User:J. C. Martinez-Garcia/Notebook/HMS Activities/2008/09/08

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On hysteresis

Today I have been reviewing some papers on the phenomenon of hysteresis in biological systems (to try to understand the results that David obtained when working with drug Zstk). Essentially:

  1. I read that in the case of a reversible dynamic enzyme model (E is the enzyme, S the substrate, ES the intermediary complex, and P is the product), the hysteresis phenomenon depends on the ratio velocity constants. Hysteresis appears when the the intermediary complex satisfies the steady state condition. Moreover CLOCKWISE HYSTERESIS (when considering the evolution of dP/dt -the rate of change in the concentration of the product- in terms of ES -the intermediary complex-) (the one that was observed in the experiments) is observed as first behavior, but then there is a crossover to COUNTERCLOCKWISE HYSTERESIS when E0 and S0 have the same order of magnitude. When Eo/S0 is relatively big (e.g. 0.2) the curve has a sigmoid form, and beyond its clockwise turn, a croosover shape. When E0/S0 is very small (0.02) the curve has a banana-shaped trajectory (counterclockwise hysteresis). I took all this stuff from the paper: Hysteresis in Dynamic Enzyme Models (by L. K. Nyiri, and G. M. Toth -Biotechnology and Bioengineering, Vol. III, 1971, pp. 697-701-, the paper is here: Media:enzyme71.pdf).
  2. In terms of energy, it seems that CLOCKWISE hysteresis may be associated to the existence of two feedback loops: a positive one, and a negative one. When the positive feedback loop (cooperative loop) rules the systems (and the negative feedback loop is less significant), the systems presents CLOCKWISE HYSTERESIS (it seems that this phenomenon is related to energy absorption, but I am not so sure, in particular when trying to describe the CLOCKWISE HYSTERESIS phenomenon in terms mechanical friction). I took this ideas from the paper: Media:ICCA03.pdf, by Yael yaniv et al, ICCA'03, 2003, pp. 456-460. I decided to include the following text from this paper, to maintain this idea in my brain: The suggested model of the intracellular control of contraction provides the explanation to the experimentally observed hystereses in the force-length relationships, at constant calcium concentration. The simulated results are in accordance with the experimental observations. At low frequencies (<2.5Hz) counterclockwise hystereses are obtained, where at a given SL the force is larger during shortening than during lengthening, while clockwise hysteresis is obtained at higher oscillation frequencies (>2.5Hz). The analysis reveals the role of each feedback loop. Without the suggested feedback loops the force is independent of the history of contraction and a unique force-length relation is obtained. The cooperativity mechanism, that regulates calcium affinity and XB recruitment, produces only counterclockwise hystereses (at all frequencies). In contrast, the mechanical feedback, that regulates the rate of XB weakening, generates clockwise hysteresis (at all frequencies). The phase of the hysteresis depends on the frequency of oscillation due to the interplay between the opposite effects of these two feedback loops. At low frequencies the cooperativity mechanism dominates. As the frequency increases, the shortening velocity increases and the role of the mechanical feedback becomes prominent. Clockwise hystereses are observed in various physical passive elements, as visco-elastic and magnetic elements. Clockwise hysteresis infers that work is done upon the muscle and energy dissipates during the cycle and more energy is consumed in stretching the muscle than is gained during muscle shortening. Hence, at high frequencies the muscle behaves as a shock absorber.
  3. Conjecture: the clockwise hysteresis behavior is driven by a high-frequency phenomenon and a dominant negative feedback loop in the enzymatic activities. I presented this ideas to David and we was very interested. I also explain in just few seconds to Pam what I an doing with David (by the way David says that he will take two weeks to finish what he is doing now, I must insist in the experimental activities).