Embed Size (px)
Citation preview
Life's Universal Scaling Laws.Geoffrey B. West and James H. Brown
2004
Presented by: Faiza and Vineeth
SummarySummary
Life is the most complex physical phenomenon in the Universe, manifesting an extraordinary diversity of form and function over an enormous scale from the largest animals and plants to the smallest microbes and sub-cellular units.
SummarySummary
A Swiss animal scientist, Max Kleiber, who performed a set of careful measures of metabolism rate of different animals. His data showed that metabolic rate scales with body mass to the three-fourths power.
SummarySummary
● West and Brown proposed a set of principles based on the observation that almost all life is sustained by hierarchical branching networks, which we assume have invariant terminal units, are space-filling and are optimized by the process of natural selection.
● Metabolic rate based on blood flow. ● Scaling laws application to molecules, trees and
forest.● They talk about Controversies and criticism.
Universal laws in biology?Universal laws in biology?
In 1917, D’Arcy Thompson began his book
On Growth and Form
with the quote:
“chemistry… was a science but not Science… for that true Science lay in its relation to mathematics.”
He then goes on to say:
math + chemistry = Science
biology + fluffy = science Picture By Culture24 Reporter | 12 January 2012
What if animals were fractals? University of Utah ACCESS 2009
Allometric scaling lawsAllometric scaling laws
Allometry is the study of changes in characteristics of organisms as body sizes grow.
accessscience.com/content/Allometry/757225
Allometric scaling lawsAllometric scaling laws
A typical allometric scaling law is usually written in the form of
Y = Y0Mb
where Y is the biological variable of interest, M is themass.Both Y0 and b are numbers to be determined from experimental data, and the scaling exponent is of particular interest as it characterizes how Y specifically changes as the mass is varied.
What if animals were fractals? University of Utah ACCESS 2009
Allometric scaling lawsAllometric scaling laws
The most studied of those variables is basal metabolic rate.
● The basal metabolic rate of mammals and birds was originally plotted by Max Kleiber in 1932.
● In this reconstruction, the slope of the best straight-line fit is 0.74, illustrating the scaling of metabolic rate with the 3/4 power of mass.
The basal metabolic rate
ExamplesExamples
Allometric scaling exponents for various biological variables as a function of mass:
What if animals were fractals? University of Utah ACCESS 2009
Scaling Exponent
Metabolic rateHeart beat rateLife SpanRadius of aortas/ tree trunksGenome length for unicellular organismBrain mass
¾ -¼¼3/8¼¾
Origins of scalingOrigins of scaling
● Natural selection evolved hierarchical fractal like branching networks that distribute energy, metabolites, and information from macroscopic reservoirs to microscopic sites.
● Scaling laws and the generic coarse-grained dynamical behavior of biological systems reflect the constraints inherent in universal properties of such networks.
Origins of scalingOrigins of scaling
These constraints were postulated as follows:● Networks service all local biologically active
regions in both mature and growing biological systems. Such networks are called space-filling.
● The networks’ terminal units are invariant within a class or taxon.
● Organisms evolve toward an optimal state in which the energy required for resource distribution is minimized.
Metabolic RateMetabolic Rate● Aerobic metabolism is fueled by oxygen
● The blood flow rate is the proxy for Metabolic Rate
● (space filling constraints)
● Two factors independently contribute to energy loss:
1)Viscous energy dissipation
2)Energy reflected at branch points●
● Poiseuille flow
● For such flow, minimization of dissipated energy leads to area-increasing branching with ratio of radius of .
Metabolic Rate Contd..Metabolic Rate Contd..
The 3/4-power law
Metabolic Rate Contd..Metabolic Rate Contd..
● Minimum weight of a mammals the smallest size that can be supported is 1 gram.
● Which is approximately the size of shrew, the smallest mammal.
● Because of the changing roles of pulsatile and Poiseuille flow with body size, as mass decreases, the exponent for B should depend weakly on M, exhibiting calculable deviations from 3/4 as observed.
From molecules to forestsFrom molecules to forests
● Metabolic energy is conserved as it flows through the hierarchy of sequential networks.
● The continuity of flow imposes boundary conditions between adjacent levels.
● Those conditions, in turn, lead to constraints on densities of the invariant terminal units, such as mitochondria and respiratory molecules, that interact between levels.
● So, for example, the total mitochondrial mass relative to body mass is correctly predicted to be
where is the mitochondrial mass, is the average cell mass, and M is in grams.
From molecules to forestsFrom molecules to forests
● Cells in vivo adjust their number of mitochondria appropriately to the size of the host mammal as dictated by the resource supply networks. In vivo cellular metabolic rate thereby scales as .
● In vitro cultured cells from different mammals, however, are predicted to develop the same metabolic rate, about watts.
● No wonder shrews live short lives!
● Metabolic rate has two components, maintenance and growth, and can be expressed as
From molecules to forestsFrom molecules to forests
The universality of growth
From molecules to forestsFrom molecules to forests
● The number of cells to be supported increases faster than the rate at which they are supplied with energy , which allows a determination of the mass at maturity. Moreover, the parameters in the growth equation are determined by fundamental properties of cells.
● Temperature has a powerful effect on those basic properties—indeed, on all of life—because of its exponential effect on biochemical reaction rates.
● The Boltzmann factor , where E is an activation energy, k is Boltzmann’s constant, and T is the temperature, describes the effect quantitatively.
From molecules to forestsFrom molecules to forests
● All times associated with metabolism should scale as
and all rates as , with approximately the same value for E. Data covering fish, amphibians, aquatic insects, and zooplankton confirm the prediction.
● The best-fit value for E, about 0.65 eV, may be interpreted as an average activation energy for the rate limiting biochemical reactions.
From molecules to forestsFrom molecules to forests
Trees and forests
c-The number of branches (closed circles) and roots (open circles) in a tree varies roughly as the predicted inverse square of the diameter.d-The number of trees of a given size as a function of trunk diameter
Criticisms and controversiesCriticisms and controversies
● This theoretical framework reviewed has now been published for long enough to have attracted a number of critical responses.
Criticisms and controversiesCriticisms and controversies
Should it be 2/3 or 3/4? How universal is this metabolic scaling anyway?
Can we really distinguish between 2/3 and 3/4?
Discussion QuestionsDiscussion Questions
Do biological phenomena obey underlying universal laws of life that can be mathematized so that biology can be formulated as a predictive, quantitative science?
“Newton’s laws of biology”
Discussion QuestionsDiscussion Questions
In the discussion of origins of scaling we had the assumption that, the terminal units are invariant. What do you think about this statement?
