|
Mailing List complex-science@necsi.org Message #9635 | |
|---|
| |||||||
| (Yaneer, if it is not too late, can you replace my previous post with this one? There were 3 minor typos. Thanks.) I just finished reading Per Bak's "How Nature Works: The Science of Self-Organized Criticality" (Springer, 1996). Self-organized criticality (SOC) refers to the property of a complex system that is slowly driven to a critical state where small perturbations lead to "avalanches" of all sizes affecting the whole system. SOC was discovered in 1987 by Bak, Tang and Wiesenfeld (BTW) and has been applied since then to 1) geophysics, 2) cosmology, 3) evolutionary biology, 4) brain physiology, 5) quantum gravity, 6) solar physics, 7) plasma physics, 8) neurobiology, 9) sociology, 10) economics, and others. BTW visualized SOC as a "sandpile" to which grains are slowly added from above to cause avalanches or slides. If the number of avalanches, N, of a given size, s, is plotted against the size of avalanches in a double logarithmic plot, one obtains an excellent straight line, indicating that a power law is involved: N(s) = As^-k . . . . . . . . . . (1) where A and k are constants. Power laws similar to Eq. (1) were found in all of the 10 fields listed above. Clearly SOC is a major discovery of the 20th century science. It may be considered to be the first mathematical theory of complex systems and hence be referred to as the 'first law of complex systems', comparable to the first and second laws of thermodynamic systems. Since the tradition is well established in physical chemistry that all self-organizing systems are named after the city where the research is carried out, followed by the suffix "-ator", we may refer to all self-organizing systems with critical properties like sandpiles as the "Brookhavenator", although the Brookhaven National Laboratory (BNL) where SOC was discovered is located in Upton, N.Y., some tens of miles Northeast of Brookhaven. It is interesting to note that, though BNL produced 6 Nobel laureates in particle physics, it is through SOC that its name may be 'immortalized' in the form of the Brookhavenator. Also interesting is the fact that SOC has never been reported in molecular biology, to the best of my knowledge. One possible reason for this conspicuous lack of any report of SOC in molecular biology so far may be that the usual criterion for SOC, namely, the power law, e.g., Eq. (1), may be too simple to capture the mechanisms of the SOC occurring in molecular dynamical systems. I have been analyzing the so-called 'dynamic heterogeneity' of rate constants observed in single-molecule cholesterol oxidase reported in 1998 by Lu, Sun and Xie [1]. These authors found that a single molecule of cholesterol oxidase catalyzes the oxidation of cholesterol to cholesterone with rate constants that are not uniform but vary widely by a factor of about 25. And the distribution of the rate constants are not Gaussian but obeys the distribution that is similar to the black-body radiation formula of M. Planck [2], which is of a mixed form, being a product of a power law and an exponential law: p(w) = (aw^-5)e^(-b/w) . . . . . . . . . . . (2) where a and b are constants, w is the waiting time (which is inversely related to rate constants), and p(w) is the probability of the occurrence of a given waiting time, w. A waiting time is the time the enzyme waits until the next catalytic event. The mixed distribution law, Eq. (2), can be derived using the sandpile as an analogy, where i) the sandpile is replaced with an enzyme, ii) sand grains with conformons (packets of energy and information), and iii) avalanches with catalytic events. So, if my analysis of SOC briefly described here turns out to be correct, there may be two kinds of SOC--the one obeying the power law, e.g., Eq. (1), and the other obeying what may be referred to as "the mixed law", e.g., Eq. (2). With all the best. Sung ___________________________________________ Sungchul Ji, Ph.D. Department of Pharmacology and Toxicology Rutgers University Piscataway, N.J,. 08855 References: [1] Lu, H. P., Xun, L., and Xie, X. S. (1998). Single-Molecule Enzymatic Dynamics. Science 282:1877-1882. [2] Ji, S. (2009). Molecular Theory of the Living Cell: Conceptual Foundations, Molecular Mechanisms and Applications. Springer, N.Y. (to appear). |
|
|
| Subscribe (FEED) | Subscribe (DIGEST) | Subscribe (INDEX) | Unsubscribe | Mail to ListMaster |
|---|
