Problems: Module 3

Graded on thought, not a single answer. Tie the structure back to function: the body is built this way because it is the most efficient, effective way to build it. Bundling lets force from many parallel fibers add up and transfer through connective tissue to the tendon, and lets nerves and vessels run between bundles. Half credit if the answer shows thought but only partly ties back.

Actin (1): the binding site for myosin, enabling contraction and force.

Myosin (1): binds actin’s binding site, enabling contraction and force.

Tropomyosin (1): covers actin’s binding site, preventing myosin binding. It regulates contraction by stopping it from happening all the time.

Troponin complex (1): pulls tropomyosin off the binding site, but only when Ca²⁺ is present, so contraction happens only under the right circumstances.

Most important (1 + 1): any choice scores if it is justified with module content. (slide 6)

Common: both form the core of their filament. Both anchor at the Z disc. (Both being elastic is also accepted.)

Different: titin is in the thick filament, nebulin in the thin filament. Titin is coiled like a spring, nebulin is not. (slide 6)

The sarcomere is the smallest structural unit in which every event of contraction occurs. It is not the smallest controllable unit, but if you understand one sarcomere you understand every contractile event in the whole muscle. Half credit for an argument with holes.

155 >>> 5, so Na⁺ current is about 31× K⁺ current. It behaves as a Na⁺ channel. 1 point per calculation, 2 points for the conclusion. (M2 slides 16, 23)

Half a point per cell. (slide 11)

Lambert-Eaton: voltage-gated Ca²⁺ channels, presynaptic on the axon terminal. Fewer channels → vesicles cannot undergo exocytosis well → less ACh released → less muscle stimulation → fewer signals for contraction.

Myasthenia gravis: nicotinic acetylcholine receptors, postsynaptic on the motor end plate. Fewer receptors → fewer places for ACh to bind → fewer end plate potentials → fewer muscle action potentials → fewer signals for contraction.

Half a point for each disease on each of the four items. (slides 11–13; M2 slide 43)

Normal: AChE breaks down ACh in the cleft, which matters for relaxation. It stops lingering ACh from stimulating further contraction.

Inhibited: ACh is not broken down.

Muscle: residual ACh keeps stimulating the muscle cell to fire after the neuron has stopped.

Useful: when the neuron releases too little ACh, chronically as in Lambert-Eaton, or acutely after tetanus toxin. Pyridostigmine does exactly this for neuromuscular weakness. Graded generously. (slides 11, 13)

One point per link:

1. Thick cell → large diffusion distance x.

2. Larger x → longer time t.

3. x is squared, so distance has a disproportionately large effect on t.

4. T tubules carry the action potential into the core and trigger local SR release, which shrinks x and so shrinks t a lot.

5. Faster diffusion → faster contractile response.

slides 4, 17

Half a point per blank. The asterisk means cocked. “·” means bound, “+” means separate. (slide 18) The other three states are in the variants below.

ATP binding is required for the myosin head to detach from actin (0.5). After death no more ATP is produced (0.5). No ATP → no detachment → no relaxation, so the body stays rigid (0.5). (slide 18)

False. That describes Type IIa. Type I fibers have few glycolytic enzymes and rely almost exclusively on oxidative pathways. (slides 28–31)

False. IIx are fastest, but their contractions are the most powerful, not the weakest.

False. Deep red does mean high myoglobin, but that is Type I. Type IIa has moderate myoglobin and is medium red.

True as written.

Type I fibers depend almost entirely on oxidative phosphorylation, which needs oxygen, and these patients are already short of it. Switching toward Type II lowers the muscle’s dependence on a scarce oxygen supply by leaning on anaerobic pathways. Half credit if the logic has gaps, or if pathways and fiber types are discussed with no actual hypothesis.

Motor units are recruited from smallest (thinnest neuron, thinnest fibers, easiest to stimulate) to largest (thickest neuron, thickest fibers, hardest to stimulate). (slide 38) The key calls it Henneman’s size principle.

Before full relaxation, residual Ca²⁺ and residual tension remain. The next stimulus starts from that elevated baseline, so later responses piggyback on earlier ones and total force climbs. (slide 36)

Threshold: 0.4 V, the first voltage that raised force. Maximal: 2.0 V, the lowest voltage giving maximal force.

Plateau: every available motor axon has been recruited. More voltage cannot recruit more motor units, so force maxes out.

99%: lab equipment carries baseline noise, so a tracing is never perfectly flat. An oscillation smaller than the noise cannot be detected, so the definition allows a little uncertainty. In the key’s data only the 40 ms and 20 ms intervals (FI 99.81% and 99.83%) counted as fused.

Bonus: yes. Fused tetanus only shows free Ca²⁺ stays above the level that keeps cross-bridging continuous between action potentials. It does not guarantee Ca²⁺ binding to troponin C is saturated, which maximal force requires.

Deadlocked: no length change, force = load, isometric. (slide 43)

Losing: muscle lengthens, force < load, isotonic eccentric. (slide 42)

Winning: muscle shortens, force > load, isotonic concentric. (slide 41)

One point each for length, force vs load, and type.

As F falls, v rises (1). With less opposing force, the only limit on how fast cross-bridges attach, detach, and reattach is the speed of myosin ATPase itself. Less resistance, faster shortening (2). (slides 45–46)

Force is its own variable. Power = force × velocity, so it includes shortening speed (1). Force covers lifting loads, like climbing stairs or carrying groceries. Velocity covers reacting quickly enough to avoid a fall or catch yourself on a trip. Independence needs both, so power is the better predictor (2, graded generously). (slide 46)

The action potential is over within a couple of milliseconds. Free Ca²⁺ peaks next, at about 10–15 ms, after the DHPR opens the RyR. Ca²⁺-troponin C peaks slightly later and stays high longer, because binding follows free Ca²⁺ by LeChatelier’s principle. Force peaks last, around 50–60 ms, and decays over about 200 ms.

Each step waits on the one before: the AP triggers release, released Ca²⁺ must bind troponin C, and only then can cross-bridges cycle and build tension. Force falls only after SERCA lowers free Ca²⁺ and troponin C unloads. Calcium is the link that couples excitation to contraction. (M3 slide 22)

Intensity vs duration: inverse. Creatine phosphate supports the most intense, shortest exercise; fatty acid oxidation the least intense, longest.

Intensity vs time to make ATP: inverse, for the same reason. The faster a pathway delivers ATP, the more intense the work it supports.

Duration vs substrate availability: direct. Little creatine phosphate is stored, more glucose, a great deal of fat. Glycolysis is the outlier: plenty of glucose exists, but lactic acid lowers muscle pH and stops the contractile proteins within about 2 minutes. Byproduct, not substrate, sets its limit. (M3 slide 29)

(a) Lateral rectus 7.5 ms (Type IIx, fastest), gastrocnemius 40 ms (Type IIa), soleus 90 ms (Type I, slowest).

(b) Shortening velocity rises linearly with myosin ATPase activity. Faster ATP hydrolysis means faster cross-bridge cycling.

(c) Type 1 motor units hold nearly full tetanic stress for 30 minutes. Type II fall to almost zero by about 5 minutes. Whole muscle drops to about half and levels off, the Type I fibers still working after the Type II have fatigued. (M3 slide 31)

(a) About 2.0–2.3 µm. Across that range thick and thin filaments overlap fully without colliding, so the maximum number of cross-bridges can form (point c).

(b) At 3.7 µm the filaments no longer overlap, so no cross-bridges form (e). At 1.3 µm thin filaments have hit the M line and thick filaments have crashed into the Z disc, wrecking the spatial arrangement (a).

(c) Past optimal length active tension falls, but passive tension from stretching rises steeply, like a stretched rubber band. Total = active + passive, so total climbs again. (M3 slide 35)

A, 5 Hz: each twitch relaxes fully before the next. B, 10 Hz: the next stimulus arrives before full relaxation, so twitches stack. C, 25 Hz: unfused tetanus, sustained high tension with ripples. D, 50 Hz: fused tetanus, smooth and maximal.

Each new stimulus arrives while residual Ca²⁺ and tension remain, so the response starts from a higher baseline and piggybacks on the last. Action potential amplitude never changes; Ca²⁺ in the sarcoplasm does. (M3 slide 36; Assignment 3 Q5b)

All three get the stimulus at 0 ms. The brackets under the axis show shortening starts later for heavier loads: the muscle must contract isometrically until force exceeds the load. The phone starts almost immediately, the backpack last.

The phone shortens most and its whole event lasts longest (about 75 ms); the backpack shortens least and finishes by about 40 ms.

The dashed tangents are velocity = distance/time. The phone’s slope is steepest and the backpack’s shallowest: shortening velocity falls as load rises. (M3 slide 44)

Above zero velocity the muscle shortens: concentric, maximum velocity about 40 cm/s at zero load. The crossing at about 40 N/cm² is isometric, zero velocity at maximum force. Below zero the muscle lengthens: eccentric, where load exceeds the force the muscle can make.

Fast-twitch fibers reach about 40 cm/s at no load against about 14 for slow twitch, and stay higher at every force. Both reach the same maximum force near 40 N/cm² at zero velocity. (M3 slide 45)

Maximum force is about 40 N/cm². Both power curves peak near 13 N/cm², and 13/40 ≈ 1/3.

Fast-twitch peaks near 380 W/kg, slow-twitch near 150 W/kg: about 2.5×, inside the 2–3× the lecture quotes. Power = force × velocity, so it is zero at zero force and at zero velocity and peaks in between. (M3 slide 46)

Threshold 0.4 V, the first rise above baseline. Maximal 2.0 V, the lowest voltage giving maximal force.

Between them each step recruits more motor axons, smallest first, so force climbs. Above 2.0 V every motor unit is already recruited, so force plateaus.

The small drop at 2.5 and 3.0 V is noise; the key notes the simulation gives slightly different values each run. Treat it as a plateau. (Assignment 3 Q5c)

FI: 400 ms 2.26%, 200 ms 4.37%, 100 ms 77.24%, 80 ms 90.87%, 60 ms 98.58%, 40 ms 99.81%, 20 ms 99.83%.

Using FI ≥ 99%, only 40 and 20 ms are fused tetanus. 400 and 200 ms are separate twitches; 100 to 60 ms are unfused.

Peak force rises from about 98 g to 582 g as the interval shortens because each stimulus lands before relaxation and piggybacks on residual Ca²⁺ and tension: wave summation. Force still climbs between 40 and 20 ms, showing fused tetanus is not necessarily maximal force. (Assignment 3 Q5d)

A-alpha somatic motor neuron action potential → voltage-gated Ca²⁺ channels open at the terminal → Ca²⁺ enters → acetylcholine released from vesicles → ACh binds nicotinic acetylcholine receptors, ligand-gated channels, on the motor end plate → Na⁺ enters → EPSP on the end plate → at the transition to regular sarcolemma, if threshold is met, voltage-gated Na⁺ channels open → muscle action potential propagates in all directions.

Ending: the neuron stops firing and acetylcholinesterase breaks down residual ACh in the cleft. (slides 10–11)

Tetrodotoxin: blocks voltage-gated Na⁺ channels in neurons and muscle → instant, lethal paralysis.

Dendrotoxin: blocks neural voltage-gated K⁺ channels → repolarization minimized, depolarization runs too long → ACh over-released → relentless sarcolemmal depolarization, cramping, convulsions.

Botulinum toxin: inhibits ACh release → no stimulation → paralysis, including respiratory muscles. Tetanus toxin acts the same way.

Myasthenia gravis: autoantibodies destroy acetylcholine-gated channels on the motor end plate → progressive weakness, eventual paralysis.

Lambert-Eaton: autoantibodies attack voltage-gated Ca²⁺ channels → eventually prevents neurotransmitter release. (slide 13)

Sarcolemmal action potential → travels down the T tubule → DHPR changes conformation → DHPR, physically connected, pulls open the RyR Ca²⁺ channel → Ca²⁺ floods from the SR into the sarcoplasm → Ca²⁺ binds troponin C → troponin pulls tropomyosin off actin’s binding site → cross-bridges form → force. (slides 17, 22)

Triad: the DHPR can only mechanically open the RyR because the T tubule and SR sit physically adjacent. (slide 4)

ATP binding detaches the head. Hydrolysis by myosin ATPase recocks it. The head binds farther up the thin filament, releases P_i, performs the power stroke, releases ADP. (slide 18)

No ATP: ATP binding is what detaches myosin, so heads stay bound to actin at A·M and cannot detach or recock.

The action potential only triggers calcium release. The twitch lasts as long as calcium stays high enough to keep troponin C bound, and then as long as SERCA takes to pump it back. The electrical event is over long before the mechanical one. (slide 22)

LeChatelier: at rest, free and bound Ca²⁺ are in equilibrium at low levels. RyR opening floods free Ca²⁺, so the reaction shifts right onto troponin C, reaching a new equilibrium at high levels. SERCA drains free Ca²⁺, so it shifts left, unloading troponin C back to low levels. (slide 21)

Two minutes: not glucose supply. At high intensity oxygen runs low, pyruvate becomes lactic acid, and muscle pH drops until contractile proteins stop working. Byproduct accumulation sets the limit. (slides 27–29)

Marathon: Type I, slow oxidative. Low ATPase, thin, dark red from myoglobin, oxidative phosphorylation, very high fatigue resistance.

Shot-put: Type IIx, fast glycolytic. High ATPase, thick, pale, creatine phosphate and glycolysis, very low fatigue resistance. (slide 30)

Length-tension relationship, frequency of stimulation, motor unit recruitment. (slide 34)

5 Hz: separate twitches, full relaxation between. 10 Hz: each twitch starts before the last relaxes, so tension climbs. 25 Hz: unfused tetanus, sustained high tension with peaks still visible. 50 Hz: fused tetanus, a smooth maximal waveform. (slide 36)

V, the voltage change needed to depolarize, is the same for every motor unit. C varies: the membrane acts as a capacitor, and smaller neurons and fibers have less membrane surface area, so lower capacitance. Lower C means less current I is needed to reach the same V, so the smallest cells are easiest to depolarize and fire first. They are also Type I and the most fatigue resistant. (slide 38)

Concentric: force greater than load, shortens, acceleration. Lifting in a bicep curl.

Eccentric: force less than load, lengthens, deceleration. Lowering the weight under control.

Isometric: force equal to or less than load, no length change, fixation. Deadlocked arm wrestling, carrying groceries, standing posture. (slides 41–43)

Power peaks at about one third of maximum force, so near 10 N. Fast-twitch muscle produces roughly 2–3× the power of slow twitch. (slide 46)

The backpack has the longer isometric phase, because more force must build before tension exceeds load. It shortens less, so the whole contraction takes less time, and its shortening velocity is lower. The phone reverses every one of these. (slide 44)

The lecture’s cycle has no bound-and-still-holding-P_i step: binding is weak until P_i is released, which gives A·M*·ADP. Full order: A·M → A + M·ATP → A + M*·ADP·P_i → A·M*·ADP → A·M·ADP → A·M.

Doubling thickness doubles x, so time rises 4×, because x is squared.

Below 99%, so unfused tetanus. Shorter intervals leave less time to relax, so FI climbs toward 100% and fused tetanus.

(a) Isotonic concentric, force > load, shortening. (b) Isotonic eccentric, force < load, lengthening, deceleration. (c) Isometric, force = load, no length change.

F = F₀ gives v = 0: the isometric point where the curve crosses zero. Maximum v occurs at F = 0: zero load, the top of the curve. (slide 45)

Below 0.4 V the stimulus is subthreshold for every motor axon, so the reading is baseline. At 0.4 V the first, smallest motor units reach threshold and are recruited. Each further voltage step recruits more until all are active near 2.0 V.

(a) IIx are pale, with little myoglobin. Type I is dark red.

(b) Type II fibers have no force left by 5 minutes. Type I are still strong after 30.

(c) Creatine phosphate is the fastest (1 ATP). Fatty acid oxidation is the most efficient (90–140 ATP).

(d) Glycolysis stops because lactic acid lowers muscle pH, not because glucose runs out.

Whole muscle (epimysium) → fascicle (perimysium) → muscle fiber (the cell, wrapped in sarcolemma) → myofibril → sarcomere → thick and thin filaments → proteins (myosin, titin, actin, nebulin, tropomyosin, troponin). (M3 slides 3–6)

The A band (full width of the thick filaments, dark) alternates with the I band (thin filaments only, light). Repeating sarcomeres line those bands up across the cell. (M3 slide 6)

Ca²⁺ entering at the surface would have to diffuse 50 µm to the core, and diffusion time grows with distance squared. T tubules carry the action potential deep into the cell so the SR can release Ca²⁺ right beside every myofibril, making contraction fast and uniform. (M3 slides 4, 17)

One T tubule flanked by two patches of SR. The DHPR in the T tubule is physically connected to the RyR on the SR; that contact lets a voltage change mechanically open the Ca²⁺ release channel. (M3 slides 4, 17)

Troponin I binds actin, troponin T binds tropomyosin, troponin C binds Ca²⁺. When Ca²⁺ binds troponin C the complex changes shape and pulls tropomyosin off actin’s binding site, letting myosin bind. (M3 slides 6, 16)

AP reaches the terminal → voltage-gated Ca²⁺ channels open → Ca²⁺ in → ACh exocytosis → ACh binds nicotinic receptors (ligand-gated) on the motor end plate → Na⁺ in → EPSP → at the edge of the end plate, voltage-gated Na⁺ channels open → muscle AP spreads in all directions. (M3 slide 11)

The end plate has ligand-gated channels, not voltage-gated Na⁺ channels, so it can only make graded potentials. The action potential begins where the end plate meets regular sarcolemma, which has voltage-gated Na⁺ channels. (M3 slide 11)

Same: shape, steep Na⁺-driven depolarization through voltage-gated Na⁺ channels, steep K⁺-driven repolarization. Different: the muscle AP lasts about 2 ms against 1 ms, and on the slide it starts from about −80 mV. (M3 slide 12)

Tetrodotoxin: voltage-gated Na⁺ channels in nerve and muscle, instant lethal paralysis. Dendrotoxin: neural voltage-gated K⁺ channels, prolonged depolarization, ACh over-release, cramps and convulsions. Botulinum toxin: blocks ACh release, paralysis including breathing muscles. (M3 slide 13)

Myasthenia gravis: ACh-gated channels on the motor end plate, progressive weakness. Neuromyotonia: neural voltage-gated K⁺ channels, poor repolarization of the neuron. Lambert-Eaton: presynaptic voltage-gated Ca²⁺ channels, too little ACh release. (M3 slide 13)

Sarcolemmal AP → down the T tubule → DHPR changes conformation → pulls open the RyR on the SR → Ca²⁺ flows down its gradient into the sarcoplasm. (M3 slide 17)

ATP binds at the first arrow, detaching the head. It is hydrolyzed by myosin ATPase at the second, recocking the head. P_i release strengthens binding, then the power stroke, then ADP release. (M3 slide 18)

The AP only triggers Ca²⁺ release. Force lasts as long as Ca²⁺ stays bound to troponin C and cross-bridges cycle, then decays only as SERCA pumps Ca²⁺ back. Those chemical and mechanical steps take far longer than the electrical one. (M3 slide 22)

At rest free and bound Ca²⁺ balance at low levels. In contraction the RyR floods free Ca²⁺; the reaction shifts right, loading troponin C to a new high equilibrium. In relaxation SERCA drains free Ca²⁺; the reaction shifts left, unloading troponin C back to the low equilibrium. (M3 slide 21)

Speed: creatine phosphate > glycolysis > oxidative (glucose) > oxidative (fatty acids). Yield: the reverse, 1, 2, 34, 90–140 ATP. More steps extract more energy but take longer, so a pathway can be fast or efficient, not both. (M3 slides 28–29)

At high intensity oxygen runs short, pyruvate becomes lactic acid, and muscle pH drops until contractile proteins stop working. The body has plenty of glucose, so byproduct buildup, not supply, ends it. (M3 slide 28)

M3 slide 30

Color tracks myoglobin, plus capillaries and mitochondria. Type I fibers, built for oxidative metabolism, are packed with myoglobin and look dark red. Type IIx rely on glycolysis, have little myoglobin, and look pale. (M3 slides 30–31)

A bell curve of active force against resting sarcomere length, peaking around 2.0–2.3 µm. Too long: little filament overlap, few cross-bridges. Too short: thin filaments hit the M line and thick filaments crash into the Z disc, wrecking the arrangement. (M3 slide 35)

Passive tension comes from stretch alone and rises with length. Total tension is the force measured during contraction. Active tension is total minus passive, the bell curve. (M3 slide 35)

5 Hz: separate twitches with full relaxation. 10 Hz: summation, each twitch starts before the last relaxes. 25 Hz: unfused tetanus, high tension with ripples. 50 Hz: fused tetanus, smooth and maximal. (M3 slide 36)

A motor unit is one somatic motor neuron and every fiber it innervates. Precision muscles (like the eye) have small innervation ratios, few fibers per neuron, for fine steps of force. Power muscles have large ratios, many fibers per neuron. (M3 slide 37)

I = CV. V, the voltage change needed to depolarize, is the same for every cell. C varies with membrane area: small cells have small capacitance and need less current. So the smallest motor units, with Type I fibers, are recruited first and the largest last. (M3 slide 38)

Concentric: force > load, shortens, accelerates. Eccentric: force < load, lengthens, decelerates. Isometric: force = load (or less than an immovable load), no length change, fixation and stability. (M3 slides 41–43)

The backpack: longer isometric phase before shortening starts, much less shortening, shorter total duration, and lower shortening velocity. The phone: the reverse on every count. (M3 slide 44)

Above the zero-velocity line: concentric. At the crossing: isometric. Below it: eccentric. Fast-twitch fibers have higher myosin ATPase activity and cycle cross-bridges faster, so they shorten faster at every load and their curve sits higher. (M3 slide 45)

Power peaks at about one third of maximum force. (M3 slide 46)