The increased thermal motion of the thin filament could reach a larger number of HMM molecules, thereby forming the increased number of cross-bridges at higher temperature.

The interaction between actin and myosin may be promoted at higher temperatures, because it is an endothermic reaction.

However, whether this increase in the number of available cross-bridges is a physiological phenomenon is still an open question.

The observed cross-bridge number increased with temperature. One possibility is that the Brownian motion may release the head portion of HMM that are inadvertently stuck to the glass surface, but it leaves the C-terminus area of HMM attached to the glass surface, so that more HMM molecules become available to interact with the actin filament to generate more force at higher temperatures. However, this increase may be specific to the in vitro motility system, because the cross-bridge number is presumably maximized during the rigor induction, hence the number should not change with temperature in a physiological experiment. 

The average force per cross-bridge does not change much with temperature in the in vitro motility assay system. The HMM molecules do not change their shape much as the temperature is increased. A change in the shape would be necessary if force per crossbridge or unbinding force were to change with the temperature, because force is presumably a result of the macromolecular architecture of the HMM and actin interrelationship. 

Sliding velocity is expected to increase with the temperature. This is because the velocity is limited by one or two steps in the cross-bridge cycle, and their rate constants almost invariably increase with the temperature. 

The temperature insensitivity of the single molecular force is a fundamental property of a motor protein, and the force is associated with a particular macromolecular architecture. ( Conclusion ) 

1. Ca2+ dependent sliding speed of unloaded thin filaments in vitro;

2. Ca2+ activation of the thin filament-myosin S1 ATPase rate.

In the normal in vitro motility assay the thin filaments are unloaded, therefore the interpretation of the results obtained from such systems is limited to comparisons with unloaded shortening in intact muscle.

The principle of novel in vitro motility assay is to place an internal load upon the thin filament to retard filament movement due to the myosin motor. This is achieved by using an actin-binding protein attached to the cover glass along with the immobilized myosin motor protein. The greater the force on an actin filament, the higher the concentration of actin-binding protein needed to stop movement.

Bing, W., A. Knott, and S.B. Marston, A simple method for measuring the relative force exerted by myosin on actin filaments in the in vitro motility assay: evidence that tropomyosin and troponin increase force in single thin filaments. Biochem J, 2000. 350 Pt 3: p. 693-9

The Hill Coefficient (n) describes the fraction of the enzyme saturated by ligand as a function of the ligand concentration; it is used in determining the degree of cooperativity of the enzyme.

1. Positively cooperative reaction (n > 1): Once one ligand molecule is bound to the enzyme, its affinity for other ligand molecules increases.
2. Negatively cooperative reaction (n < 1): Once one ligand molecule is bound to the enzyme, its affinity for other ligand molecules decreases.
3. Noncooperative reaction (n = 1): The affinity of the enzyme for a ligand molecule is not dependent on whether or not other ligand molecules are already bound.

Calcium sensitivity (pCa50): negative log of the calcium concentration at half-maximal velocity / force) of thin filament;

Cooperativity (Hill Coefficient): Values are expressed as least-square regression of the fit to the Hill equation ± SE;

Maximal activation (Vmax or Fmax): maximal calcium-activated velocity / of thin filament.

VanBuren, P., et al., Cardiac troponin T isoforms demonstrate similar effects on mechanical performance in a regulated contractile system. Am J Physiol Heart Circ Physiol, 2002. 282(5): p. H1665-71

Thin filaments were then labeled with rhodamine-phalloidin at a 1:1 actin-to-phalloidin ratio in low-salt buffer (in mM: 25 KCl, 25 imidazole, 5 MgCL2, 10 DTT, and 2 EGTA, pH 7.4) and stored overnight a 4°C before use in the in vitro motility assay.

We emphasize that two types of variability were observed: (i) variation in the average velocities of different complexes, referred to in the literature as ‘‘static disorder,’’ and (ii) variations in the velocities of single complexes in time, referred to as ‘‘dynamic disorder’’ . Although it is difficult to rule out protein degradation or instability as a contributing factor to static disorder, such effects cannot fully explain dynamic disorder because the velocity was observed to vary both up and down in time. Degradation would be expected to only cause decreases.

…, Similar levels of static and dynamic disorder in enzyme kinetics have been reported in several previous single-molecule experiments… Our data show that such behavior can also occur in a more complex, multicomponent motor. Other researchers have provided evidence that such variability can be attributed to the existence of multiple active conformational states of the enzyme complexes and slow interconversion between them. …, suggest multiple … conformers and assembly states exhibiting different levels of ATPase activity.

The NH₂-terminal segment of TnT (TnT-NH₂⁺)highly charged, and binds at the NH₂-terminal/COOH-terminal overlap of two adjacent Tm molecules in a calcium-independent manner, thus providing a tether for the entire Tn complex to the thin filament during muscle activation.

The TnT-NH₂⁺enhances the binding of the Tm to actin and thus likely facilitates the communication of movement between adjacent Tm with thin filament activation. The overlap of adjacent Tm is felt to be a critical component of thin filament-mediated cooperative activation.