Scaling Flashcards
Knut Schmidt - Neilsen
FOREVER CURIOUS. The title of one of his books, How Animals Work, captures the essence of biologist Knut Schmidt-Nielsen, who died in Durham, North Carolina, on 25 January at the age of 91. Considered the father of comparative physiology and integrative biology, the Duke University researcher endured the heat of the Sahara and the cold of the Arctic to learn how animals thrive in extreme climates. He discovered, for example, that moisture-conserving mucus in the nose—not water stored in its hump—helps protect camels against dehydration, and that special glands help seabirds and marine reptiles shed excess salt. His lab was a menagerie, including a misnamed 100-kilogram female ostrich called Pete who was a source for 1-kilo omelets. (Pete helped Schmidt-Nielsen and his colleagues learn how ostriches can run in the heat without sweating.) “Knut invoked in all of us a sense of curiosity about how animals function,” says Barbara Block of Stanford University in Palo Alto, California.
Size & Scale
“Scaling deals with the structural and functional consequences of changes in size or scale among otherwise similar organisms”
Size is measured in
Mass and linear dimensions
Symorphosis
If “animals were built reasonably”
Galileo
Galileo: animals of different sizes have different shaped bones. The cross-sectional area of the two thigh bones (pictured) is different compared to the weight of the animal and realized the strength of the bone is proportional to the cross-sectional area but the weight of the animal is dependent on the volume which is a cube (compared to cross-sectional area which is squared). 8 feet is the tallest a human can be and still stand Scaling based on allometry As the animal grows larger, the bone diameter has to grow disproportionately larger (by a 3:2 law).
Knut Schmidt-Nielsen (1916-2007)
Father of comparative physiology and integrative biology father of scaling Knut and his wife taught biology at case Studied how animals thrive in extreme climates Example: moisture-covering mucus in the nose (not water in the hump) helps protect camels against dehydration, special glands help seabirds and marine reptiles shed excess salt
Size and scale
“Scaling deals with the structural and functional consequences of changes in size or scale among otherwise similar organisms” Three parameters can be changed when size increases: Dimensions Materials Design Size measured in mass and linear dimensions
Isometric geometry
Isometric geometry Surface ∝ (length)^2 S ∝ L^2 Volume ∝ (length)^3 V ∝ L^3 Surface ∝ (volume)^2/3 S ∝ V^2/3
Linear scale vs log-log scale (linearizes the equation). Intercept becomes the constant and the slope of the line becomes the exponent.
Linear scale vs log-log scale (linearizes the equation). Intercept becomes the constant and the slope of the line becomes the exponent. S/V = kV0.67 → Slope of 0.67 S/V = kV(0.67 - 1.0) → Slope of -0.33
Allometric equation
y = axb ; or: log y = b log x + log a A is the constant; B is the slope
Allometry
Non-isometric scaling = “allometry” (allos = different)
Isometry
Similarity in triangles is linear proportional scaling = “isometry”
Blood Volume
A: Total blood volume increases in proportion to body size (slope = 1.0) y = 0.7 * mass1 Isometric Percent blood volume is the same but liters changes proportional to body size
Bone Mass
B: bone mass has to increase higher than proportional rate (slope = 1.08) Predict that as animals get larger, there must be some shape differences in animals
Overall oxygen consumption Rate/Metabolism
C: overall oxygen consumption/metabolism increases with body size (slope = 0.75) 0.75 is an observational number If you normalize the metabolic weight per g tissue, the larger the animal, the lower the metabolic rate gram tissue is. For the same organ (e.g., brain, muscle), a large animal has less oxygen consumption per gram of kidney (for example) than a small animal has.
Hematocrit
D: hematocrit is constant and does not scale with body size (slope = 0) Also: blood pressure, temperature (don’t scale)
HR
E: as body size increases, HR decreases (slope = -0.25) related to metabolism falling off
Kleibers law
is it universal and why does this make sense. Need to use it to relate mice studies to humans
West and brown
West and brown extedned the scale to 27 orders of magnitude
Metabolic rate
Met doesnt go up as fast as body mass Larger size met advantage bec cost per gram is less so u use less o2 and take less food in
Mouse to Elephant
“Mouse to elephant curve” Slope = 0.74 Pmet (Kcal/day) = 73.3 Mb0.74 Rounded to 70 Mb0.75 Max Kleiber (1932) y = axb; or log y = b log x + log a Specific - star normalized per gram using -.25
Lung and ventilation
As the animal gets larger, the lung gets larger proportionally (isometric) Tidal volume is structural (1.04) Vital capacity is structural (1.03) Ventilation rate is more related to metabolism (0.8) Compliance is physical and directly proportional (1.04) Elastic work per min is related to metabolism (0.78) Frequency of respiration (per min) (-0.26)
Tidal volume is structural
(1.04)
Vital capacity is
(1.03)
Ventilation rate
(0.8)
Compliance
(1.04)
Elastic work per min is
(0.78)
Frequency of respiration (per min)
(-0.26)
Vital capacity is
structural
Ventilation rate is more
related to metabolism
Compliance is
physical and directly proportional
Elastic work per min is
related to metabolism
Tidal Volume is
Structural
Elephants have the most
left shifted hemoglobin
Oxygen consumption rate is
Oxygen consumption rate is related to metabolism (0.76) Structural changes are proportional, metabolic ones are 0.75 (whole body) and -0.25 (normalized) Metabolism doesnt go up quiet as much as body size metabolic rate doesn increase as much so getting bigger is an advantage
Circulation
Relationship between capillary density and body weight Blood Volume = a = 7%, b = 1.0 Heart rate, b = -0.25 Hemoglobin, b = 0 Heart size, a = .6%, b = 1.0 If volume stays the same, but flow rate is changing proportional to body size with 0.75 ratio, then you’re going to calculate that the circulation time is slower for the large animal than for the small animal.
Blood Volume
= a = 7%, b = 1.0
Heart rate,
b = -0.25
Hemoglobin,
b = 0
Heart size,
a = .6%, b = 1.0
If volume stays the same, but flow rate is changing proportional to body size with 0.75 ratio, then you’re going to
calculate that the circulation time is slower for the large animal than for the small animal.
Facts
Quadrupeds much more efficient than bipeds Factorial aerobic scope: VO2max/VO2rest Mammalian average ~10 Human athlete & horse approach 10 Dog = 30 Small mammals < 10 Bat 2.5 – 3.0 Small rodents 6-8 max
Communication in neuronal networks
Ratio of white matter to grey matter (slope = 1.23) As the brain gets larger, the proportion of white matter gets larger Proportionally speaking, a human brain has much more white matter than a rat brain does Percent myelination vs brain diameter Myelin % much greater the larger the animal Increase in proportion of white matter with brain size Bigger brain has more neurons but not proportionally to the volume so the density of neurons decreases with brain size because you have more myelin filling the volume Neuron density decreases with increasing brain matter (not pertaining to synaptic connections) Human brains are proportionally larger given our body mass relative to other mammals
Symmorphosis
“If animals were built reasonably” Greek: balanced formation A state of structural design commensurate to functional needs resulting from regulated morphogenesis whereby formation of structural elements is regulated to satisfy but not exceed the requirements of the functional system - Taylor and Weibel 1981 I.e., in biological organisms, structural design is matched to functional demand
Principles: of Symorphysis
Adaptation of function Variation Allometric (genetic - e.g. body size in insects vs mammals) Adaptive (genetic - programmed adaptation to environment, lifestyle, or load) Induced (epigenetic - operating on the phenotype) Constraints Historical (natural selection to previous conditions) External (environmental pressures and resistance) Internal or constitutional (inner complexity of interconnected functions) Integration of function Economy/efficiency
Adaptation of function
Allometric variation Differences in body mass, Mb, cause VO2max/Mb to be more than 5x higher in a mouse than in a cow because metabolic rate is proportional to about Mb-0.2 Adaptive variation Animals of similar size can be adapted to different levels of endurance performance; dogs and horses can be considered to be endurance athletes as they achieve a VO2max that is 2.5x higher than that of a sedentary species of their size class such as goats and cows Weibel: oxygen consumption at the level of the mitochondria drives the entire structural change all the way up through the lungs. The system doesn’t do anything more than what it needs to do → efficient design. Electron micrograph of muscle mitochondrion shows the packing of inner mitochondrial membranes where oxidative phosphorylation takes place. The active mitochondrial surface, the inner mitochondrial membrane, where oxidative phosphorylation takes place, shows invariant density in the mitochondria both with respect to body mass and aerobic capacity. Thus, the active surface is directly proportional to mitochondrial volume.
Allometric plot of resting and maximal heart frequencies in mammalian species
The larger animal can raise its heart rate proportionately more at maximum than the small animal can.
Integration
Ventilation rate for oxygen and circulation of the blood and the utilization and production of CO2 and utilization of O2 by mitochondria are linked Requirements of the system are specified by the utilization aspect of the components of the physiology, which means that a certain amount of work being done here requires a certain amount of blood flow and ventilation there.
Extension of Keiblers Law
Metabolic Rate
Elephant to Mouse
Organ Metabolism
Blood and Gast Transport
Lung and Ventilation
Circulation
Factorial Aerobic Scope
Effect of Size and Temp on Met Rate
Communication in Neural networks
Functional Trade Off
Evolution of Increased Glia
BMC
Scaling Laws
Symorphysis adaptation of function
Mitochondria
VO2 Max
Allometric Plot
Integration
Integration Pt. 2
Economy Efficiency
Geometry
Allometry
Specific Met Rate
Allometry Plot 2
