1. Basic Mechanics
terms
mechanical advantage
For static equilibrium the in force times the in lever must equal the out force times the out lever. The result of this is that the amount of input force necessary to produce a given output force is proportional to the ratio of the out to in lever arm (dout/din). The mechanical advantage is the inverse of the ratio dout/din, which is din/dout. This makes sense...as din/dout increases, the mechanical advantage increases. The ratio din/dout is equivalent to the ratio Fout/Fin so some people use this latter ratio as the mechaical advantage (which again makes sense...the bigger the output force relative to the input force, the better the mechanical advantage).
velocity ratio (or velocity advantage)
This figure is as above but I've color coded the muscle and its effect on the movement of the bone. Note that when the blue muscle contracts 10% (from its position in the mechanical advantage figure), the bone is displaced a large amount (rotated through a large arc). By contrast, when the red muscle contracts 10% (again, relative to its position in the mechanical advantage figure), the bone is displaced (rotated) by a small amount. We say that the blue muscle is geared higher than the red muscle (which is geared lower). This is exactly equivalent to a bike.
If it takes the same duration of time for each muscle to shorten by 10%, then shortening of the blue muscle necessarily results in faster rotation of the bone than shortening of the red muscle. This velocity advantage is proportional to dout/din, or the inverse of the mechanical advantage (din/dout). More technically, the ratio dout/din is called the velocity ratio. So, the smaller the in lever, the faster the displacement. We refer to this as the gearing of the muscle, which is essentially the amount of movement per percent muscle strain. This is exactly equivalent to a bike. Low gears produce high force but a low velocity while high gears produce a small foce but a high velocity. Again, this makes sense, low gears are needed when velocity is less important than generating a large force, for example, to accelerate from rest (high acceleration), to escape snow or mud (in a car), or to climb a hill (when gravity is working against you). By contrast high gears are used when velocity is important but large forces are not, for example, speeding along a level street (only friction and some form drag working against you and the bike) or especially, a downhill street (in which gravity is working for you).
ATPase rate Ca++ cycling mitochondria capillaries aerobic (oxidative) enzymes anaerobic (glycolytic) enzymes myoglobin glycogen fatigue function
notes for above table
1. ATPase rate. Myosin is one of the major contractile proteins in muscle. It also hydrolzyzes ATP and so is an enzyme. It is this hydrolysis of ATP that converts the chemical energy in the phosphate bond to the mechanical energy of the pivoting Myosin head
2. Ca++ cycling. Ca++ is stored in the sarcoplasmic reticulum (SR) and released into the cytoplasm when the muscle fiber is stimulated. Following stimulation, the SR actively re-uptakes the Ca++ through special Ca++ channels. This cycling is dependent on the type of Ca++ channel present.
3. Mitochondria are the ATP factories but only for aerobic exercise. The more mitochondria the more ATP
4. capillaries are the smallest vessels and the sites of gas exchange between the blood and the tissues. The more capillaries the more gas can be exchanged (bringing more O2 to the muscle and removing more CO2 and other metabolic products.
5. Aerobic enzymes. These are the enzymes of the citric acid (Kreb's) cycle and the electron transport chain and oxidative phosphorylation that are located in the mitochondria
6. Anaerobic enzymes. These are the enzymes of glycolysis that are located in the cytoplasm
7. Myoglobin. These are proteins related to hemoglobin that bind to, and thus store, O2
8. Glycogen. This is a large, branching molecule of bonded glucose molecultes. This is how cells (generally muscle and liver) store glucose so that the glucose doesn't get oxidized if the cell doesn't need the ATP
9. Fatigue. This is not your brain feeling tired but the muscle fibers literally not being able to contract (or contracting with less force) because of excess phosphate or not enough ATP or ???
2. Muscle design in fish
Why are myomeres shaped the way they are? Why is there red and white muscle? Why are there myosepta?
Two contrasting behaviors: The first is steady swimming at slow and intermediate speeds using low amplitude axial undulations (i.e. the side to side displacement of the body is small). The second is burst swimming and escape responses using high amplitude axial undulation. In the escape response, a fish bends into a C-like posture then whips its tail in the opposite direction, accelerating a mass of water behind the fish, which causes the fish to accelerate forward. The key is that body bending is small in steady swimming and large in bursts and escapes. Also, the escape response can be very fast, that is less than 1/10th of a second.
Why myosepta?
Fish swim by passing a wave of contracting muscle from anterior to posterior. If there were no myosepta, but simply a series of interconnected muscle fibers, then the wave would be very damped. That is, as anterior fibers contract they would pull on posterior fibers and stretch them so the shortening of the whole side would be much less than if the anterior fibers contracted without the posterior fibers lengthening. Myosepta effectively transmit the contractile force to the backbone and skin, which keeps the posterior fibers from lengthening.
Why the myomere geometry and why red vs. white muscle?
(note: much of the discussion below is a summary of some of the elegant research from Larry Rome and his students)The geometry of muscle fibers is intimately related to the fiber type (i.e. color), hence the questions have to be answered simultaneously. Remember, the white muscle is arranged helically, with fibers pointing into or away from the midline at high angles. The red muscle is arranged in a longitudinal band near the junction of the horizontal septa and the skin, so the red fibers make very small angles with the midline.
(Click on image to get a bigger picture or here for a nice, printable PDF version)
remember the biochemical properties of red vs. white muscle. Red muscle uses the highly efficient oxidative phosphorylation pathway to get ATPs (the high hemoglobin in the abundant blood vessels of red muscle and the myoglobin in the mitochondrial membranes is what gives red muscle its color). The white muscle uses the inefficient glycolytic pathway. The oxidative phosphorylation path produces a slow twitch while the glycolytic pathway produces a fast twitch. This suggests that red muscle should be used for slow steady swimming and white muscle should be used for rapid bursts and escape swimming.
This suggestion has been tested using electromyography (EMG), in which a pair of fine-wire electrodes are inserted into a muscle enabling us to measure a voltage, which indicates that the muscle is contracting. When fish swim in a flow tank with electrodes in both the red and white muscle, it is found that the red muscles are recruited for slow, steady swimming and the white muscles are recruited for bursts and escape responses.
McNeil Alexander in 1969 suggested that the geometry differences between red and white muscles puts them in different gears and that the average gear ratio between white and red muscle for steady swimming is 4. That is, for a given amount of muscle strain, white muscle produces 4X the body bending than red muscle. So the white muscle is a lower Fout, higher Vout muscle while the red muscle is a higher Fout, lower Vout muscle. Which should be used for the fast start and which for steady swimming?
The gearing would suggest that the red muscle would have to contract a huge percentage to produce the bending seen in a fast start while the white muscle would have to contract a tiny amount to produce the bending seen in steady swimming. Is there anything bad about contracting only a tiny amount or a huge amount? See below. Otherwise, the model is consistant with the EMG recruitment data as the lower gear red muscle contraction results in only small bending but the high-gear white muscle contraction results in large bending. This theory of Alexander (gearing ratio) has been tested using a technique called sonomicrometry. In sonomicrometry, there is a pair of piezoelectric crystals, one which emits a sound and the other that receives it. The time delay between emissiona and reception is a function of the distance between the crystals. So, the crystals can be inserted in a muscle fiber and the real time muscle strain can be measured by monitoring the time delay between successive emissions and receptions during contraction. Alexander's model for a fast starting carp would predict a mean gear ratio of about 3.2. Sonomicrometry estimates the gear ratio to be 2.8 for the fast starting carp.
The important thing about the gear ratios is that white muscle bends the body much more (2-5X more) than red muscle for a given amount of muscle contraction. It also bends it faster because of its fast twitch contractile proteins.
What kind of force does red muscle generate at the lengths necessary to bend a fish the amount seen in a fast start?
Look at the length-tension curves below (you should understand why a length-tension curve is shaped the way it is. See Kardong Figure 10.6 on p. 351, which isn't very good, or click here to se a better explanation). Notice that both red and white muscles are operating near optimal lengths. But note that if red muscle were to bend the fish during a fast start, it would have to shorten to lengths in which not much force would be produced.
(Click on image to get a bigger picture or here for a nice, printable PDF version)
Can red muscle power a fast start? Can white muscle power steady swimming?
The diagrams below shows contractile force vs. muscle contractile velocity curve (the curve that decreases from left to right). The product of force and velocity is power, so the muscle power, at any shortening velocity is shown by the inverted U curve (or the curve that looks like a hill), which is easily derived from the force curve by simply multiplying the measure of force for a particular value of contraction speed by the contraction speed itself (try it...you'll see you get that inverted U curve).
Importantly, the shaded part of the power curve for red muscle shows that red muscle shortens at a speed where the power is near its peak. Because the body bends so much and at such a rapid speed during a fast start, red muscle would have to shorten at 20 ML/s to power the fast start. From the curves, it is clear that red muscle cannot shorten this quickly. Because of the 4:1 gearing ratio, white muscle only need to shorten at about 5 ML/s to power the fast start, which is where white muscle works very efficiently (near the peak on the power curve). Also, if white muscle were to power steady swimming, it would have to contract at a really slow speed, because of the slow, small deformations occurring in steady swimming. Note that at these small contractile speeds (again shaded in the lower graph), white muscle works very inefficiently (low on the power curve).
(Click on image to get a bigger picture or here for a nice, printable PDF version)
