Why We Die

Simulating the Evolution of Senescence

Kris Carlson

Continuity Logic LLC

What is aging?

Towards a precise, scientific definition based on observables:

Monotonic decreasing statistical survivorship over life history

Reduction in the ability to withstand challenges from the environment

Deterioration of function in organisms' life history relative to reproductive years

Sum total of deleterious changes occurring over an organism's life history

At the molecular, genetic, and tissue level, an apparently complex phenomenon

"...a complex process driven by diverse molecular pathways and biochemical events. The gradual decline in cellular functions associated with aging is not caused by changes in the expression or activity of just a few individual genes, but rather by the cumulative changes from many genes."

Kim, Stuart, "Common aging pathways in worms, flies, mice and humans," The Journal of Experimental Biology 210, 1607-1612.

A thought experiment to illustrate the evolution of aging

Suppose everyone in this room took a few months to write a program

It doesn't have to "do" anything—evolution has no particular goal

But it must have as many features as possible and there will be an unlimited variety of users (= niches)

It must copy (reproduce) itself at least once at 45 minutes

What would characterize the resulting ensemble of programs?

There will be no fatal or reproduction-crippling bugs for 45 minutes

There will be a distribution of bugs occurring after the reproduction point

How do we explain the paradox of aging?

Aging is an "Unsolved Problem in Biology" (Medawar, 1952)

The problem: How can fitness degradation be beneficial to individuals?

Two fallacious categories of common explanation are ruled out by evolutionary biology:

(1) No teleological thinking: evolution has no goal, no "final cause," no end toward which it is directed

Fallacy example: Death must occur to permit further evolution

However, there is an objective function present in the physical niche, and physiological, phylogenetic, and genetic constraints

(2) Group selection is far weaker than selection at the level of individuals

Fallacy example: Death of older individuals creates more room and resources for younger members

Medawar, Peter B., An Unsolved Problem of Biology (London: H. K. Lewis & Co., 1952).

The basic explanation from evolutionary biology:

The evolution of senescence results from decreasing selective pressure after reproductive maturity

Mutation, reproduction, and selection result in:

The active selection of adaptive pathways activated to maturity

Senescence is:

The passive accumulation of maladaptive pathways (bugs) activated post-maturity

Development is programmed up to maturity (advent of reproductive years)

Not the same as an earlier view of "programmed" aging because post-maturity, passive accumulation of deleterious mutations is with no goal

Development is "buggy" after maturity—from our perspective of wanting healthy longevity

Not "programmed" per se

Theories of aging

There are over 300 theories of aging

One categorization of the theories:

Ultimate theories: Why does aging exist? What are its origins? Why do species and populations age at different rates?

Thermodynamic inevitability: Entropy eventually overcomes temporary negentropic bubbles
At molecular level or organ level (the "old car theory"—the parts eventually wear out)
     Rate of living theory: energy consumption limits longevity
     Cool mice live long—but hot flies live long, too (Conti 2006; Khazaeli et al. 1997) 
     A more modern redux: inevitable metabolic bi-products, reactive oxygen species (ROS), cause cumulative molecular damage
     Low oxygen environment slows decay of trabecular meshwork causative of some glaucomas (Luna et al. 2006)

Proximate theories: What are the mechanisms of aging?

Medvedev, Z. A., An attempt at a rational classification of theories of ageing. Biological Reviews, 60 (1990), 375 - 398.
Mayr, Ernst, Cause and effect in biology. Science, 134 (1961), 1501-1506.

The evolutionary theory of aging: an emerging synthesis

"I  would emphasize that a lengthening of life is connected with an increase in the duration of reproduction, while on the other hand there is no reason to expect life to be prolonged beyond the reproductive period; so that the end of this period is usually more or less coincident with death." (Weismann, 1889)

"...the force of natural selection weakens with increasing age.... If a genetical disaster ... happens late enough in individual life, its consequences may be completely unimportant ... this dispensation may have a real bearing on the origin in innate deterioration with increasing age." (Medawar, 1952)

"...the death rate in Man takes a course generally inverse to the curve of reproductive value." (Fisher, 1958)

Fisher's "reproductive value," aka fitness, is the discounted present value of future genetic heritage:

v(x) = (∫_x^∞)(e^(-rt))(Subscript[l, t])(Subscript[m, t])dt (e^rx)/(Subscript[l, x])

Fitness is defined as reproductive success.

The earlier reproduction occurs in life, the stronger the effect it has on future generations carrying an individual's genes.

And selective pressure to mold traits with age-specific effects progressively weakens with age (Hamilton, 1966).

A second factor: the inevitability of extrinsic mortality

1. Resource shortages, predation, accidents, infectious disease, etc.: inevitably fewer individuals live to reproduce and promulgate their genes at later ages compared to earlier ages.

2. The nature of compounded growth: in theory, terrestrial bacteria could fill the habitable area of the universe in an astonishingly short time

Assumptions: 
Carrying capacity of the earth (seawater, soil, and sediment/soil subsurface) = (10^30) bacteria
Mean generation time of all bacteria (except sub-surface): ~170 days
Mean generation time of rapid-reproducing bacteria: ~20 minutes
Number of stars in the universe: (10^23)
Number of habitable planets per star (high estimate): (10^(-1))
Number of habitable planets in the universe: (10^22)
Carrying capacity of the universe based on terrestrial carrying capacity: (10^52) bacteria

In theory, without mortality, reproduction from a single terrestrial bacterium could fill the habitable area of the universe in 173 generations, or 58 days

IntegerDigits[10^52, 2]//Length

173/3//N

It is immaterial if the growth rate is slower than the fastest-reproducing bacteria rates

Based on mean generation time of 170 days for all bacteria except sub-surface, the carrying capacity of the universe would be filled in 80 days.

(173 170)/365//N

Based on mean generation time of slow-reproducing sub-surface terrestrial bacteria, of 1.5 * 10^3 years, carrying capacity would be filled in 259,500 years.

(173 1.5 10^3)//N

Whitman, William B. et al., Prokaryotes: "The unseen majority," PNAS June 9, 1998 vol. 95 no. 12, pp. 6578-6583

The origin of aging is explained by evolutionary theory

When did senescence evolve? What were the triggering factors?

The advent of sexual reproduction triggered the rapid evolution of senescence

With sexual reproduction, the somatic and reproductive genomes began evolving separately

A deleterious mutation to the genome controlling the next generation did not quickly kill the organism

Therefore late-acting, deleterious mutations could accumulate in the germ line genome

Thus the evolution of senescence began about a billion years ago

Thus some senescence genes, pathways, and processes could be among the most conserved across all eukaryotic taxa

A challenge to in silico (computer) simulation

"Only when there is an adult that produces a delimitable offspring, as opposed splitting in two, can aging evolve, and then it must always evolve. This is one of the strongest theoretical predictions in all of evolutionary biology."

Rose, Michael, Evolutionary Biology of Aging (Oxford: Oxford University Press, 1991), p. 84.

Evolution "tunes" life histories to ecological niches

Artificial evolution: Two independent experiments with flies

Selected female flies that lived long and reproduced late

Therefore artificially eliminated the effects of genes with early beneficial but late detrimental effects

Exaggerated the effects of all genes contributing to longevity and late reproduction

Result: longer-lived flies (200%) that successfully reproduced late in their life history

Stephen Austad's research on isolated population of opossums

Mainland opossums died relatively young from multiple predators (owls, coyotes, wolves, dogs, cougars, bobcats) and accidents (automobiles)

Island opossums, with no predators, died relatively older (25 - 50%, with delayed senescence)

Rose, M. R., "Laboratory evolution of postponed senescence in Drosophila melanogaster," Evolution 38 (1984): 1004-1010.
Luckinbill, S., et al., "Selection for delayed senescence in Drosophila melanogaster," Evolution 38 (1984): 996-1003.
Austad, S. N., "Retarded senescence in an insular population of Virginia opossums (Didelphis virginiana)," Journal of Zoology 229 (1993): 695-708.

Evolution "tunes" life histories, including longevity, to ecological niches

The bat is a mouse that evolved wings and can fly away from its predators

Mouse lifespan: 18-24 months    Bat lifespan: 25-30 years

Bats now comprise over 20% of mammal species

Birds, for similar reasons, are relatively long-lived

"Flying" squirrels are the longest-lived squirrels

Quahogs, buried with a very hard shell, live 200 years

Sea turtles live 180 years

Sequoias live 3200 years

Bristlecone pines live 4900 years

The start of a theoretical framework driving the evolution of senescence

Accumulation of late-acting, deleterious somatic genome mutations

The passive buildup in the genome of alleles with deleterious effects expressed post-reproductive peak

In the wild, post-maturity, there is lessening selective pressure against deleterious genes

In the wild, most animals die before senescence progresses very far

Therefore senescence has little effect on fitness, pro or con

Extrinsic mortality—e.g. predation, disease, starvation, weather, accident—exert a greater effect on fitness than senescence

Originally termed "mutation accumulation theory": the buildup of deleterious mutations expressed after maturity (late in life history)

Medawar, Peter B., An Unsolved Problem of Biology (London: H. K. Lewis & Co., 1952).

Next step in development of evolutionary theory: Antagonistic pleiotropy

Accumulation of early-beneficial, late-deleterious mutations

Active selection of alleles with beneficial early effects and by chance, deleterious late effects relative to reproductive peak

Example: MMP-13 (matrix metalloprotease 13) aka collagenase 3. Early in life, essential for formation of collagen. Mid-life, only known activity is the prevention of gingivitis. Late in life, is appropriated by the metastatic cascade.

MMP-13 and others collagenases are used by tumors to penetrate into the blood and lymphatic systems

Ala-aho, Risto, Ahonen, Matti, George, Sarah J., Heikkilä, Jari, Grénman, Reidar, Kallajoki, Markku, and Kähäri, Veli-Matti, "Targeted inhibition of human collagenase-3 (MMP-13) expression inhibits squamous cell carcinoma growth in vivo," Oncogene (2004) advance online publication 19 April 2004; doi:10.1038/sj.onc.1207678.
Coussens, Lisa M., Fingleton, Barbara, Matrisian, Lynn M., "Matrix Metalloproteinase Inhibitors and Cancer: Trials and Tribulations," Science Vol. 295 (29 March 2002), pp. 2387-2392.
Williams, G. C., Pleiotropy, natural selection and the evolution of senescence. Evolution 11 (1957), 398-411.
Hamilton, W. D., The molding of senescence by natural selection. Journal of Theoretical Biology 12 (1966), 12-45.

The "disposable soma" theory and the theory of life histories

Emphasized the trade-off between developmental resources devoted to the body (soma) versus reproduction

Life history theory: Analysis of the trade-offs in allocation of resources to development and behavior (reproduction, feeding, exploration, etc.)

The body and development are seen as an economy—constant trade-offs of scarce resources amongst competing ends

The genome is selfish and preserves itself at the expense of the body

The body (soma) is disposable, a vehicle to survive only long enough to reproduce the genome

Optimizing life histories is a "new kind of science" problem in complexity

"A complete mathematical solution to an optimal life-history problem requires enumeration of all the life-histories corresponding to local [fitness] maxima [based on a set of phenotype traits at one point in time]. This is usually a formidable task."

Add to that complexity: 1) dynamic ecologies and 2) mutating sets of phenotypic traits

Solved by evolution running many genetic programs in parallel

Kirkwood, T. B. L., Evolution of aging, Nature, 270 (1977), 301-304.
Charlesworth, Brian, Evolution in Age-Structured Populations, 2nd ed., (Cambridge: Cambridge University Press, 1980), p. 186 et seq.

The evolutionary theory can subsume all other theories of aging

Answers the "ultimate" question of why aging exists: active longevity pathway selection to maturity, passive deleterious pathway accumulation after maturity

Conventional wisdom: Diseases whose incidence increases geometrically with age are "age-related disease"

An alternative view: All 4000 diseases are age-related as are all genetic disorders

All "proximate," causal explanations are seen as devices evolution uses to "tune" life histories to ecological niches

Simulation of aging exemplifies the 'new kind of science'

"It should be emphasized, however, that with the exception of the important contributions by Hamilton and Charlesworth, there has been a surprising paucity of explicit mathematical models of evolutionary biologic theories of aging." (Martin)

Mathematical models are usually carefully caveatted about their domain of applicability

Computer simulation of model evolutionary algorithms is the natural medium for exploration of aging phenomena

Charlesworth, Brian, Evolution in Age-Structured Populations, 2nd ed., (Cambridge: Cambridge University Press, 1980) 
Martin, George M., "The evolutionary substrate of aging," Archives of Neurology Vol. 59 No. 11 (2002).
Wolfram, Stephen, A New Kind of Science (Champaign IL: Wolfram Media, Inc., 2002)

Martin's taxonomy: a "periodic table" of senescence genes

I: Longevity assurance genes

DNA repair pathways

Reactive oxygen species regulatory pathways

"Housekeeping" mechanisms pathways

II: Adaptive gene silencing

Positive: Down-regulation of rapid somatic growth mechanisms post-puberty

Negative: Decreased protein synthesis and turnover

III: Non-adaptive loss of gene silencing

Proper expression requires silencing of all non-essential genes as well as activation of required genes

Non-adaptive silencing is the loss of coordinated silencing of non-essential genes

SIR2 in yeast inversely correlated with expression of erDNA circles

IV: Good effects early, bad effects late (antagonistic pleiotropy)

Slowing of replication early in life as a tumor-suppressor

V: Good effects early, bad effects early or late

Age-specific cancers

Other senescent phenotypes resulting from random mutations

VI: Bad alleles not expressed until late in life

Late onset genetic disorders

Age-related diseases (those whose incidence increases exponentially with age)

Martin, George M., "The evolutionary substrate of aging," Archives of Neurology Vol. 59 No. 11 (2002).
Martin, George M., "Gene action in the aging brain: an evolutionary biological perspective,", Neurobiology of Aging 23 (2002) 647–654.

Representation for aging: Data structure of populations

allSpeciesFecundityMortalityLongevityMutation = {period, {..., {genome, ... {age, census, fecundity, mutationGenome, mutationFL, longevity, mortality}  } , ...}   }

ePopulation[period, {genome[age, census, fecundity, mutationGenome, mutationFL, longevity, mortality] , ...}]

Symbolic example

symbolicPopulation2=ePopulation[0, Table[genome[genomes,ages, c, f, muG, muFL, l, mo], {genomes,3}, {ages,0, 2}]]

Numerical example

samplePopulation2

Representation of evolution of senescence: Control loop

This sequence simulates having a separate germ line genome from the somatic (cellular) genome.

A different ordering simulates one genome controlling both reproduction and soma operation.

1. processLongevity (reduce the population, including newborns in age class 0 ((who are stillborn if they die) to those who can survive to be subjected to mortality)
2. processMortality (reduce the population further to those who have actually survived)
3. addZerothAgeClass (for newborns)
4. reproduce (i.e., process fecundity; those who have survived, reproduce according to their age-specific probabilities; the following 6 functions will also be included in the reproduce function as they are in vivo)
5. compute mutateGenomeNumber (mutate the newborns' genome number according to the age-specific probabilities)
6. compute mutateFecundityLongevity (mutate the fecundity and longevity values for the newborns in each genome number according to age-specific probabilities)
7. subtract mutated newborns from total newborns
8. add unmutated newborns from each genome number to that genome number's 0th age class
9. distribute mutated newborns from mutateGenomeNumber across all genome numbers' 0th age class
10 add mutated newborns from mutateFecundityLongevity in each genome number to that genome numbers' 0th age class and jiggle fecundity and longevity
11. incrementEvolutionPeriod (it's a new year)
12. incrementAllGenomesAllAgeClasses (all individuals are a year older)
13. rotate fecundity, longevity, mutationGenome and mutationFL values for all age classes to keep them with the same age class, i.e., the age class with which they were correlated before incrementing all age classes (we will correct the values for the last age class, which is a new, oldest age class if there are survivors from the previous oldest age class, in the next step)
14. copy fecundity, mutationGenomeNumber, mutationFecundityLongevity, longevity, and mortality values from next-to-last age class to last age class and mutate them (i.e., if there are survivors from the previous last age class we postulate that their fecundity, mutation and longevity values will be a little different from those of the previous age class; and see next step for what happens if there are no survivors)
15. removeSuperfluousLastAgeClasses (if any census = 0 in a last age class, delete it)

Research program: future directions

Simulation of the evolution of aging

Individual level

Population level

Simulation and verification of the emergence of Martin's categories

Simulation of the operation of senescence signaling pathways

Expansion of the representation to a network of homeostatic pathways regulating aging

Identification of intervention points and simulation of intervention operation

For example, gene silencing

Acknowledgments

Wolfram Research Inc. for Mathematica
Roman Maeder for his datatype and destructive datatyping paradigms, and many others
Michael Trott and Edgar Dijkstra for nomenclature; Trott for innumerable "cookbook" examples
Stephen Wolfram for the classic example of functional programming in Chapter 5 code of A New Kind of Science
Jeffrey Arle, Shahin Tabatabaei, and Stewart Wilson for comments on first version of the slides

General References

Austad, Steven N., Why We Age: What Science Is Discovering about the Body's Journey Through Life (New York: John Wiley & Sons, 1997)
Charlesworth, Brian, Evolution in Age-Structured Populations, 2nd ed., (Cambridge: Cambridge University Press, 1980)
Futuyma, Douglas J., Evolutionary Biology, 3rd ed., (Sunderland, MA: Sinauer Associates, 1998) 
Jacob, Christian, Illustrating Evolutionary Computation with Mathematica (San Francisco: Morgan Kaufmann, 2001)
Maeder, Roman, M220: Programming in Mathematica (Mathematica programming given by Wolfram Education Group)
Maeder, Roman, Programming in Mathematica, 3rd ed., (Reading, MA: Addison-Wesley, 1997)
Masoro, Edward J., and Austad, Steven N., eds., Handbook of the Biology of Aging, 6th edition (Boston: Academic Press, 2006)
McConnell, Steve, Code Complete, A Practical Handbook of Software Construction (Redmond, WA: Microsoft Press, 1993)
Rose, Michael, Evolutionary Biology of Aging (Oxford: Oxford University Press, 1994)
Wolfram, Stephen, A New Kind of Science (Champaign IL: Wolfram Media, Inc., 2002)