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Mitsui and Ohshima (2008) criticized the power-stroke model for muscle contraction and proposed a new model. In the new model, about 41% of the myosin heads are bound to actin filaments, and each bound head forms a complex MA_{3} with three actin molecules A1, A2 and A3 forming the crossbridge. The complex translates along the actin filament cooperating with each other. The new model well explained the experimental data on the steady filament sliding. As an extension of the study, the isometric tension transient and isotonic velocity transient are investigated. Statistical ensemble of crossbridges is introduced, and variation of the binding probability of myosin head to A1 is considered. When the binding probability to A1 is zero, the Hill-type force-velocity relation is resulted in. When the binding probability to A1 becomes finite, the deviation from the Hill-type force-velocity relation takes place, as observed by Edman (1988). The characteristics of the isometric tension transient observed by Ford, Huxley and Simmons (1977) and of the isotonic velocity transient observed by Civan and Podolsky (1966) are theoretically reproduced. Ratios of the extensibility are estimated as 0.22 for the crossbridge, 0.26 for the myosin filament and 0.52 for the actin filament, in consistency with the values determined by X-ray diffraction by Wakabayashi

_{12}transition

In 1999, Mitsui [

Now the article [

The basic ideas of our model introduced in [

Since the present study is based upon ideas that are quite different from the power stroke model and others, the basic ideas of our study are explained in some detail in Section 2. In Section 3, discussion is done of how variation in the crossbridge binding affects the muscle tension. In Section 4, discussion is done on the difference between the molecular processes in Phases 1 of the isometric tension transient and of the isotonic velocity transient, and extensibility ratios for the crossbridge, the myosin filament and the actin filament are estimated. Time course of the isometric tension transient is studied in Section 5. Time course of the isotonic velocity transient is studied in Section 6. The deviation from the Hill-type force-velocity relation is derived in Section 7. Obtained results are summarized and discussed in Section 8.

In the present study, the deviation from the hyperbolic force-velocity relation shown in _{dev} and the tension _{0obs}. The following values are determined by the data presented in

In our model, about 41% of the myosin heads are bound to actin filaments (cf. Equation 3–1–1 in [_{3} with three actin molecules. The complex MA_{3} translates along the actin filament changing the partner actin molecules. _{3}. The translation of the crossbridge along the actin filament is made possible by the structural change of MA_{3} induced by the force _{J} which exerts on the junction J between the crossbridge and the actin filament.

_{3}. There are three potential wells on the actin filament corresponding to the three binding sites A1, A2 and A3. The wells are also as called A1, A2 and A3. _{J} by _{0} − _{J} (Equation 3–5–2 in [_{dev}. this model seems close to reality when _{dev}. The deviation from the Hill-type relation when _{dev} suggests that the model in _{12} when _{dev}, and heads are distributed in A1 and A2 when _{dev}. The potential peak between A1 and A2 will be called _{12} and the potential barrier for backward movement from A2 to A1 will be denoted as _{12b} and the barrier for forward movement from A1 to A2 as _{12f}. In the followings, transitions of these types will be called _{12} transition.

The displacement of the myosin head from A2 to A1 was briefly mentioned in Section 3.6 of [_{12} transition by the statistical mechanics. Although the present study is based upon the same idea, we have found that such statistical-mechanical approach as in [

In the following discussion, a parameter _{eq} when the tilting angle of the myosin head neck domain is at the equilibrium angle _{Equation}. Then _{eq} in _{f} and _{b}, and, according to Equation 3–4–6 in [_{f} and _{b} are given in

To discuss the transition phenomena, it is important to have an idea about the mean time interval of occurrence of the _{step} in which a myosin head moves from one actin molecule to the neighboring one. This _{step} is given by
_{step} are calculated by using _{step} is about 2 ms at _{0} = 0, becomes 10 ms around _{0} = 0.5 and increases to 1 s around _{0} = 1. This result means that

In discussion of the steady filament sliding [_{c}-_{c} through filament sliding and from _{c} to _{c}-_{c} is the parameter which decreases as the tension

Suppose that all complexes MA_{3} in right half sarcomeres are collected and superposed putting A2 at the same position. This ensemble can be characterized by the ratio _{c} is defined by
_{c}-_{c}. In the following discussion, _{c}-_{c} and zero outside of the region. This will be called rectangular

The force-velocity relation deviates from Hill-type for _{dev} as shown in _{3} complex is shown. The potential at A2 is lower than that at A1, and all the myosin heads are present in well A2 in the case of _{dev} as shown in _{12} transition. Accordingly, the distribution of the myosin heads becomes as symbolically shown in _{dev}. This effect is regarded as the origin of the deviation of force-velocity relation from the Hill-type.

Symbols _{0obs} and _{cdev} are defined as _{c}’s at _{0obs} and _{dev}, respectively, on the Hill-type force-velocity relation (cf. _{c} decreases with increasing _{dev} corresponds to _{c} > _{cdev}.

_{c} > _{cdev} or _{dev}. _{c} < _{cdev} or _{dev}. In

_{c}-_{c}, and equal to zero outside of the region. Crossbridges in the red area produce positive stress, and crossbridges in the blue area produce negative stress. As the edge _{c} shifts to the left from (a2) to (b2), the red region increases and the crossbridge ensemble produce more stress and the filament sliding becomes slow (Note _{f} > _{b} in

_{dev} and thus _{c} < _{cdev}. In (c1), the blue dotted segment symbolically indicates that a portion of crossbridges of small

Now let us calculate values of _{cdev} and _{c0obs}. By definition, _{cdev} and _{c0obs} are _{c}’s for _{0obs} and _{dev} in the Hill-type force-velocity relation. The mean tension per one crossbridge is denoted as _{f}_{b}_{0} and _{0} following [_{0} = _{0} (Equation 3–1–2 in [_{0} is given by
_{dev} and _{cdev} and between _{0obs} and _{c0obs}. Combining _{cdev} and _{c0obs} are indicated by the vertical dotted red lines.

_{c} related by ^{H} and _{c}^{H}, which are in agreement with the observation when _{c}^{H} > _{cdev}. The observed _{c} are denoted as _{c}* when _{c}^{H} < _{cdev}.

_{c}^{H} < _{cdev}. _{c}^{H}. This ^{H} even though _{c} < _{cdev}. It is an imaginary state in which the _{12} transition is absent. Actually, however, the _{12} transition takes place and the violet area appears causing decrease of the red area as shown in (a2), where the width of the violet area is denoted as _{c}). Naturally _{c} in (a2) is changed into _{c}* in (a3) to make _{c} to _{c}* causes an increase of the tension while the change of the violet area from _{c}) to _{c}* and

Since the tension is the same in _{0}. _{c}* becomes negative. The brown area means that crossbridges in this area bind to A1 and produce positive stress. The width of the violet area is indicated as _{0} in (b3), _{0}. Then sum of the red area and brown area in (c) is smaller than red area in (b3) and thus the tension produced in (c) is smaller than the tension in (b3). Then the stress produced in (b3) is the maximum that the muscle machine can produce, and should be equal to _{0obs}. Accordingly, _{c}^{H} in (b1) should be equal to _{c0obs}. Since the red area in (b1) is the same as the red area in (b3), _{c}^{H} in (b1) is equal to _{0} in (b3). Thus we have
^{H} at _{c} = _{c}* = _{cdev}, and reaches its maximum at _{c}* = 0. To express such characteristics of

In _{0} _{c}* relation given by this set of equations, and the red curve shows the Hill-type ^{H}/_{0} _{c}^{H} relation. The blue curve deviates from the red curve at _{c} = _{c}* = _{cdev} and exhibits its maximum at _{c}* = 0 where ^{*}/_{0} = _{0obs}/_{0}.

Up to here, _{0} is used for the relative tension, where _{0} is the maximum tension in the extended Hill-type force-velocity relation. The experimentally observed maximum tension, however, is _{0obs} where _{0obs} = 0.88_{0} (_{0obs}. In our model _{0} = _{0} (Equation 3–1–2 in [_{0obs} is denoted as _{0obs}. Then
_{c} = _{c0obs} in _{0} = _{c0obs} (_{0obs} as

Huxley [

Phase T1 is simultaneous decrease of tension in the isometric tension transient, while Phase V1 is simultaneous shortening of muscle in the velocity transient. The length change per half sarcomere is denoted as Δ_{hs} in both transients. The experimentally measured isometric tension is _{0obs} and the relative tension is defined by _{0obs}. The relative load used in the paper by Civan and Podolsky [_{0obs} below.

At first sight, it was puzzling to see that distributions of the experimental data are quite different for the two cases, since the structural changes seem to be purely elastic both in Phases T1 and V1. Then it was reminded that the length change of sarcomere is a sum of those of the crossbridge, myosin filament and actin filament, which are proportional to each other (cf. the review by Irving [

In this connection, the experimental data reported by Julian and Sollins [_{hs} relation at different speeds of shortening. The distribution of open circles in their

It seems plausible that elastic response of crossbridge and myosin filament almost simultaneously occurs since they belong to the same molecule and elastic response of actin filament occurs with some delay. Thus it is assumed that crossbridge and myosin filament are responsible to the change in Phase T1 and that all three components are responsible to the change in Phase V1. Now changes of _{c} in Phases T1 and V1 should be different from each other even when the length change Δ_{hs} is the same. Calculation is done on this assumption by using the rectangular

_{hs} as (b). The violet areas in _{12} transition does not occur yet. Changes of the edge _{c} in Phases T1 and V1 are denoted as Δ_{cT1} and Δ_{cV1}. For the same Δ_{hs}, the tension _{cT1} in _{cV1} in (c) so as to make the red area in (b) smaller than that in (c), in accordance with the fact that the tension

Since elastic changes of the crossbridge, myosin filament and actin filament are proportional to each other [_{cT1} in (b) and Δ_{cV1} in (c) are proportional to Δ_{hs}, and expressed by
_{CBT} and _{CBV} are constants.

Let the tensions in _{T1} and _{V1}, respectively. They are given by integration of −_{b}{_{f}_{b}_{CBT} (_{CBV} (_{T1}/_{0obs} by the green curve and for _{V1}/_{0obs} by the brown curve. They are in good agreement with the experimental data.

Let us denote the ratios of extensibilities of the crossbridge, the myosin filament and the actin filament as _{CB}, _{M}, and _{A} at the elastic equilibrium respectively. Shortenings of the three per half sarcomere are denoted, respectively, as Δ_{CB}, Δ_{M} and Δ_{A,} and the length change of half sarcomere as Δ_{hs}. Then, at the elastic equilibrium, they are given by

On the above assumption, only the length changes of the crossbridge and the myosin filament contribute to Phase T1. Then we have

As assumed above, the load change period is long enough and elastic changes of the crossbridge, myosin filament and actin filament contribute to Phase V1. Thus, Δ_{cV1} is given by
_{CBT} (_{CBV} (

The extensibility ratios were investigated by X-ray diffraction by Huxley _{CB} = 0.31, _{M} = 0.27 and _{A} = 0.42. Considering approximate nature of the theory and experimental errors, our values in

In this section, it is assumed that elastic change of the actin filament does not take place during the fast length change in Phase T1. Then the elastic change of the actin filament should contribute to the next step, the tension recovery in Phase T2. This problem is discussed in next section.

As noted in Section 4, Huxley [

As in Section 4, we use the terms Phase Tn (n = 1, 2, 3, 4) in the tension transient to avoid confusion. Phases Tn are more related with molecular process rather than time sequence. Phase T1 is simultaneous drop of tension caused by elastic shortening of the crossbridge and myosin filament. Phase T2 is due to elastic shortening of the actin filament. Phase T3 is related with the _{12} transition, and divided into T3a and T3b. Phase T3a is the first part of Phase T3. Both Phases T2 and T3a contribute to the rapid early tension recovery (Phase 2 of Huxley). Phase T3b is the second part of T3 where the extreme reduction or reversal of rate of tension recovery occurs (Phase 3 of Huxley). Phase T4 is the gradual recovery of tension, with asymptotic approach to isometric tension (Phase 4 of Huxley). (There were misprints in Section 4.4 of the article [

_{cT1} < _{cdev} and _{cT1} > _{cdev}, where Δ_{cT1} is _{c} just after Phase T1. (cf.

As mentioned above, it is assumed that the elastic changes of the crossbridge and myosin filament occur in Phase T1 and then the elastic change of actin filament occurs in Phase T2. _{12} transition to occur, and its effect is neglected in Phases T1 and T2, so that the width of the violet area is kept the same as the isometric value _{0}.

As noted referring to _{step}) needed for the _{0} > 0.5). It is assumed that the potential barrier _{12f} (f: forward) is lower than _{12f} transition starts before the _{12f} transition is present but the _{12f} and _{12f} transition. Thus the red area increases and the stress is stored and the tension increases in Phase T3a. The _{c} from _{cT3a} in (c) to _{cT3b} in (d). The shift of the edge from _{cT3a} (c) to _{cT3b} (d) causes increase of the blue area and decrease of the violet area. These two effects tend to cancel each other and reduce change of the red area in the time course from (c) to (d),

_{cT1} > _{cdev}. _{cT1} > _{cdev}, the _{12f} transition does not leave the violet area and the red area significantly increases in (c). Then the

_{0obs} _{hs} relation. The solid black arrows “Phase Tn” indicate an example of change of relative tension in Phase Tn for the case of Δ_{cdev} and the dashed black arrows for the case of Δ_{cdev}. The edge Δ_{cT1} in _{hs} by combining

The tension variation _{T1}/_{0obs} in Phase T1 can be calculated as a function of Δ_{hs} by using _{cT2} in _{cV1} in _{cT2} = Δ_{cV1} means _{T2}/_{0obs} = _{V1}/_{0obs}. By using _{V1} by _{T2} and Δ_{cV1} by Δ_{cT2} in _{T2}/_{0obs} can be calculated as a function of Δ_{hs}. The calculation result is given by the brown curve in _{c} as shown in _{c} in _{c} in _{c} = _{c0obs} + Δ_{c} since Δ_{c} is the change of _{c} from the value at the isometric tension (_{c0obs}). In the steady filament sliding, all elastic elongations of the crossbridge, the myosin filament and the actin filament contribute to the muscle elongation and thus Δ_{c} (=_{c} − _{c0obs}) is equal to −Δ_{hs}/4.6 as in _{0} in _{0obs} by using the ratio _{0obs}/_{0} = 0.88 (

In _{cdev} (the case of _{cdev} (the case of _{cdev}, the solid arrow “Phase T3a” is depicted with its tip on the blue curve. As discussed above, it is plausible that the red area in _{cdev}, as discussed above, it is plausible that the red area significantly decreases from _{0obs} by the filament sliding as shown by the arrows “Phase T4”. The above argument on the solid and dashed arrows “Phase T3b” suggests that the reversal of rate of tension recovery occurs when |Δ_{hs}| is large. Supporting this conclusion, _{hs}| is large.

Ford _{0obs} during 0–9 ms, as cited by green circles in _{hs} was +1.5∼−6.0 nm in their experiment. Since our model is not applicable for positive Δ_{hs}, the case of +1.5 nm is omitted in

In _{0obs} quickly increase within about 1 ms and then gradually approach to the value at 9 ms. The mean time duration needed for one _{0} > 0.5 in _{hs} | are smaller than 7.0 nm as seen in _{hs} | range. The tension changes in Phases T1, T2 and T3a are denoted as _{1}, _{2} and _{3a}, respectively. Also symbols _{12} and _{123a} are defined as follows:

According to the scheme in _{1} is given by the green curve, and _{2} changes from the green curve to the brown curve. In _{ini2} and _{fin2} are defined as the initial and final values of _{2}/_{0obs}, which are given by the green and brown curves, respectively in _{2} is approximately expressed by a single decay constant _{T2}, _{12}/_{0obs} is given by,

The constant _{T2} is related with the elastic change of the actin filament and is independent of Δ_{hs}. The solid arrow “Phase T3b” is drawn between the brown curve and the blue curve in _{0obs} in T3b is given by the difference between these curves. It is uncertain when the _{12} transition and thus Phase T3a start. To make calculation simple, it is assumed that it starts at the same moment as Phase T2, _{3a} is approximately expressed with a single decay constant _{T3a}:
_{ini3a} − _{fin3a}) represents the magnitude of the tension variation. _{ini3a} and _{fin3a} are given by the brown and blue curves, respectively in

Now the problem is how the parameter _{T3a} changes with Δ_{hs}. In the discussion on the force-velocity relation in [_{c} for a myosin head at _{c} to cross over the potential barrier _{c}) is expressed as _{c} = (1/_{c})/_{c}) is expressed by _{c}) = _{0} − _{c} (Equations 4–2–2 in [_{c} = _{c}) where _{cT2} + _{0}. The relative relation between this boundary and A1 is similar to that between _{c} and A2. Then, in analogy to the above relation, with constants _{T3a} = _{c}’) is expected as an approximate expression, where _{c}’ = −_{cT2} + _{0} (_{0} are constants, _{T3a} in _{T3a} = _{cT2}), where _{cT2} = −Δ_{hs}/4.6 (_{3a} and _{3a} are constants. This relation implies that _{T3a} becomes small and the tension variation becomes fast when | Δ_{hs} | increases.

Trial calculations were done for _{123a} = _{12} + _{3a} (_{T2}, _{3a} and _{3a} in _{T2} = 0.7 ms is in consistency with this assumption.

Isotonic velocity transients were studied by Civan and Podolsky [

_{c} = 0 at the isometric tension (cf. _{c} in _{cV1} (cf. _{cV1} > _{cdev}, since most experiments on the velocity transient were done for Δ_{c} > _{cdev}.

In _{0} in _{12} transition does not occur yet. Then the _{12} transition starts, _{12f} transition and internal stress increases, which causes shrinkage of the _{12f} transition is over and all the violet area is turned into the red area as Δ_{cV1} > _{cdev}. The process from (a) to (b2) is related with the _{12} transition and is called Phase V2, where the red area increases and the internal stress increases. The width of

During Phase V2 the _{c} larger. The internal stress tends to expand the _{c} and accelerates the _{c} at (c). Then the frequency of the _{c} change toward their steady values from (c) to (d), where the

_{0obs}. (An example of the experimental data for small _{0obs} can be seen in _{0obs} = 0.87, _{0obs} = 0.13.) The red, blue and brown curves are the same as the curves of the same colors in _{hs} in the four Phases. As discussed above, there is the overlap between the Phases, and the arrow “Phase Vn” indicates the Phase which mainly contributes to the process.

The length change in Phase V1 occurs along the brown curve, since the elastic changes of the crossbridge, the myosin filament and the actin filament contribute to this change. The arrow “Phase V2” corresponds to the rapid decrease of muscle length from _{hsv}” symbolically represents the steady filament sliding corresponding to the state in

Now let us numerically reproduce the experimental data presented in _{hsv} which corresponds to the dashed line in _{hsv} expressed by

Here

The length change caused by the _{12} transition in Phase V2 is denoted as _{hs2}. The speed of _{hs2} depends upon the frequency of _{12} transition and will be large at the beginning and gradually decay. Its time course is approximately expressed with decay constant _{V2} by
_{V2} is a constant.

As discussed above, there is the mutual interaction between the _{c} forward and accelerates the

The interaction (a) releases the internal stress and thus elongates the muscle. As shown in _{hs2} and the length change due to the interaction (a). The combined length change is denoted as _{hs23}, which is expressed by multiplying _{hs2} by exp(−_{V3}):
_{hs23} is shown by the dotted black curve in _{hsv} (the blue line).

The decay times _{V2} and _{V3} should be functions of _{0obs} or _{V2} is proportional to the time duration of occurrence of the _{12} transition. Analogously to the manner to derive _{T3a} = _{c}’) is expected as an approximate expression, where _{c}’ is the _{c}’ = −L + Δ_{cV1}+_{0}. The tension _{cV1} becomes larger. As a simple approximation, Δ_{0obs} − _{cV1}. Then the decay time _{V2} is given approximately by
_{V2} and _{V2} are constants. The time constant _{V3} in Phase V3 is related with the _{step} = _{V3} is set as
_{V3} is a constant.

To see the characteristics of combination of _{hsv} and _{hs23}, _{hs23v} is defined by
_{hs23v} is illustrated by the dashed violet curve in

Now let us consider about the part (b) of the interaction that the internal stress tends to expand the _{c} forward and accelerates the _{cVc} in (c) larger than _{cVd} in (d). In Phase 4, _{cVc} changes into _{cVd} and the filament sliding approaches to the steady value. As shown by the overlap of the arrows of Phases V3 and V4 in _{hs4}. In analogy to the expression of _{hs23} (_{hs4} is approximately expressed by
_{hs4} expressed by this equation are illustrated by the dashed green curve in _{V4})}^{2}. The term exp(−_{V5}) corresponds to the decrease of the muscle length due to the filament sliding. Concerning the magnitude of _{V4}, it is plausible that the internal stress pushes _{c} forward more effectively when the internal stress rapidly increases, _{12} transition rapidly increases. The frequency of the _{12} transition is given by the reciprocal of the duration _{V2} given by _{v4} is expressed by
_{v4} is a constant. The time constants _{V4} and _{V5} will be mainly related with the _{4} and _{5} are constant.

Since the sum of _{hsv}, _{hs23} and _{hs4} is the total length change, it is denoted as Δ_{hs}’
_{hs}’ is the length change from the moment when Phase 1 finishes, while the abscissa Δ_{hs} in

Time course of Δ_{hs}’ was calculated with various trial values of the parameters looking for good agreement with the experimental data in the cases of (_{0obs} − _{0obs} = 0.22, 0.44 and 0.87. Calculation results with the following parameter values are shown in

Characteristic features of the series of experimental data are fairly well reproduced by the calculation. The drastic change of the curve shape for different Δ_{0obs} is mainly due to the _{12} transition, _{V2} = _{V2}exp(_{V2}_{0obs}) (

Let us consider the deviation from Hill-type force-velocity relation in connection of the _{12} transition. The deviation is determined by change of crossbridge population in well A2 and the _{0}/(_{0}) in

The relative tensions ^{H}/_{0} and _{0} are given as functions of _{c}^{H} and _{c}* in _{c}^{H} and _{c}* as functions of _{0}. From _{c}^{H} − _{c}* are shown as functions of _{0} = ^{H}/_{0} = _{0} in the range between _{dev}/_{0} and _{0obs}/_{0} in

The filament sliding velocity of Hill-type is denoted as ^{H} and the velocity in the presence of the _{12} transition as _{step} = ^{H} in _{c} = (1/^{H} = _{step} is approximately proportional to 1/exp(_{12} transition. The difference _{c}^{H} − _{c}* shown in _{3}. The potential barrier _{V}(_{c}^{H} − _{c}*) where _{V} is a constant proportional to 1/_{V}(_{c}^{H} − _{c}*)) in _{dev} < _{0obs}. Then, if we put ^{H} = _{v}(_{c}^{H} − _{c}*)) with a constant _{c}^{H} = _{c}* = _{cdev} (cf. ^{H} at _{cdev}, as required. The blue curve in _{12} transition.

In our previous paper [_{3} with three actin molecules. The complex MA_{3} translates along the actin filament changing its partner actin molecules in cooperation with _{c} determines dynamic properties of muscle in cooperation with _{12} transitions. The internal structure of the MA_{3} complex becomes temporally unstable by the sudden length change or by the sudden load change. The complex muscle behaviors observed in these transients are related with the process that the disturbed internal structure returns to its stationary state.

Results reported in the present paper are summarized as follows.

The tension variations in the first Phases in the isometric tension transient (Ford

Ratios of extensibilities of crossbridge, myosin filament and actin filament are estimated as 0.22, 0.26 and 0.52 (

The experimental data on the isometric tension transient reported by Ford

The characteristic features of muscle in the isotonic velocity transient observed by Civan and Podolsky [

The deviation from the Hill-type force-velocity relation observed by Edman [

It should be noted that the above-mentioned agreements between experimental data and calculation results are obtained by using the muscle stiffnesses _{f} and _{b} determined in [

The obtained results suggest that the ideas of the ensemble of crossbridges and the rectangular

In _{0} _{c}* relation (the blue curve) is 0 at _{c}* = 0. Accordingly, small fluctuation of tension around _{0obs} can produce significant variation of the muscle length. In this connection, the spontaneous oscillatory contraction (SPOC) of muscle (cf. the review by Ishiwata and Yasuda [

The authors are very grateful to Katsuzo Wakabayashi of Osaka University for his critical reading of manuscript and various comments, and to Hideyuki Yoshimura for his kind help in preparation of manuscript.

^{−21} at 0 °C.

_{f}: stiffness of an elongated crossbridge. 2.80 pN/nm (Equation 4–1–13 in [

_{b}: stiffness of a shrinked crossbridge. 0.26 pN/nm (Equation 4–1–14 in [

_{hs}: length of the half sarcomere.

_{0}: maximum

_{0obs}:

_{CB}: extensibility ratio of crossbridge. 0.22 (

_{M}: extensibility ratio of myosin filament. 026 (

_{A}: extensibility ratio of actin filament. 0.52 (

_{0}: maximum _{0} in [

_{0obs}: isometric tension of muscle with a full filament overlap. 4.1 × 10_{5} N/m_{2} [_{0obs}/_{0} = 0.88 (cf.

_{dev}:

_{dev}/_{0} = 0.66 (cf.

_{dev}.

_{max}: velocity of the filament sliding under no load on muscle. 2.36 μm/s at 1.8 °C [

_{c}: maximum

_{c}(0): _{c} for _{max}. 4.2 nm (Equation 4–1–11 in [

_{c0}: _{c} for

_{cdev}: _{c} for _{dev}/_{0} = 0.66. 1.60 nm (

_{c0obs}: _{c} for _{0obs}/_{0} = 0.88. 1.03 nm (

_{c}*: _{c} observed in the presence of the _{12} transition (

Force-velocity relation and definition of _{dev} and _{0obs}. The red curve is the calculation result reported in [

MA_{3} complex (shadowed) and its step motion along the actin filament (after _{3} as 1, 2 and 3. _{3}) moves to the new position;

Potential of the force exerted on the myosin head in the MA_{3} complex. The shape varies depending upon the tension _{dev}, where the force-velocity relation is Hill-type. The black circle indicates that the myosin head exists solely in well A2; _{dev} < _{0obs}, where the existence probability of the myosin head is distributed in wells A1 and A2, causing deviation of the force-velocity relation from Hill-type.

Definition of _{eq} (after _{eq}. _{eq} and

Time interval _{step} for a step motion of the myosin head as a function of _{0}. _{step} =

Statistical ensemble of crossbridges in the steady filament sliding.

Compensation of the effect of the _{12} transition by shift of _{c}^{H} to _{c}*. Magnitudes of _{c0obs} and _{cdev} are exaggerated for illustration. _{c0obs} < _{c}^{H} < _{cdev} and _{c}* > 0; _{c}* = 0; _{c}* < 0.

Relative tensions as functions of _{c}. Red line: ^{H}/_{0} as a function of _{c}^{H}. Blue line: _{0} as a function of _{c}*. (For definition of _{c0} and _{c}(0), see

_{0obs} _{hs} relations in Phase T1 and Phase V1. Circles: experimental data cited from _{0obs} calculated by _{CBT} = 2.2 (_{0obs} calculated by _{CBV} = 4.6 (

The

Changes of the _{cT1} < _{cdev}. Magnitude of _{cdev} is exaggerated for illustration.

Changes of the _{cT1} > _{cdev}.

Phases in the isometric tension transient on the _{0obs} _{hs} relation. The thick black solid and dashed arrows, respectively, indicate Phases in the cases of Δ_{cT1} < _{cdev} and Δ_{cT1} > _{cdev}. Actually the thick solid and dashed arrows are on the same vertical lines, respectively, except for the case of Phase T1.

_{0obs} as functions of time _{hs} in the isometric tension transient. The origin of _{123a}/_{0obs} calculated by using

Changes of the _{cV1} > y_{cdev}.

Phases in the isometric tension transient on the _{0obs} _{hs} relation. The black arrows indicate an example of changes of the relevant Phases in the case of Δ_{cV1} > _{cdev}. Actually the arrows are on the same horizontal lines, except for the case of Phase V1.

Characteristics of _{hs4}, _{hsv}, _{hs23}, _{hs23v} and Δ_{hs}’ are illustrated in the case of Δ_{0obs} = (_{0obs} − _{0obs} = 0.87, by using the equations and parameter values given in text.

Length change Δ_{hs}’ _{0obs}= (_{0obs} − _{0obs}. _{0obs} = 0.22; _{0obs} = 0.44; _{0obs} = 0.87. Green data points are obtained from _{hsv} = −_{hs}’ calculated by using

Explanation of the deviation of the force-velocity relation from Hill-type. _{c}^{H}, _{c}*, _{c}^{H} − _{c}* as functions of _{0}, calculated by ^{H}, the Hill-type velocity calculated in [_{12} transition calculated by