Subscriber access provided by University of Massachusetts Amherst Libraries
New Concept
On the Temperature Dependence of Enzyme-catalyzed Rates Vickery L. Arcus, Erica J. Prentice, Joanne K. Hobbs, Adrian J. Mulholland, Marc W. van der Kamp, Christopher Roland Pudney, Emily J. Parker, and Louis A. Schipper Biochemistry, Just Accepted Manuscript • DOI: 10.1021/acs.biochem.5b01094 • Publication Date (Web): 16 Feb 2016 Downloaded from http://pubs.acs.org on February 20, 2016
Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Biochemistry is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.
Page 1 of 32
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Biochemistry
On the Temperature Dependence of Enzyme-catalyzed Rates Vickery L. Arcus,*,1 Erica J. Prentice,1 Joanne K. Hobbs,†,1 Adrian J. Mulholland,3 Marc W. Van der Kamp,3,4 Christopher R. Pudney,5 Emily J. Parker2 and Louis A. Schipper1 1
School of Science, University of Waikato, Hamilton 3240, New Zealand
2
Biomolecular Interaction Centre and Department of Chemistry, University of Canterbury,
Christchurch 8041, New Zealand 3
School of Chemistry and 4School of Biochemistry, University of Bristol, Cantock’s Close,
Bristol BS8 1TS, United Kingdom 5
Department of Biology and Biochemistry, University of Bath, Claverton Down, Bath BA2 7AY,
United Kingdom *Corresponding author:
[email protected] †Present address: Department of Biochemistry and Microbiology, University of Victoria, Victoria, British Columbia, Canada
KEYWORDS Enzyme catalysis, temperature, macromolecular rate theory (MMRT), enzyme size, psychrophile, mesophile, thermophile, Eyring equation, transition state theory.
ACS Paragon Plus Environment
1
Biochemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 2 of 32
ABSTRACT
One of the critical variables that determine the rate of any reaction is temperature. For biological systems, the effects of temperature are convoluted with myriad (and often opposing) contributions from enzyme catalysis, protein stability and temperature-dependent regulation, for example. We have coined the phrase “macromolecular rate theory (MMRT)” to describe the temperature dependence of enzyme-catalyzed rates independent of stability or regulatory processes. Central to MMRT is the observation that enzyme-catalyzed reactions occur with significant values of ∆Cp‡ that are in general negative. That is, the heat capacity (Cp) for the enzyme-substrate complex is generally larger than Cp for the enzyme-transition state complex. Consistent with a classical description of enzyme catalysis, a negative value for ∆Cp‡ is the result of the enzyme binding relatively weakly to the substrate and very tightly to the transition state. This observation of negative ∆Cp‡ has important implications for the temperature dependence of enzyme-catalyzed rates. Here, we lay out the fundamentals of MMRT. We present a number of hypotheses that arise directly from MMRT including a theoretical justification for the large size of enzymes and the basis for their optimum temperatures. We rationalize the behavior of psychrophilic enzymes and describe a “psychrophilic trap” which places limits on the evolution of enzymes in low temperature environments. One of the defining characteristics of biology is catalysis of chemical reactions by enzymes and enzymes drive much of metabolism. Therefore we also expect to see characteristics of MMRT at the level of cells, whole organisms and even ecosystems.
ACS Paragon Plus Environment
2
Page 3 of 32
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Biochemistry
The rate of any chemical reaction is a function of the temperature (T) and the energy difference between the reactants and the transition state, the so-called activation energy (Ea). Arrhenius was the first to formalize this relationship in the 19th century (based on empirical observations) with his famous eponymous equation k=Aexp(−Ea/RT), where k is the rate constant and R is the universal gas constant. Early in the 20th century, the development of transition state theory (TST) by Eyring, Polanyi and others led to the Eyring equation for rate constants (equation 1 for a first order rate constant, where ∆G‡ is the change in Gibbs free energy between reactants and the transition state, kB and h are Boltzmann’s and Planck’s constants respectively, and κ is the transmission coefficient, hereafter assumed to be 1 for simplicity. For a more general definition in terms of partition functions see e.g. reference 1).1 This led to an understanding of, and statistical mechanical justification of the terms in the Arrhenius expression. The Arrhenius and Eyring equations are found in most modern (bio)chemistry textbooks and provide an excellent description of the temperature dependence of a wide array of chemical processes.1 The Eyring equation in its simplest form is sufficient for our purposes here (equation 1). An assumption often made with respect to equation 1 is that ∆H‡ and ∆S‡ are independent of temperature (and hence that ∆G‡ varies with temperature according to the Gibbs equation: ∆G‡ = ∆H‡ − T∆S‡). Indeed, this assumption holds well for many reactions involving small molecules in standard solvents. However, a number of investigators have noted deviations from linearity when plotting equation 1 for enzyme-catalysed rates suggesting that the above assumption is not valid and that there is a more complex temperature dependence for these systems.1,2 Enzymes are flexible macromolecules of high molecular weight and with correspondingly high heat capacities (Cp). For example, the heat capacity for folded proteins is estimated to be ~45 J.mol−1.K−1 per amino acid3 and thus a typical enzyme of molecular weight 65 kDa will have a
ACS Paragon Plus Environment
3
Biochemistry
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Page 4 of 32
heat capacity in water of ~25,300 J.mol−1.K−1 (for comparison, liquid water has Cp = 76 J.mol−1.K−1 at 25 °C).
=
∆ ‡
=
∆‡
∆ ‡ = ∆‡ + ∆‡ − − ∆
=
!" = !"
∆‡
‡
(1)
+ ∆‡ !" − !"
(2)
‡ ‡ ‡ ‡
∆ ∆$% ∆ '∆$% () () # & *
∆,‡ &∆-%‡ .
−+
/
(3)
∆1‡ &∆-%‡ 23.23
0++
/
0
(4)
The heat capacity (Cp) of a system is a fundamental thermodynamic parameter that quantifies the temperature dependence of the enthalpy (H) and entropy (S) according to equation 2 and incorporation of a ∆Cp‡ term into the Eyring equation (equation 1) gives equations 3 & 4. If ∆Cp‡ = 0, equation 3 collapses into equation 1. However, for reactions catalyzed by enzymes with high heat capacities, the ∆Cp‡ term may be non-zero and equations 3 & 4 should be implemented. Is there a difference in heat capacity between the enzyme-substrate and enzyme-transition state species for enzyme-catalyzed reactions (i.e. is ∆Cp‡ non-zero for enzyme-catalyzed reactions)? If so, what are the consequences for the temperature dependence of enzyme catalyzed rates? We have previously demonstrated that enzymatically catalyzed rates proceed with negative values of ∆Cp‡ ranging from −1 to −12 kJ.mol−1.K−1 (independent of denaturation)4 and we have coined the phrase macromolecular rate theory (MMRT) to reflect this unusual thermodynamic property of biochemical reactions.5,6 MMRT has significant implications for the temperature dependence of enzyme catalyzed rates and for the rates of biologically driven processes in general, such as microbial growth, respiration and photosynthesis. MMRT unifies a number of
ACS Paragon Plus Environment
4
Page 5 of 32
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Biochemistry
disparate observations with respect to thermophilic, mesophilic and psychrophilic enzymes and also presents some surprising hypotheses. Here, we lay out the basis for MMRT and present new hypotheses based on MMRT that warrant further experimental verification. We also use MMRT to provide a theoretical argument for relative size of enzymes according to the chemistry that they catalyze.
Macromolecular heat capacity The internal energy of a system is partitioned between translational, rotational, vibrational and electronic modes. The heat capacity C is formally the change in internal energy with a change in temperature and is a measure of the capacity for the translational, rotational, vibrational and electronic modes to absorb energy. For systems in water at biologically relevant temperatures (−20
