Clarification of calorimetric and van 't hoff enthalpies for evaluation of protein transition states

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SExposure of the skin and particularly the eyes to the high intensity UV light from the transilluminator is extremely hazardous: a visor should be worn ~'Marano, M R and Carrillo, N (1992) Plant Physiol 100, 1103-1113

0307-4412(94)00070-0

Clarification of Calorimetric and van 't Hoff Enthalpies for Evaluation of Protein Transition States A A SABOURY and A A MOOSAVI-MOVAHEDI

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Institute of Biochemistry & Biophysics University of Tehran Iron

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Introduction A very useful criterion for two-state behavior in equilibrium

A m o u n t of RNA 0zg) Native ~ Denatured

Figure 3 Plot of relative optical density (arbitrary units) vs amount of RNA. The autoradiogram in Figure 2 was scanned using a Gilford Response II spectrophotometer and the integrated peak areas were plotted

Discussion Classical northern protocols do not include staining R N A after electrophoresis. I,z,4 Since visualization of R N A potentially offers many advantages, we have re-evaluated and improved the staining of R N A with EtBr in our simplified procedure. The staining method described here allows evaluation of the integrity of the R N A , which can be easily recognized by the absence of smearing and the presence of high molecular weight r R N A bands (Fig 2). Addition of the dye to the gel or to the sample gave similar results with respect to the quality of visualization. In this modification we eliminate denaturation of the R N A with glyoxal or formamide I and the subsequent treatment of whole gel after electrophoresis. Omission of the denaturation step had no effect on the electrophoretic mobility of R N A molecules (Fig 2), indicating that the presence of formaldehyde in the gel is sufficient to keep the R N A molecules in a denatured state throughout electrophoresis. In addition, the r R N A bands can be directly visualized in the nylon membranes under UV light (data not shown). The modifications described here allow quicker, easier, sensitive and reproducible northern analysis. Results described here were obtained with total cellular R N A isolated from vascular plants. R N A from several different s o u r c e s , including amphibian gastrula from Bufo arenarum L, E coli and Bacillus subtilis, gave essentially the same results.

is the comparison between the calorimetric enthalpy change (AHcal), and that evaluated by the van 't Hoff equation (AHvH). If AHcal = AHvH, or on the o t h e r h a n d AHvH/AHca~ = 1, the

transition is assumed to be of the two-state type. That is, the native form of a macromolecule is converted directly to the denatured form, without passing through an intermediate. I-2 The existence of intermediates in the transition from the native form to the denatured form increases the overall equilibrium constant of process, and this tends to decrease of AHvH. Therefore, for multi-state process the behavior shown will be AHvH/AHc~I < 1.

Discussion In a two-state process the native form of macromolecule is converted directly to the denatured form: N~KD

(1)

If Y is the fraction of macromolecule in denatured form, then the equilibrium constant of this process can be written K = [D] _ Y [N] 1- Y

(2)

The enthalpy change in this process can be calculated by the van 't Hoff equation 3 I n K = - AHv_.H 1 + lna R T

Acknowledgements

(3)

In c~ = Constant

The authors would like to thank the students in the Department of

Biology for their imput and interest in this practical over the last years or

References and Notes 1Maniatis, T, Fritseh, E F and Sambrook, J (1982) Molecular Cloning. A Laboratory Manual, Cold Spring Harbor Laboratory Press, Cold

Spring Harbor, NY 2Logemann, J, SeheU, J and Willmitzer, L (1987) Anal Biochem 163, 1620 3Unless high quality phenol is available, it should be distilled before use. The working solution is neutralized by several extractions with 1 M Tris-Cl pH 8.0 and finally saturated in 0.1 M Tris-Cl pH 8.0 4Lehrach, H, Diamond, D, Wozney, J M and Boedtker, H (1977) Biochemistry 16, 4743-4751

B I O C H E M I C A L E D U C A T I O N 22(4) 1994

AHvH = In (a/K) RT

(4)

In two-state behavior, the enthalpy change that is calculated by the van 't Hoff equation is equal to that measured by calorimetry; therefore, the result AHvH/AHcal = 1

(5)

is the best evidence for two-state behavior and the lack of intermediates. 4-5

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In a three-state process the native form of a macromolecule is converted to the denatured form via an intermediate (C): K~ K, N ~-~ C ~ D (6)

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with two partial equilibrium constants K, = ([C]/[N])

K2 = ([D]/[C])

(7)

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and for the overall equilibrium constant we have

g

(8)

K' = K, K2 = ([D]/[N])

0.50

~ o.25

If Y and X are the fractions of macromolecule in the denatured and intermediate forms, respectively, then K ' will be r'=

[D] _ v [N] 1-(X+

1I)

-

(1-

Y Y)-X

From comparison of equations (2) and (9), since

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Figure 1

it is understood that the overall equilibrium constant of threestate (K') is greater than that equilibrium constant of two-state behavior (K). When the equilibrium constant becomes greater, on the basis of the van 't Hoff equation (4), AHvH is decreasing. Therefore, in three-state behavior AHvH < AHcat and the result is as follows AHvH AHea----~< 1

(11)

It is obvious when the number of intermediates in the denaturation process increases, the fraction of the macromolecules in the native form decreases, and the result is an enhancement of the value of the equilibrium constant with corresponding decreases in AHvH. The difference in the values of AHvH to A H c a I increases indicating more transition states for conversion of native to denatured form. The existence of more transition states may indicate that several domains of the macromolecule undergo independent transitions.

Conclusion A single transition is observed under conditions where AHvH and AHcal have the same value which shows that the whole macromolecule undergoes a single cooperative transition (twostate system), whereas in complex transitions the values of AHvH and AHca I a r e different which indicates multiple transition states. This is because AHca I is the algebraic sum of all heat effects occurring in the system, while the numerical value of the overall equilibrium constant, and therefore its AHvH, is dependent on the way in which the reaction is formulated. Whatever the number of intermediates as AHvH increases AHeat will decrease. A problem follows that may be set for students. Problem At the midpoint of transition (Tin), the calorimetric enthalpy change, AHcal (Tin), was measured and 88.1 kcal. mole -1 was reported for a protein. Calculate the van 't Hoff value for the enthalpy change at Tin, AH~H(Tm) from the transition curve, Fig 1, showing denatured fraction of protein against temperature.6 Is the transition of the two-state type? Solution By substituting K = Y/(1 - Y) in the differential form of the van 't Hoff equation ((dlnK/dT) = (AHvr~/RT2)), we obtain:

EDUCATION

I I 30 40 Temperature (°C)

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(1-Y)-X
BIOCHEMICAL

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(9)

22(4) 1 9 9 4

AHvtt

RT 2

/ udY x~

g(1- Y)

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dY AHvH = 4RTm 2 ( - - 7 ~ ) T m because Y = 0.5 at T = T m The slope of the transition curve is 0.0926 K -~ at Y = 0.5. Therefore, AHvH = 4 (1.987 x kcal. mo1-1. K -1) (313 K) 2 (0.0926K -I) = 72.1 kcal. mole -I Since AHvH 72.1 ------0.8<1.0 AHcaI 88.1 Thus, the transition will be the multi-state type.

References I Lapanje, S (1978) Physicochemical Aspects of Protein Denaturation chapter 3 2Hinz, H J (1988) Modern Methods in Protein Chemistry 3, 245 3Barrow, G M (1988); Physical Chemistry chapter 7 4Edsall, J T and Gutfreund, H (1983) Biothermodynamics chapter 6 s Privalov, P L (1979) Stability of Protein, Small Globular Proteins, Adv Protein Chem 33, 167 6Tsong, T Y, Hearn, R P, Wrathall, O P and Sturtevant, J M (1970) Biochemistry 9. 2666