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Theory of cell membrane organizers and pressure reversal of anesthesia
Medical Hypotheses (2001) 56(1), 26–32 © 2001 Harcourt Publishers Ltd doi: 10.1054/mehy.2000.1104, available online at http://www.idealibrary.com on
Theory of cell membrane organizers and pressure reversal of anesthesia M. Jibu Research Institute for Informatics and Science, Notre Dame Seishin University, Okayama, Japan
Summary A theory of pressure reversal of anesthesia is proposed from a modern framework of condensed matter physics. A highly ordered cooperative dynamics of ordered water in the perimembranous region of nerve cells is analyzed, and the emergence of a new phase of condensation of massive photons in the perimembranous region is derived theoretically. The critical temperature of the massive photon condensation is estimated to be higher than the body temperature. The anesthetic molecules break the order of the ordered water condensation, and decrease the critical temperature of the emergent massive photon condensation there – a possible mechanism of anesthesia. Condensed matter physics tells that the critical temperature of the condensation phase is proportional to the pressure. The critical temperature of the massive photon condensation once decreased by the anesthetic molecules increases under the high pressure, restoring the order of the massive photon condensation, thus suggesting the pressure reversal of anesthesia. © 2001 Harcourt Publishers Ltd
INTRODUCTION The phenomenon of pressure reversal of anesthesia, in which anesthetic effect is annihilated under the high pressure circumstance, has been of particular interest for investigating the mechanism of anesthesia (1). No theoretical explanations of anesthesia can be proceeded to further examination unless they clarify the mechanism of pressure reversal. Indeed, some anticipated biochemical explanation of anesthesia was not accepted because it derived the opposite property (1). The phenomenon of pressure reversal of anesthesia is a touchstone for the theory of anesthesia, but it remains unexplained by itself. The difficulty of explaining the pressure reversal seems to lie in its thermodynamical nature. Pressure is a typical thermodynamic physical variable as familiar as temperature. In physics, pressure is treated as one of the thermodynamic variables describing the thermodynamic state of a macroscopic system of matter. It is a direct and
Received 29 November 1999 Accepted 22 February 2000 Published online 8 December 2000 Correspondence to: M. Jibu, Research Institute for Informatics and Science, Notre Dame Seishin University, 2-16-9 Ifuku-cho, Okayama 700-8516, Japan. E-mail: [email protected]; Phone: +81 86 255 5636; Fax: +81 86 255 5090
26
general consequence of thermodynamics and molecular chemistry that the activity of chemical reactions becomes higher if pressure is put higher. However, the activity of chemical reactions of anesthetic molecules goes against this general thermodynamic feature. Furthermore, the number density of anesthetic molecules in the perimembranous region immediately adjacent to the nerve cells is actually very low. The mean number of anesthetic molecules in the whole perimembranous region of a single nerve cell happens to be less than 1. Such a low density of anesthetic molecules forced us to abandon the thermodynamic theory of anesthesia, and approaches from molecular biology became popular. However, the theoretical framework used in molecular biology cannot be acclimated to the thermodynamic notions and treatments. The former focuses on the individual molecular behavior taking place in the perimembranous region, while the latter on the overall average behavior emerging to the macroscopic variables. It is beyond doubt that the anesthesia is caused by the anesthetic molecules trespassing into the perimembranous region immediately adjacent to the nerve cells. So, there have been many attempts to investigate the molecular structure of the cell membrane surface (1). There, the lipid bilayer structure of membrane itself has been shown to play no principal role in anesthesia because enzymes without lipid bilayers were inactivated by anesthetics. Then,
Cell membrane organizers and pressure reversal of anesthesia
membrane proteins and membrane skeletal filaments have been investigated, though no apparent molecular biological effect of anesthetics has been found. Recently, both geometric and functional configuration dynamics of membrane proteins have been investigated in terms of the lateral diffusion process of membrane molecules in the background membrane lipid bilayer (2–3). The membrane lipid bilayer plays an underlying role as a two-dimensional field in which various molecules manifest controlled lateral diffusions. Here, a controlled lateral diffusion of a membrane molecule means a lateral diffusion of a membrane molecule suffering not only from a random thermal noise but also from a systematized drift caused by the neighboring systems. There are two neighboring systems immediately adjacent to the cell membrane; the outer and inner perimembranous regions. The cytoskeletal structure and function of cytoplasm may provide the membrane molecules with some dynamical control of a primitive level through the inner perimembranous region. However, the outer perimembranous region suffers from the trespassing of anesthetic molecules much more than the inner one. In this sense, the dynamical control of the controlled lateral diffusions of membrane molecules in the nerve cell membrane directly related to anesthetic effects should be given by the outer perimembranous region. In this paper, we investigate the physical structure and function of the outer perimembranous region, and propose a theory of anesthesia within the framework of recent condensed matter physics. There, the emergence of a new phase of condensation of massive photons (called tunneling photons or evanescent photons) in the perimembranous region is derived theoretically. The critical temperature of the massive photon condensation is estimated to be of the scale higher than the body temperature. We assume that the dynamics of the tunneling photon condensation in the outer perimembranous region controls the lateral diffusions of membrane molecules in the nerve cell membrane, and regular and ordered chemical reactions are maintained to realize the regular cell functioning of the nerve cell. The anesthetic molecules trespassing into the perimembranous region break the order of the ordered water condensation, and decrease the critical temperature of the emergent massive photon condensation. Then, the controlled lateral diffusions of membrane molecules in the cell membrane can no longer be under the control of the dynamics of the tunneling photon condensation in the outer perimembranous region, and suffer from only the control of a primitive level from the inner perimembranous region. Thus, regular and ordered chemical reactions cannot be maintained, and the regular cell functioning of the nerve cell is lost. This is a possible mechanism of anesthesia we propose. © 2001 Harcourt Publishers Ltd
27
Then we proceed to clarifying the pressure reversal of anesthesia. Condensed matter physics tells that the critical temperature of the condensation phase is proportional to the pressure. The critical temperature of the tunneling photon condensation once decreased by the anesthetic molecules increases under the high pressure, maintaining the order of the condensation. Then, the lateral diffusions of membrane molecules in the cell membrane become once again subject to the control of the dynamics of the tunneling photon condensation in the outer perimembranous region. Regular and ordered chemical reactions in the cell membrane are restored and the regular cell functioning of the nerve cell is also restored, thus explaining the mechanism of the pressure reversal of anesthesia. CONTROLLED LATERAL DIFFUSION OF MOLECULES IN CELL MEMBRANE The lipid bilayer of a cell membrane is a background twodimensional field in which such membrane molecules as membrane proteins, enzymes and transmitters manifest controlled lateral diffusions. It is the totality of those controlled lateral diffusions of membrane molecules in the lipid bilayer which specifies the overall molecular biological cell functioning. This is because the chemical reactions taking place in the whole cell membrane are all subject to those controlled lateral diffusions of membrane molecules, and the combination of those chemical reactions determines the molecular biological functioning of a cell. We developed a theoretical model of the controlled lateral diffusions of membrane molecules in the dendritic membrane of a nerve cell (4–6). This theoretical model applies equally to the controlled lateral diffusions of membrane molecules in the general cell membrane, but we are concerned with the nerve cell membrane. The geometric extent of the background lipid bilayer of the cell membrane can be regarded as a twodimensional compact manifold locally isomorphic to a domain in the two-dimensional plane: Let ρ be the distribution number density of a membrane molecule in question. Then, the changes in the distribution of the membrane molecules in the cell membrane are well described by the time evolution of the distribution number density ρ. In this sense, the distribution number density ρ is a system variable of the controlled lateral diffusions of membrane molecules. Dynamical theory of Brownian motion tells us that the time change of the distribution number density ρ is determined by the Fokker-Planck (diffusion) equation (7).
¶ρ
= −∇ . (bρ) + D∆ρ ∂τ Medical Hypotheses (2001) 56(1), 26–32
28
Jibu
The first term in the right hand side represents the time change of the distribution number density given by a certain systematic control flow, and the second term represents that given by the random force due to the thermal noise. The systematic control flow is represented by the drift vector b, and the random fluctuation is represented by the diffusion constant D. In modern languages, the same controlled lateral diffusions are usually described by a stochastic differential equation
dX = bdt + DdW or a Langevin equation
dX = b + Ö Dξ dt but those are mathematically equivalent with each other (7). The drift vector b changes its form in accordance with the neighboring control system, and so it depends on a control variable representing the control policy of the control system. Thus, the controlled lateral diffusions of membrane molecules are described by the system variable ρ and the control variable coupled with each other (4–6). The dynamical behavior of the system of membrane molecules in the cell membrane consists of two distinct parts; disordered dynamics suffering from a random thermal noise and ordered dynamics caused by a systematized drift. While the former increases the entropy of the system of geometric and functional configuration of membrane molecules in the cell membrane, the latter decreases it. Therefore, if the system of the controlled lateral diffusions of membrane molecules in the cell membrane is subject to a stronger control by a systematized drift, then its entropy decreases and the cell functioning becomes active and directional. On the other hand, if the system turns out to be out of control, then its entropy increases and the cell functioning becomes inactive and disordered. For the cell functioning to be active and directional enough to make the cell alive, it is needed to maintain an effective control system keeping a strong interaction with the system of the controlled lateral diffusions of membrane molecules in the cell membrane. Such a system, to be called a membrane organizer or controller, should exist just neighboring to the cell membrane. TUNNELING PHOTON CONDENSATION AS MEMBRANE ORGANIZER There are two neighboring systems immediately adjacent to the nerve cell membrane in which the membrane Medical Hypotheses (2001) 56(1), 26–32
organizer could exist. They are perimembranous regions just outside and inside the nerve cell, and we call them the outer and inner perimembranous regions, respectively. As the inner perimembranous region suffers from the interaction with the cytoskeletal structure and functioning of cytoplasm, it may play a role of membrane organizer in terms of a primitive intracellular informational dynamics driven by the cytoplasmic chemical and physio-chemical reactions. From a system theoretical point of view, the inner perimembranous region can be a primitive membrane organizer, meaning that it provides the membrane molecules with certain control whose control policy reflects the intracellular cytoplasmic activity of the individual cell. It is primitive in a sense that the biological activity of a primitive unicellular organism except the environmental reaction is generated by the cytoplasmic activity. The outer perimembranous region of a unicellular organism is directly connected to the environmental circumstance of the cell. It plays a role of environmental membrane organizer by which the primitive unicellular organism can modify the geometric and functional configuration dynamics of membrane molecules in the cell membrane to be adapted to the environment. Thus, the membrane organizer of a unicellular organism consists of two parts. The first one is the primitive membrane organizer which controls the geometric and functional configuration dynamics of molecules in the cell membrane with a control policy given genetically by the intracellular cytoplasmic activity. The second one is the environmental membrane organizer which controls it with a control policy driven by the environmental circumstance of the cell. In case of the multicellular organism, the primitive membrane organizer of each constituent cell remains essentially the same as in the case of a unicellular organism. However, the environmental membrane organizer changes drastically. It cannot even be called ‘environmental’ membrane organizer, because most cells forming the multicellular organism are not exposed directly to the environmental circumstance of the multicellular organism. Each constituent cell is exposed only to the local environment of the intercellular space. We call it, therefore, a local environmental membrane organizer. It exists in the outer perimembranous region in the intercellular space, and suffers from the trespassing of anesthetic molecules when the nerve tissue is subject to anesthesia. Therefore, the local environmental membrane organizer realizing the dynamical control of the controlled lateral diffusions of membrane molecules in the nerve cell membrane directly related to the anesthetic effect should be the outer perimembranous region in the intercellular space. © 2001 Harcourt Publishers Ltd
Cell membrane organizers and pressure reversal of anesthesia
Recently, for the purpose of clarifying the existence of distributed patterns of activity serving as an ideal substrate for experienced perceptual awareness and subsequent storage of that experience, we gave a detailed analysis of the dynamically ordered structure of water in the outer perimembranous region of the intercellular space (6,8). Since thermal fluctuation and dissipation of water molecules in the perimembranous region are 106 as small as that of bulk water, it is kept far from thermal equilibrium. Therefore, a new theoretical framework of condensed matter physics was needed for the detailed analysis. We have shown that the electromagnetic field plays not only secondary roles but a principal role as an ideal substrate accounting for the distributed and systematized patterns of activity in the perimembranous region of the intercellular space. Namely, the electromagnetic field manifests two distinct modes; a normal wave mode with real wave number and a tunneling or evanescent wave mode with imaginary wave number. The former is essentially the well-known part of the electromagnetic field binding atoms and molecules dynamically with each other. The latter is the damping part of the electromagnetic field corresponding to a leak field that can be usually neglected in the case of bulk water but certainly not in the case of a thin layer of water in the perimembranous region. Due to the intrinsic electric dipole moment, the water molecule interacts strongly with the electromagnetic field in the perimembranous region. We found that the electric dipoles of water molecules are systematized globally in the perimembranous region to realize a uniform configuration. It is the dynamically ordered structure of water in the perimembranous region supported by the normal wave modes of the electromagnetic field. A long-range alignment of electric dipoles cannot be extended to the whole perimembranous region, but restricted to a domain with linear dimension smaller than a characteristic length called a coherence length. It is estimated to be less than 50 µm (8). Thus, we have a distributed spatial structure of the perimembranous region composed of the non-overlapping domains of dynamically ordered states of water smaller than the coherence length. This domain structure can be understood as basic to the distributed patterns of activity in the large extent of extracellular fluid in the intercellular space with which the system of controlled lateral diffusions of membrane molecules are expected to interact. The domain structure of distributed systematized patterns in the perimembranous region was revealed to be an ideal physical substrate for the distributed patterns of activity surrounding the nerve cell membrane. It provides us with a postulated mechanism of experienced awareness and subsequent storage of that experience (8). Each stimulus driven by the experience flowing into the nerve cell membranes in terms of neurotransmitters © 2001 Harcourt Publishers Ltd
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produces a change of the geometric and functional configuration of the membrane molecules represented by the distribution number density ρ. Then, this change triggers the uniform alignment of electric dipoles of water molecules in the perimembranous region immediately adjacent to the nerve cell membrane in question. Namely, a spatial domain of the dynamically ordered structure of water with the size smaller than the coherence length is created in which the electric dipoles are aligned in one and the same direction. It is this domain of the dynamically ordered structure of water that is postulated to be a basic part of the physical substrate coordinate with perceptual awareness of the external stimuli in question. Modern condensed matter physics revealed the existence of long-range correlation waves in such a uniform alignment of electric dipoles as the dynamically ordered structure of water in the perimembranous region (9–12). Those long-range correlation waves are called NambuGoldstone modes. The Nambu-Goldstone modes were shown to be generated by a very small energy perturbation, and so each domain of the dynamically ordered structure of water postulated to be a basic part of the physical substrate coordinate with perceptual awareness of the external stimuli may generate the NambuGoldstone modes at all times thanks to the noisy thermal circumstance of the nerve cells. Those constantly produced Nambu-Goldstone modes characteristic of each domain of the dynamically ordered structure were regarded as the physical substrate coordinate with the retrieval of the perceptual awareness of the external stimuli stored in the dynamically ordered structure of water. Furthermore, it is known that the long-range correlation waves of aligned electric dipoles create a longitudinal mode of the electromagnetic field (9). This longitudinal mode is described by the electric field vector E subject not to the usual Maxwell equation
(
2
(
1 –∆ E=0 c2 t 2
but to the modified Maxwell equation with mass term
(
1 ¶ 2 Ð ∆ + M2c2 h2 c2 ¶ t 2
(
E=0
- the Planck constant divided where c is the light speed, h by 2π, and M is a positive parameter with the dimension of mass. Medical Hypotheses (2001) 56(1), 26–32
30
Jibu
The actual value of M depends on the depth δ of the perimembranous region in the intercellular space. For the typical case, we have
δ ~ ∼ 150Å
and so we have
h ~ M= ∼ 13.6 eV cδ By the modified Maxwell equation, we find that the electromagnetic field in the spatial domain of the dynamically ordered structure of water becomes a non-propagating wave mode with imaginary wave number. Photons are light quanta associated to the propagating wave modes with real wave numbers of the electromagnetic field. Light quanta associated to the non-propagating wave mode with imaginary wave number are called evanescent photons, virtual photons or tunneling photons. Due to the form of the modified Maxwell equation, they have nonvanishing mass M ≈ 13.6 eV. Namely, we have massive photons in the perimembranous region. The intercellular space between the nerve cells is filled up with not only the ordered domains of water but also the non-propagating modes of the electromagnetic field in which tunneling photons with mass M manifest a condensation. This condensation of tunneling photons overlaps the spatial domain structure of the dynamically ordered states of water in the perimembranous region (8). Each spatial domain structure of the dynamically ordered states of water in the perimembranous region is regarded as a physical substrate coordinate with perceptual awareness of the external stimuli. Like the Nambu-Goldstone mode, each condensation of tunneling photons overlapping the spatial domain structure of the dynamically ordered states of water is regarded as a physical substrate for the retrieval of the perceptual awareness of the external stimuli stored in the dynamically ordered structure of water. As the tunneling photons do not interact with each other, their condensation can be treated as an ideal Bose gas confined in each ordered domain of the perimembranous region with linear dimension of the order of the coherence length. Then, a standard calculation gives the critical temperature
h2 T = α M which is the maximum temperature for the condensation of tunneling photons maintained, where α is a constant Medical Hypotheses (2001) 56(1), 26–32
given explicitly. Putting the explicit values of constants and parameters, we find the critical temperature T lies in the range of 300–1000K which goes well along with the actual body temperature. It is of particular interest to regard the condensation of tunneling photons overlapping the spatial domain structure of distributed systematized patterns in the perimembranous region as the physical substrate for the local environmental membrane organizer. Since each tunneling photon condensation in the perimembranous region of the intercellular space is located immediately adjacent to the system of the lateral diffusions of membrane molecules in the nerve cell membrane, those membrane molecules suffer from a strong systematized drift force due to the electromagnetic field induced by the tunneling photon condensation. Such a drift force can be calculated to be proportional to the gradient of the square density of the electric field vector, obtaining
b ∇ E
2
Because each condensation of tunneling photons overlapping the spatial domain structure of the dynamically ordered states of water is regarded as a physical substrate for the retrieval of the perceptual awareness of the external stimuli stored in the dynamically ordered structure of water, the above drift force well reflects the systematized control policy in accordance with the perceptual awareness. In this sense, the tunneling photon condensation in the outer perimembranous region of the intercellular space can be regarded as a local membrane organizer of the nerve cell. ANESTHESIA AND PRESSURE REVERSAL We have seen that the dynamics of the tunneling photon condensation in the outer perimembranous region of the intercellular space controls the lateral diffusions of membrane molecules in the nerve cell membrane, and regular and ordered chemical reactions are maintained to realize the regular cell functioning of the nerve cell. We consider now the effect of trespassing of anesthetic molecules into the outer perimembranous region of the nerve cell. The crucial point is the existence of B-ions disintegrated from the anesthetic molecules. Among several kinds of ions typical for the extracellular and intracellular fluid are Na +, K+, Ca2+, etc. The effect of the presence of such ions in the dynamically ordered structure of water is clear: there are three types of ions, that is, M-ions, C-ions and B-ions. This classification is made upon the effect of the ion on the dynamically ordered structure of water. However, the effect of an ion on water molecules is essentially due to the electromagnetic interaction of Coulomb © 2001 Harcourt Publishers Ltd
Cell membrane organizers and pressure reversal of anesthesia
type, and so its strength depends highly on the distance between each water molecule and the ion in question. The above classification, therefore, can be regarded also as a classification upon the size of the ion: ions whose radius is smaller than that of the water molecule are M-ions, and they do not disturb the dynamically ordered structure of water. Na + and Ca2+ are M-ions. Those whose radius is approximately the same as that of the water molecule are C-ions, and they play the role of water molecule in realizing the dynamically ordered structure of water. In other words, C-ions can be mixed with water molecules in the dynamically ordered state. K+ is a C-ion. Those whose radius is larger than that of the water molecule are B-ions, and they disturb the dynamically ordered structure of water considerably. If there are B-ions in the perimembranous region, then the system of electric dipoles of water molecules and the electromagnetic field interacting with each other will suffer from dynamical disorder and so the dynamically ordered structure of water manifests defects. Cl – is a B-ion. Recalling the fact that K+ and Na + show higher populations inside and outside the nerve cell, respectively, the normal ionic environment of the cytoplasm and extracellular fluid might not disturb the dynamically ordered structure of water in the perimembranous region immediately adjacent to the nerve cell membrane. However, Cl – and other B-ions disintegrated from the anesthetic molecules can be thought to make many defects in the dynamically ordered structure of water, and consequently the penetration depth δ of the non-propagating evanescent modes of the electromagnetic field becomes smaller. This means that the mass M of the tunneling photon becomes larger depending inversely on the penetration depth δ. Suppose the penetration depth δ reduces to the order of 10Å due to the defect induced by the B-ions disintegrated from the anesthetic molecules, then the tunneling photon mass M becomes of the order of 100 eV. Then, the critical temperature T of the condensation of tunneling photons becomes to lie in the range of 30–100 K which is much lower than that of the actual life circumstance. Namely, the tunneling photon condensation in the outer perimembranous region of the nerve cell membrane vanishes at the body temperature due to the trespassing of anesthetic molecules. The system of controlled lateral diffusions of membrane molecules in the nerve cell membrane loses therefore the local environmental membrane organizer, and suffer from only control of a primitive level from the inner perimembranous region. Thus, regular and ordered chemical reactions in the nerve cell membrane cannot be maintained, and the regular cell functioning of the nerve cell is lost. This is a possible mechanism of anesthesia derived within the framework of modern condensed matter physics. © 2001 Harcourt Publishers Ltd
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Next, we clarify the mechanism of pressure reversal of anesthesia. As it has been revealed, the anesthetic effect is caused by the considerable decrease of the critical temperature of the tunneling photon condensation in the perimembranous region of the nerve cell membrane induced by the defects in the dynamically ordered structure of water due to the B-ions such as Cl – disintegrated from the anesthetic molecules. Condensed matter physics tells us that the critical temperature T of the condensation phase is related to the pressure P by the Kamerlingh-Onnes law
T=κ PV where κ is a constant and V is the volume of the system manifesting the condensation phase. Therefore, the critical temperature of the tunneling photon condensation in the outer perimembranous region of the nerve cell membrane decreased by the anesthetic molecules to the range of 30–100 K increases again to the range of 300–1000 K under such a high pressure circumstance as 10–100 atm. Then, the lateral diffusions of membrane molecules in the nerve cell membrane become subject to the recovered control of the local environmental membrane organizer, that is, the tunneling photon condensation in the outer perimembranous region of the nerve cell membrane. Regular and ordered chemical reactions in the nerve cell membrane are restored and the regular cell functioning of the nerve cell is also recovered, thus explaining the mechanism of the pressure reversal.
ACKNOWLEDGMENTS It is a great pleasure for the author to express her sincerest thanks to Professors Futami Kosaka and Masahisa Hirakawa of the Department of Anesthesiology and Resuscitology, Okayama University Medical School for their warmhearted advice and support. She is also indebted to Professor Yasushi Takahashi of the Department of Physics, University of Alberta, and Professor Kunio Yasue of Research Institute for Informatics and Science, Notre Dame Seishin University who kindly guided her to modern physics.
REFERENCES 1. 2. 3.
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Franks N. P., Lieb W. R. Molecular mechanisms of general anesthesia. Nature 1982; 300: 487–493. Kusumi A., Sako Y. Cell surface organization by the membrane skeleton. Curr Opinion Cell Biol 1996; 8: 566–574. Tomishige M., Sako Y., Kusumi A. Regulation mechanism of the lateral diffusion of band 3 in erythrocyte membranes by the membrane skeleten. J Cell Biol 1998; 142: 989–1000. Yasue K. Wave cybernetics: a simple model of wave-controlled nonlinear and nonlocal cooperative phenomena. Phys Rev A 1988; 38: 2671–2673.
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6. 7. 8.
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Pribram K. H. Brain and Perception. Appendices ‘A theory of nonlocal cortical processing in the brain’. New Jersey: Laurence Erlbaum, 1991. Jibu M., Yasue K. Quantum Brain Dynamics and Consciousness: An Introduction. Amsterdam: John Benjamins, 1995. Nelson E. Dynamical Theories of Brownian Motion. New Jersey: Princeton University Press, 1967. Jibu M., Pribram K. H., Yasue K. From conscious experience to memory storage and retrieval: the role of quantum brain dynamics and boson condensation of evanescent photons. Intern. J. Mod. Phys. B; 1996; 10: 1735–1754.
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9.
Umezawa H. Advanced Field Theory: Micro, Macro and Thermal Physics. New York: American Institute of Physics, 1993. 10. Ricciardi L. H., Umezawa H. Brain and physics of many-body problem. Kybernetic (Biological Cybernetics); 1967; 4: 44–48. 11. Stuart C.I.J.M., Takahashi Y., Umezawa H. On the stability and non-local properties of memory. J Theor Biol; 1978; 71: 605–618. 12. Stuart C.I.J.M., Takahashi Y., Umezawa, H. Mixed-system brain dynamics: neural memory as a macroscopic ordered state. Found Phys 1979; 9: 301–327.
© 2001 Harcourt Publishers Ltd
Theory of cell membrane organizers and pressure reversal of anesthesia M. Jibu Research Institute for Informatics and Science, Notre Dame Seishin University, Okayama, Japan
Summary A theory of pressure reversal of anesthesia is proposed from a modern framework of condensed matter physics. A highly ordered cooperative dynamics of ordered water in the perimembranous region of nerve cells is analyzed, and the emergence of a new phase of condensation of massive photons in the perimembranous region is derived theoretically. The critical temperature of the massive photon condensation is estimated to be higher than the body temperature. The anesthetic molecules break the order of the ordered water condensation, and decrease the critical temperature of the emergent massive photon condensation there – a possible mechanism of anesthesia. Condensed matter physics tells that the critical temperature of the condensation phase is proportional to the pressure. The critical temperature of the massive photon condensation once decreased by the anesthetic molecules increases under the high pressure, restoring the order of the massive photon condensation, thus suggesting the pressure reversal of anesthesia. © 2001 Harcourt Publishers Ltd
INTRODUCTION The phenomenon of pressure reversal of anesthesia, in which anesthetic effect is annihilated under the high pressure circumstance, has been of particular interest for investigating the mechanism of anesthesia (1). No theoretical explanations of anesthesia can be proceeded to further examination unless they clarify the mechanism of pressure reversal. Indeed, some anticipated biochemical explanation of anesthesia was not accepted because it derived the opposite property (1). The phenomenon of pressure reversal of anesthesia is a touchstone for the theory of anesthesia, but it remains unexplained by itself. The difficulty of explaining the pressure reversal seems to lie in its thermodynamical nature. Pressure is a typical thermodynamic physical variable as familiar as temperature. In physics, pressure is treated as one of the thermodynamic variables describing the thermodynamic state of a macroscopic system of matter. It is a direct and
Received 29 November 1999 Accepted 22 February 2000 Published online 8 December 2000 Correspondence to: M. Jibu, Research Institute for Informatics and Science, Notre Dame Seishin University, 2-16-9 Ifuku-cho, Okayama 700-8516, Japan. E-mail: [email protected]; Phone: +81 86 255 5636; Fax: +81 86 255 5090
26
general consequence of thermodynamics and molecular chemistry that the activity of chemical reactions becomes higher if pressure is put higher. However, the activity of chemical reactions of anesthetic molecules goes against this general thermodynamic feature. Furthermore, the number density of anesthetic molecules in the perimembranous region immediately adjacent to the nerve cells is actually very low. The mean number of anesthetic molecules in the whole perimembranous region of a single nerve cell happens to be less than 1. Such a low density of anesthetic molecules forced us to abandon the thermodynamic theory of anesthesia, and approaches from molecular biology became popular. However, the theoretical framework used in molecular biology cannot be acclimated to the thermodynamic notions and treatments. The former focuses on the individual molecular behavior taking place in the perimembranous region, while the latter on the overall average behavior emerging to the macroscopic variables. It is beyond doubt that the anesthesia is caused by the anesthetic molecules trespassing into the perimembranous region immediately adjacent to the nerve cells. So, there have been many attempts to investigate the molecular structure of the cell membrane surface (1). There, the lipid bilayer structure of membrane itself has been shown to play no principal role in anesthesia because enzymes without lipid bilayers were inactivated by anesthetics. Then,
Cell membrane organizers and pressure reversal of anesthesia
membrane proteins and membrane skeletal filaments have been investigated, though no apparent molecular biological effect of anesthetics has been found. Recently, both geometric and functional configuration dynamics of membrane proteins have been investigated in terms of the lateral diffusion process of membrane molecules in the background membrane lipid bilayer (2–3). The membrane lipid bilayer plays an underlying role as a two-dimensional field in which various molecules manifest controlled lateral diffusions. Here, a controlled lateral diffusion of a membrane molecule means a lateral diffusion of a membrane molecule suffering not only from a random thermal noise but also from a systematized drift caused by the neighboring systems. There are two neighboring systems immediately adjacent to the cell membrane; the outer and inner perimembranous regions. The cytoskeletal structure and function of cytoplasm may provide the membrane molecules with some dynamical control of a primitive level through the inner perimembranous region. However, the outer perimembranous region suffers from the trespassing of anesthetic molecules much more than the inner one. In this sense, the dynamical control of the controlled lateral diffusions of membrane molecules in the nerve cell membrane directly related to anesthetic effects should be given by the outer perimembranous region. In this paper, we investigate the physical structure and function of the outer perimembranous region, and propose a theory of anesthesia within the framework of recent condensed matter physics. There, the emergence of a new phase of condensation of massive photons (called tunneling photons or evanescent photons) in the perimembranous region is derived theoretically. The critical temperature of the massive photon condensation is estimated to be of the scale higher than the body temperature. We assume that the dynamics of the tunneling photon condensation in the outer perimembranous region controls the lateral diffusions of membrane molecules in the nerve cell membrane, and regular and ordered chemical reactions are maintained to realize the regular cell functioning of the nerve cell. The anesthetic molecules trespassing into the perimembranous region break the order of the ordered water condensation, and decrease the critical temperature of the emergent massive photon condensation. Then, the controlled lateral diffusions of membrane molecules in the cell membrane can no longer be under the control of the dynamics of the tunneling photon condensation in the outer perimembranous region, and suffer from only the control of a primitive level from the inner perimembranous region. Thus, regular and ordered chemical reactions cannot be maintained, and the regular cell functioning of the nerve cell is lost. This is a possible mechanism of anesthesia we propose. © 2001 Harcourt Publishers Ltd
27
Then we proceed to clarifying the pressure reversal of anesthesia. Condensed matter physics tells that the critical temperature of the condensation phase is proportional to the pressure. The critical temperature of the tunneling photon condensation once decreased by the anesthetic molecules increases under the high pressure, maintaining the order of the condensation. Then, the lateral diffusions of membrane molecules in the cell membrane become once again subject to the control of the dynamics of the tunneling photon condensation in the outer perimembranous region. Regular and ordered chemical reactions in the cell membrane are restored and the regular cell functioning of the nerve cell is also restored, thus explaining the mechanism of the pressure reversal of anesthesia. CONTROLLED LATERAL DIFFUSION OF MOLECULES IN CELL MEMBRANE The lipid bilayer of a cell membrane is a background twodimensional field in which such membrane molecules as membrane proteins, enzymes and transmitters manifest controlled lateral diffusions. It is the totality of those controlled lateral diffusions of membrane molecules in the lipid bilayer which specifies the overall molecular biological cell functioning. This is because the chemical reactions taking place in the whole cell membrane are all subject to those controlled lateral diffusions of membrane molecules, and the combination of those chemical reactions determines the molecular biological functioning of a cell. We developed a theoretical model of the controlled lateral diffusions of membrane molecules in the dendritic membrane of a nerve cell (4–6). This theoretical model applies equally to the controlled lateral diffusions of membrane molecules in the general cell membrane, but we are concerned with the nerve cell membrane. The geometric extent of the background lipid bilayer of the cell membrane can be regarded as a twodimensional compact manifold locally isomorphic to a domain in the two-dimensional plane: Let ρ be the distribution number density of a membrane molecule in question. Then, the changes in the distribution of the membrane molecules in the cell membrane are well described by the time evolution of the distribution number density ρ. In this sense, the distribution number density ρ is a system variable of the controlled lateral diffusions of membrane molecules. Dynamical theory of Brownian motion tells us that the time change of the distribution number density ρ is determined by the Fokker-Planck (diffusion) equation (7).
¶ρ
= −∇ . (bρ) + D∆ρ ∂τ Medical Hypotheses (2001) 56(1), 26–32
28
Jibu
The first term in the right hand side represents the time change of the distribution number density given by a certain systematic control flow, and the second term represents that given by the random force due to the thermal noise. The systematic control flow is represented by the drift vector b, and the random fluctuation is represented by the diffusion constant D. In modern languages, the same controlled lateral diffusions are usually described by a stochastic differential equation
dX = bdt + DdW or a Langevin equation
dX = b + Ö Dξ dt but those are mathematically equivalent with each other (7). The drift vector b changes its form in accordance with the neighboring control system, and so it depends on a control variable representing the control policy of the control system. Thus, the controlled lateral diffusions of membrane molecules are described by the system variable ρ and the control variable coupled with each other (4–6). The dynamical behavior of the system of membrane molecules in the cell membrane consists of two distinct parts; disordered dynamics suffering from a random thermal noise and ordered dynamics caused by a systematized drift. While the former increases the entropy of the system of geometric and functional configuration of membrane molecules in the cell membrane, the latter decreases it. Therefore, if the system of the controlled lateral diffusions of membrane molecules in the cell membrane is subject to a stronger control by a systematized drift, then its entropy decreases and the cell functioning becomes active and directional. On the other hand, if the system turns out to be out of control, then its entropy increases and the cell functioning becomes inactive and disordered. For the cell functioning to be active and directional enough to make the cell alive, it is needed to maintain an effective control system keeping a strong interaction with the system of the controlled lateral diffusions of membrane molecules in the cell membrane. Such a system, to be called a membrane organizer or controller, should exist just neighboring to the cell membrane. TUNNELING PHOTON CONDENSATION AS MEMBRANE ORGANIZER There are two neighboring systems immediately adjacent to the nerve cell membrane in which the membrane Medical Hypotheses (2001) 56(1), 26–32
organizer could exist. They are perimembranous regions just outside and inside the nerve cell, and we call them the outer and inner perimembranous regions, respectively. As the inner perimembranous region suffers from the interaction with the cytoskeletal structure and functioning of cytoplasm, it may play a role of membrane organizer in terms of a primitive intracellular informational dynamics driven by the cytoplasmic chemical and physio-chemical reactions. From a system theoretical point of view, the inner perimembranous region can be a primitive membrane organizer, meaning that it provides the membrane molecules with certain control whose control policy reflects the intracellular cytoplasmic activity of the individual cell. It is primitive in a sense that the biological activity of a primitive unicellular organism except the environmental reaction is generated by the cytoplasmic activity. The outer perimembranous region of a unicellular organism is directly connected to the environmental circumstance of the cell. It plays a role of environmental membrane organizer by which the primitive unicellular organism can modify the geometric and functional configuration dynamics of membrane molecules in the cell membrane to be adapted to the environment. Thus, the membrane organizer of a unicellular organism consists of two parts. The first one is the primitive membrane organizer which controls the geometric and functional configuration dynamics of molecules in the cell membrane with a control policy given genetically by the intracellular cytoplasmic activity. The second one is the environmental membrane organizer which controls it with a control policy driven by the environmental circumstance of the cell. In case of the multicellular organism, the primitive membrane organizer of each constituent cell remains essentially the same as in the case of a unicellular organism. However, the environmental membrane organizer changes drastically. It cannot even be called ‘environmental’ membrane organizer, because most cells forming the multicellular organism are not exposed directly to the environmental circumstance of the multicellular organism. Each constituent cell is exposed only to the local environment of the intercellular space. We call it, therefore, a local environmental membrane organizer. It exists in the outer perimembranous region in the intercellular space, and suffers from the trespassing of anesthetic molecules when the nerve tissue is subject to anesthesia. Therefore, the local environmental membrane organizer realizing the dynamical control of the controlled lateral diffusions of membrane molecules in the nerve cell membrane directly related to the anesthetic effect should be the outer perimembranous region in the intercellular space. © 2001 Harcourt Publishers Ltd
Cell membrane organizers and pressure reversal of anesthesia
Recently, for the purpose of clarifying the existence of distributed patterns of activity serving as an ideal substrate for experienced perceptual awareness and subsequent storage of that experience, we gave a detailed analysis of the dynamically ordered structure of water in the outer perimembranous region of the intercellular space (6,8). Since thermal fluctuation and dissipation of water molecules in the perimembranous region are 106 as small as that of bulk water, it is kept far from thermal equilibrium. Therefore, a new theoretical framework of condensed matter physics was needed for the detailed analysis. We have shown that the electromagnetic field plays not only secondary roles but a principal role as an ideal substrate accounting for the distributed and systematized patterns of activity in the perimembranous region of the intercellular space. Namely, the electromagnetic field manifests two distinct modes; a normal wave mode with real wave number and a tunneling or evanescent wave mode with imaginary wave number. The former is essentially the well-known part of the electromagnetic field binding atoms and molecules dynamically with each other. The latter is the damping part of the electromagnetic field corresponding to a leak field that can be usually neglected in the case of bulk water but certainly not in the case of a thin layer of water in the perimembranous region. Due to the intrinsic electric dipole moment, the water molecule interacts strongly with the electromagnetic field in the perimembranous region. We found that the electric dipoles of water molecules are systematized globally in the perimembranous region to realize a uniform configuration. It is the dynamically ordered structure of water in the perimembranous region supported by the normal wave modes of the electromagnetic field. A long-range alignment of electric dipoles cannot be extended to the whole perimembranous region, but restricted to a domain with linear dimension smaller than a characteristic length called a coherence length. It is estimated to be less than 50 µm (8). Thus, we have a distributed spatial structure of the perimembranous region composed of the non-overlapping domains of dynamically ordered states of water smaller than the coherence length. This domain structure can be understood as basic to the distributed patterns of activity in the large extent of extracellular fluid in the intercellular space with which the system of controlled lateral diffusions of membrane molecules are expected to interact. The domain structure of distributed systematized patterns in the perimembranous region was revealed to be an ideal physical substrate for the distributed patterns of activity surrounding the nerve cell membrane. It provides us with a postulated mechanism of experienced awareness and subsequent storage of that experience (8). Each stimulus driven by the experience flowing into the nerve cell membranes in terms of neurotransmitters © 2001 Harcourt Publishers Ltd
29
produces a change of the geometric and functional configuration of the membrane molecules represented by the distribution number density ρ. Then, this change triggers the uniform alignment of electric dipoles of water molecules in the perimembranous region immediately adjacent to the nerve cell membrane in question. Namely, a spatial domain of the dynamically ordered structure of water with the size smaller than the coherence length is created in which the electric dipoles are aligned in one and the same direction. It is this domain of the dynamically ordered structure of water that is postulated to be a basic part of the physical substrate coordinate with perceptual awareness of the external stimuli in question. Modern condensed matter physics revealed the existence of long-range correlation waves in such a uniform alignment of electric dipoles as the dynamically ordered structure of water in the perimembranous region (9–12). Those long-range correlation waves are called NambuGoldstone modes. The Nambu-Goldstone modes were shown to be generated by a very small energy perturbation, and so each domain of the dynamically ordered structure of water postulated to be a basic part of the physical substrate coordinate with perceptual awareness of the external stimuli may generate the NambuGoldstone modes at all times thanks to the noisy thermal circumstance of the nerve cells. Those constantly produced Nambu-Goldstone modes characteristic of each domain of the dynamically ordered structure were regarded as the physical substrate coordinate with the retrieval of the perceptual awareness of the external stimuli stored in the dynamically ordered structure of water. Furthermore, it is known that the long-range correlation waves of aligned electric dipoles create a longitudinal mode of the electromagnetic field (9). This longitudinal mode is described by the electric field vector E subject not to the usual Maxwell equation
(
2
(
1 –∆ E=0 c2 t 2
but to the modified Maxwell equation with mass term
(
1 ¶ 2 Ð ∆ + M2c2 h2 c2 ¶ t 2
(
E=0
- the Planck constant divided where c is the light speed, h by 2π, and M is a positive parameter with the dimension of mass. Medical Hypotheses (2001) 56(1), 26–32
30
Jibu
The actual value of M depends on the depth δ of the perimembranous region in the intercellular space. For the typical case, we have
δ ~ ∼ 150Å
and so we have
h ~ M= ∼ 13.6 eV cδ By the modified Maxwell equation, we find that the electromagnetic field in the spatial domain of the dynamically ordered structure of water becomes a non-propagating wave mode with imaginary wave number. Photons are light quanta associated to the propagating wave modes with real wave numbers of the electromagnetic field. Light quanta associated to the non-propagating wave mode with imaginary wave number are called evanescent photons, virtual photons or tunneling photons. Due to the form of the modified Maxwell equation, they have nonvanishing mass M ≈ 13.6 eV. Namely, we have massive photons in the perimembranous region. The intercellular space between the nerve cells is filled up with not only the ordered domains of water but also the non-propagating modes of the electromagnetic field in which tunneling photons with mass M manifest a condensation. This condensation of tunneling photons overlaps the spatial domain structure of the dynamically ordered states of water in the perimembranous region (8). Each spatial domain structure of the dynamically ordered states of water in the perimembranous region is regarded as a physical substrate coordinate with perceptual awareness of the external stimuli. Like the Nambu-Goldstone mode, each condensation of tunneling photons overlapping the spatial domain structure of the dynamically ordered states of water is regarded as a physical substrate for the retrieval of the perceptual awareness of the external stimuli stored in the dynamically ordered structure of water. As the tunneling photons do not interact with each other, their condensation can be treated as an ideal Bose gas confined in each ordered domain of the perimembranous region with linear dimension of the order of the coherence length. Then, a standard calculation gives the critical temperature
h2 T = α M which is the maximum temperature for the condensation of tunneling photons maintained, where α is a constant Medical Hypotheses (2001) 56(1), 26–32
given explicitly. Putting the explicit values of constants and parameters, we find the critical temperature T lies in the range of 300–1000K which goes well along with the actual body temperature. It is of particular interest to regard the condensation of tunneling photons overlapping the spatial domain structure of distributed systematized patterns in the perimembranous region as the physical substrate for the local environmental membrane organizer. Since each tunneling photon condensation in the perimembranous region of the intercellular space is located immediately adjacent to the system of the lateral diffusions of membrane molecules in the nerve cell membrane, those membrane molecules suffer from a strong systematized drift force due to the electromagnetic field induced by the tunneling photon condensation. Such a drift force can be calculated to be proportional to the gradient of the square density of the electric field vector, obtaining
b ∇ E
2
Because each condensation of tunneling photons overlapping the spatial domain structure of the dynamically ordered states of water is regarded as a physical substrate for the retrieval of the perceptual awareness of the external stimuli stored in the dynamically ordered structure of water, the above drift force well reflects the systematized control policy in accordance with the perceptual awareness. In this sense, the tunneling photon condensation in the outer perimembranous region of the intercellular space can be regarded as a local membrane organizer of the nerve cell. ANESTHESIA AND PRESSURE REVERSAL We have seen that the dynamics of the tunneling photon condensation in the outer perimembranous region of the intercellular space controls the lateral diffusions of membrane molecules in the nerve cell membrane, and regular and ordered chemical reactions are maintained to realize the regular cell functioning of the nerve cell. We consider now the effect of trespassing of anesthetic molecules into the outer perimembranous region of the nerve cell. The crucial point is the existence of B-ions disintegrated from the anesthetic molecules. Among several kinds of ions typical for the extracellular and intracellular fluid are Na +, K+, Ca2+, etc. The effect of the presence of such ions in the dynamically ordered structure of water is clear: there are three types of ions, that is, M-ions, C-ions and B-ions. This classification is made upon the effect of the ion on the dynamically ordered structure of water. However, the effect of an ion on water molecules is essentially due to the electromagnetic interaction of Coulomb © 2001 Harcourt Publishers Ltd
Cell membrane organizers and pressure reversal of anesthesia
type, and so its strength depends highly on the distance between each water molecule and the ion in question. The above classification, therefore, can be regarded also as a classification upon the size of the ion: ions whose radius is smaller than that of the water molecule are M-ions, and they do not disturb the dynamically ordered structure of water. Na + and Ca2+ are M-ions. Those whose radius is approximately the same as that of the water molecule are C-ions, and they play the role of water molecule in realizing the dynamically ordered structure of water. In other words, C-ions can be mixed with water molecules in the dynamically ordered state. K+ is a C-ion. Those whose radius is larger than that of the water molecule are B-ions, and they disturb the dynamically ordered structure of water considerably. If there are B-ions in the perimembranous region, then the system of electric dipoles of water molecules and the electromagnetic field interacting with each other will suffer from dynamical disorder and so the dynamically ordered structure of water manifests defects. Cl – is a B-ion. Recalling the fact that K+ and Na + show higher populations inside and outside the nerve cell, respectively, the normal ionic environment of the cytoplasm and extracellular fluid might not disturb the dynamically ordered structure of water in the perimembranous region immediately adjacent to the nerve cell membrane. However, Cl – and other B-ions disintegrated from the anesthetic molecules can be thought to make many defects in the dynamically ordered structure of water, and consequently the penetration depth δ of the non-propagating evanescent modes of the electromagnetic field becomes smaller. This means that the mass M of the tunneling photon becomes larger depending inversely on the penetration depth δ. Suppose the penetration depth δ reduces to the order of 10Å due to the defect induced by the B-ions disintegrated from the anesthetic molecules, then the tunneling photon mass M becomes of the order of 100 eV. Then, the critical temperature T of the condensation of tunneling photons becomes to lie in the range of 30–100 K which is much lower than that of the actual life circumstance. Namely, the tunneling photon condensation in the outer perimembranous region of the nerve cell membrane vanishes at the body temperature due to the trespassing of anesthetic molecules. The system of controlled lateral diffusions of membrane molecules in the nerve cell membrane loses therefore the local environmental membrane organizer, and suffer from only control of a primitive level from the inner perimembranous region. Thus, regular and ordered chemical reactions in the nerve cell membrane cannot be maintained, and the regular cell functioning of the nerve cell is lost. This is a possible mechanism of anesthesia derived within the framework of modern condensed matter physics. © 2001 Harcourt Publishers Ltd
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Next, we clarify the mechanism of pressure reversal of anesthesia. As it has been revealed, the anesthetic effect is caused by the considerable decrease of the critical temperature of the tunneling photon condensation in the perimembranous region of the nerve cell membrane induced by the defects in the dynamically ordered structure of water due to the B-ions such as Cl – disintegrated from the anesthetic molecules. Condensed matter physics tells us that the critical temperature T of the condensation phase is related to the pressure P by the Kamerlingh-Onnes law
T=κ PV where κ is a constant and V is the volume of the system manifesting the condensation phase. Therefore, the critical temperature of the tunneling photon condensation in the outer perimembranous region of the nerve cell membrane decreased by the anesthetic molecules to the range of 30–100 K increases again to the range of 300–1000 K under such a high pressure circumstance as 10–100 atm. Then, the lateral diffusions of membrane molecules in the nerve cell membrane become subject to the recovered control of the local environmental membrane organizer, that is, the tunneling photon condensation in the outer perimembranous region of the nerve cell membrane. Regular and ordered chemical reactions in the nerve cell membrane are restored and the regular cell functioning of the nerve cell is also recovered, thus explaining the mechanism of the pressure reversal.
ACKNOWLEDGMENTS It is a great pleasure for the author to express her sincerest thanks to Professors Futami Kosaka and Masahisa Hirakawa of the Department of Anesthesiology and Resuscitology, Okayama University Medical School for their warmhearted advice and support. She is also indebted to Professor Yasushi Takahashi of the Department of Physics, University of Alberta, and Professor Kunio Yasue of Research Institute for Informatics and Science, Notre Dame Seishin University who kindly guided her to modern physics.
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