Lecture 1
Isometry: proportions do not change in size
Humans do not grow isometrically as the proportions change, babies have
in proportion a lot bigger head size. It can be seen that the growth of the
brain is not isometric while the growth of the heart is (almost) isometric.
If you test medication, you first apply it to bigger animals after you tested
it on mice because a large animal model is much closer to humans.
In GFR you have to correct for body size (ml/min/1.73m3). This is also for
things like lung volume etc.
Voice = lower in larger animals and higher in smaller animals because of
the size of the vocal cords. Thereby they are also more sensitive to the
sound frequencies they produce themselves because of the membrane in
the ear.
Bats use ultrasonic to navigate themselves, at a frequency we can hardly
hear. The sound they produce is so loud that they will go deaf if they hear
their own sound. They prevent this by disconnecting their ears, it makes
itself deaf when making the sound.
A rat also produced ultrasonic sounds. This is why it should be taken care
of that there is not to much sound that we don’t hear of machines or
lamps which can disturb the rat.
Relatively, the bones of an elephant are much thicker than of cats which is
why cats can jumps and elephants cannot. This is also because elephants
are much more heavy and the skeleton must “carry” this weight.
The cells of an elephant are not much bigger than the cells of a mouse.
You cannot have very large cells because of the limiting factor: oxygen
diffusion. If a cell is very large, the oxygen cannot diffuse much to the
center of the cell which is why the cells of an elephant aren’t much bigger.
Y = a*xb
Y = parameter measured in relation to the size of the organism
X = measure of size used as basis of comparison
A = initial growth index (size of y when x=1)
B = scaling exponent (proportional change in Y per unit of x)
But you can also use the logarithmic form to get a linear relationship:
logY = logA + b*logx
,B = 1 -> isometry
B < 1 -> negative allometry, as x increases, y becomes relatively smaller
B > 1 -> positive allometry, as x increases, y becomes relatively larger
This is only true when we compare like dimensions (length vs length,
weight vs weight, etc.)
Mass = related to volume (L3) put in the presentation slides about this
(“isometry for different dimensions”)
Weight loading: look at cross-sectional area of the leg
“cuby family” slide: if the proportions don’t change, the weight loading on
the leg will increase by a factor of 10. To solve this you need a thicker leg
which should be an increase of mass/desired weight loading (g/cm2) = leg
cross-sectional area (cm2).
The scaling factor calculated is 1.32 (32%) but the scaling in reality is
smaller, so the weight loading on the leg of an elephant is larger than the
weight loading on the legs of a mouse. This is why you get closer to the
limits and why elephants cannot jump.
Exponential scaling relations are logarithmic which is why it is easier to
asses them on a logarithmic scale (linear relation).
This makes it possible to visualize this on a longer period.
This also spreads the data points more evenly over the graph and you can
describe the relations easier between the species.
Either 10x or ex is used on a logarithmic scale.
If you use the relation logy = loga + b*logx, logA is the intercept.
If the slope changes (b), the
In example about the flies with wing area and thorax length you expect a
slope of 1 because for both factors, the area (L2) is used.
Primary signal: intercept and slope of allometric relationship
Secondary signal: deviation from expected allometric relation. This is often
when the animal has a special adaptation. You can see if this significant by
looking at the confidence interval.
,Mheart : Mbody = 0.006 (from mouse to whales)
Mblood : Mheart = (in lecture slides)
Scaling of CV system: formulas for heart frequencies and cardiac output
compared to body mass.
, Lecture 2 – allometry scaling in pharmacology
Normal 10-15 years of drug development time:
AE = adverse effects (effects we don’t want to see)
In phases, groups become bigger each time. Along the way we lose a lot of
compounds.
Phase 1:
First time we have drug in a human being. If we are testing it in human
subjects, we’re thinking about white middle aged men. This is because
women have variations in hormone levels which can influence how the
drug acts on the body but also can affect the metabolism of the drug by
the person. Women also could be pregnant. These men are white because
we know a lot about them, they have been tested for a very long time.
In this phase 1 we mostly want to know the appropriate dose, dosing
regimen, the concentration observed in the subject and how fast it
declines, how to give the medicine (pill/nasal spray/injection).
The compound is not yet in the optimal formulation yet, it is not yet in a
pharmaceutical pure formulation. The compound is also very expensive to
manufacture at this stage.
Isometry: proportions do not change in size
Humans do not grow isometrically as the proportions change, babies have
in proportion a lot bigger head size. It can be seen that the growth of the
brain is not isometric while the growth of the heart is (almost) isometric.
If you test medication, you first apply it to bigger animals after you tested
it on mice because a large animal model is much closer to humans.
In GFR you have to correct for body size (ml/min/1.73m3). This is also for
things like lung volume etc.
Voice = lower in larger animals and higher in smaller animals because of
the size of the vocal cords. Thereby they are also more sensitive to the
sound frequencies they produce themselves because of the membrane in
the ear.
Bats use ultrasonic to navigate themselves, at a frequency we can hardly
hear. The sound they produce is so loud that they will go deaf if they hear
their own sound. They prevent this by disconnecting their ears, it makes
itself deaf when making the sound.
A rat also produced ultrasonic sounds. This is why it should be taken care
of that there is not to much sound that we don’t hear of machines or
lamps which can disturb the rat.
Relatively, the bones of an elephant are much thicker than of cats which is
why cats can jumps and elephants cannot. This is also because elephants
are much more heavy and the skeleton must “carry” this weight.
The cells of an elephant are not much bigger than the cells of a mouse.
You cannot have very large cells because of the limiting factor: oxygen
diffusion. If a cell is very large, the oxygen cannot diffuse much to the
center of the cell which is why the cells of an elephant aren’t much bigger.
Y = a*xb
Y = parameter measured in relation to the size of the organism
X = measure of size used as basis of comparison
A = initial growth index (size of y when x=1)
B = scaling exponent (proportional change in Y per unit of x)
But you can also use the logarithmic form to get a linear relationship:
logY = logA + b*logx
,B = 1 -> isometry
B < 1 -> negative allometry, as x increases, y becomes relatively smaller
B > 1 -> positive allometry, as x increases, y becomes relatively larger
This is only true when we compare like dimensions (length vs length,
weight vs weight, etc.)
Mass = related to volume (L3) put in the presentation slides about this
(“isometry for different dimensions”)
Weight loading: look at cross-sectional area of the leg
“cuby family” slide: if the proportions don’t change, the weight loading on
the leg will increase by a factor of 10. To solve this you need a thicker leg
which should be an increase of mass/desired weight loading (g/cm2) = leg
cross-sectional area (cm2).
The scaling factor calculated is 1.32 (32%) but the scaling in reality is
smaller, so the weight loading on the leg of an elephant is larger than the
weight loading on the legs of a mouse. This is why you get closer to the
limits and why elephants cannot jump.
Exponential scaling relations are logarithmic which is why it is easier to
asses them on a logarithmic scale (linear relation).
This makes it possible to visualize this on a longer period.
This also spreads the data points more evenly over the graph and you can
describe the relations easier between the species.
Either 10x or ex is used on a logarithmic scale.
If you use the relation logy = loga + b*logx, logA is the intercept.
If the slope changes (b), the
In example about the flies with wing area and thorax length you expect a
slope of 1 because for both factors, the area (L2) is used.
Primary signal: intercept and slope of allometric relationship
Secondary signal: deviation from expected allometric relation. This is often
when the animal has a special adaptation. You can see if this significant by
looking at the confidence interval.
,Mheart : Mbody = 0.006 (from mouse to whales)
Mblood : Mheart = (in lecture slides)
Scaling of CV system: formulas for heart frequencies and cardiac output
compared to body mass.
, Lecture 2 – allometry scaling in pharmacology
Normal 10-15 years of drug development time:
AE = adverse effects (effects we don’t want to see)
In phases, groups become bigger each time. Along the way we lose a lot of
compounds.
Phase 1:
First time we have drug in a human being. If we are testing it in human
subjects, we’re thinking about white middle aged men. This is because
women have variations in hormone levels which can influence how the
drug acts on the body but also can affect the metabolism of the drug by
the person. Women also could be pregnant. These men are white because
we know a lot about them, they have been tested for a very long time.
In this phase 1 we mostly want to know the appropriate dose, dosing
regimen, the concentration observed in the subject and how fast it
declines, how to give the medicine (pill/nasal spray/injection).
The compound is not yet in the optimal formulation yet, it is not yet in a
pharmaceutical pure formulation. The compound is also very expensive to
manufacture at this stage.
