and TB-Lat during 20%MVC at 60°. The RMS during force levels of ≥ 60%MVC at 120° was significantly lower than that at 60° or 90° for each muscle. The sum of difference, which represents the difference in RMS from the identical line, did not significantly differ in any of the assessed muscles in the present study. This suggests that a relatively smaller neuromuscular activation could be required when the elbow joint angle was extended. However, neuromuscular activation levels and relative force levels were matched in all three TB synergists when the elbow joint angle was at 90° or a more flexed position.

Ultra-coarse-graining of homopolymers in inhomogeneous systems

We develop coarse-grained (CG) models for simulating homopolymers in inhomogeneous systems, focusing on polymer films and droplets. If the CG polymers interact solely through two-body potentials, then the films and droplets either dissolve or collapse into small aggregates, depending on whether the effective polymer–polymer interactions have been determined from reference simulations in the bulk or at infinite dilution. To address this shortcoming, we include higher order interactions either through an additional three-body potential or a local density-dependent potential (LDP). We parameterize the two- and three-body potentials via force matching, and the LDP through relative entropy minimization. While the CG models with three-body interactions fail at reproducing stable polymer films and droplets, CG simulations with an LDP are able to do so. Minor quantitative differences between the reference and the CG simulations, namely a slight broadening of interfaces accompanied by a smaller surface tension in the CG simulations, can be attributed to the deformation of polymers near the interfaces, which cannot be resolved in the CG representation, where the polymers are mapped to spherical beads.

Sense of effort is distorted in people with chronic low back pain

Background: Proprioceptive deficits in people with low back pain (LBP) have traditionally been attributed to altered paraspinal muscle spindle afference and its central processing. Studies conducted in the upper limb demonstrated that sense of effort is also an important source of kinaesthetic information. Objectives: To better understand proprioceptive deficits in people with chronic LBP (cLBP), this study aimed to test whether sense of effort is affected in people with cLBP. Design: Cross-sectional study. Method: Fourteen participants with cLBP and fourteen healthy participants performed a 120 s force matching task with their trunk extensor muscles at a low intensity. Results: When visual feedback of the generated force was provided, both groups performed the task accurately. Removal of visual feedback resulted in an increase in error for both groups (p < 0.0001), but the increase in error was significantly larger for the cLBP group (p = 0.023). This larger error could be attributed to undershooting of the target force (p = 0.020). The control group did not consistently undershoot or overshoot the target force (p = 0.93). Furthermore, the amount of undershooting for the cLBP group increased as the task progressed (p = 0.016), which was not observed for the control group (p = 0.80). Conclusions: The results of this study revealed that sense of effort is affected in cLBP. People with cLBP overestimated the trunk extension force they generated, and the error increased as the trial progressed. With visual feedback however, people with cLBP were able to compensate and perform the task as accurately as people without cLBP.

Determining the hydration free energies of selected small molecules with MP2 and local MP2 through adaptive force matching.

Force fields for seven small solute molecules, ethanol, 2-methyl-1-propanol, 2-butanol, cyclohexene, tetrahydropyran, 1,4-dioxane, and 1,4-butanediol, in dilute aqueous solutions were created with the adaptive force matching (AFM) method using MP2 or local MP2 as reference. The force fields provide a way to predict the hydration free energies (HFEs) of these molecules with only electronic structure calculations as reference. For six of the seven molecules, the predicted HFEs are in very good agreement with experiments. For 1,4-butanediol, the model created by force matching LMP2 provides a HFE that is too positive. Further investigation suggests that LMP2 may not be sufficiently accurate for computing HFEs for alcohols with AFM. Other properties, such as enthalpy of hydration, diffusion constants, and vibrational spectra, are also computed with the force field developed. The force fields developed by AFM provide a bridge for computing ensemble properties of the reference electronic structure method. With MP2 and LMP2 as reference methods, the computed properties of the small molecular solutes are found to be in good agreement with experiments.

Functional correlates of motor control impairments in multiple sclerosis: A 7 Tesla task functional MRI study.

Upper and lower limb impairments are common in people with multiple sclerosis (pwMS), yet difficult to clinically identify in early stages of disease progression. Tasks involving complex motor control can potentially reveal more subtle deficits in early stages, and can be performed during functional MRI (fMRI) acquisition, to investigate underlying neural mechanisms, providing markers for early motor progression. We investigated brain activation during visually guided force matching of hand or foot in 28 minimally disabled pwMS (Expanded Disability Status Scale (EDSS) < 4 and pyramidal and cerebellar Kurtzke Functional Systems Scores ≤ 2) and 17 healthy controls (HC) using ultra‐high field 7‐Tesla fMRI, allowing us to visualise sensorimotor network activity in high detail. Task activations and performance (tracking lag and error) were compared between groups, and correlations were performed. PwMS showed delayed (+124 s, p = .002) and more erroneous (+0.15 N, p = .001) lower limb tracking, together with lower cerebellar, occipital and superior parietal cortical activation compared to HC. Lower activity within these regions correlated with worse EDSS (p = .034), lower force error (p = .006) and higher lesion load (p < .05). Despite no differences in upper limb task performance, pwMS displayed lower inferior occipital cortical activation. These results demonstrate that ultra‐high field fMRI during complex hand and foot tracking can identify subtle impairments in lower limb movements and upper and lower limb brain activity, and differentiates upper and lower limb impairments in minimally disabled pwMS.

Efficacy of the radial pair potential approximation for molecular dynamics simulations of dense plasmas

Macroscopic simulations of dense plasmas rely on detailed microscopic information that can be computationally expensive and is difficult to verify experimentally. In this work, we delineate the accuracy boundary between microscale simulation methods by comparing Kohn–Sham density functional theory molecular dynamics (KS-MD) and radial pair potential molecular dynamics (RPP-MD) for a range of elements, temperature, and density. By extracting the optimal RPP from KS-MD data using force matching, we constrain its functional form and dismiss classes of potentials that assume a constant power law for small interparticle distances. Our results show excellent agreement between RPP-MD and KS-MD for multiple metrics of accuracy at temperatures of only a few electron volts. The use of RPPs offers orders of magnitude decrease in computational cost and indicates that three-body potentials are not required beyond temperatures of a few eV. Due to its efficiency, the validated RPP-MD provides an avenue for reducing errors due to finite-size effects that can be on the order of ∼20%.

Development and Validation of a DFT-Based Force Field for a Hydrated Homoalanine Polypeptide.

A new force field has been created for simulating hydrated alanine polypeptides using the adaptive force matching (AFM) method. Only density functional theory calculations using the Perdew–Burke–Ernzerhof exchange–correlation functional and the D3 dispersion correction were used to fit the force field. The new force field, AFM2020, predicts NMR scalar coupling constants for hydrated homopolymeric alanine in better agreements with experimental data than several other models including those fitted directly to such data. For Ala7, the new force field shows about 15% helical conformations, 20% conformation in the β basin, and 65% polyproline II. The predicted helical population of short hydrated alanine is higher than previous estimates based on the same experimental data. Gas-phase simulations indicate that the force field developed by AFM solution-phase data is likely to produce a reasonable conformation distribution when hydration water is no longer present, such as the interior of a protein.

Distortions of the Efferent Copy during Force Perception: A Study of Force Drifts and Effects of Muscle Vibration

We used a finger force matching task to explore the role of efferent signals in force perception. Healthy, young participants performed accurate force production tasks at different force levels with the index and middle fingers of one hand (task-hand). They received visual feedback during an early part of each trial only. After the feedback was turned off, the force drifted toward lower magnitudes. After 5 s of the drift, the participants matched the force with the same finger pair of the other hand (match-hand). The match-hand consistently overshot the task-hand force by a magnitude invariant over the initial force levels. During force matching, both hands were lifted and lowered smoothly to estimate their referent coordinate (RC) and apparent stiffness values. These trials were performed without muscle vibration and under vibration applied to the finger/hand flexors or extensors of the task-hand or match-hand. Effects of vibration were seen in the match-hand only; they were the same during vibration of flexors and extensors. We interpret the vibration-induced effects as consequences of using distorted copies of the central commands to the task-hand during force matching. In particular, using distorted copies of the RC for the antagonist muscle group could account for the differences between the task-hand and match-hand. We conclude that efferent signals may be distorted before their participation in the perceptual process. Such distortions emerge spontaneously and may be amplified by the response of sensory endings to muscle vibration combined over both agonist and antagonist muscle groups.

Accurate MP2-based force fields predict hydration free energies for simple alkanes and alcohols in good agreement with experiments.

Force fields for four small molecules, methane, ethane, methanol, and ethanol, were created by force matching MP2 gradients computed with triple-zeta-quality basis sets using the Adaptive Force Matching method. Without fitting to any experimental properties, the force fields created were able to predict hydration free energies, enthalpies of hydration, and diffusion constants in excellent agreements with experiments. The root mean square error for the predicted hydration free energies is within 1 kJ/mol of experimental measurements of Ben-Naim et al. [J. Chem. Phys. 81(4), 2016–2027 (1984)]. The good prediction of hydration free energies is particularly noteworthy, as it is an important fundamental property. Similar hydration free energies of ethane relative to methane and of ethanol relative to methanol are attributed to a near cancellation of cavitation penalty and favorable contributions from dispersion and Coulombic interactions as a result of the additional methyl group.

A multi-resolution SPH method for fluid-structure interactions

In this paper, we present a multi-resolution smoothed particle hydrodynamics (SPH) method for modeling fluid-structure interaction (FSI) problems. By introducing different smoothing lengths and time steps, the spatial-temporal discretization is applied with different resolutions for fluid and structure. To ensure momentum conservation at the fluid-structure coupling, a position-based Verlet time integration scheme is introduced. Furthermore, the time-averaged velocity and acceleration of solid particles are introduced to enhance force matching in the fluid and solid equations. A set of numerical examples including several bio-mechanical problems are considered to demonstrate the efficiency, accuracy and robustness of the present method. An open-source code for all the examples is also provided.

Functional muscle synergies to support the knee against moment specific loads while weight bearing

ObjectiveExternally applied abduction and rotational loads are major contributors to the knee joint injury mechanism; yet, how muscles work together to stabilize the knee against these loads remains unclear. Our study sought to evaluate lower limb functional muscle synergies in healthy young adults such that muscle activation can be directly related to internal knee joint moments. MethodsConcatenated non-negative matrix factorization extracted muscle and moment synergies of 22 participants from electromyographic signals and joint moments elicited during a weight-bearing force matching protocol. ResultsTwo synergy sets were extracted: Set 1 included four synergies, each corresponding to a general anterior, posterior, medial, or lateral force direction. Frontal and transverse moments were coupled during medial and lateral force directions. Set 2 included six synergies, each corresponding to a moment type (extension/flexion, ab/adduction, internal/external rotation). Hamstrings and quadriceps dominated synergies associated with respective flexion and extension moments while quadriceps-hamstring co-activation was associated with knee abduction. Rotation moments were associated with notable contributions from hamstrings, quadriceps, gastrocnemius, and hip ab/adductors, corresponding to a general co-activation muscle synergy. ConclusionOur results highlight the importance of muscular co-activation of all muscles crossing the knee to support it during injury-inducing loading conditions such as externally applied knee abduction and rotation. Functional muscle synergies can provide new insight into the relationship between neuromuscular control and knee joint stability by directly associating biomechanical variables to muscle activation.

Impaired Regulation of Submaximal Force after ACL Reconstruction: Role of Muscle Spindles.

Ongoing motor deficits are routinely present following anterior cruciate ligament (ACL) reconstruction, including the ability to regulate muscle force. While such deficits are known, it is unclear why this occurs. The goal of the current study was to investigate the potential influence of muscle spindle input on submaximal force regulation and muscle activity at the knee in people following ACL reconstruction. Fourteen participants (8 female) who were 6-24 months post-ACL reconstruction and 15 control participants (8 female) undertook submaximal force matching and force modulation tasks before and after 20 min of vibration applied to the patella tendon. Across all tasks, the ACL reconstruction participants were poorer at force matching (P=0.007). The effect of vibration was not significant in either group for the force matching tasks (P=0.06), although there was a reduction in maximum voluntary contraction post-vibration in the control group (P<0.001). The ACL reconstruction group also showed evidence of greater activation of the medial hamstring muscles in comparison to controls (P=0.04). Individuals who have undergone ACL reconstruction have a diminished ability to accurately match and regulate submaximal muscle force, but this does not appear to be related to impaired muscle spindle input. Neuromuscular retraining programs that involve force regulation tasks may be necessary to optimize rehabilitation after ACL reconstruction.

Wear and Deformation Performance of W/Ta Multilayer Coatings on Pure Cu Prepared by Double Glow Plasma Alloying Technique

In this study, a multilayered hard coating with a tungsten matrix and a transition layer was deposited on pure copper by double glow plasma surface alloying technology, which aimed to provide the coating superior binding force and favorable matching of mechanical properties. The micro-hardness tester was adopted to measure the surface and cross-sectional hardness of the coatings. The nanoindentation test was used to measure the elasticity modulus of the coatings. Sliding wear tests under different conditions were performed on the W/Ta multilayer coating as well as the Cu substrate and W coating. The fairly low specific wear rate of the multilayer coating proved its excellent wear-resisting property, and the wear mechanism of the multilayer coating was mainly abrasive wear. In addition, a scratch test was executed to evaluate the deformation mechanism of the coating. Compared to the W coating, the persistence of the changing elastic–plastic deformation in the W/Ta multilayer coating improved the adhesion and resistance to plastic deformation. Moreover, the changing elastic–plastic deformation region is a benefit to the wear process, and the mechanical properties of the transition layer present a linear gradient descent instead of a vertical gradient, which makes a significant contribution in the wear stage. Further, the exploration of deformation mechanisms has a significant contribution to the design for multilayered hard coatings.

Finger Force Matching and Verbal Reports: Testing Predictions of the Iso-Perceptual Manifold Concept

We used force matching and verbal reports of finger force to explore a prediction of the iso-perceptual manifold concept, which assumes that stable percepts are associated with a manifold in the afferent-efferent space. Young subjects produced various force magnitudes with the index finger, middle finger, or both fingers together. Further, they reported the force level using a verbal scale and by matching the force with fingers of the contralateral hand. Force matching, but not verbal reports, showed larger variable errors for individual fingers in the two-finger task compared to the single-finger tasks. We discuss possible differences in afferent and efferent contributions to force perception at low and high forces based on the idea of motor control with referent coordinates for the effectors. The differences between the force matching and verbal reports are possibly related to neural circuitry differences between perceiving without action and perceiving-to-act.

Relationship between DTI Brain Connectivity and Functional Performance in Individuals with Traumatic Brain Injury.

this study examines the relationship between brain structural connectivity, and physical and cognitive performances in individuals with Traumatic Brain Injury (TBI). Nine moderate to severe TBI participants were included in the study, and regression analysis was performed to explore if DTI connectivity of 16 regions of interest can predict individuals' : 1) Maximum Voluntary Contraction (MVC), 2) time component of Wolf Motor Function Test (WMFT), 3) Reaction Time (RT) during bimanual force matching task, 4) Performance Error Measurement (PEM) during bimanual force matching task, and 5) cognitive assessment of task switching using Trail Making (TM) test. Results showed that slower WMFT, PEM, and TM can be predicted by weaker cerebrospinal tract connectivity. Higher Caudate connectivity predicted higher WMFT and slower RT, and higher right Cingulum predicted faster TM. Current results suggest that measures of cognitive-motor interference may be better indicators of functional performance than single cognitive and motor performance tests.

Intracortical Microstimulation Feedback Improves Grasp Force Accuracy in a Human Using a Brain-Computer Interface.

After a spinal cord injury, a person may grasp objects using a brain-computer interface (BCI) to control a robot arm. However, most BCIs do not restore somatosensory percepts that would enable someone to sense grasp force. Intracortical microstimulation (ICMS) in the somatosensory cortex can evoke tactile sensations and may therefore offer a viable solution to provide grasp force feedback. We investigated whether a bidirectional BCI could improve grasp force control over a BCI using only visual feedback. When evaluating the error of the applied force during a force matching task, we found that ICMS feedback improved overall applied grasp force accuracy.