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On the possible importance of relaxation processes in enzyme catalysis
J. Mol. Biol. (1968) 31, 319-321
On the Possible Importance of Relaxation Processes in Enzyme Catalysis In recent years evidence has accumulated to support the notion that conformational changes in protein structure are crucial for successful enzyme catalysis (Koshland, 1958). The enzyme-substrate complex, ES, is thought to pass through a series of successive states ES1, ESz, . . . each of which transforms to the next by means of specific atomic rearrangements and perhaps bond distortions (Eigen & Hammes, 1963; Phillips, 1966). One might expect that such geometrical rearrangements require the fulfillment of stringent energetic, or dynamical conditions: energy must be supplied in an optimal way at the right time to promote these specific conformational changes. The purpose of this note is to investigate the hypothesis that the source of this energy is collisional induced excitation of enzyme vibrational modes followed subsequently by vibrational relaxation. The enzyme is considered to be so constructed as to permit vibrational energy acquired through collisions with molecules of the environment to be funneled to centers of catalytic activity during the lifetime of the ES complex and employed there for interatomic conversions. The funneling process, furthermore, is identified primarily with the mechanism of intramolecular vibrational relaxation. Turnover numbers of enzyme systems (Amdur & Hammes, 1966) suggest that lob3 set is representative of the time during which an enzyme and substrate attach, pass through successive intermediate steps, and finally dissociate into enzyme plus products. A macromolecule such as an enzyme, with a molecular weight of about 105, might be expected to undergo on the order of 1015 collisions/set, or about 1012 collisions by ambient molecules during the ES complex lifetime. For each collision there exists a temperature-dependent probability for transfer of translational or internal energy from the colliding molecule to internal degrees of freedom within the enzyme. This excitation represents a localized energy fluctuation which instantaneously places the system thermally out of step with its environment, so that a compensating energy dissipation or relaxation must occur in order to maintain thermodynamic equilibrium. The nature of the relaxation depends upon the structure of the enzyme and upon what internal degrees of freedom have initially been excited. The enzyme contains a sufficiently large number of atoms (of the order of lo*), so that from a structural point of view it may be regarded as a “microscopic crystal” characterized by a quasi-continuous vibrational frequency distribution. The low frequency end of this distribution is associated with delocalized, collective vibrational modes readily amenable to collisional excitation at room temperature (kT-200 cm- l). Also, due to the large number of collisions during the lifetime of the ES complex, there exists an appreciable probability that quanta at the high-frequency end of the distribution be absorbed and subsequently transferred to lower-frequency modes by anharmonic couplings. In general, relaxation of the excited modes constitutes the energy-funneling process which could serve to effect conformational changes in the protein structure. Since units within the enzyme are strongly coupled to each other compared to their coupling with the environment via collisions, one might expect appreciable intramolecular relaxation prior to equilibration with the environment. 319
320
P. E. PHILLIPSON
The dynamical role of vibrational energy in enzyme catalysis can be described, then, in the following way. At a given instant, a substrate bonds with an enzyme molecule at an active site to form an ES complex. Vibrational energy which is funneled to the active site supplies the means by which conformational changes can occur. This permits the ES complex to execute the intermediate steps I%&, ESz, . . each step requiring a specific amount of energy for energetic or entropic purposes. Since there are so many vibrational pathways leading to the active site and such a large choice of vibrational quanta, it should be easy for each step to be provided with the correct energy requirements. The validity of this sequence of events rests upon the following assumptions: (1) the enzyme is typically suited by its very size and specific structure to acquire and channel vibrational energy to centers of catalytic activity; (2) intramolecular vibrational relaxation times are such that the transfer mechanism is effected by statistical energy fluctuations and subsequent relaxation; (3) the energy supplied to the active site possesses a sufficiently broad spectral distribution to meet the multitudinous energetic needs for the successful execution of the required conformational changes; (4) optimal vibrational and vibronic couplings are available for the efficient use of a given amount of supplied energy-the protein must have a specific structure not only for the channeling of the energy, but for its effective employment as well, a type of impedance matching condition. As distinct from past proposals (Moelwyn-Hughes, 1950; Weber, 1955), the point of view taken here is that whole groups of contiguous structures can be modified spatially in regions of the active sites by vibrational energy, the relaxation mechanism being of the irreversible diffusion type. While there exists a belief that electronic and protonic mechanisms familiar in organic chemistry are totally sufficient to explain the int’ricacies of enzyme catalysis (Koshland, 1960), a curious fact possibly supporting the proposed mechanism is that attempts to reproduce enzyme efficiencies with model, small-molecule catalysts have been unsuccessful (Amdur & Hammes, 1966). From an experimental point of view, isotopic substitution of heavy atoms in an enzyme should affect its catalytic activity. Substituted isotopes would constitute impurities which would modify t,he vibrational frequency distribution, tend to create vibrational energy ‘%raps,” modify the funneling process, and afortiori change the availability of vibrational energy for work at the active sites. One might expect,, then, that enzyme extracted from cells grown in an isotopic environment should behave differently as catalysts than normal enzyme. This result would be consistent with the anomalous effects of isotopic substitution on cell division and development (Rittenberg, 1963; Orgel, 1964). Infrared lasers and piezoelectric devices may be expected to provide excellent sources of energy which could be pumped into internal modes of the enzyme. It could be expected that catalytic efficiency would be changed under such influences, since here an outside source of energy would be reinforcing the vibrational processes executed by the enzyme. Experiments are now in progress and further analysis involves a quantum statistical treatment of relaxation mechanisms as they apply to intramolecular conversions in macromolecules. This communication is from the Department of Biophysics (Contribution No. 302) and the Eleanor Roosevelt Institute for Cancer Research, University of Colorado Medical Center, Denver, Colora.do and from the Department of Physics and Astrophysics, Universit,y of Colorado, Boulder, Colorado. The work has been supported in part by a fellow-
LETTERS
ship from the Alfred P. Sloan Foundation the U.S. Public Health Service.
TO
THE
331
EDITOR
and by grents HD-02080
Department of Biophysics University of Colorado Medical Center, Denver, Colorado and Depertment of Physics end Astrophysics University of Colorado, Boulder, Colorsdo, U.S.A.
and GM-l 1123 from
PAUL
E.
PHILLIPSON
Received 6 June 1967, end in revised form 7 August 1967 REFERENCES Amdur, I. L%Hammes, G. G. (1966). Chemical Kinetti: Principles and Selected Topics, p. 183. New York: McGraw-Hill Book Co. Eigen, M. t Hammes, G. G. (1963). Advanc. Enzymol. 25, 1. Koshland, D. E., Jr. (1968). Proc. Nat. Acad. Sci., Wash. 44, 98. Koshland, D. E., Jr. (1960). Advanc. Enzymol. 22, 45. Moelwyn-Hughes, E. A. (1950). In The Enzymes, ed. by J. B. Sumner and K. Myrback, 1st ed., vol. 1, pt. 1, p. 28. New York: Academic Press. Orgel. L. E. (1964). J. Mol. Biol. 9, 208. Phillips, D. C. (1966). Sci. Amer. 215, 78. Rittenberg, D. (1963). J. Chim. Phya. 60, 318. Weber, G. (1955). Discussions Faraday Sot. No. 20, 156.
On the Possible Importance of Relaxation Processes in Enzyme Catalysis In recent years evidence has accumulated to support the notion that conformational changes in protein structure are crucial for successful enzyme catalysis (Koshland, 1958). The enzyme-substrate complex, ES, is thought to pass through a series of successive states ES1, ESz, . . . each of which transforms to the next by means of specific atomic rearrangements and perhaps bond distortions (Eigen & Hammes, 1963; Phillips, 1966). One might expect that such geometrical rearrangements require the fulfillment of stringent energetic, or dynamical conditions: energy must be supplied in an optimal way at the right time to promote these specific conformational changes. The purpose of this note is to investigate the hypothesis that the source of this energy is collisional induced excitation of enzyme vibrational modes followed subsequently by vibrational relaxation. The enzyme is considered to be so constructed as to permit vibrational energy acquired through collisions with molecules of the environment to be funneled to centers of catalytic activity during the lifetime of the ES complex and employed there for interatomic conversions. The funneling process, furthermore, is identified primarily with the mechanism of intramolecular vibrational relaxation. Turnover numbers of enzyme systems (Amdur & Hammes, 1966) suggest that lob3 set is representative of the time during which an enzyme and substrate attach, pass through successive intermediate steps, and finally dissociate into enzyme plus products. A macromolecule such as an enzyme, with a molecular weight of about 105, might be expected to undergo on the order of 1015 collisions/set, or about 1012 collisions by ambient molecules during the ES complex lifetime. For each collision there exists a temperature-dependent probability for transfer of translational or internal energy from the colliding molecule to internal degrees of freedom within the enzyme. This excitation represents a localized energy fluctuation which instantaneously places the system thermally out of step with its environment, so that a compensating energy dissipation or relaxation must occur in order to maintain thermodynamic equilibrium. The nature of the relaxation depends upon the structure of the enzyme and upon what internal degrees of freedom have initially been excited. The enzyme contains a sufficiently large number of atoms (of the order of lo*), so that from a structural point of view it may be regarded as a “microscopic crystal” characterized by a quasi-continuous vibrational frequency distribution. The low frequency end of this distribution is associated with delocalized, collective vibrational modes readily amenable to collisional excitation at room temperature (kT-200 cm- l). Also, due to the large number of collisions during the lifetime of the ES complex, there exists an appreciable probability that quanta at the high-frequency end of the distribution be absorbed and subsequently transferred to lower-frequency modes by anharmonic couplings. In general, relaxation of the excited modes constitutes the energy-funneling process which could serve to effect conformational changes in the protein structure. Since units within the enzyme are strongly coupled to each other compared to their coupling with the environment via collisions, one might expect appreciable intramolecular relaxation prior to equilibration with the environment. 319
320
P. E. PHILLIPSON
The dynamical role of vibrational energy in enzyme catalysis can be described, then, in the following way. At a given instant, a substrate bonds with an enzyme molecule at an active site to form an ES complex. Vibrational energy which is funneled to the active site supplies the means by which conformational changes can occur. This permits the ES complex to execute the intermediate steps I%&, ESz, . . each step requiring a specific amount of energy for energetic or entropic purposes. Since there are so many vibrational pathways leading to the active site and such a large choice of vibrational quanta, it should be easy for each step to be provided with the correct energy requirements. The validity of this sequence of events rests upon the following assumptions: (1) the enzyme is typically suited by its very size and specific structure to acquire and channel vibrational energy to centers of catalytic activity; (2) intramolecular vibrational relaxation times are such that the transfer mechanism is effected by statistical energy fluctuations and subsequent relaxation; (3) the energy supplied to the active site possesses a sufficiently broad spectral distribution to meet the multitudinous energetic needs for the successful execution of the required conformational changes; (4) optimal vibrational and vibronic couplings are available for the efficient use of a given amount of supplied energy-the protein must have a specific structure not only for the channeling of the energy, but for its effective employment as well, a type of impedance matching condition. As distinct from past proposals (Moelwyn-Hughes, 1950; Weber, 1955), the point of view taken here is that whole groups of contiguous structures can be modified spatially in regions of the active sites by vibrational energy, the relaxation mechanism being of the irreversible diffusion type. While there exists a belief that electronic and protonic mechanisms familiar in organic chemistry are totally sufficient to explain the int’ricacies of enzyme catalysis (Koshland, 1960), a curious fact possibly supporting the proposed mechanism is that attempts to reproduce enzyme efficiencies with model, small-molecule catalysts have been unsuccessful (Amdur & Hammes, 1966). From an experimental point of view, isotopic substitution of heavy atoms in an enzyme should affect its catalytic activity. Substituted isotopes would constitute impurities which would modify t,he vibrational frequency distribution, tend to create vibrational energy ‘%raps,” modify the funneling process, and afortiori change the availability of vibrational energy for work at the active sites. One might expect,, then, that enzyme extracted from cells grown in an isotopic environment should behave differently as catalysts than normal enzyme. This result would be consistent with the anomalous effects of isotopic substitution on cell division and development (Rittenberg, 1963; Orgel, 1964). Infrared lasers and piezoelectric devices may be expected to provide excellent sources of energy which could be pumped into internal modes of the enzyme. It could be expected that catalytic efficiency would be changed under such influences, since here an outside source of energy would be reinforcing the vibrational processes executed by the enzyme. Experiments are now in progress and further analysis involves a quantum statistical treatment of relaxation mechanisms as they apply to intramolecular conversions in macromolecules. This communication is from the Department of Biophysics (Contribution No. 302) and the Eleanor Roosevelt Institute for Cancer Research, University of Colorado Medical Center, Denver, Colora.do and from the Department of Physics and Astrophysics, Universit,y of Colorado, Boulder, Colorado. The work has been supported in part by a fellow-
LETTERS
ship from the Alfred P. Sloan Foundation the U.S. Public Health Service.
TO
THE
331
EDITOR
and by grents HD-02080
Department of Biophysics University of Colorado Medical Center, Denver, Colorado and Depertment of Physics end Astrophysics University of Colorado, Boulder, Colorsdo, U.S.A.
and GM-l 1123 from
PAUL
E.
PHILLIPSON
Received 6 June 1967, end in revised form 7 August 1967 REFERENCES Amdur, I. L%Hammes, G. G. (1966). Chemical Kinetti: Principles and Selected Topics, p. 183. New York: McGraw-Hill Book Co. Eigen, M. t Hammes, G. G. (1963). Advanc. Enzymol. 25, 1. Koshland, D. E., Jr. (1968). Proc. Nat. Acad. Sci., Wash. 44, 98. Koshland, D. E., Jr. (1960). Advanc. Enzymol. 22, 45. Moelwyn-Hughes, E. A. (1950). In The Enzymes, ed. by J. B. Sumner and K. Myrback, 1st ed., vol. 1, pt. 1, p. 28. New York: Academic Press. Orgel. L. E. (1964). J. Mol. Biol. 9, 208. Phillips, D. C. (1966). Sci. Amer. 215, 78. Rittenberg, D. (1963). J. Chim. Phya. 60, 318. Weber, G. (1955). Discussions Faraday Sot. No. 20, 156.