We study cold denaturation of proteins at high pressures. Using
multicanonical Monte Carlo simulations of a model protein in a water bath, we
investigate the effect of water density fluctuations on protein stability. We
find that above the pressure where water freezes to the dense ice phase
($\approx2$ kbar), the mechanism for cold denaturation with decreasing
temperature is the loss of local low-density water structure. We find our
results in agreement with data of bovine pancreatic ribonuclease A.Comment: 4 pages for double column and single space. 3 figures Added
  references Changed conten

A. Hansen

A. Trovato

B. L. Chen

B. Lee

C -J. Tsai

C. N. Pace

C. Vanderzande

D. Chandler

E. Paci

F. H. Stillinger

G. Caldarelli

G. Hummer

G. P. Privalov

G. Panick

G. W. Robinson

H. Ludwing

H. S. Chan

H. S. Frank

J. Jonas

J. Zhang

J. Zipp

K. A. Dill

K. A. T. Silverstein

K. C. Cho

K. F. Lau

L. R. Pratt

L. Smeller

M. W. Mahoney

N. Muller

O. Collet

P. Bruscolini

P. L. Privalov

P. R. ten Wolde

P. R. ten Wolde,

R. A. Pierotti

S. A. Hawley

S. Chan

S. J. Gill

S. Kunugi

S. Shimizu

V. A. Payne

V. F. Petrenko

W. Kauzmann

Y. Nozaki

English

arXiv

We study cold denaturation of proteins at high pressures. Using multicanonical Monte Carlo simulations of a model protein in a water bath, we investigate the effect of water density fluctuations on protein stability. We find that above the pressure where water freezes to the dense ice phase (approximately 2 kbars) the mechanism for cold denaturation with decreasing temperature is the loss of local low-density water structure. We find our results in agreement with data of bovine pancreatic ribonuclease A

Marqués, Manuel I.

Borreguero, Jose M.

Stanley, H. Eugene

Dokholyan, Nikolay V.

Carolina Digital Repository

arXiv:cond-mat/0212639v3  [cond-mat.soft]  11 Jun 2003A possible mechanism for cold denaturation of proteinsat high pressureManuel I. Marqués1,∗ Jose M. Borreguero1, H. Eugene Stanley1, and Nikolay V. Dokholyan21 Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA2 Department of Biochemistry and Biophysics, University of North Carolina at Chapel Hill,School of Medicine, Chapel Hill, NC 27599, USAWe study cold denaturation of proteins at high pressures. Using multicanonical Monte Carlosimulations of a model protein in a water bath, we investigate the effect of water density fluctuationson protein stability. We find that above the pressure where water freezes to the dense ice phase(≈ 2 kbar), the mechanism for cold denaturation with decreasing temperature is the loss of locallow-density water structure. We find our results in agreement with data of bovine pancreaticribonuclease A.Some proteins become thermodynamically unstable atlow temperatures, a phenomenon called cold denatura-tion [1, 2, 3]. This phenomenon has been mainly ob-served at high pressures, ranging from approximately 200MPa up to 700 MPa [4]. An explanation of the P − Tphase diagram of a protein with cold denaturation hasbeen proposed [5], but a microscopic understanding ofthe mechanisms leading to cold denaturation has yet tobe developed, due in part to the complexity of protein-solvent interactions.Existing theories of folding and unfolding of dilutedproteins consider hydrophobicity as the driving force ofprotein stability [6, 7, 8, 9, 10]. In the case of apolarmacromolecules, hydrophobicity has been identified withthe assembly and segregation of the macromolecule tominimize the disruption of hydrogen bonds among watermolecules [6, 10, 11]. Water tends to be removed from thesurface of apolar molecules, forming a cage composed ofhighly organized water molecules around the molecule,where the disruption of hydrogen bonds is minimized[12]. The simplest hydrophobic model features an effec-tive attraction between hydrophobic molecules [13], butdoes not reproduce cold denaturation. In order to obtaincold denaturation with this model, new studies [14, 15]had to insert a temperature-dependent attraction derivedfrom experimental observations at ambient pressure [16].An explicit account of water around the hydrophobicmolecules has also been considered in order to under-stand the cold denaturation process with temperature-independent interactions. Theoretical attempts modeledthe effective water-protein interactions with the free en-ergy cost of excluding the solvent around the nonpolarmolecule [11, 17]. Numerical simulations based on theseattempts have been applied to study the pressure denat-uration found in proteins [9].Not until recently has cold denaturation been studiedat the microscopic level. Simplified models [18], based ona bimodal description of the energy of water in the shellaround the hydrophobic molecule [19], predicted cold de-naturation. Similar results were obtained using a latticemodel of a random hydrophobic-hydrophilic heteropoly-mer interacting with the solvent [20]. Several modelsmimicking the interaction between water molecules andnon-polar monomers have also been applied to the studyof cold denaturation. [21]. One possible reason for the in-ability of the previous models to capture both the molec-ular details of cold denaturation and the effect of pressureis the neglect of (i) correlations among water moleculesnear the freezing point, and (ii) the density anomalydue to the tetrahedral structure of the hydrogen bondednetwork. Here, we implement a two-dimensional latticemodel of water that captures the above mentioned waterproperties [22]. In the model, the possible orientations ofwater molecules are set by the allowed values of a q-statePotts variable σi. Only when two neighbor molecules〈i, j〉 are in the correct orientation (σi = σj) does a hy-drogen bond (HB), that increases the volume of the sys-tem by ∆V , form. This interaction mimics the incrementof volume due to the incipient formation of a tetrahedralstructure. If the two neighbor molecules 〈i, j〉 are notin the correct orientation, the interaction of the particlesdoes not imply any increment in volume. The Hamil-tonian for our model of water-water interaction may bewritten as [22]HHB = −J∑〈i,j〉δσi,σj , (1)were J > 0 is the scale of the interaction between watermolecules upon tetrahedral network formation. The to-tal volume of the system is given by V = V0 +NHB∆V ,where NHB =∑〈i,j〉 δσi,σj is the total number of hydro-gen bonds with ∆V > 0 in the system. The sum∑〈i,j〉extends only to nearest neighbors, implying that two wa-ter molecules cannot form a hydrogen bond with ∆V > 0if they are separated by one residue of the protein. Theenthalpy of the system (HHB + PV ) is given byHHB + PV = −(J − P∆V )∑〈i,j〉δσi,σj , (2)where P is the pressure applied to the system.2Our model solvent features a limiting pressure Pc =J/∆V . Above Pc, we find that NHB decreases as wedecrease the temperature, and the water model under-goes a transition to a state where all hydrogen bondswith ∆V > 0 are broken. Below Pc, we find that NHBincreases as we decrease the temperature, and the wa-ter model undergoes a sharp transition, at T = Tc =(J − P∆V )/(ln(1 + √q)) [22], to a state where all hy-drogen bonds with ∆V > 0 are formed. Thus, our watermodel reproduces the freezing of water to low and highdensity ice, since for P < Pc (Pc ≈ 200MPa in real water)water freezes to the low density ice Ih, and for P > Pc,water freezes to the high density ice II [23]. A relationbetween these two phases of ice and protein folding hasalready been suggested from a thermodynamic point ofview [24].We model the protein as a self-avoiding random walkembedded in a water bath. For simplicity, we considera non-polar homopolymer that interacts with water viathe partial ordering of water molecules, forming hydrogenbonded structures around the protein. We mimic theinteraction using the Hamiltonian,Hp = JrnHB(nmax −∑〈i,j〉ninj) , (3)where the parameter Jr > 0 is the strength of the repul-sive interaction and nHB ≡ NHB/Nwater is the numberdensity of hydrogen bonds with ∆V > 0, Nwater is thenumber of water molecules. The water–protein repulsionincreases as the water molecules tend to form the tetra-hedral, low–density, hydrogen bonded network, where anunfolded apolar macromolecule is unlikely to be embed-ded. nmax is the maximum number of residue–residuecontacts and∑〈i,j〉 ninj is the number of residue–residuecontacts, where ni = 1 if the lattice position i is oc-cupied with a residue, and zero otherwise. Therefore,nmax −∑〈i,j〉 ninj is a measure of protein compactness,and equals zero when the protein is maximally compact.Thus, Eq. (3) states that the hydrophobic repulsion driv-ing the protein to a compact state is equal to zero whenthe protein is maximally compact (∑〈i,j〉 ninj ≈ nmax)or when the water forms the high–density bond network(nHB ≈ 0).We hypothesize that the inability of water moleculesto arrange in the low density ice–like structures is theprincipal mechanism responsible for protein cold denatu-ration. At low pressures (P < Pc) and low temperatures,water molecules form a low density hydrogen bonded net-work, so the protein is forced to adopt a compact state.At high pressures (P > Pc), the water is not able to formthe low density network and forms a more dense state.In this case the effective repulsion between the residuesand the solvent decreases, and water molecules penetrateinto the protein core, unfolding the compact state. Ourhypothesis is supported by the experimental observations[4] that cold denaturation exists mainly at high pressures(of the order of kbars), where water only freezes in thedense ice II phase [25].Next we demonstrate that our model of a protein em-bedded in a water network with an enthalpy given byW = Hp +HHB + PV (4)gives rise to both cold and warm denaturation of theprotein and agrees with experimentally-observed proteindenaturation at high pressures. Since the energy land-scape of the protein interacting with the water networkis characterized by a multitude of local minima, we per-form multicanonical Monte Carlo simulations to avoidtransient trapping of our water-protein system in localenergy minima at low temperatures. Specifically, we usethe multiple-range random walk algorithm [28] to cal-culate the density of states. We adopt the algorithmin order to embed the self-avoiding protein into the lat-tice, and to calculate the two-parameter density of statesg(NHB, Nc), where Nc ≡∑〈i,j〉 ninj is the number ofresidue-residue contacts. From the density of states wecalculate the temperature and pressure dependence of theaverage number of residue-residue contactsN c =∑NHB∑NcNcg(NHB , Nc)e−W(NHB ,Nc)/TZ, (5)where Z is the partition function. We perform MonteCarlo simulations of a system of 383 water moleculesand a protein consisting of 17 non-polar residues withperiodic boundary conditions. Fig. 1 shows the depen-dence of N c/nmax on temperature for different valuesof the pressure both above and below Pc. The calcu-lated density of states g(NHB, Nc) converges to the truevalue with an accuracy of the order of 10−5. The valueof N c/nmax ranges from one (maximally compact pro-tein) to approximately 0.71 (which is the average numberof residue–residue contacts found at high temperatures).Only when P > Pc do we observe the cold denaturationof the protein.We also reconstruct the phase diagram of the water-protein system in the P − T plane (Fig. 2). We considerthe protein to be in the collapsed state if 96% of all pos-sible contacts are formed, i.e., if N c/nmax > 0.96. Foreach pressure value, the freezing lines of water shown inFig. 2 are given by the temperature at which we observea maximum in the specific heat of the water bath. Wecompare our findings to experimental observations [29]for bovine pancreatic ribonuclease A studied by 1H NMRspectroscopy. We find remarkable qualitative agreementbetween the experimental and numerical P−T phase dia-grams. In both experimental and numerical P −T phasediagrams, we observe that cold denaturation occurs athigh pressures and, as we lower the temperature, close30 0.2 0.4 0.60.70.80.910 1 2 3 4 5T/J0.70.80.91 Nc/nmaxPV0/J=2PV0/J=0FIG. 1: Normalized number of residue-residue con-tacts vs. temperature for pressure values PV0/J =0, 0.25, 0.5, 0.75, 1, 1.1, 1.125, 1.15, 1.175, 1.2, 1.25, 1.4, 1.5, 2.A magnified region where the cold denaturation takes placeis shown in the inset. The dotted line corresponds toNc/nmax > 0.96. We represent the curve corresponding toP = Pc = J/∆V by a bold line. The values of the parametersused are: J = 1, Jr = 10,∆V = 1 and q = 10.to the water–ice II freezing line and in the region wherewater molecules are not capable of forming low densityice–like structures. In addition to the study of ribonu-clease A [29], cold denaturation at very high pressures inthe kbar range has also been observed in chymotrypsino-gen [5], myoglobin [5], staphylococcal nuclease [30] andhas been proposed as the principal mechanism for theobserved pressure-inactivation of bacteria, such as Es-cherichia coli [31].Not all proteins behave equally as we decrease tem-perature at high pressure. In particular, there are someproteins that do not exhibit cold denaturation. We re-produce the variability of protein dynamics at high pres-sure and low temperature by varying the hydrophobicparameter Jr to lower values, effectively impeding a sta-ble compact state for pressures above the P = Pc line.In Fig. 3 we present the phase diagrams obtained for dif-ferent values of Jr, ranging from two to 20. The shapeof the phase diagram changes as we increase the value ofthe repulsive interaction Jr, allowing stabilization of thecompact state and cold denaturation above the P = Pcline.Within the framework of our model, we reproduce theexperimentally-observed thermodynamics of cold denat-uration, but we cannot address the kinetics of this pro-cess. It could be also feasible to investigate in future workthe dynamics with a more sophisticated model, where weconsider not just the average number of hydrogen bondswith ∆V > 0, but the actual numbers for each water0 0.5 1 1.5 2T/J00.511.5PV0/J−20 30 80T(oC)012345P(Kbar)COMPACTDENATURATEDNATIVEDENATURATEDICE IhICE IIFIG. 2: P-T phase diagram for the protein derived from Fig. 1.Dashed lines indicate the freezing lines for model water. Wa-ter freezes in low density ice Ih for PV0/J < 1 and in denseice II for PV0/J > 1. In the inset we present the experi-mental results obtained by Zhang et al. [29] for the bovinepancreatic ribonuclease A. Two typical configurations of theprotein are shown, one in the compact state and the other inthe denaturated state.0 0.5 1 1.5T/J00.511.5PV0/JJr=2Jr=5Jr=10Jr=20ICE IhICE IIFIG. 3: P-T Phase diagram for proteins with Jr = 2, 5, 10, 20.Dashed lines indicate the computed freezing lines for water.Doted line indicates the P = Pc = J/∆V line.molecule that is a neighbor to a residue.Recent computer simulations studies [32] with all-atommodels have studied the effect of pressure and averagedensity on the hydrophobic effect. The authors per-formed simulations of two Lennard-Jones (LJ) particlesin the TIP4P water model [33]. At constant tempera-ture, they found that the aggregation of the two particlesis favored with a moderate increase of pressure, or analo-gously, with a moderate increase of water density. How-4ever, this effect is reversed for pressures in the kbar range,so that aggregation becomes unstable with increasing wa-ter density. These studies support our results of a criticalpressure above which an increase of pressure leads bothto an increase of water density (because of the reductionof the number of hydrogen bonds with ∆V > 0) andto destabilization of the model protein. Following theseresults and based on previous studies [10], Shimizu etal. [15] have shown that three-body interactions have adestabilization effect on the aggregation of three LJ par-ticles. However, the inclusion of these interactions intoa model of a more complex protein did not lead to sig-nificant changes. Finally, all-atom simulations recentlyaddressed the pressure denaturation of proteins [34], butthey have not provided conclusive evidence.We conclude that the effect of pressure on water den-sity is key for understanding cold denaturation of pro-teins. The density anomaly of water arises from the lowdensity hydrogen bonded structures responsible for thehydrophobic effect, driving the protein to a compact state[2, 8, 10, 12]. At extreme pressures above Pc, loweringthe temperature implies an increasing free energy costto form a hydrogen bond with ∆V > 0, so the densityanomaly disappears. In this scenario, the hydrophobic ef-fect decreases and cold denaturation occurs. Our modelsupports this mechanism. Also, a specific arrangementof amino acids in the protein structure, determined byamino acid interactions, dictates the dynamics of pro-teins at low temperature and high pressure, thus makingsome proteins more stable than others at these P − Tconditions.We thank S. V. Buldyrev, D. Chandler, J. Hermans,G. Hummer, O. Mishima and F. Sciortino for help-ful interactions, the NSF Chemistry Program GrantCHE0096892, the Spanish Ministry of Education and thePetroleum Research Fund for support.∗ Electronic address: manuel@argento.bu.edu[1] C. N. Pace and Ch. Tanford, Biochemistry 7, 198 (1968).[2] P. L. Privalov, Crit. Rev. Biochem. Mol. Biol. 25, 281(1990); in T. E. Creighton, Protein Folding (W.H. 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Possible Mechanism for Cold Denaturation of Proteins at High Pressure

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A possible mechanism for cold denaturation of proteins at high pressure

A possible mechanism for cold denaturation of proteins at high pressure

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