Production of heat shock proteins are induced when a living cell is exposed
to a rise in temperature. The heat shock response of protein DnaK synthesis in
E.coli for temperature shifts from temperature T to T plus 7 degrees,
respectively to T minus 7 degrees is measured as function of the initial
temperature T. We observe a reversed heat shock at low T. The magnitude of the
shock increases when one increase the distance to the temperature $T_0 \approx
23^o$, thereby mimicking the non monotous stability of proteins at low
temperature. Further we found that the variation of the heat shock with T
quantitatively follows the thermodynamic stability of proteins with
temperature. This suggest that stability related to hot as well as cold
unfolding of proteins is directly implemented in the biological control of
protein folding. We demonstrate that such an implementation is possible in a
minimalistic chemical network.Comment: To be published in Physical Review Letter

A. Gragarov

A. Hansen

C. A. Gross

D. B. Straus

F. C. Neidhardt

G. M. Makhatadze

J. S. McCarthy

K. Tilly

Kim Sneppen

Kristine Bourke Arnvig

M. T. Morita

P. L. Privalov

S. L. Herendeen

S. Lindquist

S. Pedersen

S. Reeh

Steen Pedersen

Y. Zhou

English

arXiv

Crossref

Physical Review Letters

Thermodynamics of Heat-Shock Response

Production of heat-shock proteins is induced when a living cell is exposed to a rise in temperature. The heat-shock response of protein DnaK synthesis in E.coli for temperature shifts T → T + ΔT and T → T - ΔT is measured as a function of the initial temperature T. We observe a reversed heat shock at low T. The magnitude of the shock increases when one increases the distance to the temperature T ≈ 23 °C, thereby mimicking the nonmonotonous stability of proteins at low temperature. This suggests that stability related to hot as well as cold unfolding of proteins is directly implemented in the biological control of protein folding. © 2000 The American Physical Society

Arnvig, KB

Pedersen, S

Sneppen, K

UCL Discovery

VOLUME 84, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 27 MARCH 2000Thermodynamics of Heat-Shock ResponseKristine Bourke Arnvig,1 Steen Pedersen,1 and Kim Sneppen21Institute of Molecular Biology, Øster Farimagsgade 2A, 1353 Copenhagen K, Denmark2Nordita, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark(Received 29 July 1999)Production of heat-shock proteins is induced when a living cell is exposed to a rise in temperature.The heat-shock response of protein DnaK synthesis in E.coli for temperature shifts T ! T 1 DT andT ! T 2 DT is measured as a function of the initial temperature T . We observe a reversed heat shockat low T . The magnitude of the shock increases when one increases the distance to the temperature T0 23 ±C, thereby mimicking the nonmonotonous stability of proteins at low temperature. This suggests thatstability related to hot as well as cold unfolding of proteins is directly implemented in the biologicalcontrol of protein folding.PACS numbers: 87.14.Ee, 36.20.– r, 82.60.–s, 87.16.–bChaperones direct protein folding in the living cell bybinding to unfolded or misfolded proteins. The expressionlevel of many of these catalysts of protein folding changesin response to environmental changes. In particular, whenany living cell is exposed to a temperature shock the pro-duction of these evolutionary conserved proteins is tran-siently increased [1]. The heat-shock (HS) response inE.coli involves about 40 widely dispersed genes and ismediated through the s32 protein [2,3]. The s32 binds toRNA polymerase (RNAp), where it displaces the s70 sub-unit and thereby changes RNAp’s affinity to a numberof promoters. This induces production of the heat-shockproteins. If the gene for s32 is removed from the E.coligenome, the HS is suppressed [2,4] and also the cell can-not grow above 20 ±C.The HS is fast. In some cases it can be detected bya changed synthesis rate of, e.g., the chaperone proteinDnaK, about a minute after the temperature shift. Giventhat the DnaK protein in itself takes about 45 seconds tosynthesize, the observed fast change in DnaK productionmust be very close to the physical mechanism that triggersthe response. We will argue for a mechanism that does notdemand an additional synthesis of s32 and thus postulatethat a changed synthesis of s32 only plays a role in the lat-ter stages of the HS. To quantify the physical mechanismwe measure the dependence of HS with initial tempera-ture and find that the magnitude of the shock is inverselyproportional to the folding stability of a typical globularprotein.This paper measures the expression of protein DnaK.Steady state levels can be found in [5,6]; they vary fromapproximately 4000 at T  13.5 to approximately 6000at 37 ±C. DnaK is a chaperone and it has a high affinityfor hydrophobic residues [7]; as these signal a possiblemisfold, s32 controls the expression of DnaK by bindingto the RNAp. One expects at most a few hundred s32 inthe cell, a number which is dynamical adjustable becauseof the short in vivo half-life of s32 (0.7 min at 42 ±C and15 min at 22 ±C [8,9]). The lifetime s32 is known to in-crease transiently under the HS.0031-90070084(13)3005(4)$15.00The measurement was on an E.coli K12 strain grownon an A 1 B medium with a 3H labeled amino acid asdescribed in [10]. After the temperature shift we extractedsamples of the culture at subsequent times. Each samplewas exposed to radioactive labeled methionine for 30 sec-onds, after which 105-fold nonradioactive methioninewas added. Methionine absorbs very rapidly, and is thenused in protein synthesis. Protein DnaK was separated by2-dimensional gel electrophoresis, and the amount ofsynthesis during the 30 seconds of labeled methionineexposure was determined first with respect to 3H countsper minute and then with respect to total protein produc-tion. This results in an overall accuracy of about 10%.The result is a count of the differential rate of DnaKproduction (i.e., the fraction DnaK constitutes of totalprotein synthesis relative to the same fraction before thetemperature shift [10]) as a function of time after thetemperature shift. For the shift T ! T 1 DT at timet  0 we thus recordrT , t Rate of DnaK production at time tRate of DnaK production at time t  0 ,(1)where the denominator counts the steady state productionof DnaK at temperature T . In Fig. 1 we display three ex-amples, all associated with temperature changes of abso-lute magnitude DT  7 ±C. When changing T from 30 ±Cto 37 ±C, one observes that r increases to 6 after a timeof 0.07 generation. Later the expression rate relaxes to thenormal level again, reflecting that other processes coun-teract the initial response. When reversing the jump, wesee an opposite transient decrease in the expression rate.Finally, for 12 ±C ! 19 ±C we observe that the T increasegives a decrease in the expression rate. Thus the cells’ re-sponse to a positive temperature jump is opposite at lowtemperature T than it is at high T .Figure 2 summarizes our findings by plotting the valueof r  R, where the deviation from r  1 is largest for anumber of shifts T ! T 1 7 ±C. R is fitted bylnRT   aDT  T 2 T0 , (2)© 2000 The American Physical Society 3005VOLUME 84, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 27 MARCH 20000.11100 0.1 0.2 0.3 0.4r(DnaK)Generations30 to 37 C37 to 30 C12 to 19 CFIG. 1. Heat-shock response measured as DnaK rate produc-tion change as a function of time since a temperature shift. Theproduction is normalized with an overall protein production rate,as well as with its initial rate. In all cases, we use absoluteDT  7 ±C. The time scale is in units of one bacterial genera-tion at the initial temperature.where RT  T0  23 ±C  1 and aDT lnR1R2T12T2 0.2K21 (i.e., a  0.03K22).To interpret this result we first assume that the produc-tion rate of DnaK is controlled by two factors, a slowlyvarying factor C that depends on the composition of someother molecules in the cell and an instantaneous chemicalreaction constant K . Thus at time t after a shift in tem-perature the production of DnaK in the cell isdDnaKdtt,T ! T 1 DT   Ct,T ! T 1 DT3 KT 1 DT  , (3)where the initial composition of molecules, Ct  0,T !T 1 DT , equals their equilibrium number at the tempera-ture we changed from, i.e.,  CeqT.0.111010 15 20 25 30 35RInitial temperature T’Induction fold’exp(0.2*(x-23))FIG. 2. Induction fold R for positive temperature jumps as afunction of initial temperature. The dashed line corresponds tothe fit used in Eq. (2).3006To the lowest approximation, where we even ignorefeedback from changed DnaK in the cell until the DnaKproduction rate has reached its peak value,R KT 1 DT KT , (4)which implies thatlnR  lnKT 1 DT  2 lnKT   d lnKdTDT .(5)By using the linear approximation in Fig. 2,lnK  const 1 a2T 2 T02. (6)Identifying K  exp2DGT, the effective free energyassociated with the reaction isDG  G0 2aT2T 2 T02. (7)Thus DG has a maximum at T  T0  23 ±C.To interpret the fact that HS is connected to a DG thathas a maximum at T  T0  23 ±C, we note that manyproteins exhibit a maximum stability at T between 10 ±Cand 30 ±C [11,12]. Thus DG  Gfolded 2 Gunfoldedconnected to the folded state of a protein is at a minimumat T0. The corresponding maximum of stability is the resultof a balance between destabilization from entropy of poly-mer degrees of freedom at high T and destabilization due todecreased entropic contribution to hydrophobicity at low T[12,13]. One should also expect similar behavior for someparts of a protein [13], and thus expect a maximum bind-ing for hydrophobic protein-protein associations at aboutT0. Quantitatively, the size of the DG change inferredfrom the measured value of a  0.03K22 corresponds toa changed G of about 20 30 kT (about 15 kcalmol), fora temperature shift of about 40 50 ±C. This matches thechange observed for typical single domain proteins [12].Thus the HS is associated with a DG change equivalent tothe destabilization of a typical protein.The above picture still leaves us with the puzzle thatprotein binding and folding stability are at a maximum atabout T0, whereas the effective DG we observe has a mini-mum there. This can only be reconciled if the interactionwe consider is inhibitory. An inhibitory binding that con-trols the feedback is indeed possible [3]. To summarize,in Fig. 3 we display the molecular network that we be-lieve is controlling the transient heat-shock levels of DnaKin the cell. The key inhibitory control mechanism is theassociation of DnaK to s32. DnaK binds to unfolded pro-tein residues [7], and the amount of DnaK-s32 associa-tion thereby monitors cellular consequences of a shift intemperature.Impacts of mutants: We have measured the heat shockin a strain where the s32 gene is located on a high copynumber plasmid. In this strain where the synthesis ratefor s32 may approach that of DnaK, we found a HS thatVOLUME 84, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 27 MARCH 2000KDUKσ 32-U as chaperone)K32σ32σD3232KSupplySink32σHflBσ 32StorageProtease(DnaK actingDnaKDnaKDnaKRNApRNApRNApσ7070FIG. 3. Sufficient molecular network for the early heat shock.All dashed lines with arrows at both ends are chemical reactionswhich may reach equilibrium within a few seconds (they repre-sent the homeostatic response). The solid directed arrows rep-resent one-way reactions, with the production of DnaK throughthe s32-RNAp complex being the central one in this work. Thetime and temperature dependence of the early HS is reproducedwhen most DnaK is bound to unfolded proteins, and when re-maining DnaK binds to s32 to facilitate a fast depletion of s32through degradation by protease HflB.was smaller and also remained positive down to tempera-ture jumps from T well below T0  23 ±C. According toFig. 3 this reflects a situation where both s32 and DnaKare increased. The increased DnaK may then exceed theamount of unfolded proteins, and free DnaK concentra-tion thus becomes nearly independent of the overall stateof proteins in the cell. Further, an increase in the s32supply decreases the possibility for the sink to act effec-tively. Thereby, other effects such as, e.g., the temperaturedependence of the binding s32-RNAp versus the bindings70-RNAp (i.e., K32K70 from Fig. 3), may govern theresponse.The reaction network in Fig. 3 allows a more carefulanalysis of the production rate of DnaK:dDnaKdt~ RNAp-s32 s321 1 gDnaK, (8)where the s32 changes when bound to DnaK due to degra-dation by proteases (the “sink” in Fig. 3):ds32dt~ supply 2 DnaK-s32 supply 2 s321 1 gDnaK21. (9)Here g  exp2DGT  is an effective reaction constant.In the approximation where we ignore free s32, free s70,and the fraction of DnaK bound by s32, theng √K70s70K32RNAp!√KD321 1 KDUUf!. (10)The first term expresses the s’s competition for RNApbinding, whereas the second term expresses the DnaK con-trolled response. Uf, which denotes unfolded proteinsthat are not bound to DnaK, decreases with increasing[DnaK].When moving away from T0, i.e., lowering g by increas-ing Uf , the rate for DnaK production increases. For anapproximately unchanged “supply,” the extremum in pro-duction occurs when ds32dt  0 and has a value thatis approximately ~1g. With the assumption that supplydoes not have time to change before extreme response isobtained, we identify R with 1g and thereby with the freeenergy difference DG that controls the HS. The early risein r is reproduced when most s32 are bound to RNAp re-flected in the condition gDnaK ø 1. This implies a sig-nificant increase in the s32 lifetime under a positive HS,and implies that the early HS is due to a changed deple-tion rate of s32. Later, the response is modified, partlyby a changed supply and finally by a changed level of theheat-shock-induced protease HflB (HflB is a protease pro-tein, which means that it actively degrades other proteins)that depends on and counteracts the s32 level in the cell.The largest uncertainty in our analysis is the possibilityof a significant time variation in supply and HflB levelsduring the HS. As these will govern the late stages of theheat shock, the variation in “DG” for proteins in the cellmay easily be underestimated by using the peak heightvariation with T . Adding to the uncertainty in what DGprecisely represents is also the fact that, although we onlymeasure DnaK, it can be the complex of the heat-shockproteins DnaK, GrpE, and DnaJ (GrpE and DnaJ are chap-erone proteins and as DnaK they are regulated by s32)which sense the state of unfolded proteins in the cell [9,14].Such cooperativity may amplify the heat shock.For the final interpretation of DG we stress that it effec-tively counts the free energy difference between the com-plex DnaK-s32 and that of DnaK being free or being boundto unfolded proteins in the cell. Dependent on the fractionof DnaK relative to unfolded proteins U in the cell, i.e.,whether KDUUf is larger or smaller than 1, the HS mayor may not depend on the overall folding stability of pro-teins in the cell. Thus for much more unfolded proteinsthan DnaK in the cell, the measured DG reflects both anincrease of the binding to unfolded residues KDUUf aswell as a decrease of the DnaK-s32 binding KD32 whenmoving away from T0. Our data do not discriminate be-tween these processes. This discrimination can, however,be obtained in [15], where it was found that overexpres-sion of DnaK through a s32 dependent pathway repressesHS. As DnaK-s32 binding still plays a crucial role in this3007VOLUME 84, NUMBER 13 P H Y S I C A L R E V I E W L E T T E R S 27 MARCH 2000setup, the vanishing HS of [15] supports a scenario wheretoo much DnaK imply KDUUf ø 1. Then g in Eq. (10),and thereby the s32 response, becomes insensitive to theamount of unfolded proteins in the cell.We conclude that the HS is induced through the changedfolding stability of proteins throughout the cell, sensedby a changed need of chaperones. This may reflect pri-marily an increased amount of proteins that is on the wayto becoming folded, and not necessarily an increased de-naturation of already folded proteins.We now discuss related proposals of “cellular ther-mometers” for the HS. McCarthy and Walker [16]proposed that the thermometer was a change in autophos-phorylation of the DnaK protein, giving it a temperaturedependent activity. However, their data do not indicate thatthe reversed HS response that we observe at T , 23 ±Ccould be caused by such a mechanism. Gross [3] madean extensive network of possible chemical feedbackmechanisms which connect a rise in the s32 level withthe folding state of proteins in the cell: an increasedsynthesis of s32, an increased release of s32 from DnaK,as well as an increased stability of s32 when DnaK getsbound to unfolded protein residues. Figure 3 specifiesthese possibilities to a minimalistic chemical responseincluding the two latter mechanisms combined, and, ofthese, only the option of a changed stability of s32 due toa sink controlled by DnaK-s32 is able to also reproducethe fact that the maximum HS takes time to develop. Inregard to the work by Morita et al. [17], which proposedan increased synthesis of s32, we note that, for hightemperatures T , the major mechanism that controls s32synthesis, in fact, is a T dependent change in the mRNAstructure that leads to an increased translation at increasedT [17]. However, again our finding of a reversed HS atT , 23 ±C is not readily explained by such changes in thestability of mRNA structures below 23 ±C.In summary, we observed that positive heat shock is in-duced when T changes from T0  23 ±C. We found thatthe size of the heat shock qualitatively as well as quan-titatively follows the thermodynamic stability of proteinswith temperature. This suggested that stability related to3008hot as well as to cold unfolding of proteins is implementedin the HS. We demonstrated that such an implementationwas possible in a minimalistic chemical network, wherethe control is through an inhibitory binding of the centralheat-shock proteins. Finally, we saw that the temporal be-havior of the HS is reproduced when this inhibitory bindingcontrols the heat shock by exposing s32 to a protease.[1] S. Lindquist, Annu. Rev. Biochem. 55, 1151 (1986).[2] F. C. Neidhardt, R. A. VanBogelen, and V. Vaughn, Annu.Rev. Genet. 18, 295 (1984).[3] C. A. Gross, Cellular and Molecular Biology (ASM Press,Washington, D.C., 1996), p. 1382.[4] Y. Zhou, N. Kusukawa, J. W. Erickson, C. A. Gross, andT. Yura, J. Bacteriol. 170, 3640 (1988).[5] S. L. Herendeen, R. A. VanBogelen, and F. C. Neidhardt,J. Bacteriol. 139, 185 (1979).[6] S. Pedersen, P. L. Bloch, S. Reeh, and F. C. Neidhardt, Cell14, 179 (1978).[7] A. Gragarov, L. Zeng, X. Zhao, W. Burkholder, and M. E.Gottesman, J. Mol. Biol. 235, 848 (1994).[8] D. B. Straus, W. A. Walter, and C. A. Gross, Nature (Lon-don) 329, 348 (1987).[9] K. Tilly, J. Spence, and C. Georgopoulos, J. Bacteriol. 171,1585 (1989).[10] S. Reeh, S. Pedersen, and J. D. Friesen, Molec. Gen. Genet.149, 279 (1976).[11] P. L. Privalov, E. I. Tiktopulo, S. Yu. Venyaminov, Yu. V.Griko, G. I. Makhatadze, and N. N. Khechinashvili, J. Mol.Biol. 205, 737 (1989).[12] G. M. Makhatadze and P. L. Privalov, Adv. Protein Chem.47, 307 (1995).[13] A. Hansen, M. H. Jensen, K. Sneppen, and G. Zocchi, Eur.Phys. J. B 6, 157 (1998).[14] D. B. Straus, W. A. Walter, and C. A. Gross, Genes Dev. 4,2202 (1990).[15] K. Tilly, N. McKittrick, M. Zylicz, and C. Georgopoulos,Cell 34, 641 (1983).[16] J. S. McCarthy and G. C. Walker, Proc. Natl. Acad. Sci.U.S.A. 88, 9513 (1991).[17] M. T. Morita, Y. Tanaka, T. S. Kodama, Y. Kyogoku,H. Yanagi, and T. Yura, Genes Dev. 13, 655 (1999).

Thermodynamics of heat-shock response

Thermodynamics of Heat Shock Response

Thermodynamics of Heat Shock Response

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