Two Notes on the Theoretical Physics of ATP Synthase

ATP Synthase is an essential molecule in cell and molecular biology. It is responsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase’s rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total linear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.

Two Notes on the Theoretical Physics of ATP Synthase

ATP Synthase is an essential molecule in cell and molecular biology. It is responsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase’s rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total linear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.

A Methodological Analysis for the Development of a Circular-Motion Concept Inventory in a Ugandan Context by Using the Delphi Technique

Concept inventories (CI) constitute a key thread in Physics Educational Research. As such, understanding the methodology and the technique of developing a good CI is essential for all physics teachers. This research aims to develop a circular-motion concept Inventory (CMCI) that is valid in the Ugandan context. To reach a consensus, we used the Delphi technique to collect the data from eleven experts in the physics discipline. These experts were asked to rank each CI item in the inventory, based on the relevant criteria, for assigning a degree of relevance for adoption on a scale ranging from one to four, one being "not relevant" and four being "highly relevant.” Because the technique does not require experts to meet face-to-face, they remained anonymous to one another. These experts are provided with structured questionnaires of CI items from the Rotational-Kinematics Inventory (RKI) and Rolling and Rotational Motion-Concept (RRMC) inventories in the first round, in order to adopt items relevant to circular-motion concepts in the Ugandan context. They agreed to use 31 CI items in the RKI and 14 CI items in the RRMC in the second round. The mean and standard deviation of expert replies were analysed by using descriptive statistics. We used the methodological principles of CI creation, in order to create eight CI items to fill in the missing sub-concepts. Therefore, a total of 53 concept items were created. In order to analyse their qualities in a psychometric analysis, these will be evaluated by using field testing and psychometric analysis. Various physics instructors will access the CMCI, because the field testing aims to gauge the level of educational efficacy in their academic and research initiatives.

Intraoperative rotational kinematics and its influence on postoperative clinical outcomes differ according to age in Unicompartmental knee Arthroplasty

Background Although Oxford unicompartmental knee arthroplasty (UKA) is used in patients of wide age ranges, there is no clear information regarding the age differences in terms of intraoperative femorotibial rotational kinematics and its influence on clinical outcomes. Therefore, this study was conducted to examine the age differences in terms of intraoperative rotational kinematics and postoperative clinical outcomes and to analyze their relationship with classification according to the age group. Methods We investigated 111 knees of patients who underwent Oxford UKA using a navigation system and divided them into two groups: elderly (aged ≥75 years; 48 knees) and nonelderly (aged < 75 years; 63 knees). Intraoperative tibial internal rotational angles relative to the femur during passive knee flexion were measured using a navigation system, and clinical outcomes were evaluated using knee range of motion, the Knee Injury and Osteoarthritis Outcome Score (KOOS), and the Knee Society Functional Score at 2 years postoperatively. The relationships between intraoperative tibiofemoral rotational angles and clinical outcomes were also evaluated in the two groups. Results The intraoperative tibial internal rotational angle relative to the femur during knee flexion was significantly larger in the nonelderly group (13.5°) than in the elderly group (9.0°). The intraoperative tibial internal rotational angle showed a positive correlation with the pain subscale of KOOS only in the nonelderly group. Conclusion Intraoperative rotational kinematics and its influence on clinical outcomes were different between elderly and nonelderly patients, and the tibial internal rotational angle could be a more important factor for successful UKA in nonelderly patients.

Rotational Soft-Tissue Balance Is Highly Correlated with Rotational Kinematics in Total Knee Arthroplasty

Recovery of normal knee kinematics is critical for improving functional outcomes and patient satisfaction after total knee arthroplasty (TKA). The kinematics pattern after TKA varies from case to case, and it remains unclear how to reproduce normal knee kinematics. The present study aimed to evaluate rotational knee kinematics and soft-tissue balance using a navigation system and to assess the influence of intraoperative soft-tissue balance on the rotational knee kinematics. We evaluated 81 osteoarthritic knees treated with TKA using a posterior stabilized (50 knees) or cruciate retaining (31 knees) prosthesis. Rotational kinematics were assessed at 0, 30, 45, 60, and 90 degrees flexion angles by using a computer-assisted navigation system. Correlation between femorotibial rotational position and measured soft tissue balance was assessed by using Spearman's rank correlation coefficient. Rotational soft-tissue balance (the median angle of rotational stress) was significantly correlated with rotational kinematics (rotational axis of the femur relative to the tibia throughout the range of motion) at all measured angles after TKA. The correlation coefficients between the median angle of rotational stress and rotational kinematics were 0.97, 0.80, 0.74, 0.71, and 0.70 at 0, 30, 45, 60, and 90 degrees of flexion, respectively (p-values <0.0001 in all measured angles). The correlation coefficient increased as the knee approached full extension. Our findings suggest that soft-tissue balance is a key factor for rotational kinematics, following both cruciate-retaining and posterior-stabilized TKA.

Intraoperative Rotational Kinematics and Its Influence on Postoperative Clinical Outcomes Differ According to Age in Unicompartmental Knee Arthroplasty

Background: Although Oxford unicompartmental knee arthroplasty (UKA) is used in patients of wide age ranges, there is no clear information regarding the age differences in terms of intraoperative femorotibial rotational kinematics and its influence on clinical outcomes. Therefore, this study was conducted to examine the age differences in terms of postoperative clinical outcomes and intraoperative rotational kinematics and to analyze their relationship with classification according to the age group.Methods: We investigated 111 knees of patients who underwent Oxford UKA using a navigation system and divided them into two groups: elderly (aged ≥75 years; 48 knees) and nonelderly (aged <75 years; 63 knees). Intraoperative tibial internal rotational angles relative to the femur during passive knee flexion were measured using a navigation system, and clinical outcomes were evaluated using knee range of motion, the Knee Injury and Osteoarthritis Outcome Score (KOOS), and the Knee Society Functional Score at 2 years postoperatively. The relationships between intraoperative tibiofemoral rotational angles and clinical outcomes were also evaluated in the two groups. Results: The intraoperative tibial internal rotational angle relative to the femur during knee flexion was significantly larger in the nonelderly group (13.5°) than in the elderly group (9.0°). The intraoperative tibial internal rotational angle showed a positive correlation with the pain subscale of KOOS only in the nonelderly group. Conclusion: Intraoperative rotational kinematics and its influence on clinical outcomes were different between elderly and nonelderly patients, and the tibial internal rotational angle could be a more important factor for successful UKA in nonelderly patients.

Impact Performance Comparison of Advanced Snow Sport Helmets with Dedicated Rotation-Damping Systems

Rotational acceleration of the head is a principal cause of concussion and traumatic brain injury. Several rotation-damping systems for helmets have been introduced to better protect the brain from rotational forces. But these systems have not been evaluated in snow sport helmets. This study investigated two snow sport helmets with different rotation-damping systems, termed MIPS and WaveCel, in comparison to a standard snow sport helmet without a rotation-damping system. Impact performance was evaluated by vertical drops of a helmeted Hybrid III head and neck onto an oblique anvil. Six impact conditions were tested, comprising two impact speeds of 4.8 and 6.2 m/s, and three impact locations. Helmet performance was quantified in terms of the linear and rotational kinematics, and the predicted probability of concussion. Both rotation-damping systems significantly reduced rotational acceleration under all six impact conditions compared to the standard helmet, but their effect on linear acceleration was less consistent. The highest probability of concussion for the standard helmet was 89%, while helmets with MIPS and WaveCel systems exhibited a maximal probability of concussion of 67 and 7%, respectively. In conclusion, rotation-damping systems of advanced snow sport helmets can significantly reduce rotational head acceleration and the associated concussion risk.

Effects of Anterolateral Structure Augmentation on the In Vivo Kinematics of Anterior Cruciate Ligament–Reconstructed Knees

Background: Double-bundle anterior cruciate ligament (ACL) reconstruction (ACLR) is a well-known treatment that restores the stability of ACL-deficient knees. However, some isolated ACL-reconstructed knees ultimately show rotatory laxity and develop osteoarthritis. Whether combined ACLR with anterolateral structure (ALS) augmentation (ALSA) can provide better improvement in the in vivo knee rotational kinematics remains unknown. Hypothesis: When compared with isolated double-bundle ACLR, combined double-bundle ACLR with ALSA can improve knee in vivo rotational kinematics and provide better restoration of knee kinematics. Study Design: Controlled laboratory study. Methods: Sixteen patients with unilateral ACL injury were randomly divided into 2 groups to receive either combined double-bundle ACLR and ALSA (ALSA group) or isolated double-bundle ACLR (ACLR group). All patients performed a single-leg lunge using the operative and nonoperative/contralateral legs under dual-fluoroscopic imaging system surveillance during a hospital visit at a minimum 1 year (12-13 months) of follow-up to assess the 6 degrees of freedom knee kinematics. Functional evaluation using the Lysholm and Marx rating scales and clinical examinations were also performed. Results: From full extension to approximately 90° of knee flexion at 5° intervals, the mean ± SD internal rotation of the reconstructed knees in the ALSA group (1.5°± 0.9°) was significantly smaller than that of the contralateral knees (8.2°± 1.9°; P = .008). The ALSA group knees also showed significantly ( P = .045) more medial translation than the contralateral knees. In the ACLR group, the mean internal rotation of the reconstructed knee (6.0°± 2.1°) was significantly smaller than that of the contralateral knees (8.9°± 0.6°; P < .001). At full extension, the tibia was significantly more externally rotated than that of the contralateral legs (0.5°± 7.4° vs 7.6°± 3.4°, P = .049). Conclusion: When compared with isolated double-bundle ACLR, double-bundle ACLR augmented with ALS reconstruction resulted in anterolateral rotatory overconstraint during the lunge motion. Clinical Relevance: Additional ALSA of double-bundle ACL-reconstructed knees overconstrained rotatory stability. Therefore, the use of ALSA for ACL-reconstructed knees should be considered with caution for patients with ACL deficiency and anterolateral rotatory instability. Longer-term follow-up to evaluate long-term outcomes and altered kinematics over time is recommended.

Estimating Movement Smoothness From Inertial Measurement Units

Inertial measurement units (IMUs) are increasingly used to estimate movement quality and quantity to the infer the nature of motor behavior. The current literature contains several attempts to estimate movement smoothness using data from IMUs, many of which assume that the translational and rotational kinematics measured by IMUs can be directly used with the smoothness measures spectral arc length (SPARC) and log dimensionless jerk (LDLJ-V). However, there has been no investigation of the validity of these approaches. In this paper, we systematically evaluate the use of these measures on the kinematics measured by IMUs. We show that: (a) SPARC and LDLJ-V are valid measures of smoothness only when used with velocity; (b) SPARC and LDLJ-V applied on translational velocity reconstructed from IMU is highly error prone due to drift caused by integration of reconstruction errors; (c) SPARC can be applied directly on rotational velocities measured by a gyroscope, but LDLJ-V can be error prone. For discrete translational movements, we propose a modified version of the LDLJ-V measure, which can be applied to acceleration data (LDLJ-A). We evaluate the performance of these measures using simulated and experimental data. We demonstrate that the accuracy of LDLJ-A depends on the time profile of IMU orientation reconstruction error. Finally, we provide recommendations for how to appropriately apply these measures in practice under different scenarios, and highlight various factors to be aware of when performing smoothness analysis using IMU data.