Forward Jumps Research Articles

Jump performance and movement quality in 7- to 15-year-old competitive alpine skiers: a cross-sectional study

Introduction Injury rates in competitive alpine skiing are high. With current methods, identifying people at risk is expensive and thus often not feasible at the youth level. The aims of this study were (1) to describe the jump performance and movement quality of youth competitive alpine skiers according to age and sex, (2) to compare the jump distance among skiers of different sexes and movement quality grades, and (3) to assess the inter-rater grading reliability of the qualitative visual movement quality classification of such jumps and the agreement between live and video-based post-exercise grading. Materials and Methods This cross-sectional study is based on an anonymized dataset of 301 7- to 15-year-old competitive alpine skiers. The skiers performed two-legged forward triple jumps, whereby the jump distance was measured, and grades were assigned by experienced raters from the frontal and sagittal perspectives depending on the execution quality of the jumps. Furthermore, jumps were filmed and ultimately rated post-exercise. Differences in jump distance between various groups were assessed by multivariate analyses of variance (MANOVAs). Reliability was determined using Kendall’s coefficient of concordance. Results The jump distance was significantly greater in U16 skiers than in U11 skiers of both sexes and in skiers with good execution quality than in those with reduced or poor execution quality. Overall, jump distance in U16 skiers significantly differed between female (5.37 m with 95% CI [5.21, 5.53]) and male skiers (5.90 m with 95%CI [5.69, 6.10]). Slightly better inter-rater grading reliability was observed for video-based post-exercise (strong agreement) ratings than for live ratings (moderate agreement). Conclusion In competitive alpine skiers aged 7 to 15 years, jump performance increases with age, and around puberty, sex differences start to manifest. Our results highlight the importance of evaluating both jump distance and movement quality in youth skiers. To improve test-retest reliability, however, a video-based post-exercise evaluation is recommended.

Spatiotemporal jump detection during continuous film viewing: Insights from a flicker paradigm.

We investigated how sensitive visual processing is to spatiotemporal disruptions in ongoing visual events. Prior work has demonstrated that participants often miss spatiotemporal disruptions in videos presented in the form of scene edits or disruptions during saccades. Here, we asked whether this phenomenon generalizes to spatiotemporal disruptions that are not tied to saccades. In two flicker paradigm experiments, participants were instructed to identify spatiotemporal disruptions created when videos either jumped forward or backward in time. Participants often missed the jumps, and forward jumps were reported less frequently compared with backward jumps, demonstrating that a flicker paradigm produces effects similar to a saccade contingent disruption paradigm. These results suggest that difficulty detecting spatiotemporal disruptions is a general phenomenon that extends beyond trans-saccadic events.

Stochastic walker with variable long jumps.

Motivated by recent interest in the stochastic resetting of a random walker, we propose a generalized model where the random walker takes stochastic jumps of lengths proportional to its present position with certain probability, otherwise it makes forward and backward jumps of fixed (unit) length with given rates. The model exhibits a rich stochastic dynamic behavior. We obtain exact analytic results for the first two moments of the walker's displacement and show that a phase transition from a diffusive to superdiffusive regime occurs if the stochastic jumps of lengths that are twice (or more) of its present positions are allowed. This phase transition is accompanied by a reentrant diffusive behavior.

Comparative Effects of Different Physiotherapy Programs on Motor Skills of Children with Mild and Moderate Motor Impairment

Background. Children diagnosed with mild or moderate motor impairment not only face impairment of fine motor skills and problems with body balance in daily activities, they are also diagnosed with a decrease in muscle strength. Physiotherapy is prescribed to improve physical condition.
 The aim of the study was to determine the effect of different physiotherapy programs on running speed, balance and leg strength in children with mild and moderate motor impairment.
 Methods. 30 children (4–6 years old) with mild or moderate motor impairment participated in the study, and were randomly divided into two groups. The control group (n=15) received only conventional physiotherapy, while the experimental group (n=15) received a balance training program on the Abili Balance platform in addition to conventional physiotherapy. The duration of the interventions for both groups was 8 weeks. The subjects’ static and dynamic balance (according to Abili stability index and Berg scale), leg muscle strength (Broad jump) and running speed (Shuttle Run) were assessed before and after the interventions.
 Results. After 8 weeks, children in both groups had longer forward jumps and shorter shuttle run test results (p<0.05); balance indicators improved (p<0.05). After the interventions, the postural stability and leg muscle strength of the children in the study group were higher (p<0.05) than in the control group; other indicators did not differ significantly.
 Conclusions. Both applied 8-week physiotherapy programs were effective in improving children’s motor skills. Conventional physiotherapy combined with a balance training program was more effective than conventional physiotherapy in improving leg strength and postural stability in children with mild to moderate motor impairment, but not running speed and static and dynamic balance assessed by the Berg test.
 Keywords: leg, muscle strength, balance, running speed.

Full classification of dynamics for one-dimensional continuous-time Markov chains with polynomial transition rates

AbstractThis paper provides a full classification of the dynamics for continuous-time Markov chains (CTMCs) on the nonnegative integers with polynomial transition rate functions and without arbitrary large backward jumps. Such stochastic processes are abundant in applications, in particular in biology. More precisely, for CTMCs of bounded jumps, we provide necessary and sufficient conditions in terms of calculable parameters for explosivity, recurrence versus transience, positive recurrence versus null recurrence, certain absorption, and implosivity. Simple sufficient conditions for exponential ergodicity of stationary distributions and quasi-stationary distributions as well as existence and nonexistence of moments of hitting times are also obtained. Similar simple sufficient conditions for the aforementioned dynamics together with their opposite dynamics are established for CTMCs with unbounded forward jumps. Finally, we apply our results to stochastic reaction networks, an extended class of branching processes, a general bursty single-cell stochastic gene expression model, and population processes, none of which are birth–death processes. The approach is based on a mixture of Lyapunov–Foster-type results, the classical semimartingale approach, and estimates of stationary measures.

Motion extrapolation in the High-Phi illusion: Analogous but dissociable effects on perceived position and perceived motion.

A range of visual illusions, including the much-studied flash-lag effect, demonstrate that neural signals coding for motion and position interact in the visual system. One interpretation of these illusions is that they are the consequence of motion extrapolation mechanisms in the early visual system. Here, we study the recently reported High-Phi illusion to investigate whether it might be caused by the same underlying mechanisms. In the High-Phi illusion, a rotating texture is abruptly replaced by a new, uncorrelated texture. This leads to the percept of a large illusory jump, which can be forward or backward depending on the duration of the initial motion sequence (the inducer). To investigate whether this motion illusion also leads to illusions of perceived position, in three experiments we asked observers to localize briefly flashed targets presented concurrently with the new texture. Our results replicate the original finding of perceived forward and backward jumps, and reveal an illusion of perceived position. Like the observed effects on illusory motion, these position shifts could be forward or backward, depending on the duration of the inducer: brief inducers caused forward mislocalization, and longer inducers caused backward mislocalization. Additionally, we found that both jumps and mislocalizations scaled in magnitude with the speed of the inducer. Interestingly, forward position shifts were observed at shorter inducer durations than forward jumps. We interpret our results as an interaction of extrapolation and correction-for-extrapolation, and discuss possible mechanisms in the early visual system that might carry out these computations.

Falling as a strategy to decrease knee loading during landings: Implications for ACL injury prevention

Anterior cruciate ligament (ACL) injuries often occur when individuals land primarily on a single leg. Falling has been proposed as a potential strategy to decrease knee loading during landings. The purpose of this study was to compare impact forces, knee angles, and knee moments during natural landings, soft landings, and landings followed by falling after forward and vertical jumps, each under single or double-leg conditions. Sixteen male and sixteen female participants (age: 22.0 ± 2.9 years) completed each landing condition while kinematics and ground reaction forces were collected. In the natural landing condition, participants landed as they would in a sport setting. In the soft landing condition, participants landed as softly as possible with increased knee and hip flexion. In the falling condition, participants landed softly and then fell forward or backward onto a mat after forward and vertical jumps, respectively. The falling condition demonstrated the greatest initial and peak knee flexion angles, the least peak vertical ground reaction forces, and the least peak knee extension and adduction moments compared to the natural landing and soft landing conditions. The soft landing condition resulted in similar changes in landing mechanics compared to the natural landing, but the effect was limited for single-leg landings compared to double-leg landings. When the sports environment allows, falling appears to be a potential strategy to decrease knee loading when individuals must land on a single leg with sub-optimal body postures. Future studies are needed to develop progressive training of effective and safe falling techniques.

The Effect of Aspartate and Sodium Bicarbonate Supplementation on Muscle Contractile Properties Among Trained Men.

Farney, TM, MacLellan, MJ, Hearon, CM, Johannsen, NM, and Nelson, AG. The effect of aspartate and sodium bicarbonate supplementation on muscle contractile properties among trained men. J Strength Cond Res 34(3): 763-770, 2020-The focus of this investigation was to examine the effects of aspartate and NaHCO3 supplementation on muscle contractile properties within trained men. Eleven men (21.9 ± 1.5 years) ingested supplementation as 4 conditions all separated by 1 week and included the following: placebo (PLA), L-aspartate (12.5 mg) (ASP), NaHCO3 (0.3 g·kg) (SBC), or combination of ASP and SBC (CBO). For each day of testing, participants performed 1 high-intensity exercise session along with a pre- and postexercise (pre- or postex) isometric mid thigh pull test to measure peak force (PF) production and rate of force development (RFD). Blood was collected for all testing sessions before and after the high-intensity exercise to determine ammonia accumulation (AMM). Exercise sessions consisted of 4 exercises: barbell thrusters, squat jumps, lunge jumps, and forward jumps, with the total amount of work being equated for all 4 exercises across all 4 testing sessions. Participants performed the exercises in the aforementioned order, which was designated as 1 round. Each participant performed 3 rounds, with the work-to-rest ratio being 20-second work, 30-second rest. A 1-minute rest was given between the rounds. There were no treatment effects (p > 0.05) for PF, RFD, or AMM. However, there was a significant main effect for supplement consumption for the total time of work with the ASP, SBC, and CBO treatments having a lower time to completion compared with the PLA treatment. Ammonia was significantly elevated postexercise (p = 0.004), whereas there were no differences from preexercise to postexercise for PF or RFD (p > 0.05). The only significant treatment × time interaction was for RFD (p = 0.03) with CBO increasing postexercise, with the other 3 treatments all decreasing postexercise. The combination of ASP and SBC together may have the potential to reduce fatigue by mitigating the effects of metabolic by-product accumulation.

Development of vertical and forward jumping skills in typically developing children in the context of referent control of motor actions.

The empirically based referent control theory of motor actions provides a new framework for understanding locomotor maturation. Mature movement patterns of referent control are characterized by periods of minimization of activity across multiple muscles (global electromyographic [EMG] minima) resulting from transient matching between actual and referent body configurations. We identified whether locomotor maturation in young children was associated with (a) development of referent control and (b) children's frequency of participation in everyday activities evaluated by parents. Kinematics and EMG activity were recorded from typically developing children (n=15, 3-5years) and young adults (n=10, 18-25years) while walking, vertical or forward jumping. Presence and location of global EMG minima in movement cycles, slopes of ankle vertical/sagittal displacements, and shoulder displacement ratios were evaluated. Children had fewer global EMG minima compared to adults during specific phases of vertical and forward jumps. Ankle displacement profiles for walking and jumping forward were related to each other in adults, whereas those for walking and vertical jumping were related in children. Higher frequency of participation was significantly correlated with more mature jumping patterns in children. A decrease in the number of global EMG minima and changes in ankle movement patterns could be indicators of locomotor immaturity in typically developing children.

Do Stretch-Shortening Cycles Really Occur in the Medial Gastrocnemius? A Detailed Bilateral Analysis of the Muscle-Tendon Interaction During Jumping.

The effect of stretch-shortening cycles (SSCs) is often studied in laboratory settings, yet it remains unclear whether highly active muscle SSCs actually occur during in vivo movement. Nine highly trained jumping athletes performed single-leg pre-hop forward jumps at maximal effort. We hypothesized that these jumps would induce a SSC at the level of the muscle in the medial gastrocnemius. Kinematic and kinetic data were collected together with electromyography signals (EMG) and muscle fascicle length and pennation angle changes of the medial gastrocnemius of both legs and combined with a musculoskeletal model to calculate the stretch-shortening behavior of the muscle (fascicles) and tendon (series-elastic element). The length changes of the fascicles, longitudinal muscle displacement, series-elastic element, and whole muscle-tendon unit further allowed for a detailed analysis of the architectural gearing ratio between different phases of the SSC within a single movement. We found a SSC at the level of the joint, muscle-tendon unit and tendon but not at the muscle. We further found that the average architectural gearing ratio was higher during the stretching of the series-elastic element as compared to when the series-elastic element was shortening, yet this was not statistically tested because of low sample size for this parameter. However, we found no correlation when plotting the architectural gearing ratio as a function of the fascicle velocities at each instance in time. Despite the athletes having a clear preferred leg for jumping, we found no differences in any kinematic or kinetic parameter between the preferred and non-preferred leg or any parameter from the muscle-tendon interaction analysis other than a reduced longitudinal muscle shortening in the non-preferred leg (p = 0.008). We conclude that, although common at the level of the joints, MTUs, and tendon (series-elastic element), highly active SSCs very rarely occur in the medial gastrocnemius, even in movements that induce high loading. This has important implications for the translation of ex vivo findings on SSC effects, such as residual force enhancement, in this muscle. We further conclude that there is no precise tuning of the architectural gearing ratio in the medial gastrocnemius throughout the whole movement.

Changes in Floor Exercise Characteristics in World Elite Male Gymnasts

In artistic gymnastics, athletes need to compose their floor exercise routines in accordance with the Code of Points which is provided by the International Gymnastics Federation. In view of the latest rule modifications subsequent to the 2016 Olympic Games, this study investigates recent changes in judges’ scorings with respect to changes in the characteristics of floor exercise routines in world elite male gymnasts. Therefore, all floor exercise routines (n = 25) performed in the men’s floor exercise finals at the World Championships in 2013 (WC13), 2015 (WC15) and 2017 (WC17) were examined using video analysis. Gymnasts’ scores (difficulty, execution and final scores), element group distributions and further exercise characteristics (e.g., the total amount of somersaults, twists, and landing errors) were defined as variables. Decreases in difficulty and execution scores were revealed for WC17 compared to WC15 and WC13, respectively (p < .01). Additionally, a decrease in the number of backward jumped elements was observed at WC17 (p < .01), whereas the number of forward jumped elements increased (p < .01). Furthermore, a significantly increased number of landing errors (p < .05) negatively correlated with the decrease in execution (p < .001) and final scores (p < .05). To conclude, current compositional trends in men’s floor exercise encourage to include difficult forward jumps and multiple twisting connections in consideration of prudent teaching with respect to the gymnasts’ individual abilities and the decisive influence of stick landings.

Adjusted Muscle Strength Evaluation Using Directional and Continuous Jump Motion Test by 3D Motion Analysis

PURPOSE: To study adjusted muscle strength evaluation methods using directional and continuous jump motion tests (vertical,forward, backward), this study compares basketball players with general students and examines differences between the groups and directional differences. METHODS: Subjects were two groups ; General Students (14 male students) and Basketball Students (10 male students). Vertical, forward and backward jumps were each measured twice for maximum exertion (100%) and adjusted exertion (50%). The first vertical jump with full strength and then immediately after landing, adjusted exertion in each direction (50% exertion) (vertical, forward, backward) were measured using 3D motion analysis (Kinect2 (Microsoft)). Difference in average value in single jump measurement (50%) and continuous measurement (50%) using absolute values (cm) was verified and two factor ANOVA was conducted for differences between the groups (basketball vs. general) using relative values (%) and for differences among each direction (vertical, forward, backward). For the multiple comparison test, the Bonferroni method was used. The level of significance was set at 5%. RESULTS: In single jump and continuous measurements, the general student group showed close to 50% exertion in the order of forward, vertical, and backward jumps. The basketball group showed 50% exertion in the order of forward, backward, and vertical jumps. The order of superiority tended to be different between the two groups. Additionally, compared to the single jump measurement, continuous measurement showed that both the general student and basketball groups demonstrated close to 50% exertion and particularly in the continuous measurement, differences between the two groups tended to become more noticeable in the backward jump. CONCLUSIONS: For two groups, there are different directions in which adjusted exertion are likely to occur. By continuous jump measurement with initial movement maximum exertion, it is possible to evaluate accurate adjustment abilities and competitive qualities.

Professional Dancers Distinct Biomechanical Pattern during Multidirectional Landings.

This study aimed to compare lower extremity (LE) biomechanics between professional dancers (PD) and nondancers (ND) during multidirectional single-leg landings. Fifteen PD (27 ± 7 yr, 1.69 ± 0.1 m, 57.8 ± 9.3 kg) and 15 ND (25 ± 5 yr, 1.69 ± 0.1 m, 66 ± 10.2 kg) performed single-leg jumps in three directions: 1) lateral, 2) diagonal, and 3) forward. Dominant LE biomechanical data were collected using a motion capture system. Data were processed in Visual3D. LE kinematic (hip, knee, and ankle joint angles in sagittal and frontal planes, and range of motion [ROM]) and kinetics (hip and knee internal joint moments and vertical ground reaction force) variables were analyzed at initial contact (IC), peak vertical ground reaction force (PvGRF), and peak knee flexion (PKF). Repeated-measures ANOVA was conducted (P < 0.05). At IC, statistically significant interactions were found for ankle frontal and hip sagittal angles (P < 0.05). The main effects for groups and jump directions were attained (P < 0.05). PD at IC had lower hip and knee flexion and higher ankle plantarflexion than ND. PD had significantly higher knee (PD, 41 ± 6.1; ND, 33.8 ± 8.4) and ankle (PD, 53.7 ± 3.4; ND, 38.9 ± 8.9) ROM than ND. At IC, the lateral jump had higher hip abduction moment, hip abduction, and ankle inversion and lower hip flexion and ankle plantarflexion than the forward and diagonal jumps. The lateral jump (15.5 ± 7.7) had higher hip excursion than the forward jump (12.7 ± 5.4). The higher extended posture of PD at IC promoted an efficient use of the knee and ankle ROM to dissipate the landing forces. Regardless of the group, jump directions also solicited different biomechanical responses, particularly between lateral and forward directions. These strategies should be considered for implementation in prevention programs, as it can foster adequate LE neuromuscular control.

Comparison of jump-landing protocols with Biodex Balance System as measures of dynamic postural stability in athletes

The objective of the study was to determine whether a relationship exists between the two common methods for assessing postural stability in athletes: the time-to-stabilisation (TTS) via force-plate and the Biodex Balance System (BBS). The conditions under which these measurements assess dynamic postural control may not provide sufficient feedback to practitioners. Fourty-four amateur soccer players with no history of musculoskeletal disorders volunteered for the study. Pearson correlation was used to compare the anterior–posterior (AP), medio-lateral (ML), and the overall stability indexes measured by BBS, with the corresponding parameters of TTS assessed via force plate. There was no significant correlation between any parameters of dynamic stability measured by force-plate and the stability indexes. However, there was a significant correlation between the resulting vectors and the AP component of TTS for each jump protocol. Furthermore, forward drop landing exhibited shortest TTS in AP direction, while lateral drop landing resulted in longer ML TTS relative to both forward jumps (p < 0.001). These results demonstrate that the TTS and BBS stability indexes should be used as distinct measures of dynamic postural stability. TTS protocols may be modified to target a specific training conditions or athletic population.

Including Thermal Fluctuations in Actomyosin Stable States Increases the Predicted Force per Motor and Macroscopic Efficiency in Muscle Modelling.

Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges.

Neuromuscular Control Mechanisms During Single-Leg Jump Landing in Subacute Ankle Sprain Patients: A Case Control Study

BackgroundOptimal neuromuscular control mechanisms are essential for preparing, maintaining, and restoring functional joint stability during jump landing and to prevent ankle injuries. In subacute ankle sprain patients, neither muscle activity nor kinematics during jump landing has previously been assessed. ObjectiveTo compare neuromuscular control mechanisms and kinematics between subacute ankle sprain patients and healthy persons before and during the initial contact phase of a 25-cm single-leg jump. DesignCase-control study. SettingUniversity hospital. PatientsFifteen patients with grade I or II acute ankle sprains were followed up after 4 weeks of conservative management not involving physical therapy. MethodsSubjects performed alternately 3 single-leg forward jumps of 25 cm (toe-to-heel distance) barefoot. Their results were compared with the data of 15 healthy subjects. Main Outcome MeasurementsElectromyographic (EMG) activity of the musculus (m.) gastrocnemius lateralis, m. tibialis anterior, and m. peroneus longus as well as kinematics for ankle, knee, and hip joint were recorded for pre–initial contact (IC) phase, post–initial contact phase, and reflex-induced phase. ResultsThe results showed that EMG activity of the 3 muscles did not differ between ankle sprain patients (n = 15) and healthy persons (n = 15) for any of the analyzed time intervals (all P > .05). However, during the pre-IC phase, ankle sprain patients presented less plantar flexion, as well as during the post-IC phase after jump landing, compared to healthy persons (P < .05). ConclusionTaken together, these kinematic alterations of the ankle joint can lead to neuromuscular control mechanism disturbances through which functional instability might arise. Level of EvidenceIII

Interacting Gears Synchronize Propulsive Leg Movements in a Jumping Insect

Gears are found rarely in animals and have never been reported to intermesh and rotate functionally like mechanical gears. We now demonstrate functional gears in the ballistic jumping movements of the flightless planthopper insect Issus. The nymphs, but not adults, have a row of cuticular gear (cog) teeth around the curved medial surfaces of their two hindleg trochantera. The gear teeth on one trochanter engaged with and sequentially moved past those on the other trochanter during the preparatory cocking and the propulsive phases of jumping. Close registration between the gears ensured that both hindlegs moved at the same angular velocities to propel the body without yaw rotation. At the final molt to adulthood, this synchronization mechanism is jettisoned.

Effect of anticipation on knee kinematics during a stop-jump task

Knee stability during a functional assessment of the stop-jump task is a key factor to determine if an athlete is adequately rehabilitated after knee ligamentous injury. This study aimed to investigate knee stability due to the effect of anticipation on landing maneuvers during planned and unplanned stop-jump tasks. Knee kinematics of ten healthy male participants were collected using an optical motion analysis system during stop-jump tasks. Stop jumps were performed in four different landing positions either in planned movement or in an unplanned movement on a signal triggered as participants passed through a photocell gate. Kinematic data at the time of foot strike at landing in the stop-jump considered for investigating the anticipation effect during the stop-jump tasks. Two-way multivariate analysis of variance (MANOVA) with repeated measures and stratified paired t-tests were conducted to compare the knee kinematics data between planned and unplanned tasks. Statistical significance was set at the p<0.05 level. External rotational angle showed a significant decrease in unplanned stop-jump tasks during forward (p<0.05) and right (p<0.05) jumps when compared to that of planned tasks. Flexion angle and abduction angle during forward, vertical and right jumps were significantly decreased in the unplanned tasks. Anticipation significantly influenced the landing maneuvers of stop-jump task. The results indicated that both planned and unplanned stop-jump tasks should be considered when monitoring the rehabilitation progress after a ligamentous injury.

Optimum analysis of a Brownian refrigerator

A Brownian refrigerator with the cold and hot reservoirs alternating along a space coordinate is established. The heat flux couples with the movement of the Brownian particles due to an external force in the spatially asymmetric but periodic potential. After using the Arrhenius factor to describe the behaviors of the forward and backward jumps of the particles, the expressions for coefficient of performance (COP) and cooling rate are derived analytically. Then, through maximizing the product of conversion efficiency and heat flux flowing out, a new upper bound only depending on the temperature ratio of the cold and hot reservoirs is found numerically in the reversible situation, and it is a little larger than the so-called Curzon and Ahlborn COP ε(CA)=(1/√[1-τ])-1. After considering the irreversible factor owing to the kinetic energy change of the moving particles, we find the optimized COP is smaller than ε(CA) and the external force even does negative work on the Brownian particles when they jump from a cold to hot reservoir.

The elementary events underlying force generation in neuronal lamellipodia

We have used optical tweezers to identify the elementary events underlying force generation in neuronal lamellipodia. When an optically trapped bead seals on the lamellipodium membrane, Brownian fluctuations decrease revealing the underlying elementary events. The distribution of bead velocities has long tails with frequent large positive and negative values associated to forward and backward jumps occurring in 0.1–0.2 ms with varying amplitudes up to 20 nm. Jump frequency and amplitude are reduced when actin turnover is slowed down by the addition of 25 nM Jasplakinolide. When myosin II is inhibited by the addition of 20 μM Blebbistatin, jump frequency is reduced but to a lesser extent than by Jasplainolide. These jumps constitute the elementary events underlying force generation.