On anti-portfolio effects in science and technology with application to reaction kinetics, chemical synthesis, and molecular biology
- †Department of Chemistry, Stanford University, Stanford, CA 94305-5080;
- ‡Institute of Mathematical Statistics and Applied Mathematics, Casa Academiei Romane, Calea 13 Septembrie 13, Bucharest 050711, Romania;
- ¶Cardiology Research Unit, University Emergency Hospital, Romanian Academy of Medical Sciences, 169 Splaiul Independentei, Bucharest 050098, Romania; and
- ‖Institute of Physical Chemistry, Romanian Academy, Splaiul Independentei 202, Bucharest 060021, Romania
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Contributed by John Ross, September 11, 2007 (received for review August 27, 2007)
Abstract
The portfolio effect is the increase of the stability of a system to random fluctuations with the increase of the number of random state variables due to spreading the risk among these variables; many examples exist in various areas of science and technology. We report the existence of an opposite effect, the decrease of stability to random fluctuations due to an increase of the number of random state variables. For successive industrial or biochemical processes of independent, random efficiencies, the stability of the total efficiency decreases with the increase of the number of processes. Depending on the variables considered, the same process may display both a portfolio as well as an anti-portfolio behavior. In disordered kinetics, the activation energy of a reaction or transport process is the result of a sum of random components. Although the total activation energy displays a portfolio effect, the rate coefficient displays an anti-portfolio effect. For random-channel kinetics, the stability of the total rate coefficient increases with the average number of reaction pathways, whereas the stability of the survival function has an opposite behavior: it decreases exponentially with the increase of the average number of reaction pathways (anti-portfolio effect). In molecular biology, the total rate of a nucleotide substitution displays a portfolio effect, whereas the probability that no substitutions occur displays an anti-portfolio effect, resulting in faster evolutionary processes due to fluctuations. The anti-portfolio effect emerges for products of random variables or equations involving multiplicative convolution products.
Footnotes
- §To whom correspondence should be addressed. E-mail: marceluc{at}stanford.edu
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Author contributions: M.O.V. designed research; M.O.V., A.D.C., V.T.P., and J.R. performed research, analyzed data, and wrote the paper.
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The authors declare no conflict of interest.
- © 2007 by The National Academy of Sciences of the USA
