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1.
Two forms of the equation for expression of the rate constant for electron transfer through a Marcus-type treatment are discussed. In the first (exergonic) form, the Arrhenius exponential term was replaced by its classical Marcus term; in the second (endergonic) form, the forward rate constant was replaced by the reverse rate constant (the forward rate constant in the exergonic direction), which was expanded to an equivalent Marcus term and multiplied by the equilibrium constant. When the classical Marcus treatment was used, these two forms of the rate equation give identical curves relating the logarithm of the rate constant to the driving force. The Marcus term for the relation between activation free-energy, ΔG#, reorganization energy, λ, and driving force, ΔGo, derived from parabolas for the reactant and product states, was identical when starting from exergonic or endergonic parabolas. Moser and colleagues introduced a quantum mechanical correction factor to the Marcus term in order to fit experimental data. When the same correction factor was applied in the treatment for the endergonic direction by Page and colleagues, a different curve was obtained from that found with the exergonic form. We show that the difference resulted from an algebraic error in development of the endergonic equation. 相似文献
2.
Ricquier D 《Comptes rendus biologies》2006,329(8):578-86; discussion 653-5
Thermogenesis is an obligatory consequence of cellular metabolism and is identified as a unique property of homeotherms which have to maintain constant their body temperature in a cold environment. Physiologically, thermogenesis is made of basal metabolism, post-prandial thermogenesis, exercise-induced thermogenesis and adaptive thermogenesis induced by changes in the environmental temperature. Biochemically, thermogenesis comes from exergonic reactions from a loose coupling between endergonic and exergonic reactions. In cells, respiration and oxidations occur in mitochondria which ensure the coupling of oxidative energy to ATP synthesis. Identification of mitochondrial uncoupling proteins UCP allowed further understanding of the mechanism of coupling or uncoupling of respiration to ADP phosphorylation. Such data maybe of help in the understanding, or possible treatment, of certain types of obesity. 相似文献
3.
Protein folding is regarded as a quantum transition between the torsion states of a polypeptide chain. According to the quantum
theory of conformational dynamics, we propose the dynamical contact order (DCO) defined as a characteristic of the contact
described by the moment of inertia and the torsion potential energy of the polypeptide chain between contact residues. Consequently,
the protein folding rate can be quantitatively studied from the point of view of dynamics. By comparing theoretical calculations
and experimental data on the folding rate of 80 proteins, we successfully validate the view that protein folding is a quantum
conformational transition. We conclude that (i) a correlation between the protein folding rate and the contact inertial moment
exists; (ii) multi-state protein folding can be regarded as a quantum conformational transition similar to that of two-state
proteins but with an intermediate delay. We have estimated the order of magnitude of the time delay; (iii) folding can be
classified into two types, exergonic and endergonic. Most of the two-state proteins with higher folding rate are exergonic
and most of the multi-state proteins with low folding rate are endergonic. The folding speed limit is determined by exergonic
folding. 相似文献
4.
The dynamics of Brownian motion has widespread applications extending from transport in designed micro-channels up to its prominent role for inducing transport in molecular motors and Brownian motors. Here, Brownian transport is studied in micro-sized, two-dimensional periodic channels, exhibiting periodically varying cross-sections. The particles in addition are subjected to an external force acting alongside the direction of the longitudinal channel axis. For a fixed channel geometry, the dynamics of the two-dimensional problem is characterized by a single dimensionless parameter which is proportional to the ratio of the applied force and the temperature of the particle environment. In such structures entropic effects may play a dominant role. Under certain conditions the two-dimensional dynamics can be approximated by an effective one-dimensional motion of the particle in the longitudinal direction. The Langevin equation describing this reduced, one-dimensional process is of the type of the Fick-Jacobs equation. It contains an entropic potential determined by the varying extension of the eliminated channel direction, and a correction to the diffusion constant that introduces a space dependent diffusion. Different forms of this correction term have been suggested before, which we here compare for a particular class of models. We analyze the regime of validity of the Fick-Jacobs equation, both by means of analytical estimates and the comparisons with numerical results for the full two-dimensional stochastic dynamics. For the nonlinear mobility we find a temperature dependence which is opposite to that known for particle transport in periodic potentials. The influence of entropic effects is discussed for both, the nonlinear mobility and the effective diffusion constant. 相似文献
5.
Thiosulfate respiration in Salmonella enterica serovar Typhimurium is catalyzed by the membrane-bound enzyme thiosulfate reductase. Experiments with quinone biosynthesis mutants show that menaquinol is the sole electron donor to thiosulfate reductase. However, the reduction of thiosulfate by menaquinol is highly endergonic under standard conditions (ΔE°' = -328 mV). Thiosulfate reductase activity was found to depend on the proton motive force (PMF) across the cytoplasmic membrane. A structural model for thiosulfate reductase suggests that the PMF drives endergonic electron flow within the enzyme by a reverse loop mechanism. Thiosulfate reductase was able to catalyze the combined oxidation of sulfide and sulfite to thiosulfate in a reverse of the physiological reaction. In contrast to the forward reaction the exergonic thiosulfate-forming reaction was PMF independent. Electron transfer from formate to thiosulfate in whole cells occurs predominantly by intraspecies hydrogen transfer. 相似文献
6.
An analytic potential function consistent with the Marcus equation for activation energy is formulated and used to reveal new insights into the activation process in chemical reactions. As for the Marcus equation, the new potential function depends only on two parameters, the reaction energy and the activation energy (or the so-called Marcus intrinsic activation energy). Combination of the Marcus potential with the reaction force analysis provides two-parameter analytic expressions for the reaction force, reaction force constant, and reaction works. Moreover, since the parameters necessary to define the Marcus potential energy function can be obtained experimentally, the present model may produce experimental analytic potentials allowing for new and interesting applications, thus emerging as a powerful tool to characterize activation processes in chemical reactions. 相似文献
7.
Protein solubility can be adequately represented by the classical Cohn equation for the salting-out of alcohol dehydrogenase and fumarase from clarified yeast homogenate with ammonium sulfate. However, the constant β in this equation is a function of the contacting procedure employed. The kinetics of continuous salting-out were similar for alcohol dehydrogenase and fumarase. The overall rate equation for precipitation had a variable order which was high initially, up to 3.1, but approached unity on completion of precipitation. This was followed by a partial resolution stage which was first order with respect to the concentration driving force. Precipitate particle size was estimated as 0.5 to 5 μm with continuous flow precipitation producing the largest particles. 相似文献
8.
Succinate:quinone reductases are membrane-bound enzymes that catalyze electron transfer from succinate to quinone. Some enzymes in vivo reduce ubiquinone (exergonic reaction) whereas others reduce menaquinone (endergonic reaction). The succinate:menaquinone reductases all contain two heme groups in the membrane anchor of the enzyme: a proximal heme (heme b(P)) located close to the negative side of the membrane and a distal heme (heme b(D)) located close to the positive side of the membrane. Heme b(D) is a distinctive feature of the succinate:menaquinone reductases, but the role of this heme in electron transfer to quinone has not previously been analyzed. His28 and His113 are the axial ligands to heme b(D) in Bacillus subtilis succinate:menaquinone reductase. We have individually replaced these His residues with Leu and Met, respectively, resulting in assembled membrane-bound enzymes. The H28L mutant enzyme lacks succinate:quinone reductase activity probably due to a defective quinone binding site. The H113M mutant enzyme contains heme b(D) with raised midpoint potential and is impaired in electron transfer to menaquinone. Our combined experimental data show that the heme b(D) center, into which we include a quinone binding site, is crucial for succinate:menaquinone reductase activity. The results support a model in which menaquinone is reduced on the positive side of the membrane and the transmembrane electrochemical potential provides driving force for electron transfer from succinate via heme b(P) and heme b(D) to menaquinone. 相似文献
9.
Thomas Hillen 《Journal of mathematical biology》1996,35(1):49-72
If in the classical Turing model the diffusion process (Brownian motion) is replaced by a more general correlated random
walk, then the parameters describing spatial spread are the particle speeds and the rates of change in direction. As in the
Turing model, a spatially constant equilibrium can become unstable if the different species have different turning rates and
different speeds. Furthermore, a Hopf bifurcation can be found if the reproduction rate of the activator is greater than its
rate of change of direction, and oscillating patterns are possible.
Received 24 February 1995; received in revised form 6 September 1995 相似文献
10.
Crofts AR 《Biochimica et biophysica acta》2004,1655(1-3):77-92
The rate-limiting reaction of the bc(1) complex from Rhodobacter sphaeroides is transfer of the first electron from ubihydroquinone (quinol, QH(2)) to the [2Fe-2S] cluster of the Rieske iron-sulfur protein (ISP) at the Q(o)-site. Formation of the ES-complex requires participation of two substrates (S), QH(2) and ISP(ox). From the variation of rate with [S], the binding constants for both substrates involved in formation of the complex can be estimated. The configuration of the ES-complex likely involves the dissociated form of the oxidized ISP (ISP(ox)) docked at the b-interface on cyt b, in a complex in which N(epsilon) of His-161 (bovine sequence) forms a H-bond with the quinol -OH. A coupled proton and electron transfer occurs along this H-bond. This brief review discusses the information available on the nature of this reaction from kinetic, structural and mutagenesis studies. The rate is much slower than expected from the distance involved, likely because it is controlled by the low probability of finding the proton in the configuration required for electron transfer. A simplified treatment of the activation barrier is developed in terms of a probability function determined by the Br?nsted relationship, and a Marcus treatment of the electron transfer step. Incorporation of this relationship into a computer model allows exploration of the energy landscape. A set of parameters including reasonable values for activation energy, reorganization energy, distances between reactants, and driving forces, all consistent with experimental data, explains why the rate is slow, and accounts for the altered kinetics in mutant strains in which the driving force and energy profile are modified by changes in E(m) and/or pK of ISP or heme b(L). 相似文献
11.
Effects of Temperature and ΔG° on Electron Transfer from Cytochrome c2 to the Photosynthetic Reaction Center of the Purple Bacterium Rhodobacter sphaeroides
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G. Venturoli F. Drepper J.C. Williams J.P. Allen X. Lin P. Mathis 《Biophysical journal》1998,74(6):3226-3240
The kinetics of electron transfer from cytochrome c2 to the primary donor (P) of the reaction center from the photosynthetic purple bacterium Rhodobacter sphaeroides have been investigated by time-resolved absorption spectroscopy. Rereduction of P+ induced by a laser pulse has been measured at temperatures from 300 K to 220 K in a series of specifically mutated reaction centers characterized by altered midpoint redox potentials of P+/P varying from 410 mV to 765 mV (as compared to 505 mV for wild type). Rate constants for first-order electron donation within preformed reaction center–cytochrome c2 complexes and for the bimolecular oxidation of free cytochrome c2 have been obtained by multiexponential deconvolution of the kinetics. At all temperatures the rate of the fastest intracomplex electron transfer increases by more than two orders of magnitude as the driving force −ΔG° is varied over a range of 350 meV. The temperature and ΔG° dependences of the rate constant fit the Marcus equation well. Global analysis yields a reorganization energy λ = 0.96 ± 0.07 eV and a set of electronic matrix elements, specific for each mutant, ranging from 1.2 10−4 eV to 2.5 10−4 eV. Analysis in terms of the Jortner equation indicates that the best fit is obtained in the classical limit and restricts the range of coupled vibrational modes to frequencies lower than ∼200 cm−1. An additional slower kinetic component of P+ reduction, attributed to electron transfer from cyt c2 docked in a nonoptimal configuration of the complex, displays a Marcus type dependence of the rate constant upon ΔG°, characterized by a similar value of λ (0.8 ± 0.1 eV) and by an average electronic matrix element smaller by more than one order of magnitude. In all of the mutants, as the temperature is decreased below 260 K, both intracomplex reactions are abruptly inhibited, their rate being negligible at 220 K. The free energy dependence of the second-order rate constant for oxidation of cyt c2 in solution suggests that the collisional reaction is partially diffusion controlled, reaching the diffusion limit at exothermicities between 150 and 250 meV over the temperature range investigated. 相似文献
12.
First evidence for existence of an uphill electron transfer through the bc(1) and NADH-Q oxidoreductase complexes of the acidophilic obligate chemolithotrophic ferrous ion-oxidizing bacterium Thiobacillus ferrooxidans 总被引:1,自引:0,他引:1
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The energy-dependent electron transfer pathway involved in the reduction of pyridine nucleotides which is required for CO(2) fixation to occur in the acidophilic chemolithotrophic organism Thiobacillus ferrooxidans was investigated using ferrocytochrome c as the electron donor. The experimental results show that this uphill pathway involves a bc(1) and an NADH-Q oxidoreductase complex functioning in reverse, using an electrochemical proton gradient generated by ATP hydrolysis. Based on these results, a model is presented to explain the balance of the reducing equivalent from ferrocytochrome c between the exergonic and endergonic electron transfer pathways. 相似文献
13.
1. The rate of exosmosis of water was studied in unfertilized Arbacia eggs, in order to bring out possible differences between the kinetics of exosmosis and endosmosis. 2. Exosmosis, like endosmosis, is found to follow the equation See PDF for Equation, in which a is the total volume of water that will leave the cell before osmotic equilibrium is attained, x is the volume that has already left the cell at time t, and k is the velocity constant. 3. The velocity constants of the two processes are equal, provided the salt concentration of the medium is the same. 4. The temperature characteristic of exosmosis, as of endomosis, is high. 5. It is concluded that the kinetics of exosmosis and endosmosis of water in these cells are identical, the only difference in the processes being in the direction of the driving force of osmotic pressure. 相似文献
14.
Photosystem I is a large macromolecular complex located in the thylakoid membranes of chloroplasts and in cyanobacteria that catalyses the light driven reduction of ferredoxin and oxidation of plastocyanin. Due to the very negative redox potential of the primary electron transfer cofactors accepting electrons, direct estimation by redox titration of the energetics of the system is hampered. However, the rates of electron transfer reactions are related to the thermodynamic properties of the system. Hence, several spectroscopic and biochemical techniques have been employed, in combination with the classical Marcus theory for electron transfer tunnelling, in order to access these parameters. Nevertheless, the values which have been presented are very variable. In particular, for the case of the tightly bound phylloquinone molecule A(1), the values of the redox potentials reported in the literature vary over a range of about 350 mV. Previous models of Photosystem I have assumed a unidirectional electron transfer model. In the present study, experimental evidence obtained by means of time resolved absorption, photovoltage, and electron paramagnetic resonance measurements are reviewed and analysed in terms of a bi-directional kinetic model for electron transfer reactions. This model takes into consideration the thermodynamic equilibrium between the iron-sulfur centre F(X) and the phylloquinone bound to either the PsaA (A(1A)) or the PsaB (A(1B)) subunit of the reaction centre and the equilibrium between the iron-sulfur centres F(A) and F(B). The experimentally determined decay lifetimes in the range of sub-picosecond to the microsecond time domains can be satisfactorily simulated, taking into consideration the edge-to-edge distances between redox cofactors and driving forces reported in the literature. The only exception to this general behaviour is the case of phylloquinone (A(1)) reoxidation. In order to describe the reported rates of the biphasic decay, of about 20 and 200 ns, associated with this electron transfer step, the redox potentials of the quinones are estimated to be almost isoenergetic with that of the iron sulfur centre F(X). A driving force in the range of 5 to 15 meV is estimated for these reactions, being slightly exergonic in the case of the A(1B) quinone and slightly endergonic, in the case of the A(1A) quinone. The simulation presented in this analysis not only describes the kinetic data obtained for the wild type samples at room temperature and is consistent with estimates of activation energy by the analysis of temperature dependence, but can also explain the effect of the mutations around the PsaB quinone binding pocket. A model of the overall energetics of the system is derived, which suggests that the only substantially irreversible electron transfer reactions are the reoxidation of A(0) on both electron transfer branches and the reduction of F(A) by F(X). 相似文献
15.
When two or more tight-binding inhibitors are present in an enzyme assay, the equation that relates the initial velocity v to the concentration of reactants cannot be written in an algebraically explicit form. Rather, for n inhibitors it is an implicit polynomial equation of degree n + 1 with respect to v. The complexity of the polynomial coefficients dramatically increases with each added inhibitor. Solving the transcendental rate equation by traditional methods of numerical mathematics has proven tedious because of the sensitivity of these methods to initial estimates and because of the existence of multiple roots. However, the equation can be rearranged into a convenient recursive form, one in which the velocity appears on both sides and the solution is found iteratively. The algebraic form of the recursive rate equation is remarkably simple and differs from the rate equation for classical rather than tight-binding inhibition only by an added term. The numerical stability and the speed of convergence were tested on the case of two competitive inhibitors. Initial estimates of velocity that spanned 12 orders of magnitude converged within five iterations. The velocities computed with the recursive method for a single tight-binding inhibitor were identical with the values predicted by the Morrison equation. The method is used to analyze experimental data for the inhibition of rat liver dihydrofolate reductase by mixtures of the anticancer drug methotrexate and its metabolic precursor form, methotrexate-alpha-aspartate (a prodrug). 相似文献
16.
The cytochrome (cyt) subunit of the photosynthetic reaction center from Rhodopseudomonas viridis contains four heme groups in a linear arrangement in the spatial order heme1, heme2, heme4, and heme3. Heme3 is the direct electron donor to the photooxidized primary electron donor (special pair, P(+)). This heme has the highest redox potential (E(m)) among the hemes in the cyt subunit. The E(m) of heme3 has been specifically lowered by site-directed mutagenesis in which the Arg residue at the position of 264 of the cyt was replaced by Lys. The mutation decreases the E(m) of heme3 from +380 to +270 mV, i.e., below that of heme2 (+320 mV). In addition, a blue shift of the alpha-band was found to accompany the mutation. The assignment of the lowered E(m) and the shifted alpha-band to heme3 was confirmed by spectroscopic measurements on RC crystals. The structure of the mutant RC has been determined by X-ray crystallography. No remarkable differences were found in the structure apart from the mutated residue itself. The velocity of the electron transfer (ET) from the tetraheme cyt to P(+) was measured under several redox conditions by following the rereduction of P(+) at 1283 nm after a laser flash. Heme3 donates an electron to P(+) with t(1/2) = 105 ns, i.e., faster than in the wild-type reaction center (t(1/2) = 190 ns), as expected from the larger driving force. The main feature is that a phase with t(1/2) approximately 2 micros dominates when heme3 is oxidized but heme2 is reduced. We conclude that the ET from heme2 to heme3 has a t(1/2) of approximately 2 micros, i.e., the same as in the WT, despite the fact that the reaction is endergonic by 50 meV instead of exergonic by 60 meV. We propose that the reaction kinetics is limited by the very uphill ET from heme2 to heme4, the DeltaG degrees of which is about the same (+230 meV) in both cases. The interpretation is further supported by measurements of the activation energy (216 meV in the wild-type, 236 meV in the mutant) and by approximate calculations of ET rates. Altogether these results demonstrate that the ET from heme2 to heme3 is stepwise, starting with a first very endergonic step from heme2 to heme4. 相似文献
17.
The classical Michaelis-Menten model is widely used as the basis for modeling of a number of biological systems. As the model does not consider the inhibitory effect of endproducts that accumulate in virtually all bioprocesses, it is often modified to prevent the overestimation of reaction rates when products have accumulated. Traditional approaches of model modification use the inclusion of irreversible, competitive, and noncompetitive inhibition factors. This article demonstrates that these inhibition factors are insufficient to predict product inhibition of reactions that are close the dynamic equilibrium. All models investigated were found to violate thermodynamic laws as they predicted positive reaction rates for reactions that were endergonic due to high endproduct concentrations. For modeling of biological processes that operate close to the dynamic equilibrium (e.g., anaerobic processes), it is critical to prevent the prediction of positive reaction rates when the reaction has already reached the dynamic equilibrium. This can be achieved by using a reversible kinetic model. However, the major drawback of the reversible kinetic model is the large number of empirical parameters it requires. These parameters are difficult to determine and prone to experimental error. For this reason, the reversible model is not practical in the modeling of biological processes.This article uses the fundamentals of steady-state kinetics and thermodynamics to establish an equation for the reversible kinetic model that is of practical use in bio-process modeling. The behavior of this equilibrium-based model is compared with Michaelis-Menten-based models that use traditional inhibition factors. The equilibrium-based model did not require any empirical inhibition factor to correctly predict when reaction rates must be zero due to the free energy change being zero. For highly exergonic reactions, the equilibrium-based model did not deviate significantly from the Michaelis-Menten model, whereas, for reactions close to equilibrium, the reaction rate was mainly controlled by the quotient of mass action ratio (concentration of all products over concentration of all substrates) over the equilibrium constant K. This quotient is a measure of the displacement of the reaction from its equilibrium. As the new equation takes into account all of the substrates and products, it was able to predict the inhibitor effect of multiple endproducts. The model described is designed to be a useful basis for a number of different model applications where reaction conditions are close to equilibrium. 相似文献
18.
Cell suspensions of methanogenic bacteria (Methanosarcina barkeri, Methanospirillum hungatei, Methano-brevibacter arboriphilus, and Methanobacterium thermoautotrophicum) were found to form CO from CO2 and H2 according to the reaction: CO2 + H2----CO + H2O; delta G0 = +20 kJ/mol. Up to 15,000 ppm CO in the gas phase were reached which is significantly higher than the equilibrium concentration calculated from delta G0 (95 ppm under the experimental conditions). This indicated that CO2 reduction with H2 to CO is energy-driven and indeed the cells only generated CO when forming CH4. The coupling of the two reactions was studied in more detail with acetate-grown cells of M. barkeri using methanogenic substrates. The effects of the protonophore tetrachlorosalicylanilide (TCS) and of the proton-translocating ATPase inhibitor N,N'-dicyclohexylcarbodiimide (cHxN)2C were determined. TCS completely inhibited CO formation from CO2 and H2 without affecting methanogenesis from CH3OH and H2. In the presence of the protonophore the proton motive force delta p and the intracellular ATP concentration were very low. (cHxN)2C, which partially inhibited methanogenesis from CH3OH and H2, had no effect on CO2 reduction to CO. In the presence of (cHxN)2C delta p was high and the intracellular ATP content was low. These findings suggest that the endergonic formation of CO from CO2 and H2 is coupled to the exergonic formation of CH4 from CH3OH and H2 via the proton motive force and not via ATP. CO formation was not stimulated by the addition of sodium ions. 相似文献
19.
Pyruvate:ferredoxin oxidoreductase (PFOR) catalyzes the coenzyme A (CoA)-dependent oxidative decarboxylation of pyruvate. In many autotrophic anaerobes, PFOR links the Wood-Ljungdahl pathway to glycolysis and to cell carbon synthesis. Herein, we cloned and sequenced the M. thermoacetica PFOR, demonstrating strong structural homology with the structurally characterized D. africanus PFOR, including the presence of three [4Fe-4S] clusters per monomeric unit. The PFOR reaction includes a hydroxyethyl-thiamin pyrophosphate (HE-TPP) radical intermediate, which forms rapidly after PFOR reacts with pyruvate. This step precedes electron transfer from the HE-TPP radical intermediate to an intramolecular [4Fe-4S] cluster. We show that CoA increases the rate of this redox reaction by 10(5)-fold. Analysis by Marcus theory indicates that, in the absence of CoA, this is a true electron-transfer reaction; however, in its presence, electron transfer is gated by an adiabatic event. Analysis by the Eyring equation indicates that entropic effects dominate this rate enhancement. Our results indicate that the energy of binding CoA contributes minimally to the rate increase since the thiol group of CoA lends over 40 kJ/mol to the reaction, whereas components of CoA that afford most of the cofactor's binding energy contribute minimally. Major conformational changes also do not appear to explain the rate enhancement. We propose several ways that CoA can accomplish this rate increase, including formation of a highly reducing adduct with the HE-TPP radical to increase the driving force for electron transfer. We also consider the possibility that CoA itself forms part of the electron-transfer pathway. 相似文献
20.
The role of Thr-113 of Escherichia coli dihydrofolate reductase in binding and catalysis was probed by amino acid substitution. Thr-113, a strictly conserved residue that forms a hydrogen bond to the active-site Asp-27 and to the amino group of methotrexate through a fixed water molecule, was replaced by valine. The kinetic scheme is identical in form with the wild-type scheme, although many of the rate constants vary, including a decrease in the association rate constants and an increase in the dissociation rate constants for folate ligands, a decrease in the hydride-transfer rate constant in both directions, and an increase in the intrinsic pKa of Asp-27. Overall, replacement of Thr-113 by Val decreases the binding of folate substrates by approximately 2.3 kcal/mol. These multiple complex changes on various ground and transition states underscore the optimal properties of a strictly conserved residue in the evolution of catalytic function. 相似文献