2230:-based models, this problem was treated using different solvation parameters for charged atoms or Henderson-Hasselbalch equation with some modifications. However even the latter approach does not solve the problem. Charged residues can remain charged even in the nonpolar environment if they are involved in intramolecular ion pairs and H-bonds. Thus, the energetic penalties can be overestimated even using the Henderson-Hasselbalch equation. More rigorous theoretical methods describing such ionization effects have been developed, and there are ongoing efforts to incorporate such methods into the implicit solvation models.
2226:. The low energetic costs of such ionization effects have indeed been observed for protein mutants with buried ionizable residues. and hydrophobic α-helical peptides in membranes with a single ionizable residue in the middle. However, all electrostatic methods, such as PB, GB, or GBSA assume that ionizable groups remain charged in the nonpolar environments, which leads to grossly overestimated electrostatic energy. In the simplest
2158:. Unfortunately, the simplified ASA-based model cannot capture the "specific" distance-dependent interactions between different types of atoms in the solid state which are responsible for clustering of atoms with similar polarities in protein structures and molecular crystals. Parameters of such interatomic interactions, together with atomic solvation parameters for the protein interior, have been approximately derived from
690:
2074:
tend to cluster together or occupy nonpolar media, whereas polar and charged groups of the solute tend to remain in water. However, it is important to properly balance the opposite energy contributions from different types of atoms. Several important points have been discussed and investigated over
2042:. Recent work has also been done developing thermostats based on fluctuating hydrodynamics to account for momentum transfer through the solvent and related thermal fluctuations. One should keep in mind, though, that the folding rate of proteins does not depend linearly on viscosity for all regimes.
1786:
Another possibility is to use ad hoc quick strategies to estimate solvation free energy. A first generation of fast implicit solvents is based on the calculation of a per-atom solvent accessible surface area. For each of group of atom types, a different parameter scales its contribution to solvation
2162:
data. The implicit solvation model breaks down when solvent molecules associate strongly with binding cavities in a protein, so that the protein and the solvent molecules form a continuous solid body. On the other hand, this model can be successfully applied for describing transfer from water to
2149:
carbon of ~40 cal/(Ă… mol), which is 2 times bigger than ~20 cal/(Ă… mol) obtained for transfer from water to liquid hydrocarbons, because the parameters derived by such fitting represent sum of the hydrophobic energy (i.e., 20 cal/Ă… mol) and energy of van der Waals attractions of aliphatic groups in
1206:
Although this equation has solid theoretical justification, it is computationally expensive to calculate without approximations. A number of numerical
Poisson-Boltzmann equation solvers of varying generality and efficiency have been developed, including one application with a specialized computer
948:
152:
component of free energy. The continuum representation of solvent also significantly improves the computational speed and reduces errors in statistical averaging that arise from incomplete sampling of solvent conformations, so that the energy landscapes obtained with implicit and explicit solvent
2104:
scale for nonpolar atoms but intermediate between cyclohexane and octanol scales for polar atoms. Thus, different atomic solvation parameters should be applied for modeling of protein folding and protein-membrane binding. This issue remains controversial. The original idea of the method was to
1953:
It is possible to include a layer or sphere of water molecules around the solute, and model the bulk with an implicit solvent. Such an approach is proposed by M. J. Frisch and coworkers and by other authors. For instance in Ref. the bulk solvent is modeled with a
Generalized Born approach and the
1995:
of the extent of the hydrophobic effect. Most authors place the extent of this effect between 5 and 45 cal/(Ă… mol). Note that this surface area pertains to the solute, while the hydrophobic effect is mostly entropic in nature at physiological temperatures and occurs on the side of the solvent.
1364:
2004:
Implicit solvent models such as PB, GB, and SASA lack the viscosity that water molecules impart by randomly colliding and impeding the motion of solutes through their van der Waals repulsion. In many cases, this is desirable because it makes sampling of configurations and
124:(ASA) that were historically the first, and more recent continuum electrostatics models, although various modifications and combinations of the different methods are possible. The accessible surface area (ASA) method is based on experimental linear relations between
1945:. EEF1 additionally uses a distance-dependent (non-constant) dielectric, and ionic side-chains of proteins are simply neutralized. It is only 50% slower than a vacuum simulation. This model was later augmented with the hydrophobic effect and called Charmm19/SASA.
1741:. The effective Born radius of an atom characterizes its degree of burial inside the solute; qualitatively it can be thought of as the distance from the atom to the molecular surface. Accurate estimation of the effective Born radii is critical for the GB model.
2009:
much faster. This acceleration means that more configurations are visited per simulated time unit, on top of whatever CPU acceleration is achieved in comparison to explicit solvent. It can, however, lead to misleading results when kinetics are of interest.
1219:(GB) model is an approximation to the exact (linearized) Poisson-Boltzmann equation. It is based on modeling the solute as a set of spheres whose internal dielectric constant differs from the external solvent. The model has the following functional form:
2021:
and choosing an appropriate damping constant for the particular solvent. In practical bimolecular simulations one can often speed-up conformational search significantly (up to 100 times in some cases) by using much lower collision frequency
2091:
would be a much better approximation. Investigation of passive permeability barriers for different compounds across lipid bilayers led to conclusion that 1,9-decadiene can serve as a good approximations of the bilayer interior, whereas
435:
2177:
More testing is needed to evaluate the performance of different implicit solvation models and parameter sets. They are often tested only for a small set of molecules with very simple structure, such as hydrophobic and amphiphilic
1578:
1917:
705:
1749:
The
Generalized Born (GB) model augmented with the hydrophobic solvent accessible surface area (SA) term is GBSA. It is among the most commonly used implicit solvent model combinations. The use of this model in the context of
259:
153:
are different. Although the implicit solvent model is useful for simulations of biomolecules, this is an approximate method with certain limitations and problems related to parameterization and treatment of
1225:
1459:
3960:
Eriksson AE, Baase WA, Zhang XJ, Heinz DW, Blaber M, Baldwin EP, Matthews BW (Jan 1992). "Response of a protein structure to cavity-creating mutations and its relation to the hydrophobic effect".
2210:
equation and from experiments. However, since the charged protein residues are ionizable, they simply lose their charges in the nonpolar environment, which costs relatively little at the neutral
1762:, the conformational ensembles produced by GBSA models in other studies differ significantly from those produced by explicit solvent and do not identify the protein's native state. In particular,
3798:
Radzicka A, Wolfenden R (1988). "Comparing the polarities of the amino acids: side-chain distribution coefficients between the vapor phase, cyclohexane, 1-octanol, and neutral aqueous solution".
1991:. Implicit solvation models may be augmented with a term that accounts for the hydrophobic effect. The most popular way to do this is by taking the solvent accessible surface area (SASA) as a
4174:
Dao-pin S, Anderson DE, Baase WA, Dahlquist FW, Matthews BW (Dec 1991). "Structural and thermodynamic consequences of burying a charged residue within the hydrophobic core of T4 lysozyme".
4209:
Caputo GA, London E (Mar 2003). "Cumulative effects of amino acid substitutions and hydrophobic mismatch upon the transmembrane stability and conformation of hydrophobic alpha-helices".
1072:
989:
1193:
1770:
population was observed. Variants of the GB model have also been developed to approximate the electrostatic environment of membranes, which have had some success in folding the
3596:
Wang Y, Sigurdsson JK, Brandt E, Atzberger PJ (August 2013). "Dynamic implicit-solvent coarse-grained models of lipid bilayer membranes: fluctuating hydrodynamics thermostat".
1027:
1104:
1607:
330:
1631:
2716:
Shestakov AI, Milovich JL, Noy A (Mar 2002). "Solution of the nonlinear
Poisson-Boltzmann equation using pseudo-transient continuation and the finite element method".
685:{\displaystyle {\vec {\nabla }}\cdot \left=-4\pi \rho ^{f}({\vec {r}})-4\pi \sum _{i}c_{i}^{\infty }z_{i}q\lambda ({\vec {r}})e^{\frac {-z_{i}q\Psi ({\vec {r}})}{kT}}}
2040:
295:
1700:
1735:
1662:
1135:
2285:
1954:
multi-grid method used for
Coulombic pairwise particle interactions. It is reported to be faster than a full explicit solvent simulation with the particle mesh
113:
properties. These media are not necessarily uniform, since their properties can be described by different analytical functions, such as “polarity profiles” of
1467:
3825:
Mayer PT, Anderson BD (Mar 2002). "Transport across 1,9-decadiene precisely mimics the chemical selectivity of the barrier domain in egg lecithin bilayers".
943:{\displaystyle {\vec {\nabla }}\cdot \left=-\rho ^{f}({\vec {r}})-\sum _{i}c_{i}^{\infty }z_{i}q\lambda ({\vec {r}})e^{\frac {-z_{i}q\Psi ({\vec {r}})}{kT}}}
3296:
TA Keith, MJ Frisch (1994). "Chapter 3: Inclusion of
Explicit Solvent Molecules in a Self-Consistent-Reaction Field Model of Solvation". In Smith D (ed.).
1800:
387:. Thus, the needed atomic solvation parameters were initially derived from water-gas partition data. However, the dielectric properties of proteins and
1958:(PME) method of electrostatic calculation. There are a range of hybrid methods available capable of accessing and acquiring information on solvation.
2117:
types of atoms. The non-existent “hydrophobic” interactions of polar atoms are overridden by large electrostatic energy penalties in such models.
181:
2761:"Computation of electrostatic forces between solvated molecules determined by the Poisson-Boltzmann equation using a boundary element method"
2673:
Fogolari F, Brigo A, Molinari H (Nov 2002). "The
Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology".
1207:
hardware platform. However, performance from PB solvers does not yet equal that from the more commonly used generalized Born approximation.
97:
can be applied to approximate the averaged behavior of many highly dynamic solvent molecules. However, the interfaces and the interiors of
2981:
Onufriev A, Case DA, Bashford D (Nov 2002). "Effective Born radii in the generalized Born approximation: the importance of being perfect".
2109:
of organic molecules, which allows calculation of solvation free energy. However, some of the recently developed electrostatic models use
4285:
GarcĂa-Moreno EB, Fitch CA (2004). "Structural interpretation of pH and salt-dependent processes in proteins with computational methods".
3657:
Zagrovic B, Pande V (September 2003). "Solvent viscosity dependence of the folding rate of a small protein: distributed computing study".
3220:
3465:
Sharp KA, Nicholls A, Fine RF, Honig B (Apr 1991). "Reconciling the magnitude of the microscopic and macroscopic hydrophobic effects".
1926:
corresponds to a suitably chosen small molecule in which group i is essentially fully solvent-exposed. The integral is over the volume
1359:{\displaystyle G_{s}=-{\frac {1}{8\pi \epsilon _{0}}}\left(1-{\frac {1}{\epsilon }}\right)\sum _{i,j}^{N}{\frac {q_{i}q_{j}}{f_{GB}}}}
2954:
Still WC, Tempczyk A, Hawley RC, Hendrickson T (1990). "Semianalytical treatment of solvation for molecular mechanics and dynamics".
2270:
3751:"Anisotropic solvent model of the lipid bilayer. 2. Energetics of insertion of small molecules, peptides, and proteins in membranes"
3702:"Anisotropic solvent model of the lipid bilayer. 1. Parameterization of long-range electrostatics and first solvation shell effects"
3243:
Ferrara P, Apostolakis J, Caflisch A (Jan 2002). "Evaluation of a fast implicit solvent model for molecular dynamics simulations".
1375:
3328:
Lee MS, Salsbury FR, Olson MA (Dec 2004). "An efficient hybrid explicit/implicit solvent method for biomolecular simulations".
4302:
4261:
3523:
3309:
2494:
4023:"Are the parameters of various stabilization factors estimated from mutant human lysozymes compatible with other proteins?"
3095:"An implicit membrane generalized born theory for the study of structure, stability, and interactions of membrane proteins"
1975:
effects arising from solute-imposed constraints on the organization of the water or solvent molecules. This is termed the
392:
17:
1794:
19 force-field and is called EEF1. EEF1 is based on a
Gaussian-shaped solvent exclusion. The solvation free energy is
4244:
Schaefer M, van
Vlijmen HW, Karplus M (1998). "Electrostatic contributions to molecular free energies in solution".
4336:
1971:
Models like PB and GB allow estimation of the mean electrostatic free energy but do not account for the (mostly)
391:
are much more similar to those of nonpolar solvents than to vacuum. Newer parameters have thus been derived from
2087:
solution is a poor approximation of proteins or biological membranes because it contains ~2M of water, and that
2876:
Höfinger S (Aug 2005). "Solving the
Poisson-Boltzmann equation with the specialized computer chip MD-GRAPE-2".
2219:
344:
of the particular atom i per surface unit area. The needed solvation parameters for different types of atoms (
3408:"A review of methods for the calculation of solution free energies and the modelling of systems in solution"
4331:
1032:
956:
372:
of these compounds between different solutions or media using standard mole concentrations of the solutes.
1160:
4341:
2240:
3541:"Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations"
4346:
3860:
Walter A, Gutknecht J (1986). "Permeability of small nonelectrolytes through lipid bilayer membranes".
2442:
Zhou R (Nov 2003). "Free energy landscape of protein folding in water: explicit vs. implicit solvent".
1610:
1199:
to the ions in solution (often set to uniformly 1). If the potential is not large, the equation can be
994:
418:
412:
2760:
2206:
of ~3 (lipid bilayer) or 4 to 10 (interior of proteins) costs significant energy, as follows from the
1775:
1077:
47:
3982:
3910:"Interatomic potentials and solvation parameters from protein engineering data for buried residues"
3257:
2995:
1766:
are overstabilized, possibly due to insufficient electrostatic screening, and a higher-than-native
1585:
2280:
2265:
2227:
308:
298:
166:
121:
94:
2562:"Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides"
2096:
was a very poor approximation. A set of solvation parameters derived for protein interior from
3977:
3252:
2990:
1616:
38:
as a continuous medium instead of individual “explicit” solvent molecules, most often used in
2275:
2245:
2106:
2025:
2018:
1763:
369:
267:
59:
1675:
3969:
3615:
3552:
3474:
3419:
3106:
3047:
2830:
2775:
2725:
2631:
2576:
2323:
1713:
1665:
1640:
1113:
383:(gas phase). This energy can supplement the intramolecular energy in vacuum calculated in
8:
2622:
Eisenberg D, McLachlan AD (Jan 1986). "Solvation energy in protein folding and binding".
2511:
2255:
2203:
2195:
2159:
2138:
2097:
2062:. Their average energetic contribution can be reproduced with an implicit solvent model.
1771:
1754:
is termed MM/GBSA. Although this formulation has been shown to successfully identify the
1751:
1634:
696:
384:
141:
98:
87:
43:
3973:
3619:
3556:
3478:
3423:
3371:
Marini A, Muñoz-Losa A, Biancardi A, Mennucci B (Dec 2010). "What is solvatochromism?".
3110:
3051:
2834:
2779:
2729:
2635:
2580:
2382:
2327:
1573:{\displaystyle D=\left({\frac {r_{ij}}{2a_{ij}}}\right)^{2},a_{ij}={\sqrt {a_{i}a_{j}}}}
4151:
4123:
4094:
4066:
4003:
3937:
3909:
3885:
3775:
3750:
3726:
3701:
3682:
3639:
3605:
3573:
3540:
3353:
3298:
3278:
3179:
3151:
3127:
3094:
3070:
3035:
3016:
2901:
2799:
2698:
2655:
2542:
2467:
2250:
2199:
2133:
or uniform media. It is possible to express van der Waals interaction energies in the
1992:
1976:
1759:
1146:
39:
4294:
4253:
3118:
2599:
2561:
2417:
4308:
4298:
4267:
4257:
4226:
4191:
4156:
4099:
4047:
3995:
3942:
3877:
3842:
3780:
3731:
3674:
3643:
3631:
3578:
3519:
3490:
3447:
3388:
3345:
3305:
3270:
3225:
3203:
3184:
3132:
3075:
3008:
2936:
2893:
2858:
2853:
2818:
2791:
2741:
2690:
2647:
2604:
2534:
2490:
2459:
2421:
2386:
2351:
2346:
2311:
2014:
125:
4007:
3889:
3686:
3357:
3282:
3020:
2905:
2803:
2702:
2659:
2546:
2471:
1912:{\displaystyle \Delta G_{i}^{solv}=\Delta G_{i}^{ref}-\sum _{j}\int _{Vj}f_{i}(r)dr}
4290:
4249:
4218:
4183:
4146:
4138:
4089:
4081:
4037:
3987:
3932:
3924:
3869:
3834:
3807:
3770:
3762:
3721:
3713:
3666:
3623:
3568:
3560:
3482:
3437:
3427:
3380:
3337:
3262:
3215:
3174:
3166:
3152:"Atomic solvation parameters applied to molecular dynamics of proteins in solution"
3122:
3114:
3065:
3055:
3000:
2963:
2928:
2919:
Koehl P (Apr 2006). "Electrostatics calculations: latest methodological advances".
2885:
2848:
2838:
2783:
2733:
2682:
2639:
2594:
2584:
2526:
2451:
2413:
2378:
2341:
2331:
1988:
1984:
365:
4067:"Quantification of helix-helix binding affinities in micelles and lipid bilayers"
3060:
2055:
1980:
1955:
421:(PB) describes the electrostatic environment of a solute in a solvent containing
4042:
4022:
3627:
2823:
Proceedings of the National Academy of Sciences of the United States of America
2569:
Proceedings of the National Academy of Sciences of the United States of America
2316:
Proceedings of the National Academy of Sciences of the United States of America
2290:
2151:
2142:
2070:
All implicit solvation models rest on the simple idea that nonpolar atoms of a
75:
3564:
2932:
364:
fit of the calculated and experimental transfer free energies for a series of
4325:
3508:
2819:"Electrostatics of nanosystems: application to microtubules and the ribosome"
2191:
2051:
1200:
388:
361:
145:
114:
3991:
3486:
2589:
2137:
state in the surface energy units. This was sometimes done for interpreting
4312:
4230:
4160:
4103:
4051:
3946:
3846:
3784:
3735:
3678:
3635:
3582:
3451:
3392:
3349:
3274:
3229:
3221:
10.1002/(SICI)1097-0134(19990501)35:2<133::AID-PROT1>3.0.CO;2-N
3170:
3136:
3079:
3012:
2940:
2897:
2862:
2843:
2795:
2745:
2737:
2694:
2463:
2425:
2355:
2336:
1755:
129:
4271:
4195:
3999:
3881:
3494:
3188:
2651:
2608:
2538:
2530:
379:
is the free energy needed to transfer a solute molecule from a solvent to
4142:
2390:
2260:
2179:
2101:
2088:
2006:
1767:
1154:
4187:
4085:
3811:
3406:
Skyner RE, McDonagh JL, Groom CR, van Mourik T, Mitchell JB (Mar 2015).
2967:
2182:(α). This method was rarely tested for hundreds of protein structures.
254:{\displaystyle \Delta G_{\mathrm {solv} }=\sum _{i}\sigma _{i}\ ASA_{i}}
3928:
3873:
3432:
3407:
3266:
2455:
2215:
2125:
Strictly speaking, ASA-based models should only be applied to describe
154:
120:
There are two basic types of implicit solvent methods: models based on
110:
4222:
3838:
3766:
3717:
3670:
3538:
3442:
3384:
3341:
3004:
2889:
2787:
58:
interactions in structural and chemical processes, such as folding or
3539:
Anandakrishnan R, Drozdetski A, Walker RC, Onufriev AV (March 2015).
2643:
2369:
Richards FM (1977). "Areas, volumes, packing and protein structure".
2146:
2093:
2084:
341:
137:
106:
2686:
2207:
349:
149:
3610:
3370:
2058:
are important for solubility of organic molecules and especially
1972:
1195:
is a factor for the position-dependent accessibility of position
102:
63:
55:
35:
4124:"Positioning of proteins in membranes: a computational approach"
93:
The implicit solvation model is justified in liquids, where the
2202:. The transfer of an ion from water to a nonpolar medium with
2155:
2130:
2071:
1791:
357:
353:
345:
172:
133:
79:
51:
4248:. Advances in Protein Chemistry. Vol. 51. pp. 1–57.
2953:
2817:
Baker NA, Sept D, Joseph S, Holst MJ, McCammon JA (Aug 2001).
4173:
3595:
3513:
Molecular Modeling and Simulation: An Interdisciplinary Guide
3405:
2190:
Ionization of charged groups has been neglected in continuum
2165:
2134:
4121:
2100:
data was also different from octanol scale: it was close to
1948:
1454:{\displaystyle f_{GB}={\sqrt {r_{ij}^{2}+a_{ij}^{2}e^{-D}}}}
136:
molecule. This method operates directly with free energy of
4122:
Lomize AL, Pogozheva ID, Lomize MA, Mosberg HI (Jun 2006).
3515:
Interdisciplinary Applied Mathematics: Mathematical Biology
2105:
derive all solvation parameters directly from experimental
83:
4243:
3242:
2559:
2404:
Roux B, Simonson T (Apr 1999). "Implicit solvent models".
395:
or other similar data. Such parameters actually describe
2059:
426:
422:
71:
67:
4289:. Methods in Enzymology. Vol. 380. pp. 20–51.
1737:
is a quantity (with the dimension of length) termed the
175:
molecule in the simplest ASA-based method is given by:
3959:
3907:
2286:
Comparison of software for molecular mechanics modeling
2211:
160:
4064:
3748:
3699:
3464:
3036:"Folding very short peptides using molecular dynamics"
2560:
Ooi T, Oobatake M, NĂ©methy G, Scheraga HA (May 1987).
4246:
Linkage Thermodynamics of Macromolecular Interactions
4020:
2672:
2312:"Polarity and permeation profiles in lipid membranes"
2194:
models of implicit solvation, as well as in standard
2145:
energetics, which leads to “solvation” parameter for
2028:
1803:
1716:
1678:
1643:
1619:
1588:
1470:
1378:
1228:
1163:
1116:
1080:
1035:
997:
959:
708:
438:
311:
270:
184:
3204:"Effective energy function for proteins in solution"
2980:
2816:
2715:
3295:
4284:
3297:
2621:
2185:
2172:
2034:
1911:
1729:
1694:
1656:
1625:
1601:
1572:
1453:
1358:
1187:
1129:
1098:
1066:
1021:
983:
942:
684:
324:
289:
253:
3908:Lomize AL, Reibarkh MY, Pogozheva ID (Aug 2002).
3797:
3289:
368:. The experimental energies are determined from
4323:
4065:Lomize AL, Pogozheva ID, Mosberg HI (Oct 2004).
3749:Lomize AL, Pogozheva ID, Mosberg HI (Apr 2011).
3700:Lomize AL, Pogozheva ID, Mosberg HI (Apr 2011).
3327:
3201:
78:, association of biological macromolecules with
4287:Energetics of Biological Macromolecules, Part E
3859:
3323:
3321:
3149:
2758:
2512:"The "cratic correction" and related fallacies"
1781:
1744:
4117:
4115:
4113:
3903:
3901:
3899:
2371:Annual Review of Biophysics and Bioengineering
2214:: ~4 to 7 kcal/mol for Asp, Glu, Lys, and Arg
2045:
991:represents the position-dependent dielectric,
105:can also be considered as media with specific
3824:
3656:
1074:represents the charge density of the solute,
340:, i.e., a contribution to the free energy of
4278:
4208:
4202:
4021:Funahashi J, Takano K, Yutani K (Feb 2001).
4014:
3818:
3755:Journal of Chemical Information and Modeling
3742:
3706:Journal of Chemical Information and Modeling
3693:
3650:
3399:
3318:
3236:
3195:
3092:
3086:
3027:
2912:
2869:
2810:
2752:
2709:
2403:
4237:
4167:
4110:
4058:
3953:
3896:
3853:
3304:. Columbus, OH: American Chemical Society.
3143:
2666:
2484:
2437:
2435:
2397:
2303:
2120:
2065:
1110:at a distance of infinity from the solute,
46:. The method is often applied to estimate
2615:
2553:
2503:
2078:
1961:
399:energy between two condensed media or the
4150:
4093:
4041:
3981:
3936:
3774:
3725:
3609:
3572:
3441:
3431:
3256:
3219:
3178:
3126:
3069:
3059:
2994:
2852:
2842:
2598:
2588:
2362:
2345:
2335:
2271:Comparison of force field implementations
1966:
1949:Hybrid implicit-explicit solvation models
1210:
42:simulations and in other applications of
3791:
2974:
2875:
2718:Journal of Colloid and Interface Science
2432:
2368:
1790:Another strategy is implemented for the
1106:represents the concentration of the ion
1029:represents the electrostatic potential,
3507:
2759:Lu B, Zhang D, McCammon JA (Jun 2005).
2509:
2478:
2129:, i.e., energetics of transfer between
1922:The reference solvation free energy of
360:(S), etc.) are usually determined by a
14:
4324:
3033:
2150:the solid state, which corresponds to
2947:
2921:Current Opinion in Structural Biology
2918:
2309:
2013:Viscosity may be added back by using
1937:and the summation is over all groups
1787:("ASA-based model" described above).
1067:{\displaystyle \rho ^{f}({\vec {r}})}
984:{\displaystyle \epsilon ({\vec {r}})}
3093:Im W, Feig M, Brooks CL (Nov 2003).
2441:
1758:of short peptides with well-defined
1188:{\displaystyle \lambda ({\vec {r}})}
406:
393:octanol-water partition coefficients
161:Accessible surface area-based method
3412:Physical Chemistry Chemical Physics
3373:The Journal of Physical Chemistry B
3202:Lazaridis T, Karplus M (May 1999).
2383:10.1146/annurev.bb.06.060177.001055
2113:values of 20 or 40 cal/(Ă… mol) for
24:
3827:Journal of Pharmaceutical Sciences
3659:Journal of Computational Chemistry
3330:Journal of Computational Chemistry
3150:Wesson L, Eisenberg D (Feb 1992).
2983:Journal of Computational Chemistry
2878:Journal of Computational Chemistry
1834:
1804:
1702:is the distance between particles
1091:
998:
907:
845:
762:
753:
712:
649:
587:
492:
483:
442:
203:
200:
197:
194:
185:
171:The free energy of solvation of a
25:
4358:
1022:{\displaystyle \Psi ({\vec {r}})}
2675:Journal of Molecular Recognition
3862:The Journal of Membrane Biology
3589:
3532:
3501:
3458:
3364:
2768:The Journal of Chemical Physics
2186:Treatment of ionization effects
2173:Importance of extensive testing
1203:to be solved more efficiently.
1099:{\displaystyle c_{i}^{\infty }}
2220:Henderson-Hasselbalch equation
1900:
1894:
1637:of the solvent being modeled,
1182:
1176:
1167:
1061:
1055:
1046:
1016:
1010:
1001:
978:
972:
963:
925:
919:
910:
881:
875:
866:
819:
813:
804:
780:
774:
765:
756:
747:
741:
732:
715:
667:
661:
652:
623:
617:
608:
555:
549:
540:
510:
504:
495:
486:
477:
471:
462:
445:
148:methods that include only the
13:
1:
4295:10.1016/S0076-6879(04)80002-8
4254:10.1016/S0065-3233(08)60650-6
3119:10.1016/S0006-3495(03)74712-2
2418:10.1016/S0301-4622(98)00226-9
2297:
1979:and is a major factor in the
1602:{\displaystyle \epsilon _{0}}
3061:10.1371/journal.pcbi.0020027
1999:
1782:Ad hoc fast solvation models
1745:With accessible surface area
7:
3034:Ho BK, Dill KA (Apr 2006).
2241:Polarizable continuum model
2233:
2218:residues, according to the
2083:It has been noted that wet
2046:Hydrogen bonds with solvent
1141:is the charge of a proton,
1137:is the valence of the ion,
403:of two solvation energies.
325:{\displaystyle \sigma _{i}}
34:) is a method to represent
10:
4363:
3628:10.1103/PhysRevE.88.023301
3300:Modeling the hydrogen bond
3040:PLOS Computational Biology
2489:. New York: Plenum Press.
1776:integral membrane proteins
1611:permittivity of free space
419:Poisson-Boltzmann equation
413:Poisson-Boltzmann equation
410:
164:
60:conformational transitions
3565:10.1016/j.bpj.2014.12.047
2933:10.1016/j.sbi.2006.03.001
1626:{\displaystyle \epsilon }
4043:10.1093/protein/14.2.127
2487:Hydrophobic interactions
2121:Solid-state applications
2066:Problems and limitations
122:accessible surface areas
4337:Computational chemistry
3992:10.1126/science.1553543
3487:10.1126/science.2011744
2590:10.1073/pnas.84.10.3086
2281:Accessible surface area
2266:Force field (chemistry)
2228:accessible surface area
2079:Choice of model solvent
2035:{\displaystyle \gamma }
1962:Effects unaccounted for
425:. It can be written in
299:accessible surface area
290:{\displaystyle ASA_{i}}
167:Accessible surface area
95:potential of mean force
3518:. New York: Springer.
3171:10.1002/pro.5560010204
2844:10.1073/pnas.181342398
2738:10.1006/jcis.2001.8033
2510:Holtzer A (Jun 1995).
2337:10.1073/pnas.131023798
2107:partition coefficients
2036:
1967:The hydrophobic effect
1913:
1731:
1696:
1695:{\displaystyle r_{ij}}
1658:
1627:
1603:
1574:
1455:
1360:
1316:
1211:Generalized Born model
1189:
1131:
1100:
1068:
1023:
985:
944:
686:
370:partition coefficients
326:
291:
255:
2531:10.1002/bip.360350605
2406:Biophysical Chemistry
2246:COSMO solvation model
2037:
2019:Hamiltonian mechanics
1914:
1772:transmembrane helixes
1739:effective Born radius
1732:
1730:{\displaystyle a_{i}}
1697:
1659:
1657:{\displaystyle q_{i}}
1628:
1604:
1575:
1456:
1361:
1296:
1190:
1132:
1130:{\displaystyle z_{i}}
1101:
1069:
1024:
986:
945:
687:
327:
292:
256:
4143:10.1110/ps.062126106
2485:Ben-Naim AY (1980).
2310:Marsh D (Jul 2001).
2224:ΔG = 2.3RT (pH - pK)
2026:
1801:
1714:
1676:
1666:electrostatic charge
1641:
1617:
1586:
1468:
1376:
1226:
1161:
1114:
1078:
1033:
995:
957:
706:
436:
309:
268:
182:
128:of transfer and the
99:biological membranes
88:biological membranes
4332:Molecular modelling
4188:10.1021/bi00113a006
4086:10.1110/ps.04850804
4030:Protein Engineering
3974:1992Sci...255..178E
3812:10.1021/bi00405a042
3620:2013PhRvE..88b3301W
3557:2015BpJ...108.1153A
3545:Biophysical Journal
3479:1991Sci...252..106S
3424:2015PCCP...17.6174S
3111:2003BpJ....85.2900I
3099:Biophysical Journal
3052:2006PLSCB...2...27H
2968:10.1021/ja00172a038
2835:2001PNAS...9810037B
2780:2005JChPh.122u4102L
2730:2002JCIS..247...62S
2636:1986Natur.319..199E
2581:1987PNAS...84.3086O
2328:2001PNAS...98.7777M
2256:Molecular mechanics
2204:dielectric constant
2196:molecular mechanics
2160:protein engineering
2139:protein engineering
2098:protein engineering
1857:
1830:
1752:molecular mechanics
1635:dielectric constant
1435:
1414:
1095:
849:
591:
385:molecular mechanics
334:solvation parameter
142:molecular mechanics
44:molecular mechanics
32:continuum solvation
18:Continuum solvation
4342:Molecular dynamics
3929:10.1110/ps.0307002
3874:10.1007/BF01870127
3433:10.1039/C5CP00288E
3267:10.1002/prot.10001
2456:10.1002/prot.10483
2276:Poisson's equation
2251:Molecular dynamics
2200:molecular dynamics
2032:
1977:hydrophobic effect
1909:
1870:
1837:
1807:
1760:tertiary structure
1727:
1692:
1654:
1623:
1599:
1570:
1451:
1418:
1397:
1356:
1185:
1147:Boltzmann constant
1127:
1096:
1081:
1064:
1019:
981:
940:
835:
834:
682:
577:
576:
322:
287:
251:
221:
82:, or transport of
40:molecular dynamics
30:(sometimes termed
28:Implicit solvation
4347:Protein structure
4304:978-0-12-182784-7
4263:978-0-12-034251-8
4223:10.1021/bi026697d
3839:10.1002/jps.10067
3767:10.1021/ci200020k
3718:10.1021/ci2000192
3671:10.1002/jcc.10297
3598:Physical Review E
3525:978-0-387-95404-2
3385:10.1021/jp1097487
3342:10.1002/jcc.20119
3311:978-0-8412-2981-5
3005:10.1002/jcc.10126
2962:(16): 6127–6129.
2890:10.1002/jcc.20250
2788:10.1063/1.1924448
2630:(6050): 199–203.
2496:978-0-306-40222-7
2015:Langevin dynamics
1989:hydrophobic cores
1985:globular proteins
1861:
1568:
1515:
1449:
1354:
1289:
1268:
1179:
1058:
1013:
975:
937:
922:
878:
825:
816:
777:
759:
744:
718:
679:
664:
620:
567:
552:
507:
489:
474:
448:
407:Poisson-Boltzmann
366:organic compounds
234:
212:
126:Gibbs free energy
16:(Redirected from
4354:
4317:
4316:
4282:
4276:
4275:
4241:
4235:
4234:
4206:
4200:
4199:
4171:
4165:
4164:
4154:
4128:
4127:(Free full text)
4119:
4108:
4107:
4097:
4071:
4070:(Free full text)
4062:
4056:
4055:
4045:
4027:
4026:(Free full text)
4018:
4012:
4011:
3985:
3968:(5041): 178–83.
3957:
3951:
3950:
3940:
3923:(8): 1984–2000.
3914:
3913:(Free full text)
3905:
3894:
3893:
3857:
3851:
3850:
3822:
3816:
3815:
3806:(5): 1664–1670.
3795:
3789:
3788:
3778:
3746:
3740:
3739:
3729:
3697:
3691:
3690:
3654:
3648:
3647:
3613:
3593:
3587:
3586:
3576:
3536:
3530:
3529:
3505:
3499:
3498:
3462:
3456:
3455:
3445:
3435:
3403:
3397:
3396:
3379:(51): 17128–35.
3368:
3362:
3361:
3325:
3316:
3315:
3303:
3293:
3287:
3286:
3260:
3240:
3234:
3233:
3223:
3199:
3193:
3192:
3182:
3156:
3155:(Free full text)
3147:
3141:
3140:
3130:
3090:
3084:
3083:
3073:
3063:
3031:
3025:
3024:
2998:
2989:(14): 1297–304.
2978:
2972:
2971:
2951:
2945:
2944:
2916:
2910:
2909:
2873:
2867:
2866:
2856:
2846:
2829:(18): 10037–41.
2814:
2808:
2807:
2765:
2756:
2750:
2749:
2713:
2707:
2706:
2670:
2664:
2663:
2644:10.1038/319199a0
2619:
2613:
2612:
2602:
2592:
2566:
2565:(Free full text)
2557:
2551:
2550:
2516:
2515:(Free full text)
2507:
2501:
2500:
2482:
2476:
2475:
2439:
2430:
2429:
2401:
2395:
2394:
2366:
2360:
2359:
2349:
2339:
2307:
2041:
2039:
2038:
2033:
1918:
1916:
1915:
1910:
1893:
1892:
1883:
1882:
1869:
1856:
1845:
1829:
1815:
1736:
1734:
1733:
1728:
1726:
1725:
1701:
1699:
1698:
1693:
1691:
1690:
1663:
1661:
1660:
1655:
1653:
1652:
1632:
1630:
1629:
1624:
1608:
1606:
1605:
1600:
1598:
1597:
1579:
1577:
1576:
1571:
1569:
1567:
1566:
1557:
1556:
1547:
1542:
1541:
1526:
1525:
1520:
1516:
1514:
1513:
1512:
1496:
1495:
1483:
1460:
1458:
1457:
1452:
1450:
1448:
1447:
1434:
1429:
1413:
1408:
1396:
1391:
1390:
1365:
1363:
1362:
1357:
1355:
1353:
1352:
1340:
1339:
1338:
1329:
1328:
1318:
1315:
1310:
1295:
1291:
1290:
1282:
1269:
1267:
1266:
1265:
1246:
1238:
1237:
1217:Generalized Born
1194:
1192:
1191:
1186:
1181:
1180:
1172:
1136:
1134:
1133:
1128:
1126:
1125:
1105:
1103:
1102:
1097:
1094:
1089:
1073:
1071:
1070:
1065:
1060:
1059:
1051:
1045:
1044:
1028:
1026:
1025:
1020:
1015:
1014:
1006:
990:
988:
987:
982:
977:
976:
968:
949:
947:
946:
941:
939:
938:
936:
928:
924:
923:
915:
903:
902:
889:
880:
879:
871:
859:
858:
848:
843:
833:
818:
817:
809:
803:
802:
787:
783:
779:
778:
770:
761:
760:
752:
746:
745:
737:
720:
719:
711:
691:
689:
688:
683:
681:
680:
678:
670:
666:
665:
657:
645:
644:
631:
622:
621:
613:
601:
600:
590:
585:
575:
554:
553:
545:
539:
538:
517:
513:
509:
508:
500:
491:
490:
482:
476:
475:
467:
450:
449:
441:
377:solvation energy
331:
329:
328:
323:
321:
320:
296:
294:
293:
288:
286:
285:
260:
258:
257:
252:
250:
249:
232:
231:
230:
220:
208:
207:
206:
21:
4362:
4361:
4357:
4356:
4355:
4353:
4352:
4351:
4322:
4321:
4320:
4305:
4283:
4279:
4264:
4242:
4238:
4217:(11): 3275–85.
4207:
4203:
4182:(49): 11521–9.
4172:
4168:
4131:Protein Science
4126:
4120:
4111:
4080:(10): 2600–12.
4074:Protein Science
4069:
4063:
4059:
4025:
4019:
4015:
3983:10.1.1.461.7843
3958:
3954:
3917:Protein Science
3912:
3906:
3897:
3858:
3854:
3823:
3819:
3796:
3792:
3747:
3743:
3698:
3694:
3655:
3651:
3594:
3590:
3537:
3533:
3526:
3506:
3502:
3473:(5002): 106–9.
3463:
3459:
3404:
3400:
3369:
3365:
3336:(16): 1967–78.
3326:
3319:
3312:
3294:
3290:
3241:
3237:
3200:
3196:
3159:Protein Science
3154:
3148:
3144:
3091:
3087:
3032:
3028:
2979:
2975:
2952:
2948:
2917:
2913:
2884:(11): 1148–54.
2874:
2870:
2815:
2811:
2763:
2757:
2753:
2714:
2710:
2687:10.1002/jmr.577
2671:
2667:
2620:
2616:
2575:(10): 3086–90.
2564:
2558:
2554:
2514:
2508:
2504:
2497:
2483:
2479:
2440:
2433:
2402:
2398:
2367:
2363:
2322:(14): 7777–82.
2308:
2304:
2300:
2295:
2236:
2188:
2175:
2169:lipid bilayer.
2152:fusion enthalpy
2123:
2081:
2068:
2056:solvation shell
2050:Solute-solvent
2048:
2027:
2024:
2023:
2002:
1969:
1964:
1956:Ewald summation
1951:
1931:
1888:
1884:
1875:
1871:
1865:
1846:
1841:
1816:
1811:
1802:
1799:
1798:
1784:
1747:
1721:
1717:
1715:
1712:
1711:
1683:
1679:
1677:
1674:
1673:
1648:
1644:
1642:
1639:
1638:
1618:
1615:
1614:
1593:
1589:
1587:
1584:
1583:
1562:
1558:
1552:
1548:
1546:
1534:
1530:
1521:
1505:
1501:
1497:
1488:
1484:
1482:
1478:
1477:
1469:
1466:
1465:
1440:
1436:
1430:
1422:
1409:
1401:
1395:
1383:
1379:
1377:
1374:
1373:
1345:
1341:
1334:
1330:
1324:
1320:
1319:
1317:
1311:
1300:
1281:
1274:
1270:
1261:
1257:
1250:
1245:
1233:
1229:
1227:
1224:
1223:
1213:
1171:
1170:
1162:
1159:
1158:
1121:
1117:
1115:
1112:
1111:
1090:
1085:
1079:
1076:
1075:
1050:
1049:
1040:
1036:
1034:
1031:
1030:
1005:
1004:
996:
993:
992:
967:
966:
958:
955:
954:
929:
914:
913:
898:
894:
890:
888:
884:
870:
869:
854:
850:
844:
839:
829:
808:
807:
798:
794:
769:
768:
751:
750:
736:
735:
728:
724:
710:
709:
707:
704:
703:
671:
656:
655:
640:
636:
632:
630:
626:
612:
611:
596:
592:
586:
581:
571:
544:
543:
534:
530:
499:
498:
481:
480:
466:
465:
458:
454:
440:
439:
437:
434:
433:
415:
409:
316:
312:
310:
307:
306:
281:
277:
269:
266:
265:
245:
241:
226:
222:
216:
193:
192:
188:
183:
180:
179:
169:
163:
76:polysaccharides
23:
22:
15:
12:
11:
5:
4360:
4350:
4349:
4344:
4339:
4334:
4319:
4318:
4303:
4277:
4262:
4236:
4201:
4166:
4137:(6): 1318–33.
4109:
4057:
4013:
3952:
3895:
3852:
3817:
3790:
3741:
3692:
3665:(12): 1432–6.
3649:
3588:
3551:(5): 1153–64.
3531:
3524:
3500:
3457:
3418:(9): 6174–91.
3398:
3363:
3317:
3310:
3288:
3258:10.1.1.25.1195
3235:
3194:
3142:
3105:(5): 2900–18.
3085:
3026:
2996:10.1.1.107.962
2973:
2946:
2911:
2868:
2809:
2774:(21): 214102.
2751:
2708:
2665:
2614:
2552:
2525:(6): 595–602.
2502:
2495:
2477:
2431:
2396:
2361:
2301:
2299:
2296:
2294:
2293:
2291:Solvent models
2288:
2283:
2278:
2273:
2268:
2263:
2258:
2253:
2248:
2243:
2237:
2235:
2232:
2187:
2184:
2174:
2171:
2143:ligand binding
2122:
2119:
2080:
2077:
2067:
2064:
2052:hydrogen bonds
2047:
2044:
2031:
2001:
1998:
1968:
1965:
1963:
1960:
1950:
1947:
1929:
1920:
1919:
1908:
1905:
1902:
1899:
1896:
1891:
1887:
1881:
1878:
1874:
1868:
1864:
1860:
1855:
1852:
1849:
1844:
1840:
1836:
1833:
1828:
1825:
1822:
1819:
1814:
1810:
1806:
1783:
1780:
1746:
1743:
1724:
1720:
1689:
1686:
1682:
1651:
1647:
1622:
1596:
1592:
1565:
1561:
1555:
1551:
1545:
1540:
1537:
1533:
1529:
1524:
1519:
1511:
1508:
1504:
1500:
1494:
1491:
1487:
1481:
1476:
1473:
1462:
1461:
1446:
1443:
1439:
1433:
1428:
1425:
1421:
1417:
1412:
1407:
1404:
1400:
1394:
1389:
1386:
1382:
1367:
1366:
1351:
1348:
1344:
1337:
1333:
1327:
1323:
1314:
1309:
1306:
1303:
1299:
1294:
1288:
1285:
1280:
1277:
1273:
1264:
1260:
1256:
1253:
1249:
1244:
1241:
1236:
1232:
1212:
1209:
1184:
1178:
1175:
1169:
1166:
1124:
1120:
1093:
1088:
1084:
1063:
1057:
1054:
1048:
1043:
1039:
1018:
1012:
1009:
1003:
1000:
980:
974:
971:
965:
962:
951:
950:
935:
932:
927:
921:
918:
912:
909:
906:
901:
897:
893:
887:
883:
877:
874:
868:
865:
862:
857:
853:
847:
842:
838:
832:
828:
824:
821:
815:
812:
806:
801:
797:
793:
790:
786:
782:
776:
773:
767:
764:
758:
755:
749:
743:
740:
734:
731:
727:
723:
717:
714:
693:
692:
677:
674:
669:
663:
660:
654:
651:
648:
643:
639:
635:
629:
625:
619:
616:
610:
607:
604:
599:
595:
589:
584:
580:
574:
570:
566:
563:
560:
557:
551:
548:
542:
537:
533:
529:
526:
523:
520:
516:
512:
506:
503:
497:
494:
488:
485:
479:
473:
470:
464:
461:
457:
453:
447:
444:
411:Main article:
408:
405:
389:lipid bilayers
319:
315:
284:
280:
276:
273:
262:
261:
248:
244:
240:
237:
229:
225:
219:
215:
211:
205:
202:
199:
196:
191:
187:
165:Main article:
162:
159:
115:lipid bilayers
9:
6:
4:
3:
2:
4359:
4348:
4345:
4343:
4340:
4338:
4335:
4333:
4330:
4329:
4327:
4314:
4310:
4306:
4300:
4296:
4292:
4288:
4281:
4273:
4269:
4265:
4259:
4255:
4251:
4247:
4240:
4232:
4228:
4224:
4220:
4216:
4212:
4205:
4197:
4193:
4189:
4185:
4181:
4177:
4170:
4162:
4158:
4153:
4148:
4144:
4140:
4136:
4132:
4125:
4118:
4116:
4114:
4105:
4101:
4096:
4091:
4087:
4083:
4079:
4075:
4068:
4061:
4053:
4049:
4044:
4039:
4036:(2): 127–34.
4035:
4031:
4024:
4017:
4009:
4005:
4001:
3997:
3993:
3989:
3984:
3979:
3975:
3971:
3967:
3963:
3956:
3948:
3944:
3939:
3934:
3930:
3926:
3922:
3918:
3911:
3904:
3902:
3900:
3891:
3887:
3883:
3879:
3875:
3871:
3868:(3): 207–17.
3867:
3863:
3856:
3848:
3844:
3840:
3836:
3832:
3828:
3821:
3813:
3809:
3805:
3801:
3794:
3786:
3782:
3777:
3772:
3768:
3764:
3761:(4): 930–46.
3760:
3756:
3752:
3745:
3737:
3733:
3728:
3723:
3719:
3715:
3712:(4): 918–29.
3711:
3707:
3703:
3696:
3688:
3684:
3680:
3676:
3672:
3668:
3664:
3660:
3653:
3645:
3641:
3637:
3633:
3629:
3625:
3621:
3617:
3612:
3607:
3604:(2): 023301.
3603:
3599:
3592:
3584:
3580:
3575:
3570:
3566:
3562:
3558:
3554:
3550:
3546:
3542:
3535:
3527:
3521:
3517:
3514:
3510:
3504:
3496:
3492:
3488:
3484:
3480:
3476:
3472:
3468:
3461:
3453:
3449:
3444:
3439:
3434:
3429:
3425:
3421:
3417:
3413:
3409:
3402:
3394:
3390:
3386:
3382:
3378:
3374:
3367:
3359:
3355:
3351:
3347:
3343:
3339:
3335:
3331:
3324:
3322:
3313:
3307:
3302:
3301:
3292:
3284:
3280:
3276:
3272:
3268:
3264:
3259:
3254:
3250:
3246:
3239:
3231:
3227:
3222:
3217:
3214:(2): 133–52.
3213:
3209:
3205:
3198:
3190:
3186:
3181:
3176:
3172:
3168:
3165:(2): 227–35.
3164:
3160:
3153:
3146:
3138:
3134:
3129:
3124:
3120:
3116:
3112:
3108:
3104:
3100:
3096:
3089:
3081:
3077:
3072:
3067:
3062:
3057:
3053:
3049:
3045:
3041:
3037:
3030:
3022:
3018:
3014:
3010:
3006:
3002:
2997:
2992:
2988:
2984:
2977:
2969:
2965:
2961:
2957:
2956:J Am Chem Soc
2950:
2942:
2938:
2934:
2930:
2927:(2): 142–51.
2926:
2922:
2915:
2907:
2903:
2899:
2895:
2891:
2887:
2883:
2879:
2872:
2864:
2860:
2855:
2850:
2845:
2840:
2836:
2832:
2828:
2824:
2820:
2813:
2805:
2801:
2797:
2793:
2789:
2785:
2781:
2777:
2773:
2769:
2762:
2755:
2747:
2743:
2739:
2735:
2731:
2727:
2723:
2719:
2712:
2704:
2700:
2696:
2692:
2688:
2684:
2681:(6): 377–92.
2680:
2676:
2669:
2661:
2657:
2653:
2649:
2645:
2641:
2637:
2633:
2629:
2625:
2618:
2610:
2606:
2601:
2596:
2591:
2586:
2582:
2578:
2574:
2570:
2563:
2556:
2548:
2544:
2540:
2536:
2532:
2528:
2524:
2520:
2513:
2506:
2498:
2492:
2488:
2481:
2473:
2469:
2465:
2461:
2457:
2453:
2450:(2): 148–61.
2449:
2445:
2438:
2436:
2427:
2423:
2419:
2415:
2412:(1–2): 1–20.
2411:
2407:
2400:
2392:
2388:
2384:
2380:
2376:
2372:
2365:
2357:
2353:
2348:
2343:
2338:
2333:
2329:
2325:
2321:
2317:
2313:
2306:
2302:
2292:
2289:
2287:
2284:
2282:
2279:
2277:
2274:
2272:
2269:
2267:
2264:
2262:
2259:
2257:
2254:
2252:
2249:
2247:
2244:
2242:
2239:
2238:
2231:
2229:
2225:
2221:
2217:
2213:
2209:
2205:
2201:
2197:
2193:
2192:electrostatic
2183:
2181:
2180:alpha helixes
2170:
2168:
2167:
2161:
2157:
2153:
2148:
2144:
2140:
2136:
2132:
2128:
2118:
2116:
2112:
2108:
2103:
2099:
2095:
2090:
2086:
2076:
2073:
2063:
2061:
2057:
2054:in the first
2053:
2043:
2029:
2020:
2016:
2011:
2008:
1997:
1994:
1990:
1986:
1982:
1978:
1974:
1959:
1957:
1946:
1944:
1940:
1936:
1932:
1925:
1906:
1903:
1897:
1889:
1885:
1879:
1876:
1872:
1866:
1862:
1858:
1853:
1850:
1847:
1842:
1838:
1831:
1826:
1823:
1820:
1817:
1812:
1808:
1797:
1796:
1795:
1793:
1788:
1779:
1777:
1773:
1769:
1765:
1761:
1757:
1756:native states
1753:
1742:
1740:
1722:
1718:
1709:
1705:
1687:
1684:
1680:
1671:
1667:
1649:
1645:
1636:
1620:
1612:
1594:
1590:
1580:
1563:
1559:
1553:
1549:
1543:
1538:
1535:
1531:
1527:
1522:
1517:
1509:
1506:
1502:
1498:
1492:
1489:
1485:
1479:
1474:
1471:
1444:
1441:
1437:
1431:
1426:
1423:
1419:
1415:
1410:
1405:
1402:
1398:
1392:
1387:
1384:
1380:
1372:
1371:
1370:
1349:
1346:
1342:
1335:
1331:
1325:
1321:
1312:
1307:
1304:
1301:
1297:
1292:
1286:
1283:
1278:
1275:
1271:
1262:
1258:
1254:
1251:
1247:
1242:
1239:
1234:
1230:
1222:
1221:
1220:
1218:
1208:
1204:
1202:
1198:
1173:
1164:
1156:
1152:
1148:
1144:
1140:
1122:
1118:
1109:
1086:
1082:
1052:
1041:
1037:
1007:
969:
960:
933:
930:
916:
904:
899:
895:
891:
885:
872:
863:
860:
855:
851:
840:
836:
830:
826:
822:
810:
799:
795:
791:
788:
784:
771:
738:
729:
725:
721:
702:
701:
700:
698:
675:
672:
658:
646:
641:
637:
633:
627:
614:
605:
602:
597:
593:
582:
578:
572:
568:
564:
561:
558:
546:
535:
531:
527:
524:
521:
518:
514:
501:
468:
459:
455:
451:
432:
431:
430:
428:
424:
420:
414:
404:
402:
398:
394:
390:
386:
382:
378:
373:
371:
367:
363:
362:least squares
359:
355:
351:
347:
343:
339:
335:
317:
313:
304:
300:
282:
278:
274:
271:
246:
242:
238:
235:
227:
223:
217:
213:
209:
189:
178:
177:
176:
174:
168:
158:
156:
151:
147:
146:electrostatic
143:
139:
135:
131:
127:
123:
118:
116:
112:
108:
104:
100:
96:
91:
89:
85:
81:
77:
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
33:
29:
19:
4286:
4280:
4245:
4239:
4214:
4211:Biochemistry
4210:
4204:
4179:
4176:Biochemistry
4175:
4169:
4134:
4130:
4077:
4073:
4060:
4033:
4029:
4016:
3965:
3961:
3955:
3920:
3916:
3865:
3861:
3855:
3833:(3): 640–6.
3830:
3826:
3820:
3803:
3800:Biochemistry
3799:
3793:
3758:
3754:
3744:
3709:
3705:
3695:
3662:
3658:
3652:
3601:
3597:
3591:
3548:
3544:
3534:
3516:
3512:
3503:
3470:
3466:
3460:
3415:
3411:
3401:
3376:
3372:
3366:
3333:
3329:
3299:
3291:
3251:(1): 24–33.
3248:
3244:
3238:
3211:
3207:
3197:
3162:
3158:
3145:
3102:
3098:
3088:
3043:
3039:
3029:
2986:
2982:
2976:
2959:
2955:
2949:
2924:
2920:
2914:
2881:
2877:
2871:
2826:
2822:
2812:
2771:
2767:
2754:
2724:(1): 62–79.
2721:
2717:
2711:
2678:
2674:
2668:
2627:
2623:
2617:
2572:
2568:
2555:
2522:
2518:
2505:
2486:
2480:
2447:
2443:
2409:
2405:
2399:
2374:
2370:
2364:
2319:
2315:
2305:
2223:
2189:
2176:
2164:
2126:
2124:
2114:
2110:
2082:
2069:
2049:
2012:
2003:
1970:
1952:
1942:
1938:
1934:
1927:
1923:
1921:
1789:
1785:
1764:salt bridges
1748:
1738:
1707:
1703:
1669:
1668:on particle
1581:
1463:
1368:
1216:
1214:
1205:
1196:
1150:
1142:
1138:
1107:
952:
694:
416:
400:
396:
380:
376:
374:
337:
333:
302:
263:
170:
130:surface area
119:
92:
31:
27:
26:
2519:Biopolymers
2261:Water model
2102:cyclohexane
2089:cyclohexane
2075:the years.
2017:instead of
2007:phase space
1983:process of
1768:alpha helix
1155:temperature
48:free energy
4326:Categories
3443:10023/6096
3046:(4): e27.
2377:: 151–76.
2298:References
2216:amino acid
1201:linearized
429:units as:
401:difference
155:ionization
111:dielectric
3978:CiteSeerX
3644:118409341
3611:1212.0449
3509:Schlick T
3253:CiteSeerX
2991:CiteSeerX
2147:aliphatic
2127:solvation
2094:1-octanol
2085:1-octanol
2030:γ
2000:Viscosity
1933:of group
1873:∫
1863:∑
1859:−
1835:Δ
1805:Δ
1621:ϵ
1591:ϵ
1442:−
1298:∑
1287:ϵ
1279:−
1259:ϵ
1255:π
1243:−
1177:→
1165:λ
1092:∞
1056:→
1038:ρ
1011:→
999:Ψ
973:→
961:ϵ
920:→
908:Ψ
892:−
876:→
864:λ
846:∞
827:∑
823:−
814:→
796:ρ
792:−
775:→
763:Ψ
757:→
754:∇
742:→
730:ϵ
722:⋅
716:→
713:∇
662:→
650:Ψ
634:−
618:→
606:λ
588:∞
569:∑
565:π
559:−
550:→
532:ρ
528:π
522:−
505:→
493:Ψ
487:→
484:∇
472:→
460:ϵ
452:⋅
446:→
443:∇
375:Notably,
342:solvation
314:σ
224:σ
214:∑
186:Δ
157:effects.
150:enthalpic
140:, unlike
138:solvation
107:solvation
4313:15051331
4231:12641459
4161:16731967
4104:15340167
4052:11297670
4008:12278880
3947:12142453
3890:23972379
3847:11920749
3785:21438606
3736:21438609
3687:16666252
3679:12868108
3636:24032960
3583:25762327
3511:(2002).
3452:25660403
3393:21128657
3358:16996683
3350:15470756
3283:17671699
3275:11746700
3245:Proteins
3230:10223287
3208:Proteins
3137:14581194
3080:16617376
3021:12244353
3013:12214312
2941:16540310
2906:19378083
2898:15942918
2863:11517324
2804:23731263
2796:15974723
2746:16290441
2703:17184352
2695:12501158
2660:21867582
2547:45118648
2472:22977210
2464:14517967
2444:Proteins
2426:17030302
2356:11438731
2234:See also
1973:entropic
397:transfer
350:nitrogen
336:of atom
301:of atom
103:proteins
64:proteins
4272:9615168
4196:1747370
4152:2242528
4095:2286553
4000:1553543
3970:Bibcode
3962:Science
3938:2373680
3882:3735402
3776:3091260
3727:3089899
3616:Bibcode
3574:4375717
3553:Bibcode
3495:2011744
3475:Bibcode
3467:Science
3420:Bibcode
3189:1304905
3180:2142195
3128:1303570
3107:Bibcode
3071:1435986
3048:Bibcode
2831:Bibcode
2776:Bibcode
2726:Bibcode
2652:3945310
2632:Bibcode
2609:3472198
2577:Bibcode
2539:7766825
2324:Bibcode
2156:alkanes
1981:folding
1941:around
1664:is the
1633:is the
1609:is the
1153:is the
1145:is the
695:or (in
305:, and
297:is the
86:across
80:ligands
56:solvent
36:solvent
4311:
4301:
4270:
4260:
4229:
4194:
4159:
4149:
4102:
4092:
4050:
4006:
3998:
3980:
3945:
3935:
3888:
3880:
3845:
3783:
3773:
3734:
3724:
3685:
3677:
3642:
3634:
3581:
3571:
3522:
3493:
3450:
3391:
3356:
3348:
3308:
3281:
3273:
3255:
3228:
3187:
3177:
3135:
3125:
3078:
3068:
3019:
3011:
2993:
2939:
2904:
2896:
2861:
2851:
2802:
2794:
2744:
2701:
2693:
2658:
2650:
2624:Nature
2607:
2600:304812
2597:
2545:
2537:
2493:
2470:
2462:
2424:
2391:326146
2389:
2354:
2344:
2131:liquid
2111:ad hoc
2072:solute
1792:CHARMM
1710:, and
1582:where
1369:where
1157:, and
953:where
381:vacuum
358:sulfur
354:oxygen
346:carbon
264:where
233:
173:solute
134:solute
74:, and
52:solute
4004:S2CID
3886:S2CID
3683:S2CID
3640:S2CID
3606:arXiv
3354:S2CID
3279:S2CID
3017:S2CID
2902:S2CID
2854:56910
2800:S2CID
2764:(PDF)
2699:S2CID
2656:S2CID
2543:S2CID
2468:S2CID
2347:35418
2166:fluid
2135:solid
1993:proxy
1987:with
356:(O),
352:(N),
348:(C),
132:of a
84:drugs
4309:PMID
4299:ISBN
4268:PMID
4258:ISBN
4227:PMID
4192:PMID
4157:PMID
4100:PMID
4048:PMID
3996:PMID
3943:PMID
3878:PMID
3843:PMID
3781:PMID
3732:PMID
3675:PMID
3632:PMID
3579:PMID
3520:ISBN
3491:PMID
3448:PMID
3389:PMID
3346:PMID
3306:ISBN
3271:PMID
3226:PMID
3185:PMID
3133:PMID
3076:PMID
3009:PMID
2937:PMID
2894:PMID
2859:PMID
2792:PMID
2742:PMID
2691:PMID
2648:PMID
2605:PMID
2535:PMID
2491:ISBN
2460:PMID
2422:PMID
2387:PMID
2352:PMID
2208:Born
2198:and
2163:the
2141:and
2060:ions
1706:and
1464:and
1215:The
423:ions
417:The
4291:doi
4250:doi
4219:doi
4184:doi
4147:PMC
4139:doi
4090:PMC
4082:doi
4038:doi
3988:doi
3966:255
3933:PMC
3925:doi
3870:doi
3835:doi
3808:doi
3771:PMC
3763:doi
3722:PMC
3714:doi
3667:doi
3624:doi
3569:PMC
3561:doi
3549:108
3483:doi
3471:252
3438:hdl
3428:doi
3381:doi
3377:114
3338:doi
3263:doi
3216:doi
3175:PMC
3167:doi
3123:PMC
3115:doi
3066:PMC
3056:doi
3001:doi
2964:doi
2960:112
2929:doi
2886:doi
2849:PMC
2839:doi
2784:doi
2772:122
2734:doi
2722:247
2683:doi
2640:doi
2628:319
2595:PMC
2585:doi
2527:doi
2452:doi
2414:doi
2379:doi
2342:PMC
2332:doi
2154:of
2115:all
1774:of
699:):
697:mks
427:cgs
332:is
144:or
117:.
109:or
101:or
72:RNA
68:DNA
62:of
50:of
4328::
4307:.
4297:.
4266:.
4256:.
4225:.
4215:42
4213:.
4190:.
4180:30
4178:.
4155:.
4145:.
4135:15
4133:.
4129:.
4112:^
4098:.
4088:.
4078:13
4076:.
4072:.
4046:.
4034:14
4032:.
4028:.
4002:.
3994:.
3986:.
3976:.
3964:.
3941:.
3931:.
3921:11
3919:.
3915:.
3898:^
3884:.
3876:.
3866:90
3864:.
3841:.
3831:91
3829:.
3804:27
3802:.
3779:.
3769:.
3759:51
3757:.
3753:.
3730:.
3720:.
3710:51
3708:.
3704:.
3681:.
3673:.
3663:24
3661:.
3638:.
3630:.
3622:.
3614:.
3602:88
3600:.
3577:.
3567:.
3559:.
3547:.
3543:.
3489:.
3481:.
3469:.
3446:.
3436:.
3426:.
3416:17
3414:.
3410:.
3387:.
3375:.
3352:.
3344:.
3334:25
3332:.
3320:^
3277:.
3269:.
3261:.
3249:46
3247:.
3224:.
3212:35
3210:.
3206:.
3183:.
3173:.
3161:.
3157:.
3131:.
3121:.
3113:.
3103:85
3101:.
3097:.
3074:.
3064:.
3054:.
3042:.
3038:.
3015:.
3007:.
2999:.
2987:23
2985:.
2958:.
2935:.
2925:16
2923:.
2900:.
2892:.
2882:26
2880:.
2857:.
2847:.
2837:.
2827:98
2825:.
2821:.
2798:.
2790:.
2782:.
2770:.
2766:.
2740:.
2732:.
2720:.
2697:.
2689:.
2679:15
2677:.
2654:.
2646:.
2638:.
2626:.
2603:.
2593:.
2583:.
2573:84
2571:.
2567:.
2541:.
2533:.
2523:35
2521:.
2517:.
2466:.
2458:.
2448:53
2446:.
2434:^
2420:.
2410:78
2408:.
2385:.
2373:.
2350:.
2340:.
2330:.
2320:98
2318:.
2314:.
2222:,
2212:pH
1778:.
1672:,
1613:,
1149:,
90:.
70:,
66:,
4315:.
4293::
4274:.
4252::
4233:.
4221::
4198:.
4186::
4163:.
4141::
4106:.
4084::
4054:.
4040::
4010:.
3990::
3972::
3949:.
3927::
3892:.
3872::
3849:.
3837::
3814:.
3810::
3787:.
3765::
3738:.
3716::
3689:.
3669::
3646:.
3626::
3618::
3608::
3585:.
3563::
3555::
3528:.
3497:.
3485::
3477::
3454:.
3440::
3430::
3422::
3395:.
3383::
3360:.
3340::
3314:.
3285:.
3265::
3232:.
3218::
3191:.
3169::
3163:1
3139:.
3117::
3109::
3082:.
3058::
3050::
3044:2
3023:.
3003::
2970:.
2966::
2943:.
2931::
2908:.
2888::
2865:.
2841::
2833::
2806:.
2786::
2778::
2748:.
2736::
2728::
2705:.
2685::
2662:.
2642::
2634::
2611:.
2587::
2579::
2549:.
2529::
2499:.
2474:.
2454::
2428:.
2416::
2393:.
2381::
2375:6
2358:.
2334::
2326::
1943:i
1939:j
1935:j
1930:j
1928:V
1924:i
1907:r
1904:d
1901:)
1898:r
1895:(
1890:i
1886:f
1880:j
1877:V
1867:j
1854:f
1851:e
1848:r
1843:i
1839:G
1832:=
1827:v
1824:l
1821:o
1818:s
1813:i
1809:G
1723:i
1719:a
1708:j
1704:i
1688:j
1685:i
1681:r
1670:i
1650:i
1646:q
1595:0
1564:j
1560:a
1554:i
1550:a
1544:=
1539:j
1536:i
1532:a
1528:,
1523:2
1518:)
1510:j
1507:i
1503:a
1499:2
1493:j
1490:i
1486:r
1480:(
1475:=
1472:D
1445:D
1438:e
1432:2
1427:j
1424:i
1420:a
1416:+
1411:2
1406:j
1403:i
1399:r
1393:=
1388:B
1385:G
1381:f
1350:B
1347:G
1343:f
1336:j
1332:q
1326:i
1322:q
1313:N
1308:j
1305:,
1302:i
1293:)
1284:1
1276:1
1272:(
1263:0
1252:8
1248:1
1240:=
1235:s
1231:G
1197:r
1183:)
1174:r
1168:(
1151:T
1143:k
1139:q
1123:i
1119:z
1108:i
1087:i
1083:c
1062:)
1053:r
1047:(
1042:f
1017:)
1008:r
1002:(
979:)
970:r
964:(
934:T
931:k
926:)
917:r
911:(
905:q
900:i
896:z
886:e
882:)
873:r
867:(
861:q
856:i
852:z
841:i
837:c
831:i
820:)
811:r
805:(
800:f
789:=
785:]
781:)
772:r
766:(
748:)
739:r
733:(
726:[
676:T
673:k
668:)
659:r
653:(
647:q
642:i
638:z
628:e
624:)
615:r
609:(
603:q
598:i
594:z
583:i
579:c
573:i
562:4
556:)
547:r
541:(
536:f
525:4
519:=
515:]
511:)
502:r
496:(
478:)
469:r
463:(
456:[
338:i
318:i
303:i
283:i
279:A
275:S
272:A
247:i
243:A
239:S
236:A
228:i
218:i
210:=
204:v
201:l
198:o
195:s
190:G
54:-
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.