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Biodynamics for the emergence of energy consumers
ELSEVIER
BioSystems 42 (1997) 119-127
Biodynamics for the emergence of energy consumers Koichiro Matsuno Department of BioEngineering,
Nagaoka University of Technology, Nagaoka 940-21, Japan
Abstract
What is unique to biodynamics in vivo or dynamics leading to the emergence of biological organizations is a frozen aggregate of degrees of freedom in motion that can change its constituent members in time. Association and dissociation of degrees of freedom in the frozen aggregate is information-generative, in the sense that their realization proceeds in a contingent manner, with no unique pattern being predetermined. In particular, dissociation of some of the degrees of freedom from the parental aggregate becomes information-generative when the dissociative interaction initiated by thermal agitation originating in the ambient takes significantly longer time than the interval of the inverse thermal frequency. For instance, ATP hydrolysis with the help of myosin following the preceding association of an ATP molecule with the myosin happens to be a case of such a dissociative interaction, in which the duraiion of the interaction is far greater than the inverse of thermal frequency. One dominant mode of biodynamics in vivo is to effectively materialize a heat engine by preparing a local region with a temperature lower than that of the surroundings, thereby letting the duration time of the dissociative interaction be far greater than the1 in&se of thermal frequency. Evolutionary emergence of most primitive biological organizations would coincide with a de novo appearance of a heat engine that could hold thermal agitations from the surroundings locally there and could act upon the latter accordingly. 0 1997 Elsevier Science Ireland Ltd. Keywords: Biodynamics;
Consumers;
Entropy; Evolution;
1. Introduction When we consider biodynamics in vivo or dynamics leading to the emergence of biological organizations from an evolutionary perspective, two fundamental questions are raised. One is how to construct dynamic variables that can describe dynamic phenomena in biology, and the other is to uncover the nature of the forces acting upon these variables (Pattee, 1993). Mechanics is pecu-
Heat engine; Information;
liar in dismissing these questions altogether by maintaining that whatever dynamic variables may be conceived, the forces acting upon them can be uniquely determined as referring to the state of these variables at the moment (Rosen, 1991). Of course, it goes without saying that the mechanistic scheme of dynamics based upon the state description has been extremely successful in countless studies of physical processes. Nonetheless, state dynamics in the realm of mechanics has its limita-
0303-2647/97/$17.00 0 1997 Elsevier Science Ireland Ltd. All rights reserved. PII SO303-2647(97)01700-O
Thermal fluctuations
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tions when faced with influences coming from factors other than the already prescribed state variables. The environment, defined as everything besides the state variables, can influence the state dynamics either through applying external forces as in the form of Langevin random forces, or by introducing new state variables, or remaining other possibilities (Magnasco, 1993). In the present article we examine a fundamental characteristic of biodynamics in vivo, especially with regard to the kind of dynamical description that can be available, whether in the form of state dynamics with or without external supplements, or something else (Rosen, 1991). For this purpose, we shall first briefly summarize the nature of state dynamics in mechanics in terms of definite state variables with no external supplements. What characterizes mechanics as a form of state dynamics in terms only of definite state variables is that all the degrees of freedom available are completely constrained. This is equivalent to saying that all the relevant degrees of freedom in motion are frozen in the sense that every degree of freedom has its value determined uniquely in relation to all the others, which also determines theirs concurrently. Determining each variable uniquely in relation to all the others at every moment comes to imply that at the least, each would detect the states of all the others instantaneously (Ear-man, 1986). Identification of the relationships among all the available degrees of freedom by any member of them is taken to be instantaneous. And so, mechanics is peculiar in requiring that detection would proceed at an infinite velocity simply by taking instantaneous identification of the global relationship by the participants for granted, as a theoretical artifact; this in spite of the fact that there is no known material means of communication faster than the speed of light. Any dynamic of relationships has two attributes. One is for identification or detection, and the other for realization (Matsuno, 1985, 1989, 1993a). Mechanics is thus singularly peculiar in maintaining that only realization dynamics would be relevant because identification dynamics is deemed to take no time for its completion. However, whether identification or detection dynamics would take no time cannot be a matter of theoret-
42 (1997) 119-127
ical artifact, but a real physical problem to be examined in its own light. Biodynamics in vivo first concerns itself with how both detection and realization dynamics may be related to each other.
2. Initial uncertainties and their dynamic transformation Detection and realization dynamics both refer to available degrees of freedom in motion. It is highly exceptional that all the degrees of freedom are frozen into a single unit as mechanics would claim. It is the rule, and not the exception, that some degrees of freedom would be frozen and some not. For instance, as natural systems, an atomic nucleus can be seen as a frozen aggregate of nucleon-degrees of freedom and a nucleon as a frozen aggregate of quark-degrees of freedom. When a frozen aggregate of degrees of freedom does not remain invariant in its constituents, there are two possibilities for changes among its constituent members. One is to let additional degrees of freedom be further frozen into the then existing aggregate, and the other is to let some of the constituent degrees of freedom be dissociated from the frozen aggregate. Each of these is a mode of realization dynamics with regard to the constituent degrees of freedom in motion, and the consequence of realization can be detected by every other constituent degree of freedom (Denbigh and Denbigh, 1985; Matsuno, 1989; Gunji, 1992). However, detection would be sequentially local, instead of globally simultaneous, in the sense that it takes time to detect what others are doing elsewhere. Realization is global in an external record at every moment, but detection is local. That what is realized globally, cannot be detected internally as such at the very same moment, allows both realization and detection dynamics to proceed in such a manner that the conflicts between global realization and local detection may not be apparent in the external record, since detection again becomes global within that record (Pattee, 1993). In fact, both association and dissociation of degrees of freedom at their frozen ag-
K. Matsuno /BioSystems
gregates can be a process of removing the internal conflicts between realization and detection dynamics among the available degrees of freedom in motion (Matsuno, 1989). Consequently, both association and dissociation could be modeled as intrinsically stochastic in the sense that there is no definite means to predetermine how each process would proceed, though removal of the conflicts would be materialized in the effect. Energetics underlying the local detection dynamics is such that if the time interval of each successive synchronization between global realization and local detection for eliminating the conflicts between the two is Atsync,the underlying quantum mechanics suggests that energy esyncspecified by
would have to be dissipated for internal measurement of each degree of freedom involved, in which li is Planck’s constant divided 2n. The accompanied energy flow f,,,c follows
(erg/unit time/degree-of-freedom). Once a certain degree of freedom appears in associative interaction with a frozen aggregate of other degrees of freedom, the interaction can be viewed as probabilistically dichotomous between the event of association completed and not. In addition, these dichotomous probabilistic events can be parameterized in terms of information bits per unit time per degree of freedom strictly with regard to whether or not the concerned degree of freedom could have already been associated with the frozen aggregate. The association of a degree of freedom into a frozen aggregate measured in terms of the rate of information generation i,
(bits/unit time/degree-of-freedom)
implies simply that once the degree of freedom sets in associative interaction with the frozen aggregate at time t,, the probability that the association would still not have been completed by time t2( > tl) will be 2 _ ‘&*-‘I). Similarly, one can also define an information generation rate
42 (1997) 119-127
id
121
(bits/unit time/degree-of-freedom)
for the dissociation of a degree of freedom from the then available frozen aggregate. At this point, it should be emphasized that the context under which the information is defined is clearly delimited (Kiippers, 1991). The context refers to what has been realized, while the information generation points to the process of removing the internal conflicts between global realization and local detection. Information cannot properly be defined as such unless a context for defining it is available (Kuppers, 1991; Salthe, 1993). The present scheme assigning information generation to a frozen aggregate of degrees of freedom that processes their further association and dissociation is definitely context-dependent, though the context itself may be variable over time. Association and dissociation of degrees of freedom at their frozen aggregates, while ,removing the internal conflicts between global realization and local detection, require an impetus for the onset of their interactions. In this regard, Boltzmann’s statistical mechanics is suggestive though neither freezing nor dissolving degrees of freedom is permitted there. Of primary significance to Boltzmann’s statistical mechanics is its recognition that detection proceeding internally among interacting particles has to be local, in spite of the fact that mechanics in its abstract form requires global detection (Matsuno, 1996). This emphasis on local detection by Boltzmann is seen in his stosszahl ansatz, or assumption of molecular chaos, asserting that each interacting particle would lose its past memory after a few, or at most several, collisions with others in the immediate past. Boltzmann’s dynamics of local detection necessarily brings about uncertainties to any initial conditions set at an arbitrary time point. Since Boltzmann’s dynamics incorporates into itself both microstates and the probability distribution defined over the latter, there can be an identity between Boltzmann’s entropy and Shannon’s measured in units of information bit (Brooks and Wiley, 1988; Salthe, 1993). Although both refer to probability, Boltzmann’s entropy concerns the
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probability distribution of microstates whereas Shannon’s refers to that of the events of detecting those microstates occupied. It is an agent doing detection that can relate Boltzmann’s entropy to Shannon’s. Such agents doing detection are already implicit in Boltzmann’s dynamics of local detection. Boltzmann’s entropy in terms of the probability distribution of microstates can be identically related to Shannon’s in terms of the probability distribution of the events of identifying each microstate occupied through Boltzmann’s agents doing local detection. The difference between Boltzmann’s and Shannon’s entropy is observation. Boltzmann’s local detection that would decrease the uncertainty by the amount of Ah (bits/ microstate) can identically decrease Boltzmann’s entropy by As = k,Ah In 2 (erg/Kelvin/microstate), in which k, ( = 1.38 x lo- l6 erg/Kelvin) is Boltzmann’s constant. The characteristic time of Boltzmann’s local detection is of the order of the inverse thermal frequency. Furthermore, if local detection proceeds as a mode of fluctuations around thermal equilibrium as Boltzmann perceived (Johnson, 1987), the decrease of Boltzmann’s entropy -As due to the local detection in a local region would have to be compensated by the entropy increase due to the heat energy Aq coming from the immediate surroundings satisfying -As++%0 because of the second law of thermodynamics as first perceived by Szilard and Brillouin, in which T is the temperature in Kelvin (Schneider, 1991). Near thermal equilibrium, the energy driving a local detection in a local region comes from the heat energy originating in the dissipation from similar local detections already accomplished in the neighborhood. Thermal fluctuations that are constantly generated while utilizing the energy released from the dissipation of preceding fluctuations of the similar nature also apply to Boltzmann’s local detection. The minimum energy required for the local detection that can internally decrease one bit of uncertainty thus turns out to be k,T In 2, though the local detection as a form
42 (1997) 119-127
of thermal fluctuations near thermal equilibrium cannot be identified as such externally. Accordingly, whether or not a certain degree of freedom sets in interaction with others would be detected internally in a dichotomous manner by distinguishing between the event of having obtained energy by the amount of eth( 2 kBT In 2) through collisions with others, and no such event yet. The extent of uncertainties between the event of collision and no such event now turns out to be eth
(erg/bit)
because eth serves as the energy measuring the difference between the dichotomous events of detecting whether or not an arbitrary microstate may be occupied. We have estimated the degree of initial uncertainties, measured as eth (erg/bit), on the condition that there could be neither association nor dissociation of degrees of freedom in motion. In spite of that limitation, however, the estimated initial uncertainties can also be applied to the case where both association and dissociation of degrees of freedom might occur insofar as the temperature is definable. Biological phenomena as the subject matter of biodynamics in vivo undoubtedly satisfy this condition that the temperature could be defined. So far, we have observed that biodynamics in vivo can be parameterized at least in terms of two quantities. One is information generation rate, counted in terms of bits per unit time per unit degree of freedom, that measures the extent of how a frozen aggregate of degrees of freedom in motion varies its constituents in time, and the other is the initial uncertainties for each degree of freedom measured in units of energy per bit. In particular, if dissociation of a degree of freedom from a frozen aggregate is the case, that dissociation, initiated through one of the dichotomous events that has captured the initiating impetus specified by et, (erg/bit), mediates an energy flow of the order of et,& (erg/unit time/degree-of-freedom) because the mean survival time of energy eth within the frozen aggregate until dissociation would be about l/id. Put differently, the dissociation of a degree of freedom from the frozen aggregate will material-
K. Matsuno /BioSystems
ize only when there exists a material means that can capture and hold within itself the energy from thermal agitations for a certain period of time. A good example for this is the hydrolysis of ATP molecule in contact with myosin as an ATPase (Matsuno and Honda, 1991). An ATP molecule, as a frozen aggregate of its constituent degrees of freedom, will lose its individual identity when it is dissociated through hydrolysis. The measured mean time required for hydrolyzing one ATP molecule in contact with myosin has been found to be about 10 - 2 s (Yanagida et al., 1985; Funatsu et al., 1995). The contact between an ATP and a myosin molecule is initiated by thermal agitations. That the dissociation process of hydrolyzing ATP continues over a finite time interval comes to mean that the thermal energy acquired through the contact survives over the same interval. As a matter of fact, the dissociation process initiated by initial uncertainties eth (erg/bit) and their dynamic transformation specified by the information generation by the amount of id (bit/unit time/degree-of-freedom) just materializes in the energy flow f* Iv ethzd
(erg/unit time/degree-of-freedom)
that also measures the extent of energy dissipation per unit time. Fundamental to the expression of energy dissipation is that an energy flow of the magnitude of fd is allotted to each degree of freedom and that some energy source, such as a high energy chemical bond stored in an ATP molecule, is required to make the dissipation materialize in reality. Likewise, association of a degree of freedom into a frozen aggregate will turn out to materialize by way of the energy Ilow h - et&
(erg/unit time/degree-of-freedom)
which is dissipated also in the association process. The energy flow for association would certainly have to be equal to or greater than the energy flow driving the internal local detection, i.e.,
At the same time, if a stationary condition is applicable to the frozen aggregate, the equality
42 (1997) 119-127
fd
123
=fa
would be satisfied. Before closing our discussion on initial uncertainties and their dynamic transformation, it should be noted that Boltzmann’s dynamics of local detection cause no net information generation if the available degrees of freedom in motion remain invariant. This is because there is neither net association nor dissociation of degrees of freedom whatever frozen aggregates may exist. There is no net information generation at thermal equilibrium. Information generation due to local detection in an arbitrary local region would here be constantly compensated and offset completely by the reverse process of thermal decay due to the second law of thermodynamics available to Boltzmann’s dynamics. This is certainly consonant with the lack of net energy dissipation at thermal equilibrium that Boltzmann’s dynamics of local detection delivers. In contrast, net information generation yields and necessitates net energy dissipation.
3. Modulation of thermal fluctuations Initial uncertainties of the magnitude of et,, (erg/bit) due to detection dynamics that is necessarily local specify how detection proceeds internally. The time interval Atdet of each local detection is required to satisfy the uncertainty principle ethAtdet- A (Matsuno, 1993b)’ because the most dominant thermal quantum could carry the energy eth ( - k,T). That thermal quanta are internally detected lets the time interval Atdet of internal detection be of the same order as the inverse thermal frequency Atth( - h/k,T). The approximate equality between the time interval of internal detection and the inverse thermal frequency is a unique characteristic of thermal agitations, Implicit in thermal agitations is a time duration of interaction Atint between interacting degrees of freedom that is far less than the inverse thermal frequency (Wannier, 1966; Waldram, 1985), i.e., Atint <
124
K. Matsuno / BioSystems 42 (1997) 119-127
This relationship is a common denominator for any thermal agitations. The problem of how a frozen aggregate of degrees of freedom could change its constituent members subject to thermal agitations now urges us to reexamine the above relationship from a slightly different perspective, since the original derivation of thermal agitations does not take into account either association nor dissociation of degrees of freedom in motion. To examine this further, let us consider the case where a frozen aggregate of degrees of freedom floating in a sea of thermal agitations can be dissociated by them. If the frozen aggregate remains invariant with regard to its constituent degrees of freedom while floating in a sea of thermal agitations, it could be treated as a Brownian particle (Magnasco, 1993). On the other hand, however, if the frozen aggregate can dissociate some of its constituent degrees of freedom as an effect of receiving thermal agitations from its surroundings, a completely new situation would come up, quite different from the standard case of Brownian motion. A factor that can be pivotal is the time interval Atdissover which the dissociative interaction lasts after receiving the impetus from thermal agitations. If the time interval of a dissociative interaction happens to become far greater than the inverse thermal frequency, i.e., Atdiss>>Atth, as in the case of ATP hydrolysis with the help of myosin having AtdissN 10 - 2 s, the time interval of internal detection on the part of the frozen aggregate At,, that happens to be identical to the time interval for each synchronization between global realization and local detection, A&.,,=,would have to differ from the time interval A& for thermal agitations. A dominant quantum excitation compatible with the local detection proceeding internally at every interval At, would carry the energy ediss satisfying edissAtfaN h. Accordingly, that the dissociative interaction lasts over A& suggests that internal detection is successively repeated At,,,/At,, times over the interval Atdiss. Since the total energy accumulated through successive detections over Atdiss is eth, a dominant quantum that each internal detection could excite
during the dissociative interaction aggregate would carry the energy
at the frozen
ediss N
with
The time interval for each internal detection, that happens to equal Atsync of the synchronization between global realization and local detection, certainly satisfies the energy flow requirement asking that the energy flow for association is equal to or greater than the energy flow required for internal measurement when the frozen aggregate is in a stationary condition. The energy ratio fd& eth
_
p&y2 \4d
determines the effective temperature frozen aggregate as /A4 \1/2
Tfa of the
\uLdiss/
Increasing the time interval of the dissociative interaction at the frozen aggregate thus serves to decrease its effective temperature compared with the ambient while being initiated by thermal agitations originating there. For ATP hydrolysis, with a dissociative interaction lasting over 10 - 2 s, the decreasing factor (Atth/Atdiss)“2 becomes as small even as 10 -‘. Local detection that underlies the dissociative interaction at the frozen aggregate of degrees of freedom can decrease Boltzmann’s entropy, but the second law of thermodynamics must be fulfilled at the same time by whatever means (Schneider, 1991). Nonetheless, thermal agitations whose characteristic time is of the order of the inverse of thermal frequency cannot by themselves mediate those local detections that continue to survive far longer than the inverse thermal frequency. In order to facilitate these local detections, it would be required to have an energy source to be dissipated so as to fulfill the second law of thermodynamics as an effect.
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Information generation through the dissociative interaction at the frozen aggregate of degrees of freedom can materialize only when an energy source to be dissipated is available. Although Boltzmann’s local detection can be compatible with both the sustenance of thermal equilibrium and the absence of net information generation, those local detections that would last for much longer than the inverse thermal frequency can only generate information by accessing an energy gradient to be dissipated. In fact, the ATP hydrolysis with the help of myosin is just such an example exhibiting both net information generation and energy dissipation by holding the acquired thermal agitation for much longer than the interval of the inverse thermal frequency. Any local detection that can last far longer than the inverse thermal frequency can effectively lower the temperature there by decreasing Boltzmann’s entropy compared with the case otherwise. Once there appear two separate regions with different temperatures, it is possible to imagine, through their connection, a likelihood of having a heat engine that can extract positive work while modulating thermal agitations at the higher temperature side so as to match themselves with those at the lower side. In particular, ATP hydrolysis with the help of myosin in myofibrils demonstrates that thermal fluctuations excited in ATPactivated myofibrils are certainly modulated compared with those excited in non-activated ones (Honda et al., 1995). 4. Discussion A heat engine operating between two heat reservoirs with different temperatures manifests how local detection dynamics may proceed in reality. What is unique to the operation is the capacity of influencing or acting upon thermal agitations at the higher temperature side. Although the global character of a heat engine can be specified by both its thermal efficiency and the magnitude of the load, these parameters are not those that can be detected internally through local processes. Instead, energy flows crossing various interfaces can serve as local quantities detectable internally (Matsuno, 1989).
42 (1997) 119-127
125
The energy flow from the heat reservoir at the higher temperature into the heat engine is divided and transferred into two flows; one is for the reservoir at the lower temperature and the other for the work done by the heat engine. Since each of these three flows are quantities that can be detected locally, simultaneous identification of all three at the same moment cannot be available within the scheme of a local detection dynamics. Nonetheless, when these flows are realized, the realization dynamics mediated by them is certainly simultaneous in fixing them at every moment at least in the sense of fulfilling the condition of energy flow continuity among them. What is significant in this fulfllment of energy flow continuity is that local detection dynamics takes time in following the effect that realization dynamics of a global character has brought about. For instance, although the condition lof energy flow continuity must be observed internally in any event, there is a definite difference between energy flow continuity to be detected locally and that to be realized globally. When the energy flow for the work done by the heat engine happens to increase slightly due to some changes in the factors specifying the load, this increase could not be detected simultaneously by the factors determining the energy flows from and to the heat reservoirs. It takes time for the detection to be accomplished, no matter how small that may be. Furthermore, before the detection is completed, a renewed realization of energy flows has to have been made so as to fulfill the condition of flow continuity. Otherwise, violation of energy flow continuity would come to be detected internally. And a renewed realization of energy flows can again cause subsequent conflicts with the following detection dynamics. One thus observes that removal of conflicts between local detection and global realization could continue to hold indefinitely in a self-perpetuating manner. One dominant mode of removing these conflicts is for the heat engine to act upon the heat reservoir at the higher temperature, if not being restricted only to be acted upon by the latter. Needless to say, heat engines, as a well-established subject matter of thermodynamics, can be
126
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analyzed and understood by referring exclusively to the global dynamics of realization while calling attention to such global attributes as the efficiency of the engine and the magnitude of the load. This scheme is undoubtedly legitimate. Still, it is also legitimate to address oneself to the same subject matter by paying attention to the interplay of dynamics between local detection and global realthermodynamics ization, because approaching through Boltzmann’s statistical mechanics is founded upon the recognition of local detection dynamics. What heat engines suggest to biodynamics in vivo is the significance of the capacity of acting upon thermal agitations. That capacity can become legitimate and explicit once the role of local detection dynamics is considered. As a matter of principle, the outcome that the capacity of acting upon brings about in the effect cannot be preprogrammed in advance. The absence of preprogrammability is grounded upon the obvious physical fact that what will be detected cannot be identified before it has actually been detected. It is this absence of preprogrammability which makes biodynamics in vivo so distinct compared with a mechanics that constructs detection dynamics as immediately following realization dynamics. The flexibility and plasticity latent in the capacity of acting upon thermal agitations are realized within detection dynamics of a local character. Furthermore, acting upon thermal agitations to extract a positive work from them is equivalent to feeding on thermal agitations, that is heterotrophic while extracting energy from the latter (Matsuno, 1992). Evolutionary emergence of most primitive biological organizations could in fact happen to coincide with a de novo spontaneous appearance of heat engines (Matsuno, 1996) or energy consumers acting upon thermal agitations from the surroundings (Matsuno, 1995). A frozen aggregate of degrees of freedom in motion can exhibit the capacity of acting upon, that is to say, feeding on, thermal agitations originating in the ambient if it can hold the acquired thermal excitations for much longer than the interval of the inverse thermal frequency while changing its constituent members. ATP hydrolysis with the help of myosin certainly provides evi-
42 (1997) 119-127
dence that when a frozen aggregate of degrees of freedom starts to dissociate some of its constituents as a consequence of having received thermal agitations, their holding time becomes far greater than the inverse thermal frequency. One more example of acting upon thermal agitations that could be significant protobiologically would be aggregation of thermal heterocomplex molecules of amino acids in aqueous milieu in the sense that heating amino acid molecules could have been quite conceivable on the surface of the primitive earth (Fox and Dose, 1977). Forming microspherical structures of the thermal heterocomplex molecules in aqueous *milieu would be a form of holding thermal agitations locally there. In fact, the hysteretic association of those thermal heterocomplex molecules upon cyclic variations of temperature in the ambient could effectively transform the microspherical aggregates into heat engines or energy consumers acting upon thermal agitations (Sakurazawa et al., 1994). In essence, biodynamics in vivo characterizes dynamic phenomena with frozen aggregates of degrees of freedom that can hold thermal excitations from the ambient for much longer than the interval of the inverse thermal frequency while reshuffling their constituent degrees of freedom.
Acknowledgements The author wishes to thank Stanley N. Salthe for helpful comments on the draft of the present manuscript.
References Brooks, D.R. and Wiley, E.O., 1988, Evolution and Entropy: Toward a Unified Theory of Biology. 2nd edn. (University of Chicago Press, Chicago, Illinois). Denbigh, K.G. and Denbigh, J.S., 1985, Entropy in Relation to Incomplete Knowledge (Cambridge University Press, Cambridge, UK). Earman, J., 1986, A Primer on Determinism (Reidel, Dordrecht). Fox, S. W. and Dose, K., 1977, Molecular Evolution and the Origin of Life, Revised Edition (Marcel Dekker, New York).
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Funatsu, T., Harada, Y., Tokunaga, M., Saito, K. and Yanagida, T., 1995, Imaging of single fluorescent molecules and individual ATP turnovers by single myosin molecules in aqueous solution. Nature 374, 5555559. Gunji, Y.-P., 1992, The form of life: it is possible but not necessary. Appl. Math. Comp. 47, 267-288. Honda, H., Nagao, S., Hatori, K. and Matsuno, K., 1995: Slow and macroscopic modulation of thermal fluctuations in myofibrils. Biophys. Chem. 54, 61-66. Johnson, H.A., 1987, Thermal noise and biological information. Quart. Rev. Biol. 62, 141-152. Ktippers, B.-O., 1991, Information and the Origin of Life. (Bradford/The MIT Press, Cambridge, Massachusetts). Magnasco, MC., 1993, Forced thermal ratchets. Phys. Rev. Lett. 71, 147771481. Matsuno, K., 1985, How can quantum mechanics of material evolution be possible?: symmetry and symmetry-breaking in protobiological evolution. BioSystems 17, 1799192. Matsuno, K., 1989, Protobiology: Physical Basis of Biology. (CRC Press, Boca Raton, Florida). Matsuno, K., 1992, Cohesive interaction for the emergence of eukaryotic cells, in: The Origin and Evolution of the Cell, H. Hartman and K. Matsuno (eds) (World Scientific, Singapore) pp. 231-240. Matsuno, K., 1993a, Being free from ceteris paribus: a vehicle of founding physics on biology rather the other way around. Appl. Math. Comp. 56, 261-279. Matsuno, K., 1993b, Biology in the eyes of molecules. Nanobiology 2, 37741. Matsuno, K., 1995, Consumer power as the major evolutionary force. J. Theor. Biol. 173, 137-145.
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Matsuno, K., 1996, Boltzmann’s dynamics on the primitive earth about 3.8 billion years ago, in: Chemical Evolution: Physics of the Origin and Evolution of Life, J. ChelaFlares and F. Raulin (eds) (Kluwer, Dordrecht) pp. 231238. Matsuno, K. and Honda, H., 1991, Information aspects of actomyosin complex. CRC Crit. Rev. Biomed. Eng. 18, 311-321. Pattee, H. H., 1993, The limitation of formal models of measurement, control and cognition. Appl. Math. Comp. 56, lllll30. Rosen, R., 1991, Life Itself: A Comprehensive Inquiry into the Nature, Origin and Fabrication of Life (Columbia University Press, New York). Sakurazawa, S., Honda, H., Imai, E. and Matsuno, K., 1994, The hysteretic growth of microspherical particles consisting of thermal heterocomplex molecules from amino acids. Viva Origin0 22, 81-88. Salthe, S.N., 1993, Development and Evolution: Complexity and Change in Biology (Bradford/The MIT Press, Cambridge, Massachusetts). Schneider, T.D., 1991, Theory of molecular machines. II. energy dissipation from molecular machines. J. Theor. Biol. 148, 125-137. Waldram, J.R., 1985, The Theory of Thermodynamics (Cambridge University Press, Cambridge, UK). Wannier, G.H., 1966, Statistical Physics (Wiley, New York). Yanagida, T., Arata, T. and Oosawa, F., 1985, Sliding distance of actin filament induced by a myosin crossbridge during one ATP hydrolysis cycle. Nature 316, 366368.
BioSystems 42 (1997) 119-127
Biodynamics for the emergence of energy consumers Koichiro Matsuno Department of BioEngineering,
Nagaoka University of Technology, Nagaoka 940-21, Japan
Abstract
What is unique to biodynamics in vivo or dynamics leading to the emergence of biological organizations is a frozen aggregate of degrees of freedom in motion that can change its constituent members in time. Association and dissociation of degrees of freedom in the frozen aggregate is information-generative, in the sense that their realization proceeds in a contingent manner, with no unique pattern being predetermined. In particular, dissociation of some of the degrees of freedom from the parental aggregate becomes information-generative when the dissociative interaction initiated by thermal agitation originating in the ambient takes significantly longer time than the interval of the inverse thermal frequency. For instance, ATP hydrolysis with the help of myosin following the preceding association of an ATP molecule with the myosin happens to be a case of such a dissociative interaction, in which the duraiion of the interaction is far greater than the inverse of thermal frequency. One dominant mode of biodynamics in vivo is to effectively materialize a heat engine by preparing a local region with a temperature lower than that of the surroundings, thereby letting the duration time of the dissociative interaction be far greater than the1 in&se of thermal frequency. Evolutionary emergence of most primitive biological organizations would coincide with a de novo appearance of a heat engine that could hold thermal agitations from the surroundings locally there and could act upon the latter accordingly. 0 1997 Elsevier Science Ireland Ltd. Keywords: Biodynamics;
Consumers;
Entropy; Evolution;
1. Introduction When we consider biodynamics in vivo or dynamics leading to the emergence of biological organizations from an evolutionary perspective, two fundamental questions are raised. One is how to construct dynamic variables that can describe dynamic phenomena in biology, and the other is to uncover the nature of the forces acting upon these variables (Pattee, 1993). Mechanics is pecu-
Heat engine; Information;
liar in dismissing these questions altogether by maintaining that whatever dynamic variables may be conceived, the forces acting upon them can be uniquely determined as referring to the state of these variables at the moment (Rosen, 1991). Of course, it goes without saying that the mechanistic scheme of dynamics based upon the state description has been extremely successful in countless studies of physical processes. Nonetheless, state dynamics in the realm of mechanics has its limita-
0303-2647/97/$17.00 0 1997 Elsevier Science Ireland Ltd. All rights reserved. PII SO303-2647(97)01700-O
Thermal fluctuations
120
K. Matsuno / BioSystems
tions when faced with influences coming from factors other than the already prescribed state variables. The environment, defined as everything besides the state variables, can influence the state dynamics either through applying external forces as in the form of Langevin random forces, or by introducing new state variables, or remaining other possibilities (Magnasco, 1993). In the present article we examine a fundamental characteristic of biodynamics in vivo, especially with regard to the kind of dynamical description that can be available, whether in the form of state dynamics with or without external supplements, or something else (Rosen, 1991). For this purpose, we shall first briefly summarize the nature of state dynamics in mechanics in terms of definite state variables with no external supplements. What characterizes mechanics as a form of state dynamics in terms only of definite state variables is that all the degrees of freedom available are completely constrained. This is equivalent to saying that all the relevant degrees of freedom in motion are frozen in the sense that every degree of freedom has its value determined uniquely in relation to all the others, which also determines theirs concurrently. Determining each variable uniquely in relation to all the others at every moment comes to imply that at the least, each would detect the states of all the others instantaneously (Ear-man, 1986). Identification of the relationships among all the available degrees of freedom by any member of them is taken to be instantaneous. And so, mechanics is peculiar in requiring that detection would proceed at an infinite velocity simply by taking instantaneous identification of the global relationship by the participants for granted, as a theoretical artifact; this in spite of the fact that there is no known material means of communication faster than the speed of light. Any dynamic of relationships has two attributes. One is for identification or detection, and the other for realization (Matsuno, 1985, 1989, 1993a). Mechanics is thus singularly peculiar in maintaining that only realization dynamics would be relevant because identification dynamics is deemed to take no time for its completion. However, whether identification or detection dynamics would take no time cannot be a matter of theoret-
42 (1997) 119-127
ical artifact, but a real physical problem to be examined in its own light. Biodynamics in vivo first concerns itself with how both detection and realization dynamics may be related to each other.
2. Initial uncertainties and their dynamic transformation Detection and realization dynamics both refer to available degrees of freedom in motion. It is highly exceptional that all the degrees of freedom are frozen into a single unit as mechanics would claim. It is the rule, and not the exception, that some degrees of freedom would be frozen and some not. For instance, as natural systems, an atomic nucleus can be seen as a frozen aggregate of nucleon-degrees of freedom and a nucleon as a frozen aggregate of quark-degrees of freedom. When a frozen aggregate of degrees of freedom does not remain invariant in its constituents, there are two possibilities for changes among its constituent members. One is to let additional degrees of freedom be further frozen into the then existing aggregate, and the other is to let some of the constituent degrees of freedom be dissociated from the frozen aggregate. Each of these is a mode of realization dynamics with regard to the constituent degrees of freedom in motion, and the consequence of realization can be detected by every other constituent degree of freedom (Denbigh and Denbigh, 1985; Matsuno, 1989; Gunji, 1992). However, detection would be sequentially local, instead of globally simultaneous, in the sense that it takes time to detect what others are doing elsewhere. Realization is global in an external record at every moment, but detection is local. That what is realized globally, cannot be detected internally as such at the very same moment, allows both realization and detection dynamics to proceed in such a manner that the conflicts between global realization and local detection may not be apparent in the external record, since detection again becomes global within that record (Pattee, 1993). In fact, both association and dissociation of degrees of freedom at their frozen ag-
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gregates can be a process of removing the internal conflicts between realization and detection dynamics among the available degrees of freedom in motion (Matsuno, 1989). Consequently, both association and dissociation could be modeled as intrinsically stochastic in the sense that there is no definite means to predetermine how each process would proceed, though removal of the conflicts would be materialized in the effect. Energetics underlying the local detection dynamics is such that if the time interval of each successive synchronization between global realization and local detection for eliminating the conflicts between the two is Atsync,the underlying quantum mechanics suggests that energy esyncspecified by
would have to be dissipated for internal measurement of each degree of freedom involved, in which li is Planck’s constant divided 2n. The accompanied energy flow f,,,c follows
(erg/unit time/degree-of-freedom). Once a certain degree of freedom appears in associative interaction with a frozen aggregate of other degrees of freedom, the interaction can be viewed as probabilistically dichotomous between the event of association completed and not. In addition, these dichotomous probabilistic events can be parameterized in terms of information bits per unit time per degree of freedom strictly with regard to whether or not the concerned degree of freedom could have already been associated with the frozen aggregate. The association of a degree of freedom into a frozen aggregate measured in terms of the rate of information generation i,
(bits/unit time/degree-of-freedom)
implies simply that once the degree of freedom sets in associative interaction with the frozen aggregate at time t,, the probability that the association would still not have been completed by time t2( > tl) will be 2 _ ‘&*-‘I). Similarly, one can also define an information generation rate
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id
121
(bits/unit time/degree-of-freedom)
for the dissociation of a degree of freedom from the then available frozen aggregate. At this point, it should be emphasized that the context under which the information is defined is clearly delimited (Kiippers, 1991). The context refers to what has been realized, while the information generation points to the process of removing the internal conflicts between global realization and local detection. Information cannot properly be defined as such unless a context for defining it is available (Kuppers, 1991; Salthe, 1993). The present scheme assigning information generation to a frozen aggregate of degrees of freedom that processes their further association and dissociation is definitely context-dependent, though the context itself may be variable over time. Association and dissociation of degrees of freedom at their frozen aggregates, while ,removing the internal conflicts between global realization and local detection, require an impetus for the onset of their interactions. In this regard, Boltzmann’s statistical mechanics is suggestive though neither freezing nor dissolving degrees of freedom is permitted there. Of primary significance to Boltzmann’s statistical mechanics is its recognition that detection proceeding internally among interacting particles has to be local, in spite of the fact that mechanics in its abstract form requires global detection (Matsuno, 1996). This emphasis on local detection by Boltzmann is seen in his stosszahl ansatz, or assumption of molecular chaos, asserting that each interacting particle would lose its past memory after a few, or at most several, collisions with others in the immediate past. Boltzmann’s dynamics of local detection necessarily brings about uncertainties to any initial conditions set at an arbitrary time point. Since Boltzmann’s dynamics incorporates into itself both microstates and the probability distribution defined over the latter, there can be an identity between Boltzmann’s entropy and Shannon’s measured in units of information bit (Brooks and Wiley, 1988; Salthe, 1993). Although both refer to probability, Boltzmann’s entropy concerns the
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probability distribution of microstates whereas Shannon’s refers to that of the events of detecting those microstates occupied. It is an agent doing detection that can relate Boltzmann’s entropy to Shannon’s. Such agents doing detection are already implicit in Boltzmann’s dynamics of local detection. Boltzmann’s entropy in terms of the probability distribution of microstates can be identically related to Shannon’s in terms of the probability distribution of the events of identifying each microstate occupied through Boltzmann’s agents doing local detection. The difference between Boltzmann’s and Shannon’s entropy is observation. Boltzmann’s local detection that would decrease the uncertainty by the amount of Ah (bits/ microstate) can identically decrease Boltzmann’s entropy by As = k,Ah In 2 (erg/Kelvin/microstate), in which k, ( = 1.38 x lo- l6 erg/Kelvin) is Boltzmann’s constant. The characteristic time of Boltzmann’s local detection is of the order of the inverse thermal frequency. Furthermore, if local detection proceeds as a mode of fluctuations around thermal equilibrium as Boltzmann perceived (Johnson, 1987), the decrease of Boltzmann’s entropy -As due to the local detection in a local region would have to be compensated by the entropy increase due to the heat energy Aq coming from the immediate surroundings satisfying -As++%0 because of the second law of thermodynamics as first perceived by Szilard and Brillouin, in which T is the temperature in Kelvin (Schneider, 1991). Near thermal equilibrium, the energy driving a local detection in a local region comes from the heat energy originating in the dissipation from similar local detections already accomplished in the neighborhood. Thermal fluctuations that are constantly generated while utilizing the energy released from the dissipation of preceding fluctuations of the similar nature also apply to Boltzmann’s local detection. The minimum energy required for the local detection that can internally decrease one bit of uncertainty thus turns out to be k,T In 2, though the local detection as a form
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of thermal fluctuations near thermal equilibrium cannot be identified as such externally. Accordingly, whether or not a certain degree of freedom sets in interaction with others would be detected internally in a dichotomous manner by distinguishing between the event of having obtained energy by the amount of eth( 2 kBT In 2) through collisions with others, and no such event yet. The extent of uncertainties between the event of collision and no such event now turns out to be eth
(erg/bit)
because eth serves as the energy measuring the difference between the dichotomous events of detecting whether or not an arbitrary microstate may be occupied. We have estimated the degree of initial uncertainties, measured as eth (erg/bit), on the condition that there could be neither association nor dissociation of degrees of freedom in motion. In spite of that limitation, however, the estimated initial uncertainties can also be applied to the case where both association and dissociation of degrees of freedom might occur insofar as the temperature is definable. Biological phenomena as the subject matter of biodynamics in vivo undoubtedly satisfy this condition that the temperature could be defined. So far, we have observed that biodynamics in vivo can be parameterized at least in terms of two quantities. One is information generation rate, counted in terms of bits per unit time per unit degree of freedom, that measures the extent of how a frozen aggregate of degrees of freedom in motion varies its constituents in time, and the other is the initial uncertainties for each degree of freedom measured in units of energy per bit. In particular, if dissociation of a degree of freedom from a frozen aggregate is the case, that dissociation, initiated through one of the dichotomous events that has captured the initiating impetus specified by et, (erg/bit), mediates an energy flow of the order of et,& (erg/unit time/degree-of-freedom) because the mean survival time of energy eth within the frozen aggregate until dissociation would be about l/id. Put differently, the dissociation of a degree of freedom from the frozen aggregate will material-
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ize only when there exists a material means that can capture and hold within itself the energy from thermal agitations for a certain period of time. A good example for this is the hydrolysis of ATP molecule in contact with myosin as an ATPase (Matsuno and Honda, 1991). An ATP molecule, as a frozen aggregate of its constituent degrees of freedom, will lose its individual identity when it is dissociated through hydrolysis. The measured mean time required for hydrolyzing one ATP molecule in contact with myosin has been found to be about 10 - 2 s (Yanagida et al., 1985; Funatsu et al., 1995). The contact between an ATP and a myosin molecule is initiated by thermal agitations. That the dissociation process of hydrolyzing ATP continues over a finite time interval comes to mean that the thermal energy acquired through the contact survives over the same interval. As a matter of fact, the dissociation process initiated by initial uncertainties eth (erg/bit) and their dynamic transformation specified by the information generation by the amount of id (bit/unit time/degree-of-freedom) just materializes in the energy flow f* Iv ethzd
(erg/unit time/degree-of-freedom)
that also measures the extent of energy dissipation per unit time. Fundamental to the expression of energy dissipation is that an energy flow of the magnitude of fd is allotted to each degree of freedom and that some energy source, such as a high energy chemical bond stored in an ATP molecule, is required to make the dissipation materialize in reality. Likewise, association of a degree of freedom into a frozen aggregate will turn out to materialize by way of the energy Ilow h - et&
(erg/unit time/degree-of-freedom)
which is dissipated also in the association process. The energy flow for association would certainly have to be equal to or greater than the energy flow driving the internal local detection, i.e.,
At the same time, if a stationary condition is applicable to the frozen aggregate, the equality
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fd
123
=fa
would be satisfied. Before closing our discussion on initial uncertainties and their dynamic transformation, it should be noted that Boltzmann’s dynamics of local detection cause no net information generation if the available degrees of freedom in motion remain invariant. This is because there is neither net association nor dissociation of degrees of freedom whatever frozen aggregates may exist. There is no net information generation at thermal equilibrium. Information generation due to local detection in an arbitrary local region would here be constantly compensated and offset completely by the reverse process of thermal decay due to the second law of thermodynamics available to Boltzmann’s dynamics. This is certainly consonant with the lack of net energy dissipation at thermal equilibrium that Boltzmann’s dynamics of local detection delivers. In contrast, net information generation yields and necessitates net energy dissipation.
3. Modulation of thermal fluctuations Initial uncertainties of the magnitude of et,, (erg/bit) due to detection dynamics that is necessarily local specify how detection proceeds internally. The time interval Atdet of each local detection is required to satisfy the uncertainty principle ethAtdet- A (Matsuno, 1993b)’ because the most dominant thermal quantum could carry the energy eth ( - k,T). That thermal quanta are internally detected lets the time interval Atdet of internal detection be of the same order as the inverse thermal frequency Atth( - h/k,T). The approximate equality between the time interval of internal detection and the inverse thermal frequency is a unique characteristic of thermal agitations, Implicit in thermal agitations is a time duration of interaction Atint between interacting degrees of freedom that is far less than the inverse thermal frequency (Wannier, 1966; Waldram, 1985), i.e., Atint <
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This relationship is a common denominator for any thermal agitations. The problem of how a frozen aggregate of degrees of freedom could change its constituent members subject to thermal agitations now urges us to reexamine the above relationship from a slightly different perspective, since the original derivation of thermal agitations does not take into account either association nor dissociation of degrees of freedom in motion. To examine this further, let us consider the case where a frozen aggregate of degrees of freedom floating in a sea of thermal agitations can be dissociated by them. If the frozen aggregate remains invariant with regard to its constituent degrees of freedom while floating in a sea of thermal agitations, it could be treated as a Brownian particle (Magnasco, 1993). On the other hand, however, if the frozen aggregate can dissociate some of its constituent degrees of freedom as an effect of receiving thermal agitations from its surroundings, a completely new situation would come up, quite different from the standard case of Brownian motion. A factor that can be pivotal is the time interval Atdissover which the dissociative interaction lasts after receiving the impetus from thermal agitations. If the time interval of a dissociative interaction happens to become far greater than the inverse thermal frequency, i.e., Atdiss>>Atth, as in the case of ATP hydrolysis with the help of myosin having AtdissN 10 - 2 s, the time interval of internal detection on the part of the frozen aggregate At,, that happens to be identical to the time interval for each synchronization between global realization and local detection, A&.,,=,would have to differ from the time interval A& for thermal agitations. A dominant quantum excitation compatible with the local detection proceeding internally at every interval At, would carry the energy ediss satisfying edissAtfaN h. Accordingly, that the dissociative interaction lasts over A& suggests that internal detection is successively repeated At,,,/At,, times over the interval Atdiss. Since the total energy accumulated through successive detections over Atdiss is eth, a dominant quantum that each internal detection could excite
during the dissociative interaction aggregate would carry the energy
at the frozen
ediss N
with
The time interval for each internal detection, that happens to equal Atsync of the synchronization between global realization and local detection, certainly satisfies the energy flow requirement asking that the energy flow for association is equal to or greater than the energy flow required for internal measurement when the frozen aggregate is in a stationary condition. The energy ratio fd& eth
_
p&y2 \4d
determines the effective temperature frozen aggregate as /A4 \1/2
Tfa of the
\uLdiss/
Increasing the time interval of the dissociative interaction at the frozen aggregate thus serves to decrease its effective temperature compared with the ambient while being initiated by thermal agitations originating there. For ATP hydrolysis, with a dissociative interaction lasting over 10 - 2 s, the decreasing factor (Atth/Atdiss)“2 becomes as small even as 10 -‘. Local detection that underlies the dissociative interaction at the frozen aggregate of degrees of freedom can decrease Boltzmann’s entropy, but the second law of thermodynamics must be fulfilled at the same time by whatever means (Schneider, 1991). Nonetheless, thermal agitations whose characteristic time is of the order of the inverse of thermal frequency cannot by themselves mediate those local detections that continue to survive far longer than the inverse thermal frequency. In order to facilitate these local detections, it would be required to have an energy source to be dissipated so as to fulfill the second law of thermodynamics as an effect.
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Information generation through the dissociative interaction at the frozen aggregate of degrees of freedom can materialize only when an energy source to be dissipated is available. Although Boltzmann’s local detection can be compatible with both the sustenance of thermal equilibrium and the absence of net information generation, those local detections that would last for much longer than the inverse thermal frequency can only generate information by accessing an energy gradient to be dissipated. In fact, the ATP hydrolysis with the help of myosin is just such an example exhibiting both net information generation and energy dissipation by holding the acquired thermal agitation for much longer than the interval of the inverse thermal frequency. Any local detection that can last far longer than the inverse thermal frequency can effectively lower the temperature there by decreasing Boltzmann’s entropy compared with the case otherwise. Once there appear two separate regions with different temperatures, it is possible to imagine, through their connection, a likelihood of having a heat engine that can extract positive work while modulating thermal agitations at the higher temperature side so as to match themselves with those at the lower side. In particular, ATP hydrolysis with the help of myosin in myofibrils demonstrates that thermal fluctuations excited in ATPactivated myofibrils are certainly modulated compared with those excited in non-activated ones (Honda et al., 1995). 4. Discussion A heat engine operating between two heat reservoirs with different temperatures manifests how local detection dynamics may proceed in reality. What is unique to the operation is the capacity of influencing or acting upon thermal agitations at the higher temperature side. Although the global character of a heat engine can be specified by both its thermal efficiency and the magnitude of the load, these parameters are not those that can be detected internally through local processes. Instead, energy flows crossing various interfaces can serve as local quantities detectable internally (Matsuno, 1989).
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125
The energy flow from the heat reservoir at the higher temperature into the heat engine is divided and transferred into two flows; one is for the reservoir at the lower temperature and the other for the work done by the heat engine. Since each of these three flows are quantities that can be detected locally, simultaneous identification of all three at the same moment cannot be available within the scheme of a local detection dynamics. Nonetheless, when these flows are realized, the realization dynamics mediated by them is certainly simultaneous in fixing them at every moment at least in the sense of fulfilling the condition of energy flow continuity among them. What is significant in this fulfllment of energy flow continuity is that local detection dynamics takes time in following the effect that realization dynamics of a global character has brought about. For instance, although the condition lof energy flow continuity must be observed internally in any event, there is a definite difference between energy flow continuity to be detected locally and that to be realized globally. When the energy flow for the work done by the heat engine happens to increase slightly due to some changes in the factors specifying the load, this increase could not be detected simultaneously by the factors determining the energy flows from and to the heat reservoirs. It takes time for the detection to be accomplished, no matter how small that may be. Furthermore, before the detection is completed, a renewed realization of energy flows has to have been made so as to fulfill the condition of flow continuity. Otherwise, violation of energy flow continuity would come to be detected internally. And a renewed realization of energy flows can again cause subsequent conflicts with the following detection dynamics. One thus observes that removal of conflicts between local detection and global realization could continue to hold indefinitely in a self-perpetuating manner. One dominant mode of removing these conflicts is for the heat engine to act upon the heat reservoir at the higher temperature, if not being restricted only to be acted upon by the latter. Needless to say, heat engines, as a well-established subject matter of thermodynamics, can be
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analyzed and understood by referring exclusively to the global dynamics of realization while calling attention to such global attributes as the efficiency of the engine and the magnitude of the load. This scheme is undoubtedly legitimate. Still, it is also legitimate to address oneself to the same subject matter by paying attention to the interplay of dynamics between local detection and global realthermodynamics ization, because approaching through Boltzmann’s statistical mechanics is founded upon the recognition of local detection dynamics. What heat engines suggest to biodynamics in vivo is the significance of the capacity of acting upon thermal agitations. That capacity can become legitimate and explicit once the role of local detection dynamics is considered. As a matter of principle, the outcome that the capacity of acting upon brings about in the effect cannot be preprogrammed in advance. The absence of preprogrammability is grounded upon the obvious physical fact that what will be detected cannot be identified before it has actually been detected. It is this absence of preprogrammability which makes biodynamics in vivo so distinct compared with a mechanics that constructs detection dynamics as immediately following realization dynamics. The flexibility and plasticity latent in the capacity of acting upon thermal agitations are realized within detection dynamics of a local character. Furthermore, acting upon thermal agitations to extract a positive work from them is equivalent to feeding on thermal agitations, that is heterotrophic while extracting energy from the latter (Matsuno, 1992). Evolutionary emergence of most primitive biological organizations could in fact happen to coincide with a de novo spontaneous appearance of heat engines (Matsuno, 1996) or energy consumers acting upon thermal agitations from the surroundings (Matsuno, 1995). A frozen aggregate of degrees of freedom in motion can exhibit the capacity of acting upon, that is to say, feeding on, thermal agitations originating in the ambient if it can hold the acquired thermal excitations for much longer than the interval of the inverse thermal frequency while changing its constituent members. ATP hydrolysis with the help of myosin certainly provides evi-
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dence that when a frozen aggregate of degrees of freedom starts to dissociate some of its constituents as a consequence of having received thermal agitations, their holding time becomes far greater than the inverse thermal frequency. One more example of acting upon thermal agitations that could be significant protobiologically would be aggregation of thermal heterocomplex molecules of amino acids in aqueous milieu in the sense that heating amino acid molecules could have been quite conceivable on the surface of the primitive earth (Fox and Dose, 1977). Forming microspherical structures of the thermal heterocomplex molecules in aqueous *milieu would be a form of holding thermal agitations locally there. In fact, the hysteretic association of those thermal heterocomplex molecules upon cyclic variations of temperature in the ambient could effectively transform the microspherical aggregates into heat engines or energy consumers acting upon thermal agitations (Sakurazawa et al., 1994). In essence, biodynamics in vivo characterizes dynamic phenomena with frozen aggregates of degrees of freedom that can hold thermal excitations from the ambient for much longer than the interval of the inverse thermal frequency while reshuffling their constituent degrees of freedom.
Acknowledgements The author wishes to thank Stanley N. Salthe for helpful comments on the draft of the present manuscript.
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