# Four aspects of creep phenomena in striated muscle

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## Summary

Four aspects of the slow creep of tension and sarcomere lengths observed during fixed-end tetani are studied with computer simulations, using the instantaneous steady-state (adiabatic) approximation. (1) Most aspects of fixed-end creep phenomena can be simulated in the presence of the passive forces which correctly produce initially shortened end sarcomeres. However, the very large maximum tensions observed with fibres of low resting force for sarcomere lengths > 3.0*μ*m cannot be simulated within the adiabatic approximation. (2) Random variations in the passive tension-length curve between different sarcomeres can predict the reported incidence of contracting sarcomeres in the middle of the fibre, while avoiding significant tension creep when a central segment is length-clamped. They can also reverse the velocity of these sarcomeres during creep in fibres with high resting tension, as observed by Altringham and Bottinelli (1985). At sarcomere lengths of ⩾ 3.4*μ*m we find that spatial variations in passive tension strength also contribute to tension creep. (3) Crossbridge fluctuations in active tension have been estimated from the sliding-filament model, and do not contribute significantly to tension creep. (4) The need for inter-sarcomere stiffness or other mechanisms to produce an additional slow rise in tension at long times, and to smooth the sarcomere length distribution, is assessed.

## Keywords

Striate Muscle Spatial Variation Length Distribution Sarcomere Length Active Tension## Mathematical symbols used for muscle variables and parameters, including standard parameter values

- α
_{−} slope of active tension-velocity curve in contraction per unit isometric tension

- α
_{+} slope (as above) in extension per unit isometric tension

- α
_{i} equals α

_{±}for sarcomere number i, (i = 1, ...,n)- Δl
_{i} random sarcomere length shift for passive tension, sarc. no. i

- Δl
r.m.s. value of the passive length shifts

- δl
_{i} random sarcomere length fluctuation from active tension

- δl
r.m.s. value of the active length fluctuations

- γ
decay exponent per sarcomere for extra end tension strength

- i
sarcomere number [i = l(middle), ...,n(end)]

- l
_{i}(t) length of sarcomere i at time t

- l
_{end} average sarcomere length of a fibre segment at one end

- l
_{*} slack length per sarcomere

- L
total length of fibre

- μ
coefficient of viscous passive tension n number of sarcomeres in half-fibre

- η
exponent for length dependence of extra end tension

- t
time

- Τ
_{C} correlation time for active tension fluctuations

- r
overall rate of the contraction cycle

- R
_{0} isometric ATP-ase rate per half-sarcomere

- T(t)
total tension per filament at time t

- T(l, υ)
steady-state tension function (per filament)

- T
_{0}(l) isometric active tension for sarc. length l

- T
_{P}p(l) homogeneous passive tension function of sarc. length l

- T
_{P}_{i}(l_{i}) inhomogeneous passive tension for sarc. no. i, length l

_{i}- T
_{P,o} strength of passive tension function T

_{P}(l) (at 3.6 μm)- T
_{i}_{E}(l_{i}) extra end tension function for sarc. no. i

- T
_{E}_{i} strength of extra end tension function for sarc. no. i (at 3.6 μm)

- T
_{E,o} strength of extra end tension (T

_{E}^{n}) at end of fibre (i = n)- υ
extension velocity per sarcomer

- ξ
exponent for length dependence of passive tension

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