Muscles and Heat Dr. Maurissa D’Angelo

Muscle Heat Generates heat as contract Vitally important to maintaining body temperature Most of heat from skeletal muscle Release excess heat to maintain temperature

Muscles and Heat Maintenance heat source – Slow liberation of heat via resting muscle – Unrelated to contraction, “background heat” Initial Heat Liberated during contraction Byproduct of chemistry of contractile process – Activation heat, A: related to excitation-contraction coupling – Shortening heat, ax: related to shortening of muscle – Tension-time heat, f(P,t): related to cross-bridge turnover during time when muscle is maintaining tension Recover heat – heat generated at end of contraction – Largely aerobic – Related primarily to oxidation of lactate – Liberated during relaxation (if muscle can relax without bearing load) – Degradation of potential energy of lifted load into heat (i.e. no longer bearing load)

Initial Heat Extra heat – i.e. heat that exceeds maintenance heat, liberated immediately following stimulus Occurs during: – depolarization and repolarization of sarcolemma – Release of activator calcium by sarcoplasmic recticulum – Binding of calcium to troponin C Initial heat accompanies mechanical activity of activated contractile proteins Because of heat modeling, Hill equation to predict hyperbolic shape of force-velocity curve, define chemical basis of muscular contraction

Isometric Contraction i.e. muscle isn’t shortening, not performing any external work Heat – Immediately after stimulation of muscle – activation heat Brief burst of heat prior to development of significant tension – Following activation heat – slower rate heat production along with development of tension Small Ignored for modeling and discussion (in this class) Energy = (Work Produced) / (Free Energy of ATP)

Modeling Initial Heat  E = A + W i (Activation Heat + Internal Work) – Where  E is the change in external energy – A is the heat of activation – W i is the internal work which takes place in isometrically contracting muscle Even though ends of muscle are fixed, small amount of internal work done by contractile elements Still have slight shape change in muscle, stretching  E = Q – W – Energy in thermodynamic terms – Q is the activation energy (plus small amount of heat liberated during contraction) – W is the internal work

Isotonic Contraction Muscle shortens while lifting constant load, external work is performed Additional energy/heat present Total amount of heat liberated (ax) – a: amount of heat liberated for each cm of shortening (constant for given type of muscle) – x: the distance the muscle shortens – Shortening heat is therefore = a*x

10 Isotonic - Shortening Heat Shortening Heat = ax – a is muscle specific (units of force) – x is the shortening distance –  E = A + W e + ax (Energy Balance) A is Activation Heat W e is External Work ax is Shortening Heat –  E = Q + Px = Heat (A + ax) + Work (Px)

Refined Equations Refined precision of measuring heat liberation – Determined a (activation heat) is not constant during isometric contractions at different loads Found proportional to developed tension – Heat of shortening dependent on load – Mommaerts separated heat of activation into two components, A – true heat of activation and f(P,t) – heat liberation which is a function of tension of muscle (P) and length of time (t) tension is maintained

12 Tension-Time Heat Isometric –  E = A + W i + f(P, t) Isotonic –  E = A + W e + ax + f(P, t) Where f(p, t) represents the heat liberated as a function of both the muscle tension P and the time duration t that the tension is exerted.

13 Hill’s Equation “Characteristic Equation of Muscle” “Extra Energy” Let muscle lift a load P through a distance x. The energy generated as work W = Px The energy generated as Shortening Heat = ax Activation Heat A is omitted (not related to contraction) f(P, t) omitted for simplicity Extra Energy = Px + ax = (P + a) x Represents the total amount of extra energy liberated by a muscle contracting under isotonic conditions.

14 “Extra Energy” Extra Energy Liberation = (P + a) x Rate of Extra Energy Liberation = (P + a) dx/dt For an isometrically contracting muscle P = P 0 and the Rate = 0 since there is no Work (x = 0) nor is there any Shortening Heat (isometric). For an unloaded freely shortening muscle (P = 0) the rate of energy release is a maximum.

15 “Extra Energy” - continued There is a direct linear proportionality for – Rate of Extra Energy Released and the – Difference between Max Load (P 0 ) and – the Actual Load (P), i.e. E  (P 0 - P) That is to say, the smaller the load, the greater the rate of energy released. – (P + a) v = (P 0 - P) b

16 “Extra Energy” - continued (P + a) v = (P 0 - P) b P v + a v = P 0 b - P b P v + a v + P b + a b = P 0 b + a b (P + a) v + (P + a) b = (P 0 + a) b

Measuring Energy Cost via Heat Measure via direct and indirect calorimetry Direct – airtight insulated chamber – Person remains dormant or exercises – Humidified air provides oxygen – Chemical absorbents remove carbon dioxide – Heat produced picked up by stream of cold water Indirect – energy metabolism in body – Oxygen dependent – Measure oxygen consumption, calculate energy equivalent – Measured via spirometer