E139 Lecture 8: Muscle Mechanics II

calculating active muscle force

Fa = 1 -a(L-1)²

what is “a” in the active muscle force equation for most vertebrates

3 in most vertebrate muscles

how does a value change the muscle length vs force graph

greater a = more parabolic

smaller a = flatter

isometric contractions

length of the muscle is constant, but force changes

• experiment by changing length, stimulating, and finding force

why is the relationship between force and muscle length

represents an average

• in actuality it is a cubic graph

what drives the muscle length vs force relationship with active force

sarcomere interactions drive the pattern

graphing total force

active force = parabolic graph

passive force = exponential graph

total force = cubic graph

purpose titin

contributes to passive force

• longer titin isoforms are more compliant than shorter isoforms

what is PEVK in titin

ca2+ binding sight

• when bound, the titin binds to actin to shorten and make it more stiff

what does titin span

Z disk to Z disk

epimysium

intramuscular connective tissue that wraps around the muscle

perimysium

intramuscular connective tissue that wraps around the fascicles

endomysium

intramuscular connective tissue that wraps around the muscle cells

relationship between fibrotic tissue and conc

fibrotic = greater conc of intramuscular connective tissue = stiffer

calculating passive force

exponential graph

• c = slope/ stiffness constant

• k = curvature constant

c value in passive muscle force equation

high c = more stiff

low c = less stiff

k value in passive muscle force equation

high k = flatter curve

low k = more curved

Lr in passive muscle force equation

Lr = resting muscle length (L/Lo)

• low Lr = passive tension develops at a shorter length

equation for total force

Ft = Fa + Fp

isometric contractions and mechanical work

isometric contractions do not generate any mechanical work (force x displacement)

• no displacement occurs

isotonic contractions

allow muscles to shorten at a constant load, but changing length

the heat of shortening and the dynamic constants of muscle

length increases with a greater load over time

velocity vs force graph

x axis = velocity

y axis = force (g)

• logarithmic graph; decreased force = increased slope

a f huxley

studied myosin heads generate force and ratchet

proportion of attached crossbridges vs displacement away from equilibrium (mm)

positive side = force generateion

• increased speed of contraction = more crossover with negative force generation

• at vmax = there is equal + and - force

the hill equation

(F+a)(V+b) = (Fo+a)b

a/Fo = b/Vmax

what does the hill equation describe

the curvature of the force-velocity relationship

a/Fo in hill equation

greater a/Fo = flatter curve

power equation

P = F(V) = W/t