El aprendizaje es un proceso neurofisiológico

values.

In the parameter values extracted from the published in vitro data a commonly recognised [10] inconsistancy was observed. A single crossbridge displacement is ~7.9nm, the attachment time of a crossbridge according to ATPase assays (Section

3.3, Table 3.3.1) is ~34ms which gives a maximum velocity of about 0.23µm/s when

in vitro experiments have shown unloaded filaments travel at speeds up to ~8µm/s

[59,90,91] and muscle contraction’s speeds are of the order 6-7 µm/s [10].

From the work described in Section 3.5, the lever distance is consistent with that from other work therefore the slow crossbridge duration was studied using the model described in this thesis. The crossbridge forms in reaction stage k4, where M.ADP.Pi

binds to actin forming the crossbridge (Figure 3.3.1) where a myosin bond site finds and binds to an actin bond site. The strain independent duration of this is ~33ms obtained from in vitro solutions of actin and myosin fragments (Section 3.3.3). In the

shorter than random fragments in the 3-d space of an in vitro solution. Therefore, as an

apparently dominant component of the attached time, the pre-lever reaction k4 was

examined by reducing its duration (increasing its reaction rate). As the reactions were strain independent they could not go into reverse.

In Figure 4.3.1 model data for the displacement against time of the right hand end of the actin filament are plotted for different durations of reaction stage k4. The filament

moved in steps, which settled, over time, into a pattern that roughly repeated (Figure 4.3.1 inset). The step duration decreased as pre-lever times decreased, increasing the

filament’s speed. As k4’s duration decreased below ~2.5ms the filament displacement

became unstable: after a short distance no new crossbridges formed to replace those that had released and with no crossbridges remaining the restoring force of titin drew the filament back to its initial position.

Figure 4.3.1, Results from the Baseline Model; displacement of the right-hand end of the actin filament over time showing the influence of the pre-lever reaction’s duration. The inset window

shows an enlargement of the 40 to 50 msec of movement, kta set at 0.06 x 10 -5

N/m.

In order to consider the involvement of k4 in the filament movement the repeat pattern

of behaviour was examined in more detail. Figure 4.3.2 plots the position and reaction state of each bond site and crossbridge against time for k4=300s

-1

(3.3ms duration)

(filament speed = 2µm/s) between 38-52ms after the model has started (the

the reaction stages to the overall movement the position and reaction state of each of the bond sites and crossbridges were plotted against time. The x-axis aligns

longitudinally with the actin filament. Diagrams B and the enlargement C show the longitudinal positions of the actin (solid grey lines) and myosin (blue dashed lines) bond sites (x-axis) against time (y-axis) as bonds are created and broken. B shows the full length of the actin and myosin filaments. Zero on the x-axis aligns with the M-disc. Each bond site is colour coded depending on its reaction state (D). The final positions of the bond sites on the actin filament are shown as black crosses on a black line representing the actin filament's final position (B).

Figure 4.3.2 C shows multiple crossbridges lever at the same time e.g. (2) and (3) having the displacement of a single crossbridge in this low load situation. Distortion of the myosin cofilament was minimal as it is stiff compared to the actin filament and myosin arms. With a long pre-lever duration a crossbridge can travel a large distance as the actin filament is moved on by other crossbridges before it expresses its strain energy. Its lever distance then becomes ineffectual in propelling the actin forward and puts energy into straightening the myosin arm it is attached to (E). During the

crossbridge the blue-dashed line indicates the relaxed arm, S1-S2, position this allows the displacement of the crossbridge from its initial formation to be seen. Figure 4.3.2, C shows all of the crossbridges losing movement in this way with (1), (4) losing the majority of forward displacement.

Similar plots showed that as the pre-lever was shortened below ~2.5ms the duration of the levering stage, k6, (Figure 3.3.1) came to dominate the attachment cycle and the

crossbridges went into equilibrium with the forces in the actin filament. The pattern and timing of the release of these crossbridges became dependent on the probability and chance model described in Section 3.5.7.

Figure 4.3.2, The position and reaction state of individual crossbridges during the repeat cycle of behaviour observed in Figure 4.3.1. k4 = 300s

-1

(3.3ms duration). Reaction states: actin site unbound (grey), pre-lever (black), levering (red), post-lever (blue). Myosin bond sites (dashed blue) marks the S2-S1 junction if the arm was relaxed this allows the crossbridge displacement

from its natural position to be gauged (E). The distance between the red and dashed red markers indicates the lever distance of the crossbridge (E).

4.3.1

Motility with Strain Independent Reactions:

conclusions.

As discussed in Section 4.1 the pre-lever reaction time has a dominant influence on filament speed. If shortened a modest amount the speed increased (2µm/s, k4= 300s-1

(3.3ms duration)) but if over shortened the persistence of movement was lost, the actin filament stopped moving forward and the restoring force of titin returned it to its start point. Stability may not be necessary in a sarcomere where multiple filaments work together but observations made during in vitro motility [91] studies show filaments of

1µm length can maintain movement with much higher speeds (6-7µm/s). The overall

filament displacement generated per crossbridge seemed inefficient: crossbridges levered together and travelled long distances in pre-lever states potentially straining against the forward movement of other crossbridges and losing their lever input to straightening their myosin arm. To investigate these characteristics further and better match the observed data, strain dependent pre-lever reactions were applied to the

Baseline Model. These had the potential to provide long strain free times consistent with in vitro reaction data but short attachment times during motility.

The unattached reaction cycle (Section 3.3.3) will not be considered at this time; an assumption is made that the in vitro measurements of individual fragments in solution in this strain free state are representative of those in the sarcomere. In addition, the system has been modelled with two heads per myosin arm (Section 3.2.9). As the first myosin bond site releases from a crossbridge the second myosin head has had time to go through the unattached reaction stages and was then available to bond.