Volumetric Properties at High Pressures of the Nucleosides Inosine, 2

Article pubs.acs.org/jced

Volumetric Properties at High Pressures of the Nucleosides Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine and the Volumetric Properties of Guanosine Derived Using Group Additivity Methods Gavin R. Hedwig,*,† Geoffrey B. Jameson,† and Harald Høiland‡ †

Institute of Fundamental Sciences-Chemistry, Massey University, Private Bag 11222, Palmerston North 4474, New Zealand Department of Chemistry, University of Bergen, N-5020 Bergen, Norway

‡

S Supporting Information *

ABSTRACT: Sound speeds have been measured for aqueous solutions of the nucleosides inosine, 2′-deoxyinosine, and 2′deoxyguanosine at T = 298.15 K and at the pressures p = (0.1, 10, 20, 40, 60, 80, and 100) MPa. Using methods described in previous work, these sound speeds were used to derive the partial molar volumes at infinite dilution, V2o, the partial molar isentropic o compressions at infinite dilution, KS,2 , and the partial molar isothermal compressions at infinite dilution, KoT,2 {KoT,2 = −(∂Vo2/ ∂p)T}, for the nucleosides in aqueous solution at the elevated pressures. A semiempirical model was used to rationalize the KoT,2 results in terms of changes in hydration of the solutes as a function of pressure. Group additivity methods were used to derive values of Vo2 and KoT,2 over the pressure range p = (10 to 100) MPa for the sparingly soluble nucleoside guanosine.

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INTRODUCTION It is widely accepted that in the early development of life on Earth, RNA alone directed and catalyzed the chemistry of life. This hypothesis is commonly referred to as the “RNA world”.1−5 One of the challenges of prebiotic chemistry is to demonstrate a feasible synthetic route to RNA from its simple building blocks such as the nucleic-acid bases, nucleosides, and nucleotides. Recent findings that activated purine and pyrimidine ribonucleotides can be synthesized6,7 and polymerized8 under plausible prebiotic conditions is certainly encouraging. The exact primordial conditions of temperature, pressure, and pH under which such RNA syntheses may have occurred are also far from established.9−12 It is important, therefore, to determine the conditions of temperature and pressure under which RNA and its constituent molecules are both physically and chemically stable in order to define the boundary conditions necessary for an RNA world to prevail. Knowledge of the volumetric properties as a function of pressure for RNA and its constituent building blocks is essential for mapping the physical stabilities of these molecules over the (p−T) landscape. Several years ago, we reported13 a method to derive, from speed of sound measurements as a function of pressure, the partial molar volumes at infinite dilution, Vo2, the partial molar isentropic compressions at infinite dilution, KoS,2, and the partial molar isothermal compressions at infinite dilution, KoT,2 {KoT,2 = −(∂Vo2/∂p)T}, for solutes in aqueous solution over a wide pressure range. This method was subsequently14 used to determine the volumetric properties at infinite dilution for the nucleosides adenosine, cytidine, and © XXXX American Chemical Society

uridine in aqueous solution at T = 298.15 K and p = (10 to 120) MPa. These nucleosides, along with guanosine, are the major nucleoside constituents of RNA. Guanosine was not included in our previous study because its very low saturated molality in water (1.92 × 10−3 mol·kg−1 at T = 298.15 K15) precluded the determination of reliable solution thermodynamic properties from direct experimental measurements. One approach to determine the volumetric properties of guanosine is to use an indirect group additivity method. The nucleoside 2′-deoxyguanosine is of sufficient solubility in water to enable volumetric properties to be derived from experimental data. Consequently, if a contribution can be obtained for the hydroxyl group in the 2′ position of the ribose ring, then the volumetric properties of guanosine can be obtained by group additivity. The nucleosides we have chosen for this purpose are inosine and 2′-deoxyinosine. As shown in Figure 1, inosine differs structurally from guanosine only by the absence of an amino group in the 2 position of the purine ring. We report herein the results of speed of sound measurements at T = 298.15 K and at the pressures p = (10, 20, 40, 60, 80, and 100) MPa for aqueous solutions of the nucleosides inosine, 2′deoxyinosine, and 2′-deoxyguanosine. These sound speeds were analyzed to obtain the thermodynamic properties Vo2, KoS,2, and KoT,2 for the nucleosides at each of the six pressures. Received: June 7, 2014 Accepted: September 8, 2014

A

dx.doi.org/10.1021/je500458e | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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Figure 1. Structures of nucleosides guanosine and inosine and their 2′-deoxy derivatives.

Table 1. Source, Purification Method, and Mass Fraction Purity of Each Nucleoside

a

chemical name

source

purification method

mass fraction purity

method of analysis

inosine 2′-deoxyinosine 2′-deoxyguanosine monohydrate

Sigma Sigma ChemGenes Corporation

recrystallization recrystallization recrystallization

≥0.99 ≥0.98 ≥0.99

CHNa CHN CHN

Elemental analyses for C, H, and N.

A necessary requirement for the evaluation of these properties at high pressures is the availability of a range of reliable thermodynamic properties, in particular the partial molar isobaric expansion at infinite dilution, Eo2 {Eo2 = (∂Vo2 /∂T)p}, for the nucleosides at the pressure p = 0.1 MPa.13 Values of Eo2 and also the partial molar heat capacities at infinite dilution, Cop,2, for inosine, 2′-deoxyinosine, and 2′-deoxyguanosine in aqueous solution at p = 0.1 MPa and T = 298.15 K have been reported previously.16 Becauase speed of sound data for solutions of these nucleosides at p = 0.1 MPa at T = 298.15 K are also a prerequisite for the evaluation of volumetric properties at high pressures, these results are also included herein.

Because all the nucleosides have been well characterized previously,16 solution density was chosen as a criterion of purity of the recovered material used in this work. The densities at T = 298.15 K for aqueous solutions prepared using these recovered solids were in excellent agreement (within ± 3.0 × 10−3 kg·m−3) with those calculated using polynomials derived from our reported density data.16 The water used to prepare solutions and as the reference solvent was purified by reverse osmosis and deionization using an Ondeo Purite Select water purification system and was thoroughly degassed immediately prior to use. All solutions were prepared by mass using a Mettler Toledo AX205 analytical balance (readability 0.01 mg) and corrections were made for the effect of air buoyancy. The uncertainties for the solution molalities were < 2 × 10 −5 mol·kg−1. Apparatus. Sound speed measurements at atmospheric pressure were carried out using a rubidium clock sound velocity meter, the details of which have been described elsewhere.17 The temperature of the thermostat bath was maintained to ± 0.001 K using methods described in earlier work from the Bergen laboratory.18 The reproducibility of a sound speed measurement was to better than ± 0.005 m·s−1. The instrument used for the sound speed measurements at high pressures was

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EXPERIMENTAL METHODS Materials. General information on the nucleosides used in this study is given in Table 1. The samples of inosine, 2′deoxyinosine, and 2′-deoxyguanosine monohydrate used were either purified solids remaining from an earlier study16 or material recovered from aqueous solutions used for experimental measurements in this previous work. For each nucleoside, the recovered solid was recrystallized from hot water using the procedures described in detail elsewhere.16 B



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Table 2. Sound Speeds and Apparent Molar Isentropic Compressions for Aqueous Solutions of Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine at T = 298.15 K and p = 0.1 MPaa mb mol·kg

uc −1

mb

1015 KS,ϕ

−1

−1

−1

m ·mol ·Pa 3

m·s

mol·kg

uc −1

1015 KS,ϕ

−1

m ·mol−1·Pa−1 3

m·s

Inosine

a

0.08494 0.07502 0.06847 0.06500 0.06089 0.05297

1502.191 1501.578 1501.143 1500.933 1500.669 1500.162

−10.19 −10.47 −10.44 −10.60 −10.66 −10.83

± ± ± ± ± ±

0.04 0.04 0.04 0.05 0.05 0.06

0.02994 0.02896 0.02813 0.02701 0.02599

1498.669 1498.604 1498.555 1498.473 1498.407

−6.34 −6.34 −6.46 −6.29 −6.32

± ± ± ± ±

0.10 0.10 0.11 0.11 0.12

0.01070 0.01057 0.01051 0.01048

1497.459 1497.444 1497.443 1497.442

−11.67 −11.33 −11.53 −11.60

± ± ± ±

0.28 0.28 0.29 0.29

0.04489 0.03696 0.03395 0.02885 0.02048 0.01854 2′-Deoxyinosine 0.02493 0.02400 0.02301 0.02199

−11.01 ± −11.07 ± −11.19 ± −11.23 ± −11.42 ± −11.56 ±

1499.643 1499.122 1498.930 1498.594 1498.046 1497.921

2′-Deoxyguanosine 0.01030 0.01028 0.01011 0.009827

0.07 0.08 0.09 0.10 0.15 0.16

1498.343 1498.274 1498.213 1498.146

−6.46 −6.28 −6.40 −6.41

± ± ± ±

0.12 0.13 0.13 0.14

1497.434 1497.426 1497.415 1497.396

−11.86 −11.49 −11.56 −11.64

± ± ± ±

0.29 0.29 0.30 0.31

The standard uncertainty for T is 0.01 K. bThe standard uncertainty for m is 1 × 10−5 mol·kg−1. cThe repeatability of u is ± 0.005 m·s−1.

Table 3. Coefficients of Eq 8 Used to Calculate Solution Densities, Specific Heat Capacities, and Isentropic Compressibilities for Aqueous Solutions of Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine at p = 0.1 MPa ρ

T K

kg·m

κS

cp −3

−1

−1

Pa−1

J·K ·g

a1

a2

a2

11

10 a1

1011a2

0.546 ± 0.016

−8.5912 ± 0.0059

3.242 ± 0.089

0.64 ± 0.40

−7.957 ± 0.025

1.90 ± 0.94

b

−8.6951 ± 0.0057

b

a1 Inosine

± ± ± ±

0.07 0.07 0.07 0.09

−15.3 −17.0 −16.2 −15.4

288.15 298.15 303.15 313.15

104.41 102.33 101.60 100.18

288.15 298.15 303.15 313.15

90.108 ± 0.03 88.62 ± 0.2 88.08 ± 0.2 86.87 ± 0.2

a

288.15 298.15 303.15 313.15

100.35 ± 0.07 98.02 ± 0.04 97.34 ± 0.05 96.01 ± 0.08

b

± ± ± ±

1.0 1.0 1.2 1.5

−0.7323 ± 0.0013

2′-Deoxyinosine −8.4 ± 7.7 −14.0 ± 9.1 −20.3 ± 6.7

−0. 699 ± 0.010

2′-Deoxyguanosine

a

b

−0.7183 ± 0.0033

b b

b

See text. The linear form of eq 8 was used because of the narrow molality range accessible for this sparingly soluble compound.

δ = κT − κS = (Tα 2V )/Cp = (Tα 2)/σ

designed and constructed at the University of Bergen. Details of the apparatus and operational procedures used have been described previously.13 The operating temperature (T = 298.15 K) was stable to ± 0.001 K, and the pressure was adjustable to within ± 0.15 MPa of any nominal value.13 The estimated uncertainty for a measured sound speed was ± 0.03 m·s−1.

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(1)

where Cp is the isobaric heat capacity, σ is the heat capacity per unit volume, and α is the isobaric expansibility,19 which is defined by the equation α = (∂V /∂T )p /V

RESULTS

(2)

Because the difference between Cp and the isochoric heat capacity, Cv, is given by21

Thermodynamic Formalism. The difference between the isothermal compressibility, κT {κT = −(∂V/∂p)T/V}, and the isentropic compressibility, κS {κS = −(∂V/∂p)S/V}, which is usually represented by the symbol δ,19,20 can be written in the form19−21

Cp − Cv = (Tα 2V )/κT

(3)

it follows from eqs 1 and 3 that the ratio of Cp to Cv, which is often expressed using the symbol γ, is given by C



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Table 4. Partial Molar Isentropic Compressions at Infinite Dilution, the Sk(S) Values, and the Partial Molar Isothermal Compressions at Infinite Dilution for Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine in Aqueous Solution at T = 298.15 K and p = 0.1 MPa 1015 KoS,2

solute

1015 Sk(S)

m3·mol−1·Pa−1 −11.83 ± 0.06 −11.1 ± 1.0b −13.8 ± 0.8c −6.37 ± 0.07a −7.2 ± 1.0b −11.58 ± 0.16a −5.0 ± 1.0b −5.8 ± 0.9c

inosine

2′-deoxyinosine 2′-deoxyguanosine

a

a

1015 KoT,2

m3·kg·mol−2·Pa−1

m3·mol−1·Pa−1

19.1 ± 0.9

−5.05 ± 0.29a

a

d

−0.30 ± 0.14a

d

−4.44 ± 0.50a

This work. bFrom ref 30. cFrom ref 31. dSee text.

γ = Cp/Cv = κT /κS

where κS,1 * is the isentropic compressibility for solvent water (κ*S,1 = 4.47736 × 10−10 Pa−1 at T = 298.15 K),25 M2 is the solute molar mass, and the remaining symbols are as defined vide supra. The KS,ϕ results along with their uncertainties, which were estimated using propagation of errors methods26 applied to eqs 5 and 9, are given in Table 2. For dilute solutions of nonelectrolytes, the molality dependence of KS,ϕ can usually be represented by the simple linear equation27−29

(4)

The isentropic compressibilities of fluids are conveniently evaluated from speed of sound measurements. In the absence of sound dispersion, the isentropic compressibility is related to the speed of sound, u, by the Newton−Laplace equation22 κS = 1/(u 2ρ)

(5)

where ρ is the density of the fluid. Combining the isothermal compressibility recast in terms of density, {κT = (∂ρ/∂p)T/ρ}, with eqs 4 and 5 leads to the equation (∂ρ /∂p)T = γ /u 2

KS , ϕ = KSo,2 + Sk(S)m

where is the partial molar isentropic compression of the solute at infinite dilution and Sk(S) is the experimental slope. Values of KoS,2 and Sk(S) and their standard deviations obtained from the weighted least-squares analyses of KS,ϕ using eq 10 are given in Table 4. The weighting factors used in the analyses were the inverse squares of the uncertainties for the apparent molar isentropic compressions. For 2′-deoxyinosine and 2′deoxyguanosine, the values for Sk(S) were not statistically significant because the accessible molality ranges are too narrow. The KoS,2 results given in Table 4 are actually the means of the KS,ϕ values and the uncertainties given are the standard deviations. Included in Table 4 for the purposes of comparison are the KoS,2 values at T = 298.15 K reported in previous studies.30,31 Our results for inosine and 2′-deoxyinosine are in agreement with those reported by Lee and Chalikian,30 within the admittedly large uncertainty limits. However, our KoS,2 value for 2′-deoxyguanosine is significantly more negative than either of the two values available from the literature.30,31 This result is not unexpected given that similarly large differences were observed between the literature values30,31 of Vo2 for 2′deoxyguanosine at T = 298.15 K and that we obtained.16 The state of hydration of the solid material used may be the source of these discrepancies. Only in our studies has the sample of 2′deoxyguanosine been well characterized as a monohydrate. The values of Eo2 and Cop,2 for the three nucleosides at T = 298.15 K and p = 0.1 MPa reported in previous work,16 along with various properties of the solvent, were used to convert the KoS,2 values for the nucleosides into the more useful partial molar isothermal compressions at infinite dilution, KoT,2, {KoT,2 = −(∂Vo2 /∂p)T}. The expression used for this conversion is19,20

(6)

Integration of eq 6 at constant temperature between the limits of p = 0.1 MPa and a pressure p gives the expression p

ρ(p) − ρ(p = 0.1) =

∫p=0.1 (γ /u2)dp

(7)

This relationship provides a route for the evaluation of volumetric properties at high pressures. If the quantities ρ, γ, and u are known for a system at p = 0.1 MPa, and if the pressure dependence of the quantity (γ/u2) can be determined, then the density ρ at any pressure p, ρ(p) can be obtained using eq 7. Partial Molar Isentropic and Isothermal Compressions at p = 0.1 MPa. The measured sound speeds for aqueous solutions of the nucleosides at T = 298.15 K and p = 0.1 MPa are given in Table 2. The isentropic compressibility, κS, for each solution was obtained using eq 5, with the density calculated using a power series in solution molality, m, of the generic form y = y 1∗ + a1(m /mo) + a 2(m /mo)2

(8)

where a1 and a2 are the fitted coefficients, m = 1.0 mol·kg−1, and y*1 is the respective property for pure water (ρ*1 = 997.047 kg·m−3 at T = 298.15 K23). For each nucleoside, the parameters a1 and a2 and their estimated uncertainties, which are the results taken from previous work,16 are summarized in Table 3. For each solution, the value of κS was used to calculate the apparent molar isentropic compression, KS,ϕ, which is defined by the relation19,24 o

KS , ϕ = (M 2κS /ρ) −

o KTo ,2 = KSo,2 + δ1∗(2E2o /α1∗ − Cp,2 /σ1∗)

(11)

where the quantities δ1*, α1*, and σ1* are all properties of pure water: σ1* is the heat capacity per unit volume, σ1* = 4.1670 J· K−1·cm−3 at T = 298.15 K,32 α*1 is the isobaric expansibility {α*1

(κS∗,1ρ − κSρ1∗ ) (mρρ1∗ )

(10)

KoS,2

(9) D



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Table 5. Calculated Values of Isentropic Compressibility, Density, Sound Speed, Specific Heat Capacity, α, and γ for Aqueous Solutions of Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine at T = 298.15 K and p = 0.1 MPa m

1010κSa

ρb

uc

cpd

106α

mol·kg−1

Pa−1

kg·m−3

m·s−1

J·K−1·g−1

K−1

0.08535 0.07798 0.07008 0.06399 0.05598 0.04902 0.04096 0.03399 0.02602

4.40639 4.41234 4.41875 4.42371 4.43028 4.43603 4.44272 4.44854 4.45523

1005.657 1004.922 1004.134 1003.525 1002.722 1002.022 1001.210 1000.505 999.698

0.02944 0.02877 0.02755 0.02749 0.02661 0.02481 0.02390 0.02283

4.45410 4.45462 4.45558 4.45563 4.45632 4.45774 4.45845 4.45929

999.648 999.590 999.482 999.477 999.399 999.240 999.160 999.065

0.010750 0.010678 0.010615 0.010591 0.010483 0.010429 0.010360 0.010302

4.46801 4.46808 4.46813 4.46815 4.46824 4.46829 4.46835 4.46840

998.101 998.094 998.088 998.085 998.075 998.069 998.063 998.057

Inosine 1502.220 1501.755 1501.255 1500.868 1500.355 1499.907 1499.385 1498.931 1498.410 2′-Deoxyinosine 1498.637 1498.593 1498.512 1498.508 1498.450 1498.331 1498.271 1498.200 2′-Deoxyguanosine 1497.461 1497.456 1497.452 1497.450 1497.442 1497.438 1497.433 1497.429

± ± ± ± ± ± ± ± ±

γe

4.12078 4.12552 4.13067 4.13468 4.14002 4.14472 4.15022 4.15504 4.16062

270.53 269.36 268.12 267.16 265.90 264.81 263.55 262.46 261.23

4.15929 4.15973 4.16054 4.16058 4.16116 4.16236 4.16297 4.16368

261.213 261.106 260.912 260.903 260.766 260.487 260.348 260.186

± ± ± ± ± ± ± ±

0.078 0.078 0.077 0.077 0.076 0.074 0.073 0.071

1.010985(7) 1.010974(7) 1.010955(6) 1.010954(6) 1.010940(6) 1.010911(6) 1.010897(6) 1.010881(6)

4.17158 4.17163 4.17168 4.17169 4.17177 4.17181 4.17186 4.17190

258.973 258.962 258.951 258.947 258.930 258.921 258.909 258.900

± ± ± ± ± ± ± ±

0.088 0.088 0.087 0.087 0.086 0.086 0.085 0.085

1.010749(7) 1.010748(7) 1.010746(7) 1.010746(7) 1.010744(7) 1.010743(7) 1.010742(7) 1.010741(7)

0.72 0.64 0.56 0.49 0.42 0.35 0.28 0.23 0.17

1.01195(6) 1.01183(6) 1.01169(5) 1.01159(4) 1.01146(4) 1.01135(3) 1.01122(2) 1.01111(2) 1.01098(1)

The uncertainties for κS are typically (3.2 to 3.3) · 10−15 Pa−1. bThe uncertainty for ρ is ± 3.0 · 10−3 kg·m−3. cThe uncertainty for u is ± 0.005 m·s−1. The uncertainties for cp are typically: inosine, (1.3 to 2.3) · 10−4 J·K−1·g−1; 2′-deoxyinosine, (1.0 to 1.7) · 10−4 J·K−1·g−1; 2′-deoxyguanosine, (0.6 to 1.5) · 10−4 J·K−1·g−1. eThe digit in parentheses is the uncertainty in the last digit of γ.

a

d

= (∂V*1 /∂T)p/V*1 }, 106 α*1 = 257.21 K−1 at T = 298.15 K,33 δ*1 is the difference between the isothermal compressibility κ*T,1 {κ*T,1 = −(∂V*1 /∂p)T/V*1 } and the isentropic compressibility κ*S,1 {κS,1 * = −(∂V1*/∂p)S/V1*}, δ1* = κT,1 * − κS,1 * = 0.4736 · 10−11 Pa−1 25,33 o at T = 298.15 K. The values of KT,2 for the nucleosides, and their uncertainties estimated by the application of propagation of errors methods to eq 11, are given in Table 4. Evaluation of γ at p = 0.1 MPa. Values of γ for solutions of the nucleosides at p = 0.1 MPa were obtained using the expression derived from eqs 1 and 4 (κ + α 2T /σ ) γ= S κS

in the calculations are those reported by Kell23,33 {ρ*1 = (999.101, 997.047, 995.650, and 992.219) kg·m−3 at T = (288.15, 298.15, 303.15, and 313.15) K, respectively}. For 2′deoxyinosine at T = 288.15 K, the linear form of eq 8 was used because the value obtained initially for the a2 coefficient was statistically insignificant. The coefficients given in Table 3 were used to calculate solution densities for the molalities used in this study. For each solution the equation ρ − ρ1∗ = b1 + b2(T − Tm) + b3(T − Tm)2

(13)

was fitted to the density data, where Tm is the midpoint temperature of the range used (Tm = 300.65 K), and bi, i = 1 to 3, are the fitted coefficients. Differentiation of eq 13 with respect to temperature at constant pressure leads to

(12)

The isentropic compressibilities that were used to derive the KS,ϕ values given in Table 2 were analyzed using eq 8. The a1 and a2 coefficients obtained, along with their estimated uncertainties, are given in Table 3. These coefficients were then used to generate values of κS for solutions at the molalities used for the measurements at high pressures. The results obtained are given in Table 5. In a previous paper,16 densities were reported for aqueous solutions of inosine, 2′-deoxyinosine, and 2′-deoxyguanosine at ambient pressure and four temperatures. Each of these (ρ, m) data sets was analyzed using eq 8 to give the a1 and a2 coefficients shown in Table 3. The values of ρ*1 for water used

(∂ρ /∂T )p = (∂ρ1∗ /∂T )p + b2 + 2b3(T − Tm)

(14)

The derivatives (∂ρ/∂T)p obtained using eq 14 were used to calculate the isobaric expansibilities for the various solutions at p = 0.1 MPa and T = 298.15 K using eq 2 transformed as α=−

(∂ρ /∂T )p ρ

(15)

These α results and their uncertainties, which were assessed by the application of propagation of errors methods to eq 14, are given in Table 5. The larger α uncertainties for inosine arise E



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simply because of less satisfactory fits of the density data to the second-order polynomial in temperature (eq 13). Values of the specific heat capacity, cp, for aqueous solutions the nucleosides at T = 298.15 K obtained in previous work,16 were analyzed using eq 8 to give the a1 and a2 coefficients, and their estimated uncertainties, shown in Table 3. The value for the specific heat capacity for water, cp,1 * , was taken as 4.1793 J· K−1·g−1.32 The specific heat capacities calculated using eq 8 for the molalities used in this study are given in Table 5. These cp results, when converted into heat capacities per unit volume by multiplying by the solution densities given in Table 5, were combined with the values of α and κS to obtain γ, the values of which are also included in Table 5. The uncertainties for γ given in Table 5 were estimated by the application of propagation of errors to eq 12. Sound speeds for the various solutions at p = 0.1 MPa are required in the analyses of data at high pressures. These were calculated using eq 5 and the solution densities and isentropic compressibilities given in Table 5. The results obtained are also included in Table 5. Solution Densities at High Pressures. The rigorous application of eq 7 to obtain from measured sound speeds the solution densities at high pressures is not possible because the pressure dependence of γ is not known. However, given some suitable assumption about the pressure dependence of γ, solution densities at high pressures can be estimated using eq 7. Because the solutions used in this work are relatively dilute, a reasonable assumption that can be made is that the difference between the γ values for a given solution at any two pressures is approximately the same as that for the pure solvent, that is

assumption upon which eq 16 is based is indeed reasonable, at least for dilute solutions and at moderate pressures. The measured sound speeds for aqueous solutions of inosine, 2′-deoxyinosine, and 2′-deoxyguanosine at T = 298.15 K and p = (10.0 to 100.0) MPa are given in Table 7. In previous work,13,14,36 we chose to analyze the quantity γ/u2 by weighted least-squares using a third-order polynomial in the independent variable (p − 0.1). For the sytems studied previously, integration of this polynomial using eq 7 gave solution densities from which quite satisfactory thermodynamic properties were derived. For the systems in this study, however, we found that a slightly different approach ultimately gave thermodynamic properties that were of better internal consistency. For each solution, the quantity (γ/u2 − γ1/u12) was analyzed by weighted least-squares using a second-order polynomial of the form γ /u 2 − γ1/u12 = c0 + c1(p − 0.1) + c 2(p − 0.1)2

where γ1/u12 is the quantity for the pure solvent and ci, i = 0 to 2, are the fitted coefficients. The weighting factor for each value of (γ/u2 − γ1/u12) was taken as 1/(δ(γ/u2))2, where δ(γ/u2) is the uncertainty for the quantity γ/u2. In estimating the uncertainty for γ, no account was taken of the contribution from the right-hand side of eq 16. In other words, the estimated errors are relative to those for water. The polynomial coefficients, ci, i = 0 to 2, and their standard deviations obtained from the least-squares analyses are given in Supporting Information Table S1. For all but one of the solutions of inosine, and for several of the solutions of 2′deoxyguanosine, the values obtained for c2 were not statistically significant. In these cases, the linear form of eq 17 was used in the analyses. The solution densities at p = (10 to 100) MPa were obtained by integration between the limits of p = 0.1 MPa and a pressure p of the expression that follows from combining eqs 6 and 17, viz.

γ(p) − γ(p = 0.1MPa) ≈ γH O(p) − γH O(p = 0.1MPa) 2

2

(16)

where γ(p) and γH2O(p) represent, respectively, the γ values for the solution and pure water at the pressure p given in parentheses. The values for γH2O(p) over the range p = (0.1 to 100.0) MPa can be calculated using the literature data summarized in Table 6. The sound speeds were calculated

(∂ρ /∂p)T − (∂ρ1∗ /∂p)T = c0 + c1(p − 0.1) + c 2(p − 0.1)2

Table 6. Values of Sound Speed, Density, Isentropic and Isothermal Compressibility, and γ for Water at T = 298.15 K and at p = (0.1 to 100) MPa p

u1a

ρ1*b

1010κS,1 *

1010κT,1 *b

MPa

m·s−1

kg·m−3

Pa−1

Pa−1

0.1 10.0 20.0 40.0 60.0 80.0 100.0

1496.69 1513.29 1530.07 1563.64 1597.14 1630.51 1663.66

997.047 1001.465 1005.836 1014.317 1022.466 1030.304 1037.850

4.47736 4.36034 4.24668 4.03231 3.83409 3.65079 3.48126

4.52463 4.41179 4.30227 4.09658 3.90686 3.73151 3.56916

(17)

(18)

The results obtained are given in Supporting Information Table S2. Included in Table S2 are the estimated uncertainties for the solution densities, which were obtained by the application of propagation of errors to eq 18. At the pressures p = (10 to 60) MPa, the uncertainty for the density at p = 0.1 MPa (3.0 · 10−3 kg·m−3) is the predominant contributor to the estimated uncertainty for the calculated solution density. At p = (80 and 100) MPa, small contributions arise for some solutions from the estimated uncertainties for the ci coefficients of eq 18. It is worth noting that the differences between the solution densities obtained from analyses based on eq 17 and those based on the third order polynomial used in previous work are in the range (1 to 3)·10−3 kg·m−3. Thus, for most solutions the differences are less than the estimated uncertainty in solution density. Apparent and Partial Molar Volumes at High Pressures. The apparent molar volumes, Vϕ, of the nucleosides at T = 298.15 K and p = (10.0 to 100.0) MPa were calculated from the solution densities given in Table S2 using the equation

γH2O 1.01056 1.01180 1.01309 1.01594 1.01898 1.02211 1.02525

a

Calculated using the equation given in ref 34. bCalculated using the equation of state given in ref 35.

using the equation reported by Chen and Millero.34 The densities and isothermal compressibilities, κT,1 * , for water were obtained using the equation of state given by Chen et al.35 The isentropic compressibilities and the γH2O values given in Table 6 were calculated using eqs 5 and 4, respectively. Evidence presented in previous work13 suggests that the underlying

Vϕ = (M 2 /ρ) − F

(ρ − ρ1∗ ) (mρρ1∗ )

(19)



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Table 7. Sound Speeds for Aqueous Solutions of Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine at T = 298.15 K and p = (10.0 to 100.0) MPaa mb

uc

mol·kg−1

m·s−1 10.0 MPa

20.0 MPa

0.08535 0.07798 0.07008 0.06399 0.05598 0.04902 0.04096 0.03399 0.02602

1518.73 1518.28 1517.79 1517.43 1516.92 1516.44 1515.97 1515.55 1514.96

1535.60 1535.12 1534.66 1534.22 1533.79 1533.28 1532.81 1532.39 1531.78

0.02944 0.02877 0.02755 0.02749 0.02661 0.02481 0.02390 0.02283

1515.21 1515.18 1515.11 1515.13 1515.05 1514.94 1514.87 1514.80

1532.02 1531.99 1531.92 1531.92 1531.86 1531.72 1531.68 1531.58

0.01075 0.01068 0.01062 0.01059 0.01048 0.01043 0.01036 0.01030

1514.08 1514.09 1514.07 1514.06 1514.05 1514.04

1530.86 1530.86 1530.86 1530.86 1530.85 1530.84 1530.83 1530.81

1514.02

40.0 MPa Inosine 1569.26 1568.81 1568.28 1567.92 1567.36 1566.89 1566.37 1565.96 1565.39 2′-Deoxyinosine 1565.64 1565.60 1565.52 1565.51 1565.47 1565.32 1565.27 1565.19 2′-Deoxyguanosine 1564.44 1564.44 1564.43 1564.44 1564.41 1564.41

60.0 MPa

80.0 MPa

100.0 MPa

1602.78 1602.26 1601.83 1601.42 1600.83 1600.42 1599.91 1599.47 1598.87

1636.13 1635.66 1635.19 1634.77 1634.20 1633.81 1633.28 1632.85 1632.27

1669.19 1668.72 1668.28 1667.88 1667.30 1666.92 1666.38 1665.92 1665.37

1599.15 1599.12 1599.01 1599.03 1598.96 1598.86 1598.77 1598.72

1632.53 1632.47 1632.39 1632.39 1632.33 1632.19 1632.14 1632.09

1665.62 1665.59 1665.50 1665.51 1665.45 1665.33 1665.27 1665.18

1597.94 1597.94 1597.93 1597.94 1597.94 1597.94 1597.92 1597.92

1631.31 1631.31 1631.32 1631.30 1631.30 1631.30 1631.30 1631.28

1664.47 1664.46 1664.46 1664.46 1664.44 1664.44 1664.43 1664.43

The standard uncertainties for T and p are 0.01 K and 0.2 MPa, respectively. bThe standard uncertainty for m is 1 · 10−5 mol·kg−1. cThe standard uncertainty for u is 0.03 m·s−1.

a

Table 8. Partial Molar Volumes at Infinite Dilution for Inosine, 2′-Deoxyinosine, and 2′-Deoxyguanosine and the Sv Values for Inosine at T = 298.15 K and p = (0.1 to 100) MPa Vo2

p MPa

Vo2

Sv −1

cm ·mol 3

−2

Inosine 0.1 10 20 40 60 80 100 a

166.103 ± 166.121 ± 166.152 ± 166.195 ± 166.200 ± 166.172 ± 166.109 ±

0.054a 0.006 0.008 0.011 0.016 0.020 0.023

cm ·mol−1

cm ·kg·mol 3

0.205 ± 0.083 b

−0.49 −0.91 −1.27 −1.53

± ± ± ±

0.16 0.23 0.29 0.33

3

2′-Deoxyinosine

2′-Deoxyguanosine

± ± ± ± ± ± ±

169.26 ± 0.11a 169.270 ± 0.027 169.306 ± 0.034 169.335 ± 0.039 169.337 ± 0.036 169.306 ± 0.038 169.245 ± 0.038

163.677 163.672 163.660 163.618 163.549 163.453 163.330

0.073a 0.025 0.025 0.026 0.028 0.029 0.020

From ref 16. bSee text.

where Vo2 is the partial molar volume of the solute at infinite dilution and Sv is the experimental slope. The Vo2 and Sv values, together with their standard errors obtained from weighted least-squares analyses of the Vϕ data, are given in Table 8. The inverse squares of the uncertainties of the apparent molar volumes were used as the weighting factors. The value of Sv obtained from an analysis of the Vϕ data for p = 20 MPa was not statistically significant. The Vo2 result reported in Table 8 is the mean value of the Vϕ data and the uncertainty given is the standard deviation.

where the symbols used are as defined vide supra. The values used for ρ1* at the various pressures are those given in Table 6. The Vϕ results, together with their uncertainties estimated using the procedures described previously,37 are given in Supporting Information Table S3. At each pressure, the molality dependence of Vϕ for inosine was analyzed using the linear equation

Vϕ = V 2o + Svm

(20) G



Article

Table 9. Partial Molar Isentropic and Isothermal Compressions at Infinite Dilution for Inosine, 2′-Deoxyinosine, and 2′Deoxyguanosine and the Sk(S) and Sk(T) Values for Inosine at T = 298.15 K and p = (10 to 100) MPa 1015 KoS,2

p

−1

1015 Sk(S) −1

MPa

m ·mol ·Pa

10 20 40 60 80 100

−10.24 ± 0.36 −9.76 ± 0.49 −7.21 ± 0.26 −5.10 ± 0.41 −3.65 ± 0.28 −1.51 ± 0.27

10 20 40 60 80 100

−5.05 ± 0.27 −4.24 ± 0.29 −2.91 ± 0.16 −1.20 ± 0.20 0.343 ± 0.20 2.15 ± 0.13

3

1015 KoT,2

−2

−1

m ·kg·mol ·Pa 3

−1

1015 Sk(T) −1

m ·mol ·Pa 3

Inosine 23.7 ± 5.2 27.4 ± 7.0 15.7 ± 3.8 14.4 ± 5.9 17.6 ± 4.1 13.4 ± 3.8 2′-Deoxyinosinea

−3.38 ± 0.41 −3.22 ± 0.52 −0.980 ± 0.26 0.786 ± 0.40 1.85 ± 0.28 3.87 ± 0.25 1.11 1.72 2.73 4.12 5.40 7.00

± ± ± ± ± ±

m ·kg·mol−2·Pa−1 3

24.9 30.1 17.3 15.9 20.3 13.9

± ± ± ± ± ±

6.4 8.1 4.1 6.3 4.5 4.0

0.30 0.29 0.16 0.22 0.22 0.14

2′-Deoxyguanosinea 10 20 40 60 80 100 a

−10.55 ± 0.73 −9.62 ± 0.50 −7.95 ± 0.37 −5.52 ± 0.37 −3.65 ± 0.30 −2.00 ± 0.22

−3.00 ± 0.75 −2.34 ± 0.51 −1.04 ± 0.37 0.975 ± 0.37 2.49 ± 0.31 3.86 ± 0.23

See text.

The apparent molar isothermal compressions, KT,ϕ, for the nucleosides at T = 298.15 K and pressures over the range p = (10 to 120) MPa were calculated using the isothermal equivalent of eq 9, that is, with KS,ϕ, κS, and κS,1 * replaced by KT,ϕ, κT, and κT,1 * , respectively. The κT values were calculated from the κS and γ data using eqs 4 and 16. The κ*T,1 values used in the calculations are given in Table 6. The KT,ϕ results, along with their uncertainties estimated using propagation-of-errors methods applied to eqs 4 and 9, are given in the Supporting Information Table S5. At each pressure, the molality dependence of KT,ϕ for inosine was analyzed by weighted least-squares using the isothermal equivalent of eq 10. The partial molar o isothermal compressions at infinite dilution, KT,2 , the experimental slope Sk(T) values, and the standard errors obtained from the least-squares analyses are given in Table 9. The KoT,2 values for 2′-deoxyinosine and 2′-deoxyguanosine shown in Table 9 are the means of the KT,ϕ results.

The molality ranges accessible for both 2′-deoxyinosine and 2′-deoxyguanosine are too narrow for reliable Vo2 and Sv results to be obtained using eq 20. The Vo2 values given in Table 8 are the means of the Vϕ data and the uncertainties are the standard deviations. For completeness, the Vo2 results for the nucleosides at p = 0.1 MPa that were reported in previous work16 are also included in Table 8. The analysis of Vϕ data for inosine at p = 0.1 MPa also gave a value for Sv that was statistically insignificant.16 Apparent and Partial Molar Isentropic and Isothermal Compressions at High Pressures. The isentropic compressibilities for solutions of the nucleosides over the range p = (10 to 100) MPa were calculated using eq 5 and the sound speeds and solution densities given in Table 7 and Supporting Information Table S2, respectively. These κS values were used to calculate the apparent molar isentropic compressions using eq 9. The values used for the density and isentropic compressibility of water at the various pressures are those given in Table 6. The KS,ϕ results obtained are given in Supporting Information Table S4. Included in Table S4 are the uncertainties for the KS,ϕ values, which were estimated by the application of propagation of errors to eqs 5 and 9, but with the exclusion of contributions from the thermodynamic properties of the solvent. The uncertainty for u was taken as ± 0.03 m·s−1 and the uncertainties used for the solution densities are those given in Table S2. The molality dependence of KS,ϕ for inosine at each pressure was analyzed by weighted least-squares using eq 10 to give the values for KoS,2 and Sk(S), and their standard errors obtained from the least-squares analysis, shown in Table 9. The KS,ϕ data for 2′-deoxyinosine and 2′-deoxyguanosine cannot be analyzed using eq 10 for the reasons as outlined above for the apparent molar volumes. The KoS,2 values for these nucleosides given in Table 9 are the means of the KS,ϕ values and the uncertainties are the standard deviations.

■

DISCUSSION The partial molar volumes at infinite dilution for inosine, 2′deoxyinosine, and 2′-deoxyguanosine in aqueous solution over the pressure range p = (0.1 to 100) MPa are shown in Figure 2. The changes in V2o with changes in pressure for these nucleosides are rather small, as was observed previously14 for the nucleosides adenosine, cytidine, and uridine. For 2′deoxyinosine, the value of Vo2 is approximately constant over the pressure range (0.1 to 20) MPa, but then decreases as the pressure increases over the range (20 to 100) MPa. In contrast, the Vo2 values for both inosine and 2′-deoxyguanosine increase with increasing pressure over the range (0.1 to 40) MPa but decrease with increasing pressure over the range (60 to 100) MPa. These trends in Vo2 with pressure for the three nucleosides are best rationalized with reference to the partial molar isothermal compressions at infinite dilution. H



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Figure 2. Pressure dependences of the partial molar volumes at infinite dilution and T = 298.15 K for inosine, 2′-deoxyinosine, and 2′deoxyguanosine in aqueous solution.

Figure 3. Pressure dependences of the partial molar isothermal compressions at infinite dilution and T = 298.15 K for inosine, 2′deoxyinosine, and 2′-deoxyguanosine in aqueous solution.

The KoT,2 values for the nucleosides as a function of pressure are displayed in Figure 3. For each nucleoside, the change in KoT,2 with pressure is approximately linear over the pressure range studied, as indicated by the dashed lines shown in Figure 3. The values of KoT,2 for 2′-deoxyinosine at low pressures are close to zero, which accounts for the approximately constant value of Vo2 at low pressures. As the pressure increases, the value of KoT,2 for 2′-deoxyinosine becomes more positive which, as a consequence of the thermodynamic relation KoT,2 = −(∂Vo2 /∂p)T, accounts for the trend in Vo2 with pressure displayed in o Figure 2. The values of KT,2 for both inosine and 2′deoxyguanosine change sign at pressures of about 50 MPa. This accounts for the maxima that occur at about p ≈ 50 MPa for the plots of Vo2 against pressure shown in Figure 2. Semiempirical models38−40 are often used to rationalize the volumetric properties of small solutes in aqueous solution. In previous work,13,14,41 we have used a model38 that explores hydration effects based on the expression V 2o = Vint + nh(Vh − V1∗)

differentiating eq 21 with respect to pressure at constant temperature gives KTo ,2 = −(∂V 2o/∂p)T = −(∂Vint /∂p)T + nh(Kh − K1∗) (22)

where Kh {Kh = −(∂Vh/∂p)T} is the partial molar isothermal compression of water in the hydration shell of the solute and K*1 {K*1 = −(∂V*1 /∂p)T} is the molar isothermal compression of water in the bulk solvent. Because the intrinsic volume of a solute molecule of low molar mass is, to a first approximation, independent of pressure,14,38 eq 22 reduces to

KTo ,2 = nh(Kh − K1∗)

(23)

KoT,2

It follows from this expression that a negative value of for a solute indicates that the water molecules in the hydration shell are, on average, less compressible than those in the bulk solvent and conversely, if KoT,2 is positive water molecules of hydration are more compressible than those in the bulk solvent. For inosine and 2′-deoxyguanosine, the negative values of KoT,2 at the lower pressures imply that Kh < K1*. As the pressure increases, the differences between Kh and K*1 get smaller until at a pressure of about 50 MPa the values of Kh and K*1 are about the same (using the data in Table 6, K1* = 7.08 × 10−15 m3· mol−1·Pa−1 at p = 50 MPa). At this particular pressure, the water molecules in the hydration shells of inosine and 2′-

(21)

where Vint is the intrinsic volume of the solute molecule, and Vh and V1* are, respectively, the partial molar volumes of water in the hydration shell of the solute and in the bulk solvent. The value of the “hydration number”, nh, is determined largely by the number of water molecules in the first hydration shell. Assuming that the value of nh does not vary significantly with pressure, at least for moderate pressure changes, then I



Article

Table 10. Partial Molar Volumes and Isothermal Compressions at Infinite Dilution for the Hydroxyl Functional Group and Guanosine at T = 298.15 K and p = (0.1 to 100) MPa −1

m ·mol−1·Pa−1

cm ·mol 3

MPa OH Group 0.1 10 20 40 60 80 100

1015 KoT, 2

Vo2

p

2.43 2.45 2.49 2.58 2.65 2.72 2.78

± ± ± ± ± ± ±

0.09 0.03 0.03 0.03 0.03 0.04 0.04

3

Guanosine 171.68 ± 171.72 ± 171.80 ± 171.91 ± 171.99 ± 172.02 ± 172.02 ±

OH Group

0.15 0.04 0.04 0.05 0.05 0.05 0.05

−4.75 −4.50 −4.94 −3.71 −3.34 −3.55 −3.12

± ± ± ± ± ± ±

0.32 0.51 0.60 0.31 0.46 0.36 0.29

Guanosine −9.19 ± 0.60 −7.50 ± 0.90 −7.28 ± 0.79 −4.75 ± 0.48 −2.36 ± 0.60 −1.06 ± 0.47 0.74 ± 0.37

V 2o(OH) = V 2o(inosine) − V 2o(2′‐deoxyinosine)

deoxyguanosine are, on average, essentially the same as those in the bulk solvent, at least with regard to isothermal compression. Over the pressure range p = (0.1 to 100) MPa, the KoT,2 values for 2′-deoxyinosine are significantly more positive than those for inosine. The absence of a hydroxyl functional group in the 2′ position of a ribose ring reduces the extent to which cooperative hydrogen bonding can occur between water molecules and closely associated polar groups on the ribose ring. Water molecules involved in this type of hydrogen bonding are less compressible than those in the bulk solvent.40,42 Consequently, any reduction in such cooperative hydrogen bonding will make to a positive contribution to the value of KoT,2. The nucleoside 2′-deoxyinosine differs structurally from 2′deoxyguanosine only by the absence of an amino functional group in the 2 position of the purine ring (see Figure 1). Over the range p = (0.1 to 100) MPa, the values of KoT,2 for 2′deoxyinosine are more positive than those for 2′-deoxyguanosine. This observation is consistent with a greater degree of cooperative hydrogen bonding between water molecules and adjacent polar functional groups on the purine base moiety of 2′-deoxyguanosine than is the case for 2′-deoxyinosine. Following previous work,16 an empirical group additivity model can be used to evaluate the partial molar volumes at infinite dilution for the sparingly soluble nucleoside guanosine in aqueous solution at T = 298.15 K and p = (0.1 to 100) MPa. Using this model, Vo2 for guanosine is obtained from a summation of the properties derived for chosen constituent groups of the molecule. The underlying assumption for this simple group additivity model is that each constituent group interacts with the solvent more or less independently of adjacent groups.16 Because the molecular structures of guanosine and 2′-deoxyguanosine differ only by a hydroxyl functional group in the 2′ position of the ribose ring, it is convenient to consider guanosine as being comprised of just two groups, 2′-deoxyguanosine and the hydroxyl group. Thus, the partial molar volume of guanosine can be evaluated using the simple expression

(25)

The results obtained are given in Table 10 and plotted as a function of pressure in Figure 4. The dashed line, which represents a second-order polynomial, illustrates that the Vo2 (OH) values all lie on a smooth curve.

Figure 4. Pressure dependences of the partial molar volumes at infinite dilution for the hydroxyl functional group and for guanosine in aqueous solution at T = 298.15 K.

For the purposes of comparison, it would be desirable to have volumetric data for appropriate solutes in aqueous solution at elevated pressures from which values for Vo2(OH) could be derived. Unfortunately, such data are scarce. Values of Vo2 at T = 298.15 K and at the nominal pressures of 15 and 30 MPa have been reported for propan-1-ol43 and propan-1,2diol.44 The values of Vo2(OH) estimated using these Vo2 results are (0.46 ± 0.04) and (0.53 ± 0.04) cm3·mol−1 at p = (15 and 30) MPa, respectively. These results differ significantly from those obtained herein, which is perhaps not surprising given that they are derived using Vo2 data for open-chain solutes.

V 2o(guanosine) = V 2o(2′‐deoxyguanosine) + V 2o(OH) (24)

where Vo2(OH) is the change in the property Vo2 on replacing a hydrogen atom in the 2′ position of a ribose ring by a hydroxyl group, and the other terms are the partial molar volumes at infinite dilution of the species in parentheses. Values of Vo2(OH) over the range p = (0.1 to 100) MPa were evaluated from Vo2 data given in Table 8 for the pair of nucleosides inosine and 2′-deoxyinosine using the equation J



Article

Nevertheless, it is interesting to note that the change in the value of Vo2(OH) with pressure parallels that obtained in this study. The Vo2 results for guanosine, which were obtained using eq 24, are given in Table 10. At each pressure, Vo2 for guanosine is greater than that for inosine. The differences between the Vo2 values for these two nucleosides range from (5.58 ± 0.16) cm3· mol−1 at p = 0.1 MPa to (5.91 ± 0.06) cm3·mol−1 at p = 100 MPa. These differences represent the changes in volume on replacing a hydrogen atom in the 2 position of the purine ring of inosine by an amino group. The Vo2 results for guanosine are displayed as a function of pressure in Figure 4. The trend in Vo2 with increasing pressure is similar to those for both inosine and 2′-deoxyguanosine, except that the maximum is shifted to a higher pressure of about 90 MPa. The application of simple group additivity methods to the o o thermodynamic properties KS,2 and KT,2 has not been universally successful. In our previous work,45 the prediction of KoS,2 values for polypeptides using a peptide-based group additivity scheme was not quantitative, primarily because of specific interactions between adjacent functional groups and their associated solvent cospheres. On the other hand, KoS,2 data in aqueous solution for a selection of 31 small amphiphilic molecules that have no vicinal polar functional groups were successfully analyzed recently46 using a group additivity model. In this work, the evaluation of KoT,2 for guanosine using expressions analogous to eqs 24 and 25 should indeed yield reliable results. Assuming that there are minimal interactions between the base unit and the ribose moiety for both inosine and guanosine, as has been suggested by the results of previous studies,30,31 then the hydration of the hydroxyl group in the 2′ position of the ribose ring for each nucleoside will be identical, as will be the hydroxyl group contributions to KoT,2. Values of the hydroxyl group contributions to KoT,2 and o KT,2(OH), over the range p = (0.1 to 100) MPa were evaluated from the KoT,2 data for inosine and 2′-deoxyinosine given in Table 9 using an expression analogous to eq 25. The quantity KoT,2(OH) represents the change in the property KoT,2 on replacing a hydrogen atom in the 2′ position of a ribose ring by a hydroxyl group. The KoT,2(OH) results are given in Table 10 and are plotted as a function of pressure in Figure 5. With the possible exception of the result at p = 20 MPa, the KoT,2(OH) results lie more or less on a smooth curve, as indicated by the dashed line, which represents a second-order polynomial. The KoT,2 results for guanosine, which were obtained using a relationship analogous to eq 24, are given in Table 10 and are plotted as a function of pressure in Figure 5. The change in KoT,2 with pressure is approximately linear over the pressure range studied, as indicated by the dashed line shown in Figure 5. At the lower pressures, water molecules in the hydration shell of guanosine are, on average, less compressible than those in the bulk solvent. At a pressure of about 90 MPa, the values of Kh and K1* are about the same (K1* = 6.36 × 10−15 m3·mol−1·Pa−1 at p = 90 MPa), that is, the water of hydration is essentially the same as water in the bulk solvent. In conclusion, the successful application of group additivity methods has enabled the evaluation of the partial molar volumes and isothermal compressions at infinite dilution in aqueous solution for the sparingly soluble nucleoside guanosine. A comparison of the KoT,2 results for guanosine with those for inosine highlights the significance of cooperative hydrogen bonding in the hydration of the base moiety of guanosine.

Figure 5. Pressure dependences of the partial molar isothermal compressions at infinite dilution for the hydroxyl functional group and for guanosine in aqueous solution at T = 298.15 K.

■

ASSOCIATED CONTENT

S Supporting Information *

Tables containing coefficients of eq 17, calculated densities, apparent molar volumes, apparent molar isentropic compressions, and apparent molar isothermal compressions. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Einar Hogseth for his technical expertise in the design and maintenance of the sound speed equipment. Two of us (G.R.H. and G.B.J.) are grateful for financial assistance from the Marsden Fund (contract number 09-MAU-140).

■

REFERENCES

(1) Robertson, M. P.; Joyce, G. F. The Origins of the RNA World. Cold Spring Harb. Perspect. Biol. 2012, 4, a003608. (2) Dworkin, J. P.; Lazcano, A.; Miller, S. L. The Roads to and From the RNA World. J. Theor. Biol. 2003, 222, 127−134. (3) Bartel, D. P.; Unrau, P. J. Constructing an RNA World. Trends Cell Biol. 1999, 9, M9−M13. (4) Joyce, G. F. The Antiquity of RNA-based Evolution. Nature 2002, 418, 214−221. (5) Cech, T. R. The RNA Worlds in Context. Cold Spring Harb. Perspect. Biol. 2012, 4, a006742.

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Volumetric Properties at High Pressures of the Nucleosides Inosine, 2

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