1 23

Food Biophysics ISSN 1557-1858 Food BiophysicsDOI 10.1007/s11483-013-9310-7

Water at Biological and InorganicInterfaces

Giancarlo Franzese & Valentino Bianco

1 23

Your article is protected by copyright and all

rights are held exclusively by Springer Science

+Business Media New York. This e-offprint is

for personal use only and shall not be self-

archived in electronic repositories. If you wish

to self-archive your article, please use the

accepted manuscript version for posting on

your own website. You may further deposit

the accepted manuscript version in any

repository, provided it is only made publicly

available 12 months after official publication

or later and provided acknowledgement is

given to the original source of publication

and a link is inserted to the published article

on Springer's website. The link must be

accompanied by the following text: "The final

publication is available at link.springer.com”.

Food BiophysicsDOI 10.1007/s11483-013-9310-7

SPECIAL ISSUE ARTICLE

Water at Biological and Inorganic Interfaces

Giancarlo Franzese · Valentino Bianco

Received: 6 May 2013 / Accepted: 12 July 2013© Springer Science+Business Media New York 2013

Abstract We analyze the role of water at biological andinorganic interfaces. In fields like food processing, foodpreservation or bionanotechnology the fluctuations in den-sity and entropy due to hydration water have consequencesthat go from damaging the tissues to reducing the cell deathfor dehydration to regulating the food stability to controllingthe heat-exchange at the nanoscale. We focus on the ther-modynamics of hydration water at cryopreservation temper-atures and its effects on the dynamics of nano-confined andprotein-hydration water. We consider the relevance of con-fining heterogeneities for controlling the physical propertiesof hydration water and the effects of interfacial water onprotein stability. To this aim, we describe a coarse-grainedmodel of water that allows us to perform theoretical cal-culations and numerical simulations, presenting our latestresults and the work in progress. Our investigation is atthe frontier of knowledge in Physics, Chemistry and Biol-ogy, with a potential impact on fields such as Nanoscience,Nanotechnology and Food Science.

Keywords Hydration · Interfacial water · Biologicalwater · Confined water · Theory

Introduction

Water covers 2/3 of the Earth, affects its climate and mor-phology, it is critical in many technologies and dissolvesalmost all chemicals, at least in part [1]. Despite being the

G. Franzese (�) · V. BiancoDepartament de Fısica Fonamental,Universitat de Barcelona,Diagonal 647, 08028 Barcelona, Spaine-mail: gfranzese@ub.edu

most corrosive substance, it is physiologically harmless andis the main component of living beings: approximately 60 %by weight of an adult human body is due to its water con-tent. Most of this water (� 60 %) are confined in cells,while the remaining water flows below tissues and in narrowblood vessels [2, 3]. Living beings need water because it isinvolved in most biological processes: in the metabolism ofnutrients and their transport to the tissues, in the disposal ofcellular waste, and in the communication between cells [4].Enzymes and proteins need to be suspended in solution tochange their conformation and to adopt their active struc-tures, and water governs the rate of recognition that proteins,nucleic acids and membranes have of ligands and drugs [5].Our failure in fully understanding the behavior of water isone of the main limitation we have in predicting proteinstructures and in designing drugs. For example, recent datashow that the dynamics of water plays a fundamental rolein biological processes, such as determining the proteins-folding rate [6]. Also, the hydrophobic collapse of proteinsand the rapid folding of their secondary structure are medi-ated by the water molecules that are in the proximity of theamino acids [7]. Other examples come from the protein-protein interactions that are affected by the dynamics of thehydration-water layer [8].

In Food Science water is important for its contributionto the texture (crispness or tenderness) of foods and for itsimportance in the majority of food processing techniques.In particular, the water content is important in determiningthe shelf-life and food safety.

Despite its importance and countless studies, the behav-ior of water remains poorly understood with respect tosimple fluids, such as argon [9]. Water has more thansixty anomalies. For example, its diffusion increases withincreasing pressure and its density decreases with decreas-ing temperature below 4 ◦C. As a consequence, the ice floats

Author's personal copy

Food Biophysics

on liquid water and lakes freeze from the top when theoutside temperature goes down, while water at 4 ◦C sinkstoward the bottom allowing the fish to keep swimming andliving. Water has, also, an extraordinary capacity to absorbheat, essential for regulating the temperature of engines, ofour body and of our planet [10]. Again, this property isessential for the life in cold waters, because it makes water,near freezing, not much susceptible to temperature changes,keeping the bottoms of lakes at 4 ◦C despite the outside tem-perature can go far below 0 ◦C, thanks to the ice layer onthe surface.

The anomalous behavior of heat transfer and volumechanges in water is emphasized by its heat capacity andcompressibility that have a minimum at 35 ◦C and 46 ◦C,respectively. Both quantities increase upon decreasing tem-perature as if they were diverging at a temperature around–45 ◦C [10]. Furthermore, its thermal expansion coefficientturns negative below 0 ◦C [10] (Fig. 1).

Another peculiar property of water is that, contrary towhat we could think, water does not freeze easily at 0 ◦Cand tends to stay liquid at moderately negative temperatures.How far below 0 ◦C water can remain liquid in a super-cooled, metastable state depends on several conditions. Forexample, water can be liquid at temperatures as low as–20 ◦C when confined in insects bodies, or –37 ◦C in thedrops forming the clouds [11], or –47 ◦C when confined inplants [12]. The best records for bulk are achieved in lab-oratory where it is possible to observe supercooled waterat –41 ◦C at atmospheric pressure [13] and at –92 ◦C at2 kbar [14].

Polymorphism and Polyamorphism

The possible explanations for this anomalous behavior arenumerous and controversial [15]. It is clear that the maincharacteristic of the molecules of H2O is its ability to formhydrogen bonds (HB), but the very definition of this type ofbond is controversial as much as its experimental measure-ment [16]. The common understanding is that on averageeach molecule forms four HBs, each with very short life-time in such a way that they are continuously formed andbroken while water molecules diffuse in the liquid phase.

These bonds strengthen the attraction among molecules,resulting in values for the melting point, boiling point andenthalpy of vaporisation of H2O higher than what wouldbe expected by comparing with hydrides of elements in thesame groups as O, i.e. S, Se, and Te [16]. Being the typicalbond distance smaller than the van der Waals radius, the for-mation of HBs implies a balance among dispersive forces–attheir repulsive distance–and electrostatic attractive forces[17] with a partial covalent nature [18]. As a consequence,the four water molecules, that are H-bonded to a central one,tend to repel each other and to form a tetrahedral structure.

Fig. 1 Schematic dependence on temperature at atmospheric pressureof (a) the isothermal compressibility KT ≡ −(1/V )(∂V/∂P )T pro-portional to fluctuations of molar volume, (b) the specific heat CP ≡(∂H/∂T )P proportional to the fluctuations of entropy and (c) the ther-mal expansion coefficient αP ≡ (1/V )(∂V/∂T )P proportional to thecross-fluctuations of volume and entropy. The behavior of a normalfluid (indicated by the dashed line) is approximately an extrapola-tion of the behavior of liquid water at high temperature. Anomaliesexhibited by water are apparent above the melting temperature Tm andbecome more striking when the fluid is supercooled below Tm

This structure possibly propagates at the second shell of thecentral water molecule, giving origin to an “open” structure.This tetrahedral structure is characterized by a density thatis lower than the “closed” structure achieved when the HBsare broken at high pressure [19]. A fully developed tetrahe-dral network is well observed in ice Ih (hexagonal ice) andIc (cubic ice). These are only two of the more than 16 crystalforms of water. Water is, therefore, a polymorph [20].

Author's personal copy

Food Biophysics

Just as there are crystalline polymorphs, there are alsopolyamorphic forms of water, i.e. different forms of amor-phous ice (glass) of water. These are observable below–123 ◦C when the liquid is cooled with a rate of 106 ◦C/sec.To date, there have been observed at least three distinctforms of amorphous ice: low, high and very high density(LDA, HDA and VHDA) with discontinuity in volume of27 % (LDA -HDA) and 11 % (VHDA-HDA) [21, 22].

The presence of open and closed structures, has led to dif-ferent interpretations of the behavior of supercooled water(Fig. 2). These can be divided into two main categories:

(i) one hypothesizes that water separates into two liquidphases of different density through a transition analo-gous to the transformation between gas and liquid andwith a possible singularity;

(ii) another assumes that the two local configurations arenever separated into two phases.

Interpretations of type (i) account for the coexistence ofa low density liquid (LDL) phase, with a structure similar toLDA ice, and a high density liquid (HDL) phase, similar toHDA ice. Due to the anti-correlation between the fluctuationof molecular volume and entropy, the HDL-LDL transitionhas a negative slope in the pressure-temperature (P − T )plane. Among the scenarios that involve the liquid-liquid(LL) phase transition are

(a) the scenario with a LL critical point at P > 0 [23];(b) the scenario with a LL critical point at P < 0 [24];(c) the “critical point-free” scenario, in which the LL tran-

sition extends to the limit of stability (spinodal) of theliquid with respect to the gas at P < 0 [15].

P

T

meltin

g lin

e

stablegas

stablewater

LG W

idom

line

LG spinodal

HDL

LL

Wid

om

line

P

T

meltin

g lin

e

stablegas

stablewater

LG W

idom

line

LG spinodal

LL coexistenceLL spinodal

P

T

stablegas

LG W

idom

line

LG spinodal

TMD

P

T

meltin

g lin

e

stablegas

stablewater

LG W

idom

line

supercooledwater

LG s

pino

dal

LG coexistence

K extrema

T

LG critical point

LL critical

LG coexistence

LG coexistence

LG critical point

LG critical pointLG critical point point

LDL

a b

c d

Fig. 2 Schematic view of different thermodynamic models about theorigin of water anomalies in the T − P plane. a The stability limitscenario [27] hypothesizes that the liquid-to-gas spinodal, with pos-itive slope at high T, merges with the stability limit of stretchedand supercooled water, with negative slope at low T. The reentrantbehavior originates from the intersection of the spinodal with the tem-perature of maximum density (TMD) line. b The liquid-liquid criticalpoint scenario [23] supposes the existence of a second critical pointfor liquid water in the supercooled region as ending point of a neg-atively sloped first order transition line, separating two metastable

liquids at different densities: the low-density liquid (LDL) at lowP and T, and the high-density liquid (HDL) at high P and T. Sev-eral numerical results with different water models are consistent withthis scenario [23, 24, 30–37]. c The critical-point-free scenario [15]hypothesizes an order-disorder transition, with a possible discontinu-ity in density, that extends at negative pressure up to the stability limitof supercooled water. d The singularity-free scenario [38] relates theanomalous increase in KT with the reentrant behavior of the TMD line,without any divergence in KT and with a locus of constant maximain CP

Author's personal copy

Food Biophysics

In these scenarios the anomalous increase of responsefunctions is a consequence of approaching the LL coexis-tence line, with a real divergence at the LL critical pointor along the LL spinodal line. For the cases (a) and (b), attemperatures above the LL critical temperature the thermo-dynamic response functions increase near the temperatureTW (P ) of maximum correlation length. The line TW(P )

in the P − T plane is called “Widom line” [25, 26] anddeparts from the critical point, being its analytic continua-tion. Extremely close to the Widom line, the functions arerounded and remain finite.

In the critical point-free scenario [15], on the other hand,the liquid-gas spinodal at P < 0 crosses the LL spin-odal leading to a change of slope of the stability limit ofthe liquid. A similar mechanism, with a reentrant spinodalwas originally proposed in the “stability-limit” scenario[27], that relates the increase in response functions to thereentrant behavior of the temperature of maximum den-sity (TMD) line. Nevertheless this scenario reveals somethermodynamic inconsistencies [28], that can be cured byinterpreting the low-T spinodal as a LL spinodal. Hence,although absent in its original formulation, the LL transitionphase was introduced later for thermodynamic consistencyalso in the stability-limit scenario [29].

To the category (ii) belongs the “singularity-free” inter-pretation [38]. In this scenario the anomalies are the effectof anti-correlation between the fluctuation of molecularvolume and entropy, due to the fact that forming a H-bonded structure leads to a volume increase with an entropydecrease. The large increase in the response functions(Fig. 1) observed in experiments, in this interpretation, is anapparent singularity rounded in a maximum in correspon-dence to the continuous density change.

Recently, it has been shown [39] that the singularity-free interpretation holds for a coarse-grained water-likemodel (the monoatomic-water model [40]), in contrast toanother scenario called “weak crystallization theory” [41].In Ref. [39] it is shown that the coupling constant requiredfor fitting the results with the weak crystallization the-ory would be unphysical. The weak crystallization theoryhas been proposed also for another water model [41], theST2 model [42], however several works have shown withdifferent approaches that the ST2 model follows the sce-nario with a metastable LL critical point [33, 35, 37,43–47].

Recently, it has been shown [48] that the all the scenar-ios in categories (i) and (ii) result from a common physicalmechanism, and that two key physical quantities determinewhich scenario describes water: (i) the strength of the direc-tional component of the HB and (ii) the strength of thecooperative component of the HB. Furthermore, estimatesfrom experimental data for HBs [48] lead to predict theoccurrence of the scenario described in (a).

State of the Art on Hydration Water at LowTemperature

All these scenarios rationalize the anomalies of water andcompare well with the experimental data, but predict dif-ferent phase diagrams, with different implications for thebehavior of the water interface. For example, the presenceof a LL critical point implies the presence of a Widom line.Along this line the density fluctuations determine struc-tural changes that could explain recent experimental resultsof water confined in nanoscopic structures [49–51] andhydration water of proteins and DNA to almost –53 ◦C[52–57].

At these low temperatures, “bulk” water exists only inthe solid state, but the confinement and the presence ofinterfaces distorts the formation of the network of HBsand lowers the freezing temperature [58]. This allows toexplore the dynamics and thermodynamics of confinedwater, although the interpretation of experimental results isstill controversial [52, 55, 58–65].

Liquid water hydrating proteins has been found at tem-peratures as low as –113 ◦C, at atmospheric pressure[51]. At these extremely low temperatures some interestingdynamic phenomena occur [50, 66–69] suggesting a possi-ble relationship between the dynamics of biological macro-molecules and water around them [70, 71], with implicationalso in Food Science [54].

At low T, proteins exist in a state without conformationalflexibility and are biologically inactive. In the literature, thisstate is commonly called “glass”. At approximately –53 ◦Chydrated proteins regain their flexibility and their biolog-ical activity. This dynamic transition is common to manybiopolymers and is understood to be due to the strong cou-pling with the mobility of hydration water, which shows asimilar dynamic transition at the same T [52, 55, 56, 61,62, 68, 72–74]. Experiments studying the translational cor-relation time of the hydration water of a lysozyme protein[52], DNA [55] and RNA [56] have shown that at about–53 ◦C (220 K) the dynamics of hydration water changesfrom non-Arrhenius (at high T) to Arrhenius (at low T), i.e.the dynamics has an activation energy that depends on T athigh T, and is a constant at low T.

Simulations of lysozyme and DNA in hydration water(using the TIP5P-water model) [75] have found (i) that thefluctuations of the mean square deviation for the hydrogensof lysozyme and DNA change functional form at Tp ∼245 K, (ii) the specific heat of the total system (water andbiopolymer) exhibits a maximum at T ∼ 250 ± 10 Kfor both molecules, (iii) the structure of hydration water,as measured by a local tetrahedral order parameter, has amaximum increase around the same temperature, TQ =245 ± 10 K, (iv) the diffusivity of hydration water exhib-ited a dynamic change from a non-Arrhenius to Arrhenius

Author's personal copy

Food Biophysics

at a temperature Tx ∼ 245 ± 10 K for lysozyme andTx ∼ 250 ± 10 K for the DNA. These temperatures aremuch higher than the glass transition temperature, estimatedfor TIP5P at Tg = 215 K [76]. The coincidence of thesetemperatures, all higher than the Tg , suggests an interest-ing relationship between the thermodynamics and structuralchanges of the hydration water and the fluctuations ofproteins.

Similar results have been found also in confined water.Confined water is of fundamental importance in biological,geological and technological processes, including disci-plines such as electro-chemistry or photocatalysis [77]. Inthe past years experiments have revealed a dynamic changeat T � 223 ± 2 K for water confined in silica nanopores(with a radius of 2 nm) by studying the structural relaxationtime (with neutron scattering) [49] and the self-diffusioncoefficient (with nuclear magnetic resonance) [51]. Thesedynamical changes observed in water confined in silicananopores disappear at a pressure between 1200 and 1600bar [50].

Results from simulations of water models (TIP5P andST2) and of water-like models [25] have suggested thata possible explanation for disappearance of the dynamicalchanges may be the presence of a LL critical point. Thesimulations exhibit the same physical behavior as the exper-iments, and the change in the diffusion coefficient in thesimulations vanishes at pressures higher than the pressureof the LL critical point. The authors interpret their simu-lation results as a consequence of the shape of the low-TLL spinodal line that flattens out above the LL criticalpoint [25].

Therefore, although the results are argument of debate[59–62, 75], numerical and experimental evidences pointto a strong dynamic effect of the first layers of watermolecules on macromolecules, due to the hydration inter-action. Understanding these interactions, which play adominant role in many physical, chemical and biologicalagents requires knowledge of the structure of the first layersof interfacial water at the molecular level [78]. Depend-ing on whether the surface is hydrophilic or hydrophobic,the structure of the network of HBs of water is affected,giving water its unique interface properties (e.g., surfacetension) [79].

The study of the properties of water near a hydrophobicsurface is a strong topic of debate, e.g. [80–85]. Understand-ing the water structure at the interface of a hydrophobicsurface of nanoscopic size [86, 87] has important implica-tions for the folding of proteins [88–91] or for Food Science[92, 93] and pharmaceuticals [94].

Experiments for water hydrating hydrophobic surfaceshave been interpreted sometimes in favor of the formation ofa depletion layer of water molecules [95–97], sometimes infavor of the reorientation of molecules [6, 83, 98–100] and

sometimes only indicating the formation of “nano-bubbles”of local depletion [101, 102].

Water near hydrophilic surfaces behaves in a way thatcould be quite different from water at hydrophobic inter-faces. Some authors suggest that near a hydrophobic surfacewater has a local LDL structure (low density and tetra-hedral), while near a hydrophilic surface is more closed,as in regions of high density (HDL) [103]. Experimentsshow that water molecules close to hydrophilic surfaceshave residence times longer than near hydrophobic surfaces[104], and that water confined between two hydrophilic sur-faces, separated by 2nm, has a viscosity several orders ofmagnitude greater than “bulk” water [105, 106]. These dif-ferences have important implications in applications suchas microfluidics or the development of biomaterials, wherewater produces a hydrophilic pressure that favors the adher-ence of bone grafts [107].

Simulations can substantiate hypothesis (see for exampleref. [108]), but are based on specific models [109] and it isdifficult to see whether their results have the character ofuniversality that experimental data suggest. To this goal itcould be relevant to analyze the results of a coarse-grainedwater model that can be studied analytically and, by tuninga few parameters, could be able to reproduce the results ofdifferent atomistic models.

A Many-Body Model for Hydration Water

In 2000 Franzese et al. proposed a coarse-grain model fora water monolayer, such as surface-hydration water or con-fined water between nano-separated surfaces [26, 110–113].The model is able to reproduce a large variety of water prop-erties and to make predictions that can be compared withexperiments [48, 57, 90, 91, 114–131]. The model is basedon the idea of describing the HB as the sum of a direc-tional (covalent) component and a many-body (cooperative)term.

To define the model:

1) We introduce a density-field, coarse graining the totalavailable volume V into a fixed number N0 of cells,each with volume v ≡ V/N0. Because we consider theconstant pressure P, constant temperature T, constantnumber of molecules N, the volume V is a functionof P and T, with V ≥ Nv0 where v0 is the hard-corevolume of a molecule (Fig. 3).

To simplify the model, we choose N0 = N andconsider that in each cell there is one water molecule,i.e. we consider that the system has a homogeneousdensity at our coarse-graining resolution. We neglectthe position of the water molecules inside the cell andassociate to the cell a variable n = 0 if the cell density

Author's personal copy

Food Biophysics

Fig. 3 Schematic representation of the coarse-graining of the watermonolayer. The space is divided into cells with size correspondingto the average distance between neighbor molecules. The cell sizechanges with P and T. In the simplified version of the model all thecell are occupied by a molecule

v0/v ≤ 0.5 (gas-like cell) and n = 1 if v0/v > 0.5(liquid-like cell).

2) We associate to each water molecules i four bond-ing variables σij = 1, . . . , q facing nearest neighborsmolecules j. Each variable σij can participate to a HB,being four the maximum number of HBs. From exper-iments we learn that a water molecule can form morethan four HBs, but that only four can be associatedto the low-energy tetrahedral configuration made ofa water molecule and its hydration shell. Additional(“bifurcated”) HBs will increase the energy associatedto the molecule and will form at angles that are incon-sistent with the tetrahedral configuration. We includein our description only “tetrahedral” HBs. The tetrahe-dral HBs can be associated to a configuration where theO-H–O atoms deviates less than 30◦ from the perfectalignment. Hence, the bonded state corresponds to 1/6of all the possible configurations of the O-H–O atomsin the plane they define. We, therefore, choose q = 6 insuch a way that only 1/6 of the σij states is associatedto a bonded state. As a consequence each molecule hasq4 = 1296 bonding states.

From the experiments we know that the formation ofa HB decreases the energy of the system and its entropy[28]. The model includes this behavior by assumingthat two nearest neighbor molecules i and j form a HB,reducing the energy of the system by a quantity J > 0,if the variables σij and σji , one on each molecule andeach facing the other, are in the same state.

3) Experiments suggest that the formation of HB isa cooperative process [132, 133], as discussed inRef. [48]. To include this effect, the model assumes

that the energy decreases of a quantity 0 < Jσ < J

when any two of the four variables σij on the samemolecules i are in the same state. The fact that Jσ < J

guarantees that this interaction implies a rearrange-ment of all the HBs formed by the molecule i, being aneffective many-body interaction.

4) Experimental interpretations suggest that tetrahedrallybonded water molecules form locally a low densitystructure up to the second shell [19]. Increasing thepressure or the temperature, the local density increasesas a consequence of the disruption of the tetrahedralstructure, i.e. as a consequence of the breaking ofthe tetrahedral HBs considered here. A simple wayto include this effect in the model is to assume thatthe volume per molecule V/N depends linearly on thenumber of HBs NHB

V/N ≡ (V0 + NHBvHB)/N (1)

where V0/N is the molecular volume without accountingfor the HBs, depending on P and T, and vHB is the volumeincrease per HB given by the difference in volume betweenthe local low-density tetrahedral structure and the compactstructure in absence of HBs.

All the above considerations are summarized by thefollowing expression for the enthalpy of the system [26,110–113]

H +PV ≡∑

ij

U(rij )−(J −PvHB)NHB−JσNcoop+PV0,

(2)

where rij is the distance between molecules i and j andU(r) ≡ 4ε[(r0/r)12 − (r0/r)6] accounts for the van derWaals attraction, involving different shells of molecules,and the short-range repulsion of molecules.

The second term represents the directional (covalent)component of the HB, with a characteristic energy J < 4ε,where NHB ≡ ∑

〈ij〉 ninj δσij ,σj i is the number of HBs, withthe sum running over next neighbors and δa,b = 1 if a = b,or 0 otherwise.

The third term accounts for the cooperative componentof the HBs, with a characteristic energy Jσ < J , whereNcoop ≡ ∑

i ni

∑(l,k)i

δσik,σil , is the number of pairs (l, k)iof bonding variables in the same state and belonging to thesame molecules i.

The model has been studied within the mean-fieldapproximation using cavity method approach [26, 111],finding functional relationships that qualitatively predictthe phase diagram. The thermodynamic and dynamic prop-erties of the model have been analyzed in details usingMonte Carlo (MC) simulations in the NPT ensemble (i.e.,

Author's personal copy

Food Biophysics

with number of molecules, pressure, and temperature con-stant) [113, 116], with efficient cluster MC [90, 118] andKawasaki MC [117, 119, 120, 125, 127].

The model reproduces the experimental phase diagram ofwater in its gaseous phase, liquid and the supercooled liquidregion with the line of temperatures of maximum density(TMD) and the increase in the response functions. In addi-tion, by changing the model parameters one can reproducethe different scenarios for the anomalies of water. This capa-bility offers the possibility to test numerically the theoreticalpredictions of different scenarios to lower T, where theexperiments on bulk water are difficult for the inevitable for-mation of ice, and to compare with more detailed simulationmodels, minimizing by orders of magnitude the computa-tional cost, while maintaining the possibility of comparingthe simulations with analytical calculations.

Tuning the Parameters: the Effect of Cooperativityon Hydration Water

Tuning the parameters J/(4ε), Jσ /(4ε), vHB/v0 implies norelevant differences in the gas and liquid phase above theTMD line. However, a change of parameters has impor-tant consequences for the phase diagram at very low T.Stokely et al. have shown that all the proposed theoriesfor the origin of water anomalies, described in the Intro-duction and summarized in Fig. 2, are reproduced by themodel by tuning the ratio between the covalent componentof the HB J and its cooperative component Jσ [48]. In thelimit Jσ → 0, i.e. without any cooperative behavior ofHBs, Stokely et al. recover the singularity free scenario.Increasing the value of Jσ with respect to J they find theliquid-liquid critical point scenario (LLCP) scenario witha critical point at P > 0. Further increase of Jσ /J leadsto the LLCP scenario with a critical point at P < 0. Byincreasing even more Jσ /J the critical point free scenario isrecovered.

Hence, the model allowed Stokely et al. to show that themechanism underling the different scenarios is the same andis due to the cooperativity of water. In particular, Stokelyet al. estimated the value of Jσ /J from experiments andpredicted a LLCP at positive pressure [48].

The Behavior of Hydration Water at CryopreservationTemperatures

In Food Science is relevant to understand how water behavesat extreme low temperatures, i.e. at temperatures that arerelevant for frozen food. Under these conditions, bulk liq-uid water would freeze into ice or would be supercooled, i.e.would stay in a metastable state with respect the ice phases.

On the other hand, confined water, such as water in bio-logical cells or food, can be liquid also at extremely lowtemperatures, depending on the confinement conditions. Inboth cases the anomalous density behavior of water playsa key role in the preservation of the properties of frozenbiological matter. Indeed, water thermal expansion coeffi-cient αP at constant P become negative for T < 4 ◦C andhas a large increase in absolute value for T < 0 ◦C. As aconsequence, intra-cellular and extracellular water expandsrapidly at sub-zero temperatures with possible damages forthe biological matter.

A large increase for T < 0 ◦C is observed experimen-tally also for the compressibility KT , i.e. for the densityfluctuations, and for the specific heat CP , i.e. for theentropy fluctuations of water. The increase of these fluctu-ations is deleterious for food preservation and, in general,cryopreservation. Hence, it is important to understand theunderlying mechanisms to develop strategies to control theproblem.

The coarse-grained model for hydration water presentedabove offers the possibility to gain insight into thesephenomena. Once established that the model-parametersextracted from experiments are consistent with the LLCPscenario [48], the model has been studied in details [26, 48,111–113, 116–118, 120]. For example, it has been foundthat the TMD line merges, in the deep supercooled region,with the temperature of minimum density line [131] as seenin the experiments [134].

In particular, our study of the increasing thermodynamicresponse functions KT , CP and the absolute value |αP |reveals unexpected properties, as shown by the new resultsthat we present here in Figs. 4 and 5. For P smaller thanthe critical pressure PC of the LLCP the maxima of theresponse functions are related to the Widom line [25, 26],i.e. the locus of maxima in correlation length. The Widomline emanates from the LLCP and extends in the one-phase region of supercooled liquid. We have found thatthe Widom line has a sharp negative slope in the P − T

plane, until it reaches the limit of stability of the stretchedliquid with respect to the gas phase at negative pressures(liquid-to-gas spinodal) [131]. Recently, this prediction hasbeen shown to be consistent with experimental data [135–138].

This property of the Widom line is a consequence of anovel feature that has been predicted by the coarse-grainmodel for hydration water: Mazza et al. have found two lociof extrema for each quantity KT , αP and CP [126, 130,131]. They find a broader and weaker maximum at high Tand a stronger maximum at lower T. All these maxima formloci in the P − T plane that converge toward the LLCP atPC − TC , where all the response functions increase largelyfor finite systems and diverge in the thermodynamic limit,as expected at a critical point.

Author's personal copy

Food Biophysics

Fig. 4 The CP calculated by cluster MC dynamics along isobars(lines at constant P), as in Ref. [131]. The color code along the linesrepresents the value of CP . The points in the plane P −CP are the pro-jections of the maxima of CP . Lines connecting the points are guidesfor eyes, showing a large increase at PC � 0.6 and TC � 0.06. ForP < PC the locus of maxima of CP in the P − T plane overlapswith the Widom line, as discussed in the text. All the quantities areexpressed in internal units: T in 4ε/kB ; P in 4ε/vHB; CP in kB

The Widom line coincides with the locus of strongestmaxima of CP , KT and |αP | that occur at lower T and arealmost P-independent. The Widom line marks the largestchange at P < PC in the thermodynamics and structuralproperties, from LDL-like region at lower T to HDL-likeregion at higher T. It converges to the loci of weaker maximaof CP , KT and |αP | only near the LLCP, because the loci ofweaker maxima have a much stronger P-dependence. It isnoteworthy that in the literature the loci of weaker maximahave been often considered as a manifestation of the Widomline [25, 116]. This is probably due to the fact that in manyof the previous works the extremely low-T (approximately180 K at 1 atm) was difficult to explore numerically for theglassy behavior of system [45].

Fig. 5 The KT calculated by cluster MC dynamics along isotherms(line at constant T ), as in Ref. [131]. The color code along the linesrepresents the value of KT . The points in the plane T −KT are the pro-jections of the maxima of KT . Lines connecting the points are guidesfor eyes, showing a large increase in the same region of apparent diver-gence in CP . All the quantities are expressed in internal units: T in4ε/kB ; P in 4ε/vHB; KT in vHB/(4ε)

Along the loci of both weak and strong maxima ofresponse functions hydration water has structural changesthat are continuous without any real phase transition. How-ever, these changes have important consequences in thedynamics of the system. In particular, recent experimentalresults for hydrated proteins [126] show that the existenceof two maxima in CP is consistent with two differentcrossovers in the dynamics of the water layer adsorbed onthe protein.

The Dynamics of Nano-Confined or Protein-HydrationWater

Transport and dynamics in nanostructured and highly con-fined systems presents peculiarities and counterintuitivebehavior that are starting to be explored [139, 140]. Waterin zeolites, nano-porous materials, gels, or organic fibers areexamples that not only have a scientific interest but havealso practical uses.

Normal liquids diffuse less upon increasing pressure,however water is anomalous in this respect: its diffusivityincreases with increasing pressure, reaching a maximum athigher pressures. Above the pressure of maximum diffusiv-ity water recovers the behavior of a normal liquid and itsdiffusion constant decreases with increasing P. This phe-nomenon is most evident in confined water, where it ispossible to observe liquid water at cryopreservation tem-peratures, and in particular, when water is confined at thenanometric scale. This scale, of interest for nanofluidicsstudies [141], is comparable to the scale below which thefluids lose their character as a continuum and show theirmolecular characteristics. At these scale the dynamics offluids is strongly affected by the geometry of the confine-ment, chemical composition and its molecular structure. Inthe case of water additional complexity comes from theinteractions of water molecules with the hydrophobic orhydrophilic interface [140].

The many-body model described above has been usedto study the dynamic behavior and transport of supercooledwater in confined nanostructures [116, 127], allowing anumber of theoretical predictions that have been verified[57] in experiments with Quasi Elastic Neutron Scattering(QENS) technique for hydration water of a protein at pres-sures up to 1600 bar [142], and with dielectric spectroscopyon protein hydration water [126]. The results comparewell also with experiments for water confined in silicananopores [50].

In particular, the model reproduces the anomaly of waterin the diffusion coefficient D [125, 127], i.e. the increaseof D along isotherms upon increasing the pressure due tothe reduction of the average number of HBs resulting in apromotion of the molecule motion. However, the number

Author's personal copy

Food Biophysics

of defects solely does not account for the peculiar diffusionof water, with maxima and minima along isotherms. In arecent study [127], de los Santos and Franzese calculatea relation that quantitatively reproduces the behavior of Dparallel to the confining surface in highly confined water.In particular, they focus on the high-T regime and clarifyhow the interplay between breaking of HBs and cooperativerearranging regions gives rise to the diffusion extrema innanoconfined water.

The competition between the free volume available fordiffusion and HB formation takes place in a cooperativeregion of approximately 1-nm size. This results is consistentwith the average dimension of the rearranging regions ofglass-forming substances close its glass temperature [143].

Furthermore, it offers a natural explanation for theincrease of diffusion found in simulations of water whenconfined in nanotubes with diameter smaller than 1 nm[144] and in experiments for water in sub-nonometric con-finement [145, 146]. As a consequence of the results ofthe many-body model of confined water, when the confin-ing channels are less than 1-nm in diameter, the numberof water molecules forming the cooperative rearrangingregions decreases progressively until reduces to isolatedmolecules, which diffuse more quickly, despite the reducedavailable space.

In particular, the calculations fit the experimental resultsabout the permeability of certain membranes of grapheneoxide and amorphous carbon [145, 146]. Although thesemembranes prevent the passage of all types of liquids andgases, it has been observed that water flows through themwith almost total freedom, up to 1010 times faster thanhelium. This amazing property can be explained by themicroscopic structure of the membranes: the diameter of itsinterstices amounts in fact to a nanometer, consistent withthe size of cooperative rearranging regions found with themany-body model. Therefore, the application of this resultcould multiply by thousand the desalination rate of currentmembranes.

The calculations of the many-body model have alsoshown that the cooperativity of the HB network can beheld accountable for the peculiar behavior of water hydrat-ing proteins. For example, the model predicts [117] thatat cryopreservation T, i.e. approaching TC of the LLCP,the hydration water dynamics becomes extremely non-exponential, as can be characterized by a parameter called“stretched exponent” β. The predicted value for β is inagreement with experimental results on water hydratingmyoglobin [147, 148].

Moreover, by decreasing T at constant P, Kumar et al.[116] found a dynamic crossover for the HB network ofa hydration monolayer at the same T as the occurrence ofthe broad maxima of the response functions. They showby analytic calculations and numerical simulations that the

crossover is a consequence of the structural change ofthe HB network. Such predictions are in agreement withthe experiments on the hydrated lysozyme [62, 142] anddielectric spectroscopy in confined supercooled water [58].

By further decreasing T in the simulations, Mazza et al.have been able to show that there is a second crossover forthe HBs correlation time of hydration water. Their predic-tion compare well with experiments for lysozyme hydrationwater [126]. Their results further clarify that both crossoversare related to structural changes in the HB network. Thehigh-T crossover (T ∼ 250 K) is due to the maxima influctuation of the number of HBs and corresponds to theweaker maxima in CP [126, 130, 131]. The low-T crossover(T ∼ 180 K) is consequence of the cooperative reorganiza-tion of the HBs and coincides with the strongest maxima inCP and with the Widom line.

Confining Heterogeneities and Their Relevancefor Controlling the Physical Propertiesof Hydration Water

A relevant question across a wide range of nanotechno-logical applications, biological systems, and in particularFood Science is how to control the physical properties ofhydration water. For example, an issue is how to reducethe undesirable effects that water expansion at freezingtemperature has on food properties.

The effect of an interface between water and a organic orinorganic surface could extend over nanometers due to thepropagation of disturbance in the network of HBs causedby the surface, possibly showing a difference betweenthe response to hydrophobic and hydrophilic surfaces. Animportant question that is emerging in areas such as the pro-tein folding and nanotechnology is how the heterogeneityof the hydrated surface affect the properties of water aroundthem [86, 109]. We consider here how the structure of thenanoconfinement may change the anomalous behavior ofwater at cryopreservation temperatures.

As a reference (homogeneous) case we study by MC sim-ulations water confined between flat walls that interact withthe liquid through a Lennard-Jones potential or excludedvolume. In particular, we focus on the response functionsapproaching the LLCP and on the definition of an appropri-ate order parameter for the LDL-HDL phase transition. Tothis aim, we follow the mixed-field approach [149, 150] anddefine as order parameter M a linear combination of den-sity ρ and energy E, M ≡ ρ + sE, where s is the mixingparameter. Such order parameter accounts for the change indensity and energy between the HDL and LDL close thecritical point (Fig. 6).

Bianco et al. have shown that the LLCP belongs to theIsing universality class in two dimension (2d) in the case of

Author's personal copy

Food Biophysics

Fig. 6 Color-coded Gibbs free energy G/kBT in the energy-densityplane, close the liquid-liquid critical point. We calculate G from therelation G/kBT = − ln P (E, ρ), where kB is the Boltzmann constantand P (E, ρ) is the probability distribution of states with given valuesof E (in units of ε) and ρ (in units of a3). The Gibbs free energy underthese conditions has two basins separated by a barrier G � kBT .This is the order of magnitude of the free-energy barrier expected neara critical point, where the system has enough thermal energy kBT tofreely cross the barrier G between the two coexisting phases. Theorder parameter M characterizing the phase transition is related to theline joining the two minima of Gibbs free energy

infinite walls. However, by increasing the confinement, i.e.reducing the wall size L with respect the thickness of thesystem, the system displays a behavior that is surprising: theLLCP approaches the behavior of a system following theuniversality class of an Ising model in three dimensions (3d)[131]. We understand such unexpected behavior as due tothe strong cooperativity of HB network. This cooperativityenhances the spreading of fluctuations in the system, lead-ing to the broader critical distribution of the order parameterthat characterizes the 3d universality class with respect tothe 2d universality class.

The comparison of these results with those, by Strekalovaet al., for a water monolayer confined in a fixed disor-dered matrix of hydrophobic nanoparticles at differentparticle concentrations c [123, 128], offers a way to under-stand how to control the fluctuations at cryopreservationtemperatures. Strekalova et al. find that the presence ofhydrophobic nanoparticles, even at volume concentrationas low as 2.4 %, reduces of 90 % and more the maximaof KT , CP and αP and of the associated fluctuations indensity, entropy and cross-correlated entropy and density.The result is interpreted as consequence of disruption of theHB network due to the presence of the nanoparticles [123]and is qualitatively consistent with recent experiments onwater confined in a hydrophobic mesoporous material withaverage pore diameter 1.4 nm [151]. Under these conditionsthe author of the experiments find that αP shows a much

broader peak with respect to the sharp peak observed inhydrophilic confinement [151], reminiscent of Strekalovaet al. results on the reduction of the response functions withrespect to the c = 0 case.

A further study [152] about the effect of the hetero-geneity in the nanoconfinement of liquids with water-likeproperties, shows clear differences between a confinementwith an ordered structure and a disordered confinement.While in the ordered nanoconfinement the large fluctuationsin density are preserved at cryopreservation T, in the dis-ordered nanoconfinement the density fluctuations becomeweaker as the disorder increases. These results qualitativelyexplain recent experiments for water confined in a regularhydrophilic matrix or in a disordered hydrophobic meso-porous material. In the ordered confinement the anomalousbehavior of water is easier to observe at low T with respectto bulk water [153], while in the disordered confinement theanomalous behavior is suppressed [151].

Therefore, these analysis of the model suggest a way tocontrol the fluctuations and their effects at freezing temper-atures. In particular, the inclusion of small concentrations ofa heterogeneous distribution of hydrophobic nano-sized par-ticles or aggregate of bio-molecules, such as hydrophobinproteins commonly used in food processing, could regulatethe large density fluctuations of the frozen water inside thepreserved food.

Effect of Interfacial Water on Protein Stability

The way a surface interacts with water affects the biolog-ical response to the material. For example, hydrophobicsurfaces help the absorption of surfactants and proteinsbecause the process is energetically favorable. The absorp-tion on the hydrophobic surface determines the reductionof interface energy for the expulsion of water moleculesfrom the surface and its replacement with molecules of theabsorbed solute.

On the other hand, the hydrophilic surfaces are veryefficient activators of blood coagulation, in contrast to thehydrophobic surfaces. They are also more effective thenhydrophobic surfaces for the process of implantation ofmammalian cells.

It is, therefore, clear that water plays a role in the free-energy balance that rules the stability of a folded protein andthat its contribution depends on the hydropathy index, i.e.the degree of hydrophobicity/hydrophilicity, of the exposedamino acids [154]. Nevertheless, in biology, as well as inmaterial science, many of the hydrated surfaces have a het-erogeneous hydropathy. For example, proteins have polarand apolar groups on the surface depending on their config-uration. Therefore, the effect of interfacial water on proteinstability is difficult to evince.

Author's personal copy

Food Biophysics

Several interpretations have been proposed in the lastdecades [90]. Here we focus on two interpretations of thehydrophobic effect: one based on the idea that “cages”(clathrates) of water form around the hydrophobic solute,giving rise to a solute-solute force of attraction due tothe increase of entropy upon overlap of the cages. Thesestructures reduce the entropy with respect to the bulk andcompensate, approximately, the enthalpy cost for the cre-ation of a cavity which can be occupied by the solute. Thisinterpretation is supported by theoretical analysis for smallapolar atoms (e.g., rare gases).

In an alternative interpretations, large hydrophobic sur-faces repel water (depletion) and attract each other to offsetthe free-energy cost due to “dehydration”. This hypothesis issupported by experimental observations of nanobubbles andwater density depletion on hydrophobic environment [101,155]. Lum et al. [156] have developed a mean-field theory,suggesting that the crossover from the “cage” regime to the“dehydration” phenomenon occurs when the solute size isof the order of 1 nm.

In simulations the effect of dehydration is evident onlywhen the component of the attractive interaction betweenwater molecules and hydrophobic surfaces is disregarded[157] and Hotta et al. have shown, with TIP4P-water andhydrophobic fullerene C60 and C60H60 [158] or carbon nan-otubes [159] with nanoscopic size, that if one considersan attractive LJ interaction between carbon and oxygen ofwater (i) there are fluctuations between the formation ofcages and dehydration, and (ii) the regime of dehydrationis stabilized when creating regions where the solute couldform a network of H bonds that will cost too much freeenergy [159].

How these observations help us to understand proteinstability and denaturation is matter of debate. Denatura-tion is a process that determines the loss of functionalityof the protein and is observed at temperatures that are usu-ally higher than 60 ◦C (melting process due to increasedkinetic energy) and in general well below 0 ◦C (whenthere is no energy in the thermal bath to break bonds: colddenaturation).

In the low-T case the physical interpretation is unclear[90, 160, 161]. Some models propose that the denat-uration is determined by the different energies asso-ciated with different configurations [7, 9] by show-ing that when cold denaturation occurs more HBsbetween the molecules of hydration water are formed[8].

Other models identify the cause in the density fluctua-tions of interface water [11, 13] or in the destabilizationof hydrophobic contacts because of the displacement ofwater molecules inside the protein [161]. The latter mech-anism is also proposed for high pressures denaturation[162].

A long-debated idea is that the folded state is stabilizedby a strongest network of HBs at the protein interface [163–165]. These stronger HBs would form a quasi–ordered net-work of water molecules hydrating the nonpolar monomersof the protein.

In order to understand the effect that the fluctuationsin the hydration water structure has on the processes ofcold (and pressure) denaturation, we propose a coarsegrain-model for water-protein interaction. For sake of sim-plicity, following other authors [160, 161, 166–170], herewe approximate the protein as a self-avoiding hydrophobichomopolymer. Therefore, we do not discuss here the effectof water hydrating polar monomers.

Our approach is based on the many-body model forwater we presented before. We add to the enthalpy ofwater, described by the Eq. (2), a term for the water-waterinteraction at the hydrophobic interface [90, 123]

Hs = −λJ∑

<ij>s

ninj δσij δσj i , (3)

where λ is a parameter and the sum is taken over watermolecules that are hydrating the exposed polymer surface.

We consider λ > 0. In this case the enthalpy decreasefor the HB formation in the hydration shell is −J (λ +1) + PvHB , larger than the enthalpy decrease for the HBin the bulk. The water protein interaction is represented byexcluded volume with no monomer-monomer direct interac-tion. This oversimplification allows us to better test the roleplayed by hydration water in the folding-unfolding process.

We simulate the system via Monte Carlo simulations,using different algorithms:

(i) Metropolis algorithms that reproduces the local Brow-nian dynamic of water molecules and polymermonomers;

(ii) “parallel-motion” algorithm where polymer macro-movements are allowed in order to explore in a fastway the accessible protein configurations.

In both cases, we study the unfolding of the proteinadopting an initial condition with the polymer is in its foldedstate. To check the stability of the folded state under specificthermodynamic conditions, we set the bath temperature Tand the external pressure P and equilibrate first the waterin the system, without changing the protein configuration.Next, we allow for protein-configurations changes, equi-librating both water and the protein in contact with thethermal bath at the given P. By following heating or coolingprotocols at constant P, we calculate the limits of stabilityof the initial folded state with respect to the unfolded states.

In our preliminary results we observe that a foldedprotein unfolds upon cooling, giving rise to the cold denat-uration process. The folded state is stable in a finite rangeof pressures. Indeed it unfolds by increasing the pressure as

Author's personal copy

Food Biophysics

expected by pressure denaturation, and we also observe theunfolding by decreasing pressure, a phenomena that is pre-dicted by general theoretical considerations. Further work isin progress to give definitive results.

Conclusions

Water has an anomalous behavior compared to other fluids.Four possible scenarios have been proposed to explain wateranomalous properties. The theoretical study of the many-body model for hydration water, described here, performedwith analytic and simulation techniques [48] at cryogenictemperatures, of the order of −100 ◦C, allows us to concludethat the four scenarios are particular cases of a more generaltheory. A relevant result of this analysis is that there are twophysical quantities that rule which of these scenarios holdfor water. These two quantities are (i) the value of the direc-tional component of the hydrogen bonds and (ii) the valueof their cooperative component. According to experimentalestimates, it is possible to conclude that of the four scenar-ios, the one with a critical point between two liquids betterfits the experiments. A recent confirmation of this predic-tion of a critical point between two liquids comes fromsimulations of an atomistic model of water [45]. This resultapplies to disciplines such as cryobiology or cryopreser-vation of organic material, e.g., stem cells or food, wherethe knowledge of the thermodynamics of hydration water isfundamental for the optimization of the processes.

Specifically, as a consequence of this understanding ithas been possible to reveal, with a combination of experi-mental and theoretical techniques, that the water moleculesthat hydrate a lysozyme protein have a new thermodynamicproperty at low temperatures. This property is characterizedby two specific-heat maxima at ambient pressure: one, atapproximately 252 K, is due to fluctuations in the forma-tion of hydrogen bonds; the other, at approximately 181 K,is due to the cooperative rearrangement of the network ofhydrogen bonds [126]. As a consequence of these two struc-tural changes of the hydration water network, the dynamicsof the water-protein complex presents two crossovers at thesame two low temperatures. Therefore, the thermodynam-ics of hydration water directly affects the dynamics and,as a consequence, the activity of the protein at these lowtemperatures.

Further understanding of the role of the thermodynamicsof hydration water in food-processing and in applicationsfor biological matter comes from the theoretical studyof nanoconfined water. We have shown that hydrationwater behaves as a two-dimensional system as long as theconfinement is strong only along one spatial dimension.By increasing the confinement along all the three spacialdimensions, we observe a crossover of the thermodynamics

from two-dimensional to three-dimensional. Therefore,increasing the confinement makes water thermodynamicsmore consistent with that of bulk water. This result has arelevant practical effect because the density fluctuationsin three dimensions are stronger than in two dimensions.Therefore, a stronger confinement could induce a largerdamage of the confining biological matter as a consequenceof density fluctuations [131].

Nevertheless, the degree of heterogeneity of the confin-ing matrix can represent a way to control the fluctuationsand their deleterious effects. Simulations of the many-bodymodel of hydration water presented here in a hydropho-bic heterogeneous matrix have revealed a strong decrease,between 90 % and 99 %, at all the considered pressures,of water compressibility, thermal expansion coefficient andspecific heat [123].

Furthermore, simulations for a water-like system at cry-opreservation temperatures, within a hydrophobic matrix,show that depending on the degree of heterogeneity ofthe matrix the fluctuations, and the anomalous water-likebehavior are largely affected. In particular, the order matrixenhances the water-like fluctuations, while the disorderedconfinement suppresses the anomalous behavior [152].

In addition, the combination of theoretical analysis andsimulation methods has been useful to shown that anoma-lous diffusion of hydrophobically nanoconfined water isa consequence of the interaction between the rupture ofhydrogen bonds and the cooperative reorganization ofmolecules in regions of a characteristic size of 1 nm. Thisresult explains why water diffuses faster when is confinedbetween hydrophobic surfaces that are separated by lessthan 1 nm, a phenomenon relevant for the practical real-ization in the near future of desalination processes andwater filtering by nanoscale graphene membranes or carbonnanolayers [127].

The extension of these analysis to study the stabilityof folded protein with respect to variation of temperatureand pressure is now in progress. At the same time, weare considering the complex problem of water-mediatedinteractions between proteins and nanoparticles in physio-logical solutions. Our aim is to better understand the roleof hydration water in these processes. Reports about thesecalculations will be released soon.

Acknowledgments We thank M.C. Barbosa, M. Bernabei, S.V.Buldyrev, F. Bruni, S.-H. Chen, K.A. Dawson, P. Debenedetti,P. Kumar, F. Leoni, J. Luo, G. Malescio, F. Mallamace, M.I.Marques, M. G. Mazza, A.B. de Oliveira, S. Pagnotta, D. Reguera,F. de los Santos, F. Sciortino, H.E. Stanley, F.W. Starr, K. Stokely,E.G. Strekalova, O. Vilanova and P. Vilaseca for helpful discussions.We thank for support the Spanish Ministerio de Ciencia e InnovacionGrant FIS2009-10210, the Spanish Ministerio de Economia y Com-petitividad Grant FIS2012-31025, the Generalitat de Catalunya Grant2010 FI- DGR, the European Commission Grant FP7-NMP-2010-EU-USA.

Author's personal copy

Food Biophysics

References

1. C.W. Kern, M. Karplus, Water, A Comprehensive Treatise, vol. 1(Plenum Press, New York, 1972), pp. 21–91

2. G. Franzese, M. Rubi, Aspects of Physical Biology, Biologi-cal Water, Protein Solutions, Transport and Replication. LectureNotes in Physics, vol. 752 (Springer, Berlin/Heidelberg, 2008)

3. P. Ball, Life’s, Matrix, A Biography of Water (Farrar, Straus andGiroux, New York, 2000)

4. S. Zou, J.S. Baskin, A.H. Zewail, Molecular recognition ofoxygen by protein mimics: dynamics on the femtosecond tomicrosecond time scale. Proc. Natl. Acad. Sci. USA 99, 9625–9630 (2002)

5. P. Ball, Water as an active constituent in cell biology. Chem. Rev.108, 74–108 (2008)

6. K.A. Dill, T.M. Truskett, V. Vlachy, B. Hribar-Lee, Modelingwater, the hydrophobic effect, ion solvation. Annu. Rev. Biophys.Biomol. 34, 173–199 (2005)

7. L.D. Barron, L. Hecht, G. Wilson, The lubricant of life: a pro-posal that solvent water promotes extremely fast conformationalfluctuations in mobile heteropolypeptide structure. Biochemistry36, 13143–13147 (1997)

8. V. Kurkal-Siebert, R. Agarwal, J.C. Smith, Hydration-dependentdynamical transition in protein: protein interactions at ∼240 K.Phys. Rev. Lett. 100, 138102 (2008)

9. P. Ball, Water: water—an enduring mystery. Nature 452(7185),291–292 (2008)

10. P.G. Debenedetti, H.E. Stanley, Supercooled and glassy water.Phys. Today 56, 40–46 (2003)

11. W.L. Rosenfeld, D. Woodley, Deep convective clouds with sus-tained supercooled liquid water down to −37.5◦ . Nature 405,440–442 (2000)

12. P.G. Debenedetti, Metastable Liquids. Concepts and Principles(Princeton University Press, Princeton, 1996)

13. B.M. Cwilong, Sublimation in a wilson chamber. Proc. R. Soc.Lond. A Mat. 190, 137–143 (1947)

14. H. Kanno, R.J. Speedy, C.A. Angell, Supercooling of water to−92 ◦C under pressure. Science 189, 880–881 (1975)

15. C.A. Angell, Insights into phases of liquid water from study of itsunusual glass-forming properties. Science 319, 582–587 (2008)

16. P. Needham, Hydrogen bonding: homing in on a tricky chemicalconcept. Stud. Hist. Philos. Sci. A 44, 51–65 (2013)

17. J. Poater, X. Fradera, M. Sol, M. Duran, S. Simon, On theelectron-pair nature of the hydrogen bond in the framework ofthe atoms in molecules theory. Chem. Phys. Lett. 369, 248–255(2003)

18. E.D. Isaacs, A. Shukla, P.M. Platzman, D.R. Hamann, B.Barbiellini, C.A. Tulk, Compton scattering evidence for cova-lency of the hydrogen bond in ice. J. Phys. Chem. Solids 61, 403–406 (2000)

19. A.K. Soper, M.A. Ricci, Structures of high-density and low-density water. Phys. Rev. Lett. 84, 2881–2884 (2000)

20. E.A. Zheligovskaya, G.G. Malenkov, Crystalline water ices.Russ. Chem. Rev. 75, 57–76 (2006)

21. T. Loerting, N. Giovambattista, Amorphous ice: experiments andnumerical simulation. J. Phys. Condens. Matter 18, R919–R977(2006)

22. K. Amann-Winkel, F. Low, P.H. Handle, W. Knoll, J. Peters, B.Geil, F. Fujaraband, T. Loerting, Limits of metastability in amor-phous ices: the neutron scattering Debye-Waller factor. Phys.Chem. Chem. Phys. 14, 16386–16391 (2012)

23. P.H. Poole, F. Sciortino, U. Essmann, H.E. Stanley, Phase-behavior of metastable water. Nature 360, 324–328 (1992)

24. H. Tanaka, A self-consistent phase diagram for supercooledwater. Nature 380, 328 (1996)

25. L. Xu, P. Kumar, S.V. Buldyrev, S.-H. Chen, P.H. Poole, F.Sciortino, H.E. Stanley, Relation between the Widom line andthe dynamic crossover in systems with a liquid-liquid phasetransition. Proc. Natl. Acad. Sci. USA 102, 16558–16562 (2005)

26. G. Franzese, H.E. Stanley, The widom line of supercooled water.J. Phys. Condens. Matter 19, 205126 (2007)

27. R.J. Speedy, Limiting forms of the thermodynamic divergencesat the conjectured stability limits in superheated and supercooledwater. J. Phys. Chem. 86, 3002–3005 (1982)

28. P.G. Debenedetti, Supercooled and glassy water. J. Phys. Con-dens. Matter 15, R1669–R1726 (2003)

29. P.G. Debenedetti, M.C. D’Antonio, Stability and tensile strengthof liquids exhibiting density maxima. AIChE J. 34, 447–455(1988)

30. P.H. Poole, F. Sciortino, T. Grande, H.E. Stanley, C.A. Angell,Effect of hydrogen bonds on the thermodynamic behavior ofliquid water. Phys. Rev. Lett. 73, 1632–1635 (1994)

31. H. Tanaka, Phase behaviors of supercooled water: reconcilinga critical point of amorphous ices with spinodal instability. J.Chem. Phys. 105, 5099–5111 (1996)

32. D. Paschek, A. Ruppert, A. Geiger, Thermodynamic and struc-tural characterization of the transformation from a metastablelow-density to a very high-density form of supercooled TIP4P-ew model water. Chem. Phys. Chem. 9, 2737–2741 (2008)

33. Y. Liu, A.Z. Panagiotopoulos, P.G. Debenedetti, Low-temperature fluid-phase behavior of ST2 water. J. Chem. Phys.131, 104508 (2009)

34. J.L.F. Abascal, C. Vega, Widom line and the liquid-liquid criti-cal point for the TIP4P/2005 water model. J. Chem. Phys. 133,234502 (2010)

35. Y. Liu, J.C. Palmer, A.Z. Panagiotopoulos, P.G. Ebenedetti,Liquid-liquid transition in ST2 water. J. Chem. Phys. 137,214505 (2012)

36. T. Kesselring, G. Franzese, S.V. Buldyrev, H. Herrmann, H.E.Stanley, Nanoscale dynamics of phase flipping in water nearits hypothesized liquid-liquid critical point. Sci. Rep. 2, 474(2012)

37. P.H. Poole, R.K. Bowles, I. Saika-Voivod, F. Sciortino, Freeenergy surface of ST2 water near the liquid-liquid phase transi-tion. J. Chem. Phys. 138, 034505-7 (2013)

38. S. Sastry, P.G. Debenedetti, F. Sciortino, H.E. Stanley,Singularity-free interpretation of the thermodynamics of super-cooled water. Phys. Rev. E 53, 6144–6154 (1996)

39. V. Holten, D.T. Limmer, V. Molinero, M.A. Anisimov, Nature ofthe anomalies in the supercooled liquid state of the mW modelof water. J. Chem. Phys. 138, 174501 (2013)

40. V. Molinero, E.B. Moore, Water modeled as an intermediate ele-ment between carbon and silicon. J. Phys. Chem. B 113, 4008–4016 (2009)

41. D.T. Limmer, D. Chandler, The putative liquid-liquid transitionis a liquid-solid transition in atomistic models of water. J. Chem.Phys. 135, 134503 (2011)

42. F.H. Stillinger, A. Rahman, Improved simulation of liquid waterby molecular-dynamics. J. Chem. Phys. 60, 1545 (1974)

43. F. Sciortino, I. Saika-Voivod, P.H. Poole, Study of the ST2 modelof water close to the liquid-liquid critical point. Phys. Chem.Chem. Phys. 13, 19759–19764 (2011)

44. P.H. Poole, S.R. Becker, F. Sciortino, F.W. Starr, Dynamicalbehavior near a liquid–liquid phase transition in simulationsof supercooled water. J. Phys. Chem. B 115, 14176–14183(2011)

45. T.A. Kesselring, G. Franzese, S.V. Buldyrev, H.J. Herrmann,H.E. Stanley, Nanoscale dynamics of phase flipping in waternear its hypothesized liquid-liquid critical point. Sci. Rep. 2, 474(2012)

Author's personal copy

Food Biophysics

46. E. Lascaris, T.A. Kesselring, G. Franzese, S.V. Buldyrev, H.J.Herrmann, H.E. Stanley, in Response Functions Near the Liquid-Liquid Critical Point of ST2 Water. AIP Conf. Proc. 1, 4th Inter-national Symposium on Slow Dynamics in Complex Systems,vol. 1518, pp. 520–526 (2013)

47. T.A. Kesselring, E. Lascaris, G. Franzese, S.V. Buldyrev, H.J.Herrmann, H.E. Stanley, Finite-size scaling investigation of theliquid-liquid critical point in ST2water and its stability withrespect to crystallization. J. Chem. Phys. 138, 244506 (2013)

48. K. Stokely, M.G. Mazza, H.E. Stanley, G. Franzese, Effect ofhydrogen bond cooperativity on the behavior of water. Proc. Natl.Acad. Sci. USA 107, 1301–1306 (2010)

49. A. Faraone, L. Liu, C.-Y. Mou, C.-W. Yen, S.-H. Chen, Fragile-to-strong liquid transition in deeply supercooled confined water.J. Chem. Phys. 121, 10843–10846 (2004)

50. L. Liu, S.-H. Chen, A. Faraone, C.-W. Yen, C.-Y. Mou, Pressuredependence of fragile-to-strong transition and a possible secondcritical point in supercooled confined water. Phys. Rev. Lett. 95,117802 (2005)

51. F. Mallamace, M. Broccio, C. Corsaro, A. Faraone, U.Wanderlingh, L. Liu, C.-Y. Mou, S.-H. Chen, The fragile-to-strong dynamic crossover transition in confined water, nuclearmagnetic resonance results. J. Chem. Phys. 124, 161102 (2006)

52. S.-H. Chen, L. Liu, E. Fratini, P. Baglioni, A. Faraone, E.Mamontov, Observation of fragile-to-strong dynamic crossoverin protein hydration water. Proc. Natl. Acad. Sci. USA 103,9012–9016 (2006)

53. E. Mamontov, Observation of fragile-to-strong liquid transitionin surface water in CeO2. J. Chem. Phys. 123, 171101 (2005)

54. H. Jansson, W.S. Howells, J. Swenson, Dynamics of fresh andfreeze-dried strawberry and red onion by quasielastic neutronscattering. J. Phys. Chem. B 110, 13786–13792 (2006)

55. S.-H. Chen, L. Liu, X. Chu, Y. Zhang, E. Fratini, P. Baglioni,A. Faraone, E. Mamontov, Experimental evidence of fragile-to-strong dynamic crossover in DNA hydration water. J. Chem.Phys. 125, 171103 (2006)

56. X.Q. Chu, E. Fratini, P. Baglioni, A. Faraone, S.-H. Chen, Obser-vation of a dynamic crossover in rna hydration water whichtriggers a dynamic transition in the biopolymer. Phys. Rev. E 77,011908 (2008)

57. G. Franzese, K. Stokely, X.-Q. Chu, P. Kumar, M.G.Mazza, S.-H. Chen, H.E. Stanley, Pressure effects in super-cooled water, comparison between a 2d model of waterand experiments for surface water on a protein. J. Phys.Condens. Matter 20, 494210 (2008)

58. R. Bergman, J. Swenson, Dynamics of supercooled water inconfined geometry. Nature 403, 283–286 (2000)

59. S. Cerveny, J. Colmenero, A. Alegrıa, Comment on “pressuredependence of fragile-to-strong transition and a possible secondcritical point in supercooled confined water”. Phys. Rev. Lett. 97,189802 (2006)

60. J. Swenson, Comment on “pressure dependence of fragile-to-strong transition and a possible second critical point in super-cooled confined water”. Phys. Rev. Lett. 97, 189801 (2006)

61. S. Pawlus, S. Khodadadi, A.P. Sokolov, Conductivity in hydratedproteins: no signs of the fragile-to-strong crossover. Phys. Rev.Lett. 100, 108103 (2008)

62. M. Vogel, Origins of apparent fragile-to-strong transitionsof protein hydration waters. Phys. Rev. Lett. 101, 225701(2008)

63. Y. Zhang, A. Faraone, W.A. Kamitakahara, K.-H. Liu, C.-Y.Mou, J.B. Leao, S. Chang, S.-H. Chen, Density hysteresis ofheavy water confined in a nanoporous silica matrix. Proc. Natl.Acad. Sci. USA 108, 12206–12211 (2011)

64. A.K. Soper, Density minimum in supercooled confined water.Proc. Natl. Acad. Sci. USA 108, E1192 (2011)

65. Y. Zhang, A. Faraone, W.A. Kamitakahara, K.-H. Liu, C.-Y.Mou, J.B. Leao, S. Chang, S.-H. Chen, Reply to Soper, “Densitymeasurement of confined water with neutron scattering”. Proc.Natl. Acad. Sci. USA 108, E1193–E1194 (2011)

66. P.W. Fenimore, H. Frauenfelder, B.H. McMahon, R.D. Young,Bulk-solvent and hydration–shell fluctuations, similar to α- andβ–fluctuations in glasses, control protein motions and functions.Proc. Natl. Acad. Sci. USA 101, 14408–14413 (2004)

67. P.W. Fenimore, H. Frauenfelder, B.H. McMahon, R.D. Young,Proteins are paradigms of stochastic complexity. Phys. A 351, 1–13 (2005)

68. V. Lubchenko, P.G. Wolynes, H. Frauenfelder, Mosaic energylandscapes of liquids and the control of protein conformationaldynamics by glass-forming solvents. J. Phys. Chem. B 109,7488–7499 (2005)

69. J. Swenson, H. Jansson, R. Bergman, Relaxation processes insupercooled confined water and implications for protein dynam-ics. Phys. Rev. Lett. 96, 247802 (2006)

70. A. Oleinikova, N. Smolin, I. Brovchenko, Origin of the dynamictransition upon pressurization of crystalline proteins. J. Phys.Chem. B 110, 19619–19624 (2006)

71. I. Brovchenko, A. Krukau, A. Oleinikova, A.K. Mazur, Waterpercolation governs polymorphic transitions and conductivity ofDNA. Phys. Rev. Lett. 97, 137801-4 (2006)

72. L. Zhang, L. Wang, Y.-T. Kao, W. Qiu, Y. Yang, O. Okobiah, D.Zhong, From the cover: mapping hydration dynamics around aprotein surface. Proc. Natl. Acad. Sci. USA 104, 18461–18466(2007)

73. D. Liu, X.-q. Chu, M. Lagi, Y. Zhang, E. Fratini, P. Baglioni,A. Alatas, A. Said, E. Alp, S.-H. Chen, Studies of phononlikelow–energy excitations of protein molecules by inelastic x-rayscattering. Phys. Rev. Lett. 101, 13 (2008)

74. J.M. Zanotti, G. Gibrat, M.C. Bellissent-Funel, Hydration waterrotational motion as a source of configurational entropy drivingprotein dynamics. Crossovers at 150 and 220 K. Phys. Chem.Chem. Phys. 10, 4865–4870 (2008)

75. P. Kumar, Z. Yan, L. Xu, M.G. Mazza, S.V. Buldyrev, S.-H.Chen, S. Sastry, H.E. Stanley, Glass transition in biomoleculesand the liquid-liquid critical point of water. Phys. Rev. Lett. 97,177802 (2006)

76. I. Brovchenko, A. Geiger, A. Oleinikova, Multiple liquid–liquidtransitions in supercooled water. J. Chem. Phys. 118, 9473–9476(2003)

77. G.E. Brown, V.E. Henrich, W.H. Casey, D.L. Clark, C.Eggleston, A. Felmy, D.W. Goodman, M. Gratzel, G. Maciel,M.I. McCarthy, K.H. Nealson, D.A. Sverjensky, M.F. Toney,J.M. Zachara, Metal oxide surfaces and their interactions withaqueous solutions and microbial organisms. Chem. Rev. 99, 77–174 (1999)

78. P. Jungwirth, B.J. Finlayson-Pitts, D.J. Tobias, Introduction:structure and chemistry at aqueous interfaces. Chem. Rev. 106,1137–1139 (2006)

79. N. Ji, V. Ostroverkhov, C.S. Tian, Y.R. Shen, Characterizationof vibrational resonances of water-vapor interfaces by phase-sensitive sum-frequency spectroscopy. Phys. Rev. Lett. 100,096102 (2008)

80. S.J. Marrink, M. Berkowitz, H.J.C. Berendsen, Moleculardynamics simulation of a membrane/water interface: the order-ing of water and its relation to the hydration force. Langmuir 9,3122–3131 (1993)

81. F. Zhou, K. Schulten, Molecular dynamics study of a membrane-water interface. J. Phys. Chem. 99, 2194–2207 (1995)

Author's personal copy

Food Biophysics

82. A. Poynor, L. Hong, I.K. Robinson, S. Granick, Z. Zhang, P.A.Fenter, How water meets a hydrophobic surface. Phys. Rev. Lett.97, 266101 (2006)

83. B.M. Ocko, A. Dhinojwala, J. Daillant, Comment on “how watermeets a hydrophobic surface”. Phys. Rev. Lett. 101, 039601(2008)

84. A. Poynor, L. Hong, I.K. Robinson, S. Granick, P.A. Fenter, Z.Zhang, Poynor et al. reply. Phys. Rev. Lett. 101, 039602 (2008)

85. O. Chara, A.N. McCarthy, C.G. Ferrara, E.R. Caffarena, J.R.Grigera, Water behavior in the neighborhood of hydrophilicand hydrophobic membranes: lessons from molecular dynamicssimulations. Phys. A 388, 4551–4559 (2009)

86. S. Granick, S.C. Bae, Chemistry: a curious antipathy for water.Science 322, 1477–1478 (2008)

87. X. Gao, L. Jiang, Biophysics: water-repellent legs of waterstriders. Nature 432, 36–36 (2004)

88. P. Liu, X. Huang, R. Zhou, B.J. Berne, Observation of a dewet-ting transition in the collapse of the melittin tetramer. Nature 437,159–162 (2005)

89. D.M. Huang, D. Chandler, Temperature and length scale depen-dence of hydrophobic effects and their possible implicationsfor protein folding. Proc. Natl. Acad. Sci. USA 97, 8324–8327(2000)

90. V. Bianco, S. Iskrov, G. Franzese, Understanding the role ofhydrogen bonds on water dynamics and protein stability. J. Biol.Phys. 38, 27–48 (2011)

91. G. Franzese, V. Bianco, S. Iskrov, Water at interface with pro-teins. Food Biophys. 6, 186–198 (2011)

92. S. Nakai, E.-L. Chan, Hydrophobic Interactions in Food Systems(CRC Press, Boca Raton, 1988)

93. M. Le Meste, G. Roudaut, D. Champion, G. Blond, D. Simatos,in Ingredient Interactions: Effects on Food Quality, ed. by A.G.Gaonkar, A. McPherson. Interaction of Water with Food Com-ponents. CRC Press (2005), Press and references therein

94. R. Patil, S. Das, A. Stanley, L. Yadav, A. Sudhakar, A.K. Varma,Optimized hydrophobic interactions and hydrogen bonding atthe target-ligand interface leads the pathways of drug-designing.PLoS ONE 5, e12029 (2010)

95. D.A. Doshi, E.B. Watkins, J.N. Israelachvili, J. Majewski,Reduced water density at hydrophobic surfaces: effect of dis-solved gases. Proc. Natl. Acad. Sci. USA 102, 9458–9462(2005)

96. Z. Ge, D.G. Cahill, P.V. Braun, Thermal conductance ofhydrophilic and hydrophobic interfaces. Phys. Rev. Lett. 96,186101 (2006)

97. L.B.R. Castro, A.T. Almeida, D.F.S. Petri, The effect of wateror salt solution on thin hydrophobic films. Langmuir 20, 7610–7615 (2004)

98. Y. Takata, J.-H.J. Cho, B.M. Law, M. Aratono, Ellipsometricsearch for vapor layers at liquid-hydrophobic solid surfaces.Langmuir 22, 1715–1721 (2006)

99. M. Mao, J. Zhang, R.-H. Yoon, W.A. Ducker, Is there a thin filmof air at the interface between water and smooth hydrophobicsolids? Langmuir 20, 1843–1849 (2004)

100. Y.-S. Seo, S. Satija, No intrinsic depletion layer on a polystyrenethin film at a water interface. Langmuir 22, 7113–7116(2006)

101. J.W.G. Tyrrell, P. Attard, Images of nanobubbles on hydropho-bic surfaces and their interactions. Phys. Rev. Lett. 87, 176104(2001)

102. N. Ishida, T. Inoue, M. Miyahara, K. Higashitani, Nano bubbleson a hydrophobic surface in water observed by tapping-modeatomic force microscopy. Langmuir 16, 6377–6380 (2000)

103. E.A. Vogler, Structure and reactivity of water at biomaterialsurfaces. Adv. Colloid Interf. 74, 69–117 (1998)

104. M.-C. Bellissent-Funel, Water near hydrophilic surfaces. J. Mol.Liq. 96, 287–304 (2002)

105. R.C. Major, J.E. Houston, M.J. McGrath, J.I. Siepmann, X.-Y.Zhu, Viscous water meniscus under nanoconfinement. Phys. Rev.Lett. 96, 177803 (2006)

106. T.-D. Li, J. Gao, R. Szoszkiewicz, U. Landman, E. Riedo, Struc-tured and viscous water in subnanometer gaps. Phys. Rev. B 75,115415 (2007)

107. L.F. Boesel, R.L. Reis, The effect of water uptake on thebehaviour of hydrophilic cements in confined environments.Biomaterials 27, 5627–5633 (2006)

108. F. Bresme, E. Chacon, P. Tarazona, K. Tay, Intrinsic structureof hydrophobic surfaces: the oil-water interface. Phys. Rev. Lett.101, 056102 (2008)

109. N. Giovambattista, C.F. Lopez, P.J. Rossky, P.G. Debenedetti,Hydrophobicity of protein surfaces, Separating geometry fromchemistry. Proc. Natl. Acad. Sci. USA 105, 2274–2279(2008)

110. G. Franzese, M. Yamada, H.E. Stanley, Hydrogen-bonded liq-uids: effects of correlations of orientational degrees of freedom.AIP Conf. Proc. 519, 281–287 (2000)

111. G. Franzese, H.E. Stanley, Liquid-liquid critical point in a hamil-tonian model for water: analytic solution. J. Phys. Condens.Matter 14, 2201–2209 (2002)

112. G. Franzese, H.E. Stanley, A theory for discriminating the mech-anism responsible for the water density anomaly. Phys. A 314,508–513 (2002)

113. G. Franzese, M.I. Marques, H.E. Stanley, Intramolecular cou-pling as a mechanism for a liquid-liquid phase transition. Phys.Rev. E 67, 011103 (2003)

114. P. Kumar, G. Franzese, S.V. Buldyrev, H.E. Stanley, Dynamics ofWater at Low Temperatures and Implications for Biomolecules.Aspects of Physical Biology, vol. 752 of Lecture Notes in Physics(Springer, 2008), pp. 3–22

115. P. Kumar, G. Franzese, H.E. Stanley, Dynamics and thermody-namics of water. J. Phys. Condens. Matter 20, 244114 (2008)

116. P. Kumar, G. Franzese, H.E. Stanley, Predictions of dynamicbehavior under pressure for two scenarios to explain wateranomalies. Phys. Rev. Lett. 100, 105701 (2008)

117. G. Franzese, F. de los Santos, Dynamically slow processes insupercooled water confined between hydrophobic plates. J. Phys.Condens. Matter 21, 504107 (2009)

118. M.G. Mazza, K. Stokely, E.G. Strekalova, H.E. Stanley, G.Franzese, Cluster monte carlo and numerical mean field anal-ysis for the water liquid-liquid phase transition. Comput. Phys.Commun. 180, 497–502 (2009)

119. F. de los Santos, G. Franzese, in Influence of Intramolecular Cou-plings in a Model for Hydrogen-Bonded Liquids. Proceedings ofModeling and Simulation of New Materials, vol. 1091 of AIP,Granada (Spain, 2009), pp. 185–197

120. G. Franzese, A.H. Martınez, P. Kumar, M.G. Mazza, K. Stokely,E.G. Strekalova, F. de los Santos, H.E. Stanley, Phase transitionsand dynamics of bulk and interfacial water. J. Phys. Condens.Matter 22, 284103 (2010)

121. K. Stokely, M.G. Mazza, H.E. Stanley, G. Franzese, inMetastable Systems Under Pressure Chapter Metastable WaterUnder Pressure. NATO Science for Peace and Security Series A,Chemistry and Biology (Springer, 2010), pp. 197–216

122. G. Franzese, H.E. Stanley, Understanding the Unusual Proper-ties of Water. Chapter 7 (CRC Press, Boca Raton, 2010)

123. E.G. Strekalova, M.G. Mazza, H.E. Stanley, G. Franzese, Largedecrease of fluctuations for supercooled water in hydrophobicnanoconfinement. Phys. Rev. Lett. 106, 145701 (2011)

124. O. Vilanova, G. Franzese, Structural and dynamical properties ofnanoconfined supercooled water, arXiv:1102.2864 (2011)

Author's personal copy

Food Biophysics

125. F. de los Santos, G. Franzese, Understanding diffusion anddensity anomaly in a coarse-grained model for water confinedbetween hydrophobic walls. J. Phys. Chem. B 115, 14311–14320(2011)

126. M.G. Mazza, K. Stokely, S.E. Pagnotta, F. Bruni, H.E. Stanley,G. Franzese, More than one dynamic crossover in protein hydra-tion water. Proc. Natl. Acad. Sci. USA 108, 19873–19878(2011)

127. F. de los Santos, G. Franzese, Relations between the diffusionanomaly and cooperative rearranging regions in a hydrophobi-cally nanoconfined water monolayer. Phys. Rev. E 85, 010602(2012)

128. E.G. Strekalova, M.G. Mazza, H.E. Stanley, G. Franzese,Hydrophobic nanoconfinement suppresses fluctuations in super-cooled water. J. Phys. Condens. Matter 24, 064111 (2012)

129. E. Strekalova, D. Corradini, M. Mazza, S. Buldyrev, P. Gallo, G.Franzese, H. Stanley, Effect of hydrophobic environments on thehypothesized liquid-liquid critical point of water. J. Biol. Phys.38, 97–111 (2012)

130. M.G. Mazza, K. Stokely, H.E. Stanley, G. Franzese, Effectof pressure on the anomalous response functions of a con-fined water monolayer at low temperature. J. Chem. Phys. 137,204502-13 (2012)

131. V. Bianco, G. Franzese, Critical behavior of a water monolayerunder hydrophobic confinement, arXiv:1212.2847 (2012)

132. R. Ludwig, Water: from clusters to the bulk. Angew. Chem. In.Ed. 40, 1808–1827 (2001)

133. L.H. de la Pena, P.G. Kusalik, Temperature dependence of quan-tum effects in liquid water. J. Am. Chem. Soc. 127, 5246–5251(2005)

134. D. Liu, Y. Zhang, C.-C. Chen, C.-Y. Mou, P.H. Poole, S.-H.Chen, Observation of the density minimum in deeply super-cooled confined water. Proc. Natl. Acad. Sci. USA 104, 9570–9574 (2007)

135. D.A. Fuentevilla, M.A. Anisimov, Scaled equation of state forsupercooled water near the liquid-liquid critical point. Phys. Rev.Lett. 97, 195702 (2006)

136. C.E. Bertrand, M.A. Anisimov, Peculiar thermodynamics of thesecond critical point in supercooled water. J. Phys. Chem. B 115,14099–14111 (2011)

137. V. Holten, C.E. Bertrand, M.A. Anisimov, J.V. Sengers, Thermo-dynamics of supercooled water. J. Chem. Phys. 136, 094507-18(2012)

138. V. Holten, M.A. Anisimov, Entropy-driven liquid-liquid separa-tion in supercooled water. Sci. Rep. 2, 10 (2012)

139. N.E. Levinger, Water in confinement. Science 298, 1722–1723(2002)

140. C.I. Bouzigues, P. Tabeling, L. Bocquet, Nanofluidics in thedebye layer at hydrophilic and hydrophobic surfaces. Phys. Rev.Lett. 101, 114503 (2008)

141. J.C.T. Eijkel, A. Berg, Nanofluidics: what is it and what can weexpect from it? Microfluid. Nanofluid. 1, 249–267 (2005)

142. X.-Q. Chu, A. Faraone, C. Kim, E. Fratini, P. Baglioni, J.B. Leao,S.-H. Chen, Proteins remain soft at lower temperatures underpressure. J. Phys. Chem. B 113, 5001–5006 (2009)

143. E. Donth, The size of cooperatively rearranging regions at theglass transition. J. Non-Crystal. Solids 53, 325–330 (1982)

144. Y.-g. Zheng, H.-f. Ye, Z.-q. Zhang, H.-w. Zhang, Water dif-fusion inside carbon nanotubes: mutual effects of surfaceand confinement. Phys. Chem. Chem. Phys. 14, 964–971(2012)

145. R.R. Nair, H.A. Wu, P.N. Jayaram, I.V. Grigorieva, A.K.Geim, Unimpeded permeation of water through helium–leak–tight graphene-based membranes. Science 335, 442–444(2012)

146. S. Karan, S. Samitsu, X. Peng, K. Kurashima, I. Ichinose, Ultra-fast viscous permeation of organic solvents through diamond-likecarbon nanosheets. Science 335, 444–447 (2012)

147. M. Settles, W. Doster, Anomalous diffusion of adsorbed water,a neutron scattering study of hydrated myoglobin. Faraday Dis-cuss. 103, 269–279 (1996)

148. W. Doster, The protein-solvent glass transition. Biochim. Bio-phys. Acta 1804, 3–14 (2010)

149. A.D. Bruce, N.B. Wilding, Scaling fields and universality of theliquid-gas critical point. Phys. Rev. Lett. 68, 193–196 (1992)

150. N.B. Wilding, Critical-point and coexistence-curve properties ofthe Lennard-Jones fluid: a finite-size scaling study. Phys. Rev. E52, 602–611 (1995)

151. Y. Zhang, K.H. Liu, M. Lagi, D. Liu, K.C. Littrell, C.Y. Mou,S.-H. Chen, Absence of the density minimum of supercooledwater in hydrophobic confinement. J. Phys. Chem. B 113, 5007–5010 (2009)

152. E.G. Strekalova, J. Luo, H.E. Stanley, G. Franzese, S.V.Buldyrev, Confinement of anomalous liquids in nanoporousmatrices. Phys. Rev. Lett. 109, 105701 (2012)

153. F. Mallamace, C. Branca, M. Broccio, C. Corsaro, C.-Y. Mou,S.-H. Chen, The anomalous behavior of the density of water inthe range 30 K < T < 373 K. Proc. Natl. Acad. Sci. USA 104,18387–18391 (2007)

154. J. Kyte, R.F. Doolittle, A simple method for displaying thehydropathic character of a protein. J. Mol. Biol. 157, 105–132(1982)

155. T.R. Jensen, M.Ø. Jensen, N. Reitzel, K. Balashev, G.H.Peters, K. Kjaer, T. Bjørnholm, Water in contact with extendedhydrophobic surfaces: direct evidence of weak dewetting. Phys.Rev. Lett. 90, 086101 (2003)

156. K. Lum, D. Chandler, J.D. Weeks, Hydrophobicity at smalland large length scales. J. Phys. Chem. B 103, 4570–4577(1999)

157. X. Huang, R. Zhou, B.J. Berne, Drying and hydrophobic col-lapse of paraffin plates. J. Phys. Chem. B 109, 3546–3552(2005)

158. T. Hotta, M. Sasai, Fluctuating hydration structure aroundnanometer-size hydrophobic solutes i. Caging and drying aroundC60 and C60H60 spheres. J. Phys. Chem. B 109, 18600–18608(2005)

159. T. Hotta, M. Sasai, Fluctuating hydration structure aroundnanometer-size hydrophobic solutes ii. Caging and drying aroundsingle-wall carbon nanotubes. J. Phys. Chem. C 111, 2861–2871(2007)

160. M.I. Marques, J.M. Borreguero, H.E. Stanley, N.V. Dokholyan,Possible mechanism for cold denaturation of proteins at highpressure. Phys. Rev. Lett. 91, 138103 (2003)

161. C.L. Dias, T. Ala-Nissila, M. Karttunen, I. Vattulainen, M. Grant,Microscopic mechanism for cold denaturation. Phys. Rev. Lett.100, 118101-4 (2008)

162. F. Meersman, C.M. Dobson, K. Heremans, Protein unfolding,amyloid fibril formation and configurational energy landscapesunder high pressure conditions. Chem. Soc. Rev. 35, 908–917(2006)

163. H.S. Frank, M.W. Evans, Free volume and entropy in con-densed systems iii. entropy in binary liquid mixtures; partialmolal entropy in dilute solutions; structure and thermody-namics in aqueous electrolytes. J. Chem. Phys. 13, 507–532(1945)

164. N. Muller, Search for a realistic view of hydrophobic effects.Acc. Chem. Res. 23, 23–28 (1990)

165. K.A.T. Silverstein, A.D.J. Haymet, K.A. Dill, A simple model ofwater and the hydrophobic effect. J. Am. Chem. Soc. 120, 3166–3175 (1998)

Author's personal copy

Food Biophysics

166. K.F. Lau, K.A. Dill, A lattice statistical mechanics model ofthe conformational and sequence spaces of proteins. Macro-molecules 22, 3986–3997 (1989)

167. G. Caldarelli, P. de los Rios, Cold and warm denaturation ofproteins. J. Biol. Phys. 27, 229–241 (2001)

168. B.A. Patel, P.G. Debenedetti, F.H. Stillinger, P.J. Rossky, Awater-explicit lattice model of heat-, cold-, and pressure–inducedprotein unfolding. Biophys. J. 93, 4116–4127 (2007)

169. S.V. Buldyrev, P. Kumar, P.G. Debenedetti, P.J. Rossky, H.E.Stanley, Water-like solvation thermodynamics in a sphericallysymmetric solvent model with two characteristic lengths. Proc.Natl. Acad. Sci. USA 104, 20177–20182 (2007)

170. S. Matysiak, P.G. Debenedetti, P.J. Rossky, Role of hydrophobichydration in protein stability: a 3d water-explicit protein modelexhibiting cold and heat denaturation. J. Phys. Chem. B 116,8095–8104 (2012)

Author's personal copy