The Theral Dependence and Urea Concentration Dependence of Rnase A Denaturant Transition Bin LI Departent of Physics & Astronoy, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A Feb.20 th, 2001 Abstract: In this paper, we discuss the unfolding transition of protein Rnase A at soe external potential ------ increasing teperature or urea concentration. We use the change of absorbance as index of denaturant transition, and use therodynaic quantities change to describe the transition in detail. In theral dependence experient, we got the o transition specific heat change of Rnase A is: C = 1.138kCal / ole K, which is closed to the data of quite a few previous experients. p Introduction Ribonuclease A is a very iportant protein, which has been discussed in detail for any years. People are very interested in the internal structures of protein and often asked such kind of questions: What deterines the structure of acroolecules and why should the native structure of Rnase A be ore stable or ore favorable than those of derivatives? We will use Ribonuclease A to study the protein s denaturated transition (fro the folded native state to unfolded denaturant), and try to figure out the essential issues that are related to the stability of protein. There are quite a few different indexes to show the protein transition. Aong the, fluorescence, circular dichrois and absorbance are frequently used ones. Here we will use absorbance as our index to show the Rnase A unfolding transition. We will discuss unfolding transition due to increasing of teperature (theral denaturation) first, eanwhile we will show how different PH values affect our transition curves and the transition therodynaic quantities; secondly, we will discuss about the urea concentration dependence of Rnase A denaturation. Fro the plot Transition of Rnase A at PH 3.5 on the attached Page 13, we can see there is a huge difference of the absorbance in teperature range fro 50 Deg to 65 Deg, and the whole curve can be divided into three different parts: (1) Fro the low
teperature to about 50 deg, where the absorbance is high and is a slightly negatively proportional to teperature. This region is called previous transition region. (2) Fro the teperature about 65 deg to higher teperatures, where absorbance is low but slightly positively proportional to teperature. This is called post transition region. (3) The region between the teperature 50 to 65 deg, where there is a steep change of absorbance to teperature, it is called transition region. Now we can use derivative calculation ethod to obtain the teperature where the derivative of absorbance of Rnase A to teperature is axial. This teperature is called T, protein-elting teperature. In fact, this teperature is also the specific teperature where the Gibbs free energy change G = 0. Stabilization Gibbs free energy G is the free energy required to convert protein fro its ordered native conforation state to an unfolded polypeptide chain state, so it is a very iportant quantity for us to pay attention here. Fro the definition of Gibbs free energy for denatured transition, we get G=-T S (for constant pressure), and eanwhile U we know the change of entropy S= R Ln( ), where U and F are the nuber of F icroscopic state of unfolded protein and the nuber of icroscopic state of folded protein respectively. Since we use absorbance as our denaturant index, the U and F ust be related to the absorbance coefficient K, where K could be expressed in ter of f : app f K = 1 f app. f app is the apparent fractional denaturant. If we define y, yf and y U as the absorbance of Rnase for the transition region, pre-transition and post-transition, we y yf have f app =, which is the ratio of the unfolded denatured protein to the total y y U F protein close to the transition region. Input the expression of forula, we will get K = f app in ter of y into the K app yf y. By doing so, we have two assuptions: (1) Protein y yu olecules are in either one of two conforational states ----- folded or unfolded; that is to say, there is no large population of interediates. (2) Reaction is reversible. Previous experients already have shown that those two assuptions are satisfied. Now we have G= - T R Ln [K (y)]. However, we know when the teperature T is very closed to the elting teperature T, G = H T S is approxiately true, H S so we easily get Ln( K) = +. Fro the relation G= H T S, at the R T R H elting teperature T, we have H T S = G = 0, so we get S =, T input it into G= H T S, we see G = H H T T, which shows the
negatively linear relationship between G and T when T is closed to the elting teperature T. We will see later, under the condition of different PH values, we will get different elting teperatures T. And we will find out our experiental data of and T are in exactly good linear relationship: H = C p T + H (0), fro the slope of our curve we will get the change of specific heat during the denaturant transition. Fro the graph on the attached Page 8, we find besides the therodynaic denaturation, increasing the concentration of urea will also achieve the sae result. The higher the concentration of urea, the lower the teperature the native Rnase A will denature. Here all the previous calculations are also satisfied, the only difference is the transition here is on longer due to the teperature, but due to the urea concentration. So we will have the relation: Gu, [ urea] = G( H ) [ urea] 2O. During the denaturant transition, we also have the so-called Gibbs-Helholtz T equation: G = H r T S r + CP ( T Tr ) CP [ T Ln( )], which predicted a Tr strong dependence on the teperature of the enthalpy and entropy of hydrophobic interaction. Here the T r is any reference teperature and can be chosen as T, so we will T T get the following forula: G( T ) = H (1 ) + C P ( T T ) C P [ T Ln( )]. T T Now, if we know the accurate values of H, T and C P, we can calculate G(T) at teperature T; on the other hand if we know the values of other quantities, we also can calculate the C P fro this equation. H Experiental ethod and procedures Prepared and titrated the buffer (30M potassiu acetate) to different PH values: 2.0, 2.2, 2.5, 2.8, 3.0, 3.5, 4.0, 4.5, eanwhile diluted Rnase A stock solution into 1.0 g/l and with various PH values: 2.0, 2.2, 2.5, 2.8, 3.0, 3.5, 4.0, 4.5. Put the buffer and Rnase A stock solution into the suitable cells of Cary Spectrophotoeter. After zeroing the instruent, we can use it to process the theral elting curves with different PH values at the wavelength of 287n. After acquiring the experiental data, we use a data processing progra ----- Siga Plot to do calculation and analysis. For urea dependence experient, we prepared a buffer of PH=3.5 with 30M potassiu acetate, then use a urea solution with initial concentration of 10M and ixed it with the appropriate aount of buffer and Rnase A stock solution and titrated to the PH=3.5. We ake Rnase A stock solutions (1g/l) with urea concentrations: 0M, 1M, 2M, 2.5M, 3M, 3.5M, 4M, 4.5M, 5M, 6M, 7M, 8M. Siilarly, we use Spectrophotoeter to get the theral elting curves at different urea concentrations. (Please refer to the plot on the attached Page 8, and you will see the different urea concentrations are atching to different elting curves). Now, if you draw a vertical line at a fixed teperature,
you ll get a curve The absorbance of Rnase A vs. Urea concentration at that teperature. (Please see the two plots on the attached Page 9 and Page 10 ). Then, we will still use Siga Plot to do the following calculation! Experiental Data Analysis (1) Theral Melting Experient Fro the attached Page 1, we can see the whole absorbance curve and see the huge change during the transition. We can estiate our transition region at PH 2.2 is fro about T=28 Deg to T=50 Deg, and if we use the derivative ethod, we can obtain the elting teperature is about T =40.46 Deg. In the attached Page 2 and Page 3, we pick up the appropriate ranges for the previous transition region and the post transition region of Rnase A fro the whole elting curves respectively. We let the pre-transition fro T=10 Deg to T=26 Deg, and the post-transition fro T=30 Deg to 50 Deg. And after data processing, we get the fitted curves: Previous Transition: y F = y 0 F 0 U + a T = 4.696 10 7.583 10 1 5 1 4 Post Transition: y = y + b T = 2.966 10 9.264 10 T U Then we will go back to the transition region again, this tie we choose a narrower yf y range (fro T=38.5 Deg to T=43 Deg), where all the K value K = is greater than y yu zero. So after that, we can change the unit of teperature fro Deg to K o, and calculate Ln (K), then we will get the curve G vs. T, fro the slope we can get the change of enthalpy during the Rnase A denaturant transition at PH 2.2 ----- H is about 83796.6 cal/ol (Please see the attached Page 4 ). Nerveless, we can also plot Ln (K) vs. T 1, T fro the slope H R = 4.213 4 10, we get a close value for H =83712.3 cal/ol (Attached Page 5 ). So the average H is equal to 83754 cal/ol. Then cobining the transition enthalpies H of the other PH values with their corresponding elting teperatures T, we can get a linear regression line: H = C p T + H (0), so fro that we can get the teperature-independent transition specific heat change C = 1.138kCal / ole K p. (Please see the attached Page 6 and Page 7. Meanwhile we also can easily get the conclusion The higher the PH value, the higher the transition teperature, and the larger energy required to ake the transition. ). o
(2) Urea Concentration Dependence Experient After finishing the theral elting experient, we begin to deal with the urea dependence of Rnase A transition. Fro the attached Page 8, we can see the denaturant curves of different urea concentration are obviously different. But as the concentration of urea increases, this kind of difference will becoe less apparent and even diinish since ost of Rnase A will becoe denatured at low teperature if the urea concentration is high enough. So we can only get the urea dependence curve in soe sall range where teperature is neither too high nor too low (if teperature is too low, the urea will crystallize; if the teperature is too high, Rnase A has already denatured) and the urea concentration is not too high. Here, our teperature range for the urea dependence experient is fro 16 Deg to 25 Deg. Attached Page 9 and Page 10 show how the Rnase A processes denaturant transition at teperature 17 Deg and 21.5 Deg separately as the concentrations of urea increase. Based on the two plots, in both of these two cases, we can choose the previous transition region as [urea] fro 0.5 M to 3M, and the post transition region as [urea] fro 7M to 8M. After calculation, we will get the following fitted curves for the urea dependence absorbance. (a) At teperature T=17.0 Deg, we have: 0 1 3 Pre-transition: y = y + a [ urea] = 3.600 10 9.557 10 [ urea] F F + 0 1 U = yu + b [ urea] = 2.201 10 3 Post transition: y 6.368 10 [ urea] (b) At teperature T=21.5 Deg, we have: 0 1 3 Pre-transition: y = y + a [ urea] = 3.593 10 8.984 10 [ urea] F F + 0 1 U = yu + b [ urea] = 1.940 10 3 Post transition: y 2.686 10 [ urea] Now we can use the sae ethod as what we have used in the theral elting experient to get the entropy change, enthalpy change, Gibbs free energy change, and so on. Fro the attached Page 11 and Page 12, we can see the urea dependence of Gibbs free energy change during denaturant transition at two different teperatures! And fro the vertical axes intercepts of these two plots, we can get the free energy changes at zero urea concentration are: At teperature 17 Deg : G 2685.0cal ol At teperature 21.5 Deg : G H O = / 2 H O = 2970.0cal / 2 Then, we can cobine the urea dependence transition experient data fro other groups, which are using different teperatures. But there is still one ore job for us to do o if we want to get the whole curve of vs. Teperature ( K ). Reeber, we G 2 H O choose PH fixed at 3.5 when we processed the urea dependence elting curves. So in order to get the GH 2 O at high teperature, we have to do the theral dependence transition experient at PH 3.5 again (refer to attached Page 13 ), where the urea ol
concentration is zero. After data processing, we get the closed to the elting teperature T (Please refer to the data table on attached page 14, so the teperatures are higher copared to those used in urea dependence experient). On the attached o Page 15, we can see the curve vs. Teperature ( K ) at PH 3.5 for the whole GH 2 O teperature range including both the low teperature (fro urea dependence) and high teperature (fro theral dependence). By using the Gibbs-Helholtz equation: G( T ) = H (1 T T and the known quantities: ) + C P ( T T ) C energy change at different teperature, we can get fitted curve. And we can see the which we obtained fro theral elting curve! P T [ T Ln( T G 2 H O o T = 330.83( K ), H =99.4880 (Kcal/ol), G(T ) free )] C = 3.695kCal / ole K fro the o p C p here is far fro (by factor 3) the value of C p Discussion and Conclusion Our experient was successful since we see the apparent difference of the absorbance curve of the native state of Rnase A before unfolding transition and of its denatured state after unfolding transition. And we also calculated the transition therodynaic quantities for different cases. Most of our experiental data were good and reasonable, except the data of at PH 3.5 vs. Urea Concentration, where our GH 2 O experiental data were walking off the expectation values. After fitting the curve, we o obtained specific heat change C = 3.695kCal / ole K, which is quite different with p which we got in PH dependence experient. As we know, the forer specific heat o change C = 1.138kCal / ole K has already been proved, so it deonstrated the p second set of data is bad. And the large experiental data deviation is the ain reason. So accurate easureent and correct data analysis ethod are two essential factors to ake experient successful and get good experiental data. More-over, fro the absorbance curve on the attached Page 16 and attached Page 17, we can see there is a blue shift for the peak position of the PH 3.5, 8M urea copared with that of PH 3.5, 4M urea. We will discuss the reason briefly. Rnase A has 6 tyrosine, three of the are exposed to solvent; three are buried. Aong the three buried tyrosine, two are fully buried in the interior, and the other one is less buried. Various urea concentrations will result in exposing different nubers of buried tyrosine. 8M urea plus 3.5 PH will expose all the three buried tyrosines, but the 4M urea at PH 3.5 can only expose the buried tyrosine residue partially. So due to different internal structure, the absorbance curve ust be different. The larger nuber of exposed buried tyrosine case will contribute ore energy for absorbance through additional dipole oentu, so we can see this blue shift. Coparing the two plots on the
attached Page 18 and Page 19, we can presuably ake a conclusion: Under the condition of larger PH value, we will get a larger absorbance difference between the native state and denaturant state. Acknowledgeent This experient was perfored in the laboratory of Professor Jen-Jacobson, Dept. of Biological Science, Univ. of Pittsburgh. The siulation work was done in the departent coputational lab. Many thanks to Professor Jen-Jacobson and her graduate student Ms Arabela Grigorescu s nice tutoring and discussion.