## Population Genetics Department

### Lloyd Demetrius

MCZ Associate

617.493.7489

### Research interests

Two main themes describe my current research interests:

- Ergodic theory of dynamical systems and its applications to the analysis of biological processes at molecular, cellular and population levels.
- Quantum statistics as a formalism to investigate the dynamics of electron transport and proton transduction in cellular metabolism.

These themes involve work of a methodological nature — which is primarily mathematical — and studies of biological models using computational and empirical methods. The methodological studies draw from areas such as the theory of large deviation, non-linear dynamical systems, game theory, products of random matrices. The biological processes investigated include: evolutionary genetics and evolutionary dynamics, biological networks, allometric relations and demography.

*Methodological studies:* An important challenge in the
study of biological systems is to understand in quantitative terms the
relation between macroscopic patterns and processes, and the behavior
of the individual components of the system. This problem arises, for
example, in studies of life-history evolution, where the issue is to
understand the evolutionary dynamics of life-history variables in terms
of the mechanisms which operate primarily on the individual birth and
death rates. The analysis of this problem has led to the development of
a mathematical structure — called the evolutionary formalism — which
studies the relation between microscopic variables and related
macroscopic parameters in certain classes of dynamical processes in
biology.

One of the tenets of the evolutionary formalism is the following analytical fact: The growth rate parameter in models of certain classes of dynamical systems in biology satisfies a variational principle which is formally analogous to the minimization of the free energy in statistical thermodynamics. This principle implies a precise correspondence between certain concepts in thermodynamic theory, and certain macroscopic variables that characterize the behavior of dynamical systems in biology. The evolutionary formalism has led to the discovery of the concept evolutionary entropy, an analogue of the Gibbs-Boltzmann entropy, as a descriptor of the structure and behavior of certain classes of biological systems at the molecular, cellular and population levels. The variational principle entails that the methods of equilibrium statistical mechanics, which revolve around thermodynamic concepts such as free energy and temperature, can be exploited to study the non-equilibrium behavior of biological systems, which are described by processes defined by parameters such as growth rate and cycle time.

*Biological networks:* Large scale studies in
functional genomics now show that the networks which describe the
gene-regulatory systems, protein-DNA interactions, signal transduction
pathways are characterized by certain statistical signatures, in
particular robustness, the capacity of the network to remain functional
in the face of random deletion of nodes and edges. Elucidating the
relation between the topology of the networks and their statistical
properties has emerged as one of the central problems in the new
activity called Systems Biology. These problems are currently being
addressed in terms of the evolutionary formalism. The important
parameter which has emerged from these studies is the concept, network
entropy — a special case of the evolutionary entropy concept.
Analytical and computational studies have shown that network entropy, a
quantitative measure of the rate of information flow within the network
is a precise measure of the property robustness. This relation between
entropy and robustness is being used to explore the relation between
the structure and function of biological networks.

*Life-history evolution:* One of the central issues in
evolutionary genetics is the development of quantitative models to
explain the diversity of life-history in natural population, that is,
the large variability in fecundity and mortality rates which exist
within and between species. R.A. Fisher, one of the pioneers in
evolutionary theory, realized that any solution of this problem
requires a quantitative measure to predict the outcome of competition
between an invading type and the resident population, and proposed the
population growth rate — the Malthusian parameter — as the predictor of
competitive success. Since Fisher’s proposal the population growth rate
has become the dominant parameter in both theoretical and empirical
studies of life-history evolution.

Studies based on the ergodic theory of dynamical systems and diffusion processes showed that growth rate determines invasion success only in populations of effectively infinite size: In finite populations it was shown that the dynamics of invasion is a stochastic process which is predicted by the parameter evolutionary entropy, a measure of the demographic stability or robustness of the population. This demographic parameter has been integrated with Mendelian genetics to develop a dynamical theory of evolution called directionality theory. This theory predicts relations between ecological constraints and life-history variables and provides a framework for explaining the diversity of physiological and morphological properties which exist in natural populations.

*Allometric relations:* Allometric studies which began
with the work of Kleiber in 1930’s show that the metabolic rate of
organisms: uni-cells, plants and animals satisfies certain scaling laws
with respect to body mass. I have developed a class of models to
explain these empirical rules. These models, in sharp contrast to
earlier attempts to addresss this problem, explain both the diversity
in proportionality parameters and the variation in scaling exponents
observed. The models recognize that energy transduction in organisms
occurs by means of electron transfer between redox centers in
biomembranes and that this electron transfer process occurs by quantum
tunnelling. The methods of quantum statistics were exploited to derive
a scaling relation between the metabolic flux in biomembranes and the
cycle time of the metabolic process in uni-cells. The scaling relation
is the basis for investigating both theoretically and empirically,
relations between body size, and physiological and life-history
variables such as metabolic rate and life span, respectively.

*The origin and evolution of aging:* Maximal life span
potential is defined as the maximum observed life span of a species.
There is about a 50-fold range of variation of this parameter within
the mammalian species. The problem of explaining this range of
variation has been an important issue in studies of gerontology.
Efforts to address this problem and to explain the large differencies
in the rate of aging between species have been driven to a large extent
by the rate of living theory oxidative stress theory. This theory
essentially asserts that metabolic rate determines the rate of aging. I
have appealed to new models of the aging process to propose the
hypothesis that metabolic stability, the capacity of metabolic networks
in the cell to maintain steady state concentrations of metabolites, is
the prime determinant of aging. This new class of models has been
integrated with evolutionary models to develop a new theory of aging
which is able to (a) predict the maximum life span potential of
species, (b) evaluate the effect of interventions such as caloric
restriction on species life span.

### Selected publications

- Demetrius, Lloyd and D. Simon (2012) An inverse-Warburg effect and the origin of Alzheimer's disease
*Biogerontology*13, 583-594

- Demetrius, Lloyd and D. Simon (2013) The inverse association of cancer and Alzheimer's: a bioenergetic mechanism
*Interface - Jour. Royal Society*10, 82

- Demetrius, Lloyd and S. Legendre (2013) Evolutionary entropy predicts the outcome of selection: Competition for resources that vary in abundance and diversity Theor. Pop.
*Biology*83, 39-54

- Davis, Paul C., L.A. Demetrius and J.A. Tuszynski (2012) Implications of quantum metabolism and natural selection for the origin of cancer cells and tumor progression
*AIP Advances*2, 011002

- Davis, Paul C., L.A. Demetrius and J.A. Tuszynski (2011) Cancer as dynamical phase transition
*Theor. Biol. And Medical Modelling*8, 30 - Demetrius, L., Coy, J. F. and Tuszynski, J. A. (2010): Cancer proliferation and therapy: the Warburg effect and quantum metabolism. J.R. Soc. Interface.
- Demetrius, L. and Tuszynski, J. A. (2009): Quantum metabolism explains the allometric scaling of metabolic rates. J.R. Soc. Interface .
- Demetrius, L., Harremöes, P. and Legendrec, S. (2009): Evolutionary Entropy: A Predictor of Body Size, Metabolic Rate and Maximal Life Span. Bulletin of Mathematical Biology, 71: 800 - 818 .
- Adjaye, J., Brink, T.C., Demetrius, L. and Lehrach, H. (2008): Age-related transcriptional changes in gene expression in different organs of mice support the metabolic stability theory of aging. Biogerontology .
- Demetrius, L. and Ziehe, M. (2007): Darwinian fitness. Theoretical Population Biology, 72: 323 - 345 .
- Demetrius, L. (2006): Aging in Mouse and Human Systems. Ann. N.Y. Acad. Sci., 1067: 66 82.
- Demetrius L., and Manke, T. (2005): Robustness and network evolution. Physica A, 346: 682 - 696 .
- Kowald, A. and Demetrius, L. (2005): Directionality theory: a computational study of an entropic principle in evolution. Proc. Royal Soc. B. London, 272: 741 - 749 .
- Demetrius, L. and Ziehe, M. (2005): Directionality theory: an empirical study of an entropc principle in life-history evolution. Proc. Royal Soc. B. London, 272: 1185 - 1194 .
- Demetrius, L., Gundlach, M., and Ochs, M. (2004): Complexity and demographic stability. Theor. Pop. Biol. 65: 211 - 225 .
- Demetrius, L. (2002): Quantum statistics and allometric scaling of organisms. Physica A, 322: 477 - 490 .
- Demetrius, L., Gundlach, V.M. and Ochs, G. (2002): Complexity and demographic stability in population models. Theoretical Population Biology, 65: 211 - 225 .
- Demetrius, L. (2001): Mortality plateaus and directionality theory. Proc. Royal Soc. B London, 268: 2029 - 2037 .
- Demetrius, L. and Gundlach, V.M. (2000): Game theory and evolution: finite size and absolute fitness measures. Mathematical Biosciences, 168: 9 - 38 .
- Demetrius, L. (1997): Directionality principles in thermodynamics and evolution. Proc. Natl. Acad. Sci. USA, 94: 3491 - 3498 .
- Arnold, L., Demetrius, L. and Gundlach, V.M. (1994): Evolutionary formalism for products of positive random matrices. The Annals of Applied Probability, Vol. 4, No. 3: 859 - 901 .
- Demetrius, L. (1983): Statistical Mechanics and Population Biology. Journal of Statistical Physics, Vol. 30, No. 3: 709 - 753 .
- Demetrius, L. (1978): Adaptive value, entropy and survivorship curves. Nature, 275: 213 - 214 .