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Three-Dimensional Lattice Monte Carlo Simulations of Model Proteins. IV. Proteins at an Oil-Water Interface K. Leonhard,*,† J. M. Prausnitz,‡,§ and C. J. Radke‡,| Lehrstuhl fu¨r Technische Thermodynamik, Schinkelstrasse 8, 52062 Aachen, Germany, Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720-1462, and Chemical Sciences and Earth Sciences DiVisions, Lawrence Berkeley National Laboratory, Berkeley, California 94720 ReceiVed September 16, 2005. In Final Form: December 21, 2005 Lattice Monte Carlo simulations describe the adsorption of protein-like heteropolymer chains at an oil/water interface. The heteropolymers are designed sequences of 27 and 64 amino acid-type lattice sites taken from a 20-letter alphabet. We use our recently suggested energy scale to model oil and water. We investigate the effect of the oil parameters on adsorption properties of a single chain and on the aggregation of adsorbed chains while keeping the water parameters fixed to their optimum values found previously. By varying the oil parameters, we can cause a large range of adsorption behavior: from no adsorption to reversible adsorption to irreversible adsorption. We compare adsorption at a liquid/ solid interface to that at a liquid/liquid interface. A liquid interface leads to stronger adsorption and denaturation than a solid interface with the same water and oil interaction parameters. We propose “optimal” oil parameters and use them to study multichain adsorption at a liquid interface.
Introduction Because of the importance of adsorption in biology, drug production and formulation, and food processing, much experimental and theoretical effort has been directed toward studying how proteins adsorb at interfaces. Despite these efforts, many questions concerning protein adsorption remain. An important question concerns the change in conformation of the protein as a function of sequence, solvent properties, and interface properties. An overview of previous theoretical and simulation work on the topic can be found in the introduction of a study by Anderson et al.1 Since then, additional aspects of protein adsorption have been studied by Otsuka et al., who measured the height versus time of adsorption of a single adsorbed glucose oxidase protein using tapping-mode atomic-force microscopy.2 They suggest a primary unfolding step of the protein chain toward R-helices and a secondary step that leads to further unfolding. Similarily, using sum frequency generation vibrational spectroscopy, Wang et al. provide evidence for a “dramatic” change in conformation of BSA at an air-solution interface. The extent of unfolding increases as the surface coverage falls.3 The same dependence of the extent of unfolding on protein concentration has been reported by Jones and Middelberg, who measured the stressstrain curve at water-oil interfaces with adsorbed proteins.4 They exclude covalent bonds as the origin of the interfacial forces, and they assume hydrophic interactions as the main protein-protein interactions at the interface.4 Using FTIR spectroscopy, Lefe`vre and Subirade find the formation of intermolecular antiparallel β-sheets for proteins adsorbed to an oil-water interface.5 The films of adsorbed proteins are more viscous and rigid than those * Corresponding author. E-mail:
[email protected]. † Lehrstuhl fu ¨ r Technische Thermodynamik. ‡ University of California. § Chemical Sciences Division, Lawrence Berkeley National Laboratory. | Earth Sciences Division, Lawrence Berkeley National Laboratory. (1) Anderson, R. E.; Pande, V. S.; Radke, C. J. J. Chem. Phys. 2000, 112, 9167-9185. (2) Otsuka, I.; Yaoita, M.; Higano, M.; Nagashima, S.; Kataoka, R. Appl. Surf. Sci. 2004, 235, 188-196. (3) Wang, J.; Buck, S. M.; Chen, Z. Analyst 2003, 128, 773-778. (4) Jones, D. B.; Middelberg, A. P. J. Langmuir 2002, 18, 5585-5591. (5) Lefe`vre, T.; Subirade, M. J. Colloid Interface Sci. 2003, 263, 59-67.
formed by smaller molecules (2D network); the data show that adsorbed proteins contain significant amounts of residual native structures. According to Lefe`vre and Subirade, the protein entropy is not increased upon adsorption. Because the interface provides a denaturing condition, the content of β-sheets increases. The investigated protein (β-lactoglobulin) is insoluble in n-hexadecane used as the oil phase. Using explicit-(SPC)-water simulations, Mungikar et al. simulate a polymer consisting of 8-to-20-residue-long, charged, ASP-ILE diblock units that adsorbs on a charged surface.6 They study inter- and intramolecular hydrogen bonds with their model based on LJ interactions and point charges. These simulations show that electrostatic interactions and an entropy gain are the driving forces for adsoption on the surface of the proteins used in their simulations. Liu and Haynes use an HP model with explicit hydrophobic, polar, inert wall and hydrophobic wall segments plus implicit water in two dimensions.7 Solid walls impose constrains on the movement of chain beads of adsorbed chains and restrict their conformational freedom as does the limited dimensionality (2D). Adsorption is first reversible and then irreversible. Whereas the authors find a reduction in entropy when the chain adsorbs to a strongly hydrophobic surface, they performed those simulation above the midpoint temperature, which corresponds to a dominating unfolded state in the bulk liquid. To study the effect of increased surface protein concentration, they use inert segments for walls to confine the space available to an individual chain. They do not consider intermolecular contacts, however. In this model, the lowest-energy state of an adsorbed protein is degenerate in most cases. The authors also report experimental results on hen egg-white lysozyme (HEWL); these show reduced (but not completely vanishing) activity of the adsorbed protein, especially for low surface coverage. The authors conclude that any meaningful adsorption model for globular proteins must account for the dependence of protein conformation on surface coverage. When the hydrophobicity of the interface is similar to that of the hydrophobic beads, adsorption is energetically and entropically (6) Mungikar, A. A.; Forciniti, D. Biomacromolecules 2004, 5, 2147-2159. (7) Liu, S. M.; Haynes, C. A. J. Colloid Interface Sci. 2005, 282, 283-292.
10.1021/la052535h CCC: $33.50 © 2006 American Chemical Society Published on Web 03/01/2006
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favored. For very stable proteins (weak adsorption), adsorption is favored only energetically. A different model has been applied by Euston and Naser to study protein adsorption.8 They distinguish two types of proteins used to stabilize emulsions: random coil and globular proteins. In this study, a protein consists of 125 identical beads not necessarily arranged as a chain. All subunits remain in contact with at least one other bead (which one is not fixed, however). The definition of contact includes contacts over edges and corners in addition to the usually defined face contacts. The protein may be athermal (random coil) or may have attractive interaction between beads or between beads and the solid interface. Surface pressure is modeled by a force driving beads toward an axis perpendicular to the interface and running through the center of mass of the protein. Interchain interactions between different proteins are not considered. A transition between particlelike and chainlike adsorption is found depending on the attraction between chain beads. The qualitative behavior is correlated to forces holding together the tertiary structure in a real protein. At low surface pressure, protein conformation is independent of pressure. Then, there is a transition where a higher surface pressure deformes the protein. Using lattice Monte Carlo simulations of 27-mer model proteins,9 Castells and Van Tassel studied kinetic aspects of protein adsorption via an investigation of free-energy barriers to adsorption. They found that a hard surface stabilizes the unfolded state. Only when the surface is strongly attractive is there no free-energy barrier between the folded adsorbed and unfolded adsorbed states. In the first case, the final state is reached via initial unfolding followed by partial refolding. When we studied multichain simulations with the model proposed by Anderson et al., we found qualitatively unreasonable aggregation in bulk water. Therefore, we changed the interaction model. In previous studies, we devised a modified MiyazawaJernigan10 amino acid-water interaction energy scale and applied it to protein folding and protein aggregation.11-13 In the present work, we introduce additional interaction energy parameters to model amino acid-oil interactions. The objective of this work is to determine the effect of the oil parameters and of interface softness (liquid/solid or liquid/liquid interface) on adsorption to estabish a more realistic oil model and to use that model to study multichain aggregation at the interface. Because experiment indicates7 that interchain contacts are important, in contrast to previous studies, we consider interchain contacts.
Interaction Model We have proposed the following expression for the amino acid-solvent interaction energy Ei0 (ref 11)
Cs n 1 Ei0 ) (1 - Cs)Eii + ω j+ Ejj 2 2n j)1
∑
(1)
where the amino acid-amino acid self-interaction energy Eii is taken from Table 5 of Miyazawa and Jernigan.10 All other nonself-interaction energies Eij are also taken from Table 5 of that work. Cs is a contrast parameter. When it is zero, the solvent solvates hydrophobic amino acids as well (or as poorly) as (8) Euston, S. R.; Abu Naser, M. Langmuir 2005, 21, 4227-4235. (9) Castells, V.; Yang, S.; Van Tassel, P. R. Phys. ReV. E 2002, 65, 031912. (10) Miyazawa, S.; Jernigan, R. L. Macromoleules 1985, 18, 534-552. (11) Leonhard, K.; Prausnitz, J. M.; Radke, C. J. Protein Sci. 2004, 13, 358369. (12) Leonhard, K.; Prausnitz, J. M.; Radke, C. J. Biophys. Chem. 2003, 106, 81-89. (13) Leonhard K.; Prausnitz, J. M.; Radke, C. J. Phys. Chem. Chem. Phys. 2003, 5, 5291-5299.
hydrophilic amino acids. The more positive Cs, the more favorable are contacts between the solvent and hydrophilic amino acids. When Cs is negative, contacts between the solvent and hydrophobic amino acids are favored. Hence we can model hydrophilic solvents (e.g., water) with Cs > 0 and hydrophobic solvents (e.g., oil) with Cs < 0. ω j describes the average interaction of an amino acid with the solvent. When ω j is negative, amino acids interact on average attractively with the solvent. When ω j is positive, they repel the solvent and hence effectively attract each other. Because it is more convenient to think in terms of amino acid interactions than amino acid-solvent interactions, in the rest of this article we call ω j the “effective amino acid-amino acid mean attraction” or briefly “mean attraction”. However, on the basis of exchange energies a positive ω j means an effective attraction in this context. When simulations with more than one solvent are performed to study proteins at a fluid-phase interface, we have to introduce more parameters to describe the properties of all solvents. For multiple-solvent simulations, three kinds of solvent parameters are necessary: Csi and $i are single-solvent parameters necessary for each solvent, and E0i0j is the binary solvent-solvent interaction energy for solvents i and j. All solvent-solvent self-interaction energies E0i0i are set equal to zero; therefore, the oil-water interaction energy corresponds to an exchange energy.11 To keep the number of parameter combinations manageable in this study, we fix the water parameters to the optimal values (Cs,H2O ) 0.2 and ω j H2O ) 0.16) found in earlier studies.11-13 We also fix the contrast parameter for oil, Cs,oil to -0.1. This parameter needs to be negative to model a hydrophobic solvent. We arbitrarily choose the absolute value for oil to be half of that for water because we expect oil-amino acid interactions to be less specific than water-amino acid interactions. Anyway, a change in the contrast parameter for water has only quantitative effects on the results in pure water and does not lead to a qualitative change in behavior in the range 0.1 e Cs,H2O e 0.4. The mean attraction in oil, ω j oil, and the oil-water interaction, Eoil-water, are the independent variables that we vary to study their effect on the behavior of a protein adsorbed at an oil-water interface.
Simulation Technique The details of our simulations have been described in depth in a previous paper.11 Here, we give only a brief overview of the simulation techniques already described in that paper and more detailed information on the methods used to model the interface. All simulations are performed on a 3D cubic lattice with periodic boundary conditions and a size of 20 × 20 × 20 sites. Each site of the lattice protein molecule corresponds to a collection of residues, yielding an effective residue or a bead. Beads are arranged along a self-avoiding chain, and the distance between beads, the so-called Kuhn segment distance, is sufficient to permit freely jointed moves.14 All sites that are not occupied by a chain group are occupied by an effective solvent molecule.10 An effective solvent molecule is a lattice site of the same size as a Kuhn segment and can represent any number of solvent molecules that correspond to the size of the segment. An effective solvent molecule can be either a water kind or an oil kind. At the beginning of a simulation, all solvent sites at a location z < zinter are of the water kind, and those at z g zinter are of the oil kind. zinter defines the location of the interface along the z axis. During the simulation, mixing between oil and water sites is allowed only within dinter/2 sites from the center of the interface, hence dinter determines the (14) Boyd, R. H.; Phillips, P. J. The Science of Polymer Molecules; Cambridge University Press: New York, 1993.
Model Proteins at Interfaces
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thickness or softness of the interface. Unless otherwise indicated, zinter ) 10 and dinter ) 6 in the rest of this article. The system energy is defined as the sum of the interaction energies over all pairs of adjacent sites on the lattice that are not neighbors on a chain. Accordingly, the system energy is described by the Hamiltonian that has the following form: L
H)
L
L
∑ ∑ ∑ E(i,j,k),(i+1,j,k) + E(i,j,k),(i,j+1,k) + E(i,j,k),(i,j,k+1) i)1 j)1 k)1
(2)
L is the size of the lattice in lattice units, and E(i,j,k),(l,m,n) is the interaction energy between an amino acid or solvent bead on site (i, j, k) and one on site (l, m, n). Only nearest-neighbor interactions are non-zero. During the simulation, end-flip, kink-bend, and crank-shaft Monte Carlo moves are attempted. If we try to move a chain bead to a site occupied by another chain bead, then the move is immediately rejected because we use self-avoiding chains. Otherwise, we try to exchange the protein bead with a solvent bead on this site. Then, the move is accepted or rejected depending on the energy change ∆E associated with the move in accordance with the Metropolis criterion
∆E e 0: always accept
( )
∆E > 0: accept with probability exp -
∆E kBT
(3) (4)
where kB, the Boltzmann constant, has the value of 1 MJ-energy unit/1 associated temperature unit. MJ energies are based on contact frequencies, hence they are only relative energies. To our knowledge, no conversion to conventional energy units is available. Therefore, for our purpose here, temperature can be expressed in any arbitrary unit. Within dinter/2 sites from the center of the interface, we try to exchange adjacent solvent sites along a random direction, when they are of different types, and apply the Metropolis criterion to decide whether the exchange is accepted or not. Moves of chain beads are prohibited if they involve a movement of a oil site more than dinter/2 sites away from the interface into the water phase and when they require the respective movement of a water bead. The types of amino acid beads for a chain are chosen to reflect a composition corresponding to a typical real protein. Then the sequence is obtained by simulated annealing in sequence space for a given structure.11 Its one-letter abbreviation code is TRMKQKNSLYEIEASVGVHRLTAPGFD for our 27-mer and KEKSTAGRVASGVLDSVACGVLGDIDTLQGSPIAKLKTFYGNKFNDVEASQAHMIRWPNYTLPE for the 64-mer. The native state of the 27-mer in water is a compact 3 × 3 × 3 cube with 28 non-bonded contacts when ω j H2O > 0.1, and it is a non-compact structure with 26 such contacts otherwise. We use ω j H2O ) 0.16 throughout this work because it turned out to be the most reasonable water parameter.11 The native state in water of the 64-mer is a compact 4 × 4 × 4 cube for all water models studied by us previously.12 Extensive simulations have shown that the native states are global minima of the free-energy landscapes. Details of the native states, including sketches of them and folding kinetics as well as thermodynamics, can be found in refs 11 and 12.
Free Energy In a Monte Carlo simulation, it is not possible to calculate absolute free energies. However, it is posssible to calculate freeenergy differences between states that can be observed in MC
Table 1. One Chain at an Oil-Water Interfacea Fads
Fads(folded)
Fads(unfolded)
ω j oil
Nnat
RG
kBT
0.1 0.2 0.3 0.5 0.7
0.16 0.16 0.16 0.16 0.16
21.3 9.1 7.2 7.0 6.0
1.5 2.1 2.6 2.8 3.0
-1.1 -8.4 -13.2 -19 -27
-0.5 -5.1 -6.2 -9 -18.0
-2.5 -9.8 -14.6 -20 -28
0.3 0.3 0.3 0.3 0.3
-0.04 0.06 0.16 0.26 0.36
4.1 5.6 7.2 16.4 21.0
3.0 2.9 2.6 1.8 1.5
-7.8 -25 -13.2 -5.0 -1.1
4.8 -16 -6.2 -3.3 -1.1
-9.2 -26 -14.6 -6.4 -2.2
Eoil-water
kBT
k BT
a T ) 0.9Tm, Cs,water ) 0.2, ω j water ) 0.16, and Cs,oil ) -0.1 for all simulations. At this temperature, Nnat ) 22.1 and RG ) 1.5 for a chain in bulk water.
Table 2. One Chain at an Oil-Water Interfacea Fads Eoil-water ω j oil dinter Nnat 0.1 0.1 0.1 0.3 0.3 0.3 0.3 0.3 0.5 0.5 0.7 0.7
0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16 0.16
0 2 6 0 2 4 6 8 0 6 0 6
22.5 21.6 21.3 16.5 7.2 7.2 7.2 7.1 9.9 6.7 6.0 6.0
RG
kBT
1.5 1.5 1.5 1.9 2.6 2.6 2.6 2.6 2.5 2.8 3.0 3.0
-1.9 -1.1 -1.1 -6.8 -12.9 -13.2 -13.2 -13.2 -16 -19 -28 -27
Fads(folded) Fads(unfolded) kBT
kBT
-2.0
-3.0
-0.5 -6.1 -6.2 -6.8 -6.2 -6.4 -9.6 -8.7 -18.5 -18.0
-2.5 -8.1 -14.3 -14.6 -14.6 -14.6 -17.4 -20.4 -29.5 -28
a T ) 0.9Tm, Cs,water ) 0.2, ω j water ) 0.16, and Cs,oil ) -0.1 for all simulations. The softness of the interface is varied.
simulations by counting the number of occurrences of the states. We use the number of native contacts, Nnat, the number of intermolecular contacts, Ninter, and the z coordinate of the center of mass of the protein, which are called order parameters, to create a 3D histogram for each chain in a simulation and count how often the chain is in each state corresponding to a combination of the three order parameters. The z coordinate is rounded to a tenth of a lattice spacing unit, and all beads have the same mass. After the simulation, the relative free energy F(A) of state A can be calculated from the number of times the chain was found in state Z(A)
F(A) ) - kBT ln Z(A)
(5)
where Z(A) is the canonical partition function of the system in state A. It is composed of the configurational part of the partition sum, Zconf, and the translational part, Ztrans. For a chain moving around freely in a box of length L, Ztrans ) 6L3 or, equivalently, Ftrans/kBT ) -10.78 (with L ) 20) per free object. For a chain confined to a 2D interface, Ztrans ) 4L2 and Ftrans/kBT ) -7.38 per free object, whereas the translational part of the partition sum for a chain adsorbed to a soft interface is difficult to separate from the configurational part. A single isolated chain is a free object as is an aggregated multiple chain. Reported free energies of aggregation in Table 3 correspond to the particular concentrations employed here. They can be converted to different concentrations by the formula given above for the translational partition sum.
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Table 3. Free Energies for the Eight States Possible in a Multichain Simulation at an Oil-Water Interfacea number of chains 2 3 4
F/kBT single unfolded bulk
F/kBT aggregated folded bulk
F/kBT aggregated unfolded bulk
F/kBT single folded interface
F/kBT single unfolded interface
F/kBT aggregated folded interface
F/kBT aggregated unfolded interface
-1.2
-1.2
-2.8
-7.0 -7.0 -7.0
-14.3 -14.4 -15.2
-8.6 -8.0 -8.8
-14.7 -15.4 -16.7
a T ) 0.9Tm, Cs,water ) 0.2, ω j water ) 0.16, Cs,oil ) -0.1, Eoil-water ) 0.3, and ω j oil ) 0.16 for all simulations. The free energy of the single folded chain in the bulk is set to zero for the two-chain simulation. The free energy of the single folded adsorbed chain is set to -7.0 for the three- and four-chain simulations.
State A can be a histogram bin. However, a more general definition of a state is also possible. For example, we can define an aggregated and an isolated state in multichain simulations. In this case, we add the number of occurrence in all histogram bins that correspond to zero intermolecular contacts to obtain Z(isolated) and add all others to obtain Z(aggregated). More generally, a state can also be any combination of histogram bins. In this manner, we compute free energies of adsorption, distinguishing between the native and non-native state and between aggregated and non-aggregated states. The precise definitions of the states that we use to analyze our simulation data are presented later in the section entitled Aggregation at the Interface. In the case of strong adsorption, the free energy cannot be sampled satisfactorily in a single simulation. Therefore, we perform biased simulations to force our system to sample a specific portion of the free-energy landscape. The bias potential V has the form
V ) R(z - zb)2
(6)
where zb is the z coordinate that the chain is forced toward and R determines the strength of this force. This procedure leads to biased results for the simulation, but the unbiased free energy for a state can be easily recoverd from the biased free energy, Fbiased(A), and the bias potenial applied to state A, V(A),
F(A) ) Fbiased(A) - V(A)
Figure 1. Free-energy profile for single chains at the interface. Effect of the oil-water interaction energy at a constant ω j oil ) 0.16 and T ) 0.9Tm. The thin, dotted line symbolizes the interface at z ) 0.
(7)
Because any single simulation can provide only free-energy differences between the states sampled during that simualtion, we can add an arbitrary constant to the free energies obtained from a simulation. By creating free-energy landscapes overlapping in the order parameter z, one can add constants to every simulation to obtain a continuous free-energy landscape that covers the whole range of the order parameter of interest. This is not possible in a single simulation.15 We collect 3D histograms of the energy of each chain, of the total energy, and of the radius of gyration, RG ) n (rcm-ri)2, where the sum runs over all beads of a chain. x1/n∑i)1
rcm is the location of the center of mass of a chain, and ri is the position of bead i in lattice units. The order parameters of the histograms are the number of total contacts, Ntot, the number of contacts between the beads of one chain and all other amino acid beads on any chain, omitting contacts between the two neighbors that are consecutive on the same chain (one neighbor for a terminal bead), the number of native contacts, Nnat, and the z coordinate of the center of mass of the protein, as in the free-energy calculations. We use the collected data to present profiles of these quantities as a function of the distance of the chain from (15) Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academinc Press: New York, 1996.
the interface to reveal information about the structural and energetic changes associated with adsorption. The lattice spacing introduces strong periodicity into F, Ntot, Nnat, and RG because, for example, the chain can be fully folded only when its center of mass is at an integer position. Therefore, we perform a correctly weighted averaging using the four bins immediately preceding and following a bin and the bin itself. Neverthless, some spikes remain on the profiles. They are rather small but can distract from the main features. Therefore, we performe an unweighted averaging, again over nine bins, on the results obtained from the first averaging and computation of the quantity of interest. The error introduced by this procedure is much smaller than the statistical error of the simulations.
Results Effect of the Interaction between Oil and Water, Eoil-water, and of the Effective Mean Attraction in Oil, $oil, on the Adsorption of a Single Chain. As mentioned before, we perform simulations with different mean attractions for oil and different oil-water interactions. Table 1 shows the effects of these parameters on the number of native contacts, Nnat, the radius of gyration, RG, and free energies of adsorption. We use two different reference states for the free energies reported in Tables 1 and 2. The reference state for Fads is the chain in bulk water in any form (i.e., folded or unfolded). Hence, Fads is what is usually referred to as the free energy of adsorption. This definition of the free energy is also used in Figures 1 and 6. When we take into account the number of native contacts, as in Fads(folded) and Fads(unfolded), the reference state is the fully folded chain in bulk water. At 0.9Tm, the free energy of a fully folded chain is 1.4kBT higher than that of the chain in any state because the chain is in equilibrium with the unfolded state, which has a free energy that is 1.1kBT higher than that of the folded chain.11 We can see
Model Proteins at Interfaces
Figure 2. Profile of the number of native contacts for single chains at the interface. Effect of the oil-water interaction energy at a constant ω j oil ) 0.16 and T ) 0.9Tm. The thin, dotted line symbolizes the interface at z ) 0.
Figure 3. Schematic of a 27-mer at the oil-water interface (Eoil-water ) 0.5 and ω j oil ) 0.16). The water phase is in the uncolored bottom part of the figure, and the oil phase is on the top illustrated by a very light gray. Light gray is used for hydrophilic amino acid beads, medium gray for neutral, and dark gray for hydrophobic beads. Each bead is labeled with the one-letter abbreviation for the amino acid that it represents.
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Figure 5. Schematic of a 27-mer at the oil-water interface (Eoil-water ) 0.1 and ω j oil ) 0.16). The water phase is in the uncolored bottom part of the figure, and the oil phase is on the top illustrated by a very light gray. Light gray is used for hydrophilic amino acid beads, medium gray for neutral, and dark gray for hydrophobic beads. Each bead is labeled with the one-letter abreviation for the amino acid that it represents.
Figure 6. Free-energy profile for single chains at the interface. Effect of the mean attraction in oil at a constant Eoil-water ) 0.3 and T ) 0.9Tm. The thin, dotted line symbolizes the interface at z ) 0.
from bulk to interface. Therefore, a z value, zseparate, that separates the bulk region from the interface has to be arbitrarily chosen. We want very little influence of the interface in the region that we define as bulk, but at the same time we want to minimize the possibility that a chain that has no contact with the interface is considered to be adsorbed. We found that the results for the adsorbed chain are rather independent of the position of zseparate in the range from 6 to 9 when the interface is at zinter ) 10. Therefore, we choose zseparate ) 7.
Figure 4. Schematic of a 27-mer at the oil-water interface (Eoil-water ) 0.3 and ω j oil ) 0.16). The water phase is in the uncolored bottom part of the figure, and the oil phase is on the top illustrated by a very light gray. Light gray is used for hydrophilic amino acid beads, medium gray for neutral, and dark gray for hydrophobic beads. Each bead is labeled with the one-letter abbreviation for the amino acid that it represents.
from the free-energy profiles for a single chain (Figures 1 and 6) that there is no precise definition of when a chain is adsorbed and when it is in the bulk because there is a continuous transition
In those cases of reversible adsorption, the results for Nnat and RG depend on the thickness of the water phase because the time that the chain spends in that phase depends on the thickness of the phase. (Reversible adsorption means that a chain adsorbs and desorbs several times during a simulation (typical simulations are longer than 108 MC steps). When the adsorption is irreversible, we do not observe any desorption events during a simulation. The transition from reversible to irreversible behavior is at a free energy of adsorption of about 10kBT.) Hence, the data in Table 1 give an idea what happens under weakly adsorbing conditions, but more precise information will be provided in the form of free-energy profiles and other distance-dependent data for representative interaction sets.
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In the upper half of Table 1, the effect of Eoil-water is highlighted. Figures 1 and 2 show the impact of Eoil-water on the free energy and the number of native contacts as a function of the distance from the interface, which is indicated by a thin dotted line at z ) 0. In these figures, we use the multiple-histogram method to combine results from several simulations for a single condition (i.e., a set of parameters ω j i, Csi and Eoil-water). This leads to approximately but not identically overlapping lines in the figures. The discrepancies between two overlapping lines give an idea of the statistical uncertanites of the corresponding property. If oil and water dislike each other very much (i.e., Eoil-water g 0.5), then the protein chain adsorbs irreversibly to the interface, loses its native stucture to a great extent, and has a large radius of gyration, meaning that it spreads out very widely on the interface (Figure 3). The valley of the free energy of asdorption is very deep and narrow compared to other conditions studied. The steepness of this valley on the oil side is caused by the strong oil-water dislike that prevents oil beads from moving into the water and offering space to chain beads. This dislike is also the reason for the strong unraveling effect of the interface, which makes the free energy of the unfolded adsorbed chain about 10kBT lower than that of the folded adsorbed chain. When this dislike decreases, Eoil-water ) 0.3, the configurations of the protein at the interface become more compact (Figure 4), the free-energy valley becomes wider and more shallow, and the denaturing power of the interface becomes weaker. When Eoil-water decreases further, for example, to 0.1 (Figure 5), the force driving the adsorption vanishes, and the chain penetrates both phases at intermediate temperatures and stays only in water, preferably away from the interface and highly folded, at low temperatures. Under this last combination of parameters, there is barely an attractive area associated with the interface, and the oil phase causes a very soft repulsion extending several sites into the water phase. This is because oil and water are close to the critical point of the corresponding liquid-liquid Ising system and mix relatively well. This oil-water mixture is penetrable by the chain but provides an environment that is unfavorable compared to water. The profiles of the native contacts look very similar for all different water-oil interactions studied, with relatively large statistical errors. The main difference between the conditions is that the chain can move more into the oil phase when the oilwater dislike is weak. The strong differences in the average numbers of native contacts in Table 1 are, therefore, mainly caused by the different amounts of time that the chain spends at a certain position and not so much by the structure it has at that position. The bottom half of Table 1 and Figures 6 and 7 show the effect of the effective mean attraction in oil. By varying ω j oil, we can make the protein prefer either the water or the oil phase and be adsorbed to the interface reversibly or irreversibly. For a given oil-water interaction Eoil-water, the protein adsorption is the strongest when the mean attraction of the amino acid residues in water is slightly stronger than in oil (i.e. ω j oil ) 0.06). A weaker mean attraction in oil means at the same time a more favorable average amino acid interaction with oil than with water. However, the free energy for the chain is the same in both phases not when the mean attraction is the same but when it is somewhat weaker in oil because the sequence is optimized for the native structure in water, which causes the chain to gain stabilization energy when it folds to the native structure in water. This is not possible in oil because the native structure, which exposes hydrophilic beads to a large extent, is not beneficial in the oil phase. Therefore, only when the mean attraction in oil is very weak (e.g., ω j oil ) -0.04) does the chain prefer to be in the oil
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Figure 7. Profile of the number of native contacts for single chains at the interface. Effect of the mean attraction in oil at a constant Eoil-water ) 0.3 and T ) 0.9Tm. The thin, dotted line symbolizes the interface at z ) 0.
Figure 8. Schematic of a 27-mer at the oil-water interface (Eoil-water ) 0.3 and ω j oil ) -0.04). The water phase is in the uncolored bottom part of the figure, and the oil phase is on the top illustrated by a very light gray. Light gray is used for hydrophilic amino acid beads, medium gray for neutral, and dark gray for hydrophobic beads. Each bead is labeled with the one-letter abbreviation for the amino acid that it represents.
phase (Figure 8). In this case, we observe the fewest native contacts of all conditions studied and a large radius of gyration. Even when the chain penetrates into water, it cannot fold into its native structure because the hydrophobic beads are tied too strongly to the oil (cf. Figure 7). For a mean attraction in oil that equals the mean attraction in water, we observe the condition already discussed in the previous section. When the oil environment is moderately to strongly unfavorable compared to water, ω j oil ) 0.26 to 0.36, water is preferred enough by the chain to adsorb reversibly and very weakly; the chain retains much of its native structure. For ω j oil ) 0.36 and Eoil-water ) 0.3, the free energy of adsorption, the average number of native contacts, and the average radius of gyration are very similar to those for the system with ω j oil ) 0.16 and Eoil-water ) 0.1, but the profiles of Fads and Nnat look quite different. For a strong mean attraction in oil, the chain wants to avoid any contact with oil. Therefore, it does not even come close to the interface and retains most of its native structure wherever it moves. When we study the free-energy difference between the folded and unfolded adsorbed chain as a function of the mean attraction in oil, we find a maximum at ω j oil ) 0.06, where adsorption is strongest and the chain is adsorbed most flatly. When ω j oil < 0.06 the chain tends to prefer the oil phase where the native chain is also not very stable, but at least compact structures are preferred over non-compact ones. When ω j oil > 0.06 the attraction between
Model Proteins at Interfaces
Figure 9. Free-energy profile for single chains at the interface. Effect of the interface thickness on the free energy of adsorption. Eoil-water ) 0.3, ω j oil ) 0.16, and T ) 0.9Tm. The thin, dotted line symbolizes the interface at z ) 0.
oil and the chain, even with hydrophobic beads, becomes weaker and weaker, and the effect of the interface on the chain, even when the chain is close to the interface, becomes weaker. In general, the unfolding strength is correlated with the strength of adsorption. Effect of Interface Softness. We vary the interface softness for a range of oil-water interaction energy parameters to characterize possible effects of the interface softness. When the interface thickness, dinter, is zero, we do not allow oil beads to penetrate into water and vice versa. Because of excluded volume restrictions, this means that the protein chain cannot penetrate into the oil phase when the simulation is started with the chain in water and vice versa. In this case, we simulate a solid interface. When dinter > 0, the restriction of excluded volume is relaxed, and the chain can penetrate any distance into any phase, not only dinter/2 sites. Only the mixing of the solvents is restricted to a band next to the interface and is dinter sites thick. Results are shown in Table 2, which is organized in the same way as Table 1 except that we introduce the thickness of the interface as an additional parameter. Table 2 shows that there is a difference between a solid and a fluid interface for all conditions studied and that it is most pronounced when the oil-water dislike is intermediate. We also demonstrate the effect of the interface thickness in Figure 9 in form of the free-energy profiles for Eoil-water ) 0.3. For a solid interface, under the conditions studied, the distance where the interface attracts the protein chain is shorter than that for a fluid interface. This is caused by oil beads that, in the case of a fluid-fluid interface, move into the water phase and attract the protein chain over a longer range. When the chain moves closer to the interface, at a distance of one to two beads, the steric repulsion of the solid interface begins to play an important role. Note that an adsorption where the chain is flat (at z ) 0) is in principle possible and should have a finite positive free energy. However, under the conditions at which we performed the simulation, the simulation did not sample those high freeenergy states. As long as the interface is a fluid-fluid interface, there is barely any effect of the interface thickness in the range studied, dinter ) 2-8. The adsorption seems to be slightly weaker for d ) 2 than for a thicker interface; for all other thicknesses, the free-energy profiles are indistinguisable within the statistical accuracy of the simulation. When the oil-water dislike is strong (Eoil-water > 0.3), even local mixing of water and oil barely takes place because of the large energy penalty of additional oil-water contacts. Therefore, even if we allow mixing, the results are not very different from those for a solid interface. This explains the smaller effect of the interface thickness for a large oil-water dislike than for Eoil-water
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) 0.3. Finally, Figure 9 displays a small but significant energy barrier to adsorption at the solid interface (i.e., for d ) 0) not found for adsorption at the oil-water interface. Apparently, the presence of oil solubilized into the protein near the oil-water interface allows it to unfold partially with a favorable free energy that is not available for adsorption at the solid-water interface. When we compare the general behavior of proteins designed to function in water (i.e., irreversible adsorption to an oil-water interface, denaturation upon aggregation, and the liquidliquidlike behavior of the interface), we conclude that we should use ωoil ≈ ωwater and Eoil-water ) 0.3-0.5 in our simulations to obtain the most qualitatively realistic behavior of the protein chains. We therefore will use ωoil ) 0.16 and Eoil-water ) 0.3 for our multichain simulations at the interface. Aggregation at the Interface. We performed simulations with two, three, and four chains at an oil-water interface. The results of such a simulation are, in principle, contained in multidimensional histograms that give the energy and the free energy as a function of the z position of the chain, the number of native contacts, and the number of intermolecular contacts. The information can either be presented as a series of 2D or 3D projections of the 4D hypersurface or by defining a few useful states and contracting the histogram into these states. We choose the latter way to present our data and define the following eight states: separated and native in the bulk, separated and unfolded in the bulk, aggregated and native in the bulk, aggregated and unfolded in the bulk, separated and native at the interface, separated and unfolded at the interface, aggregated and native at the interface, and aggregated and unfolded at the interface. A chain is considered to be native when Nnat ) 28 and otherwise unfolded, separated when Ninter ) 0 and otherwise aggregated, and adsorbed at the interface when z g 7; otherwise, it is considered to reside in the bulk. The eight states are defined by the possible combinations of the three order parameters. The reader not familiar with these order parameters is referred to ref 13 for a more detailed description and sketches of the four bulk states. Here, we just add four more states that are discriminated from the four bulk states by their proximity to the interface. We use the same definition of adsorbed as in the one-chain adsorption section. In our previous study on bulk aggregation,13 we found reversible aggregation at T ) 0.9Tm for two 27-mers with the interaction parameters for water that we use in this work, and we have been able to determine the free energies for the four states of a chain in the bulk. In simulations with more than two chains in bulk water, we found the system in glasslike states at T ) 0.9Tm, and it was not possible to determine free energies of the four states with reasonable accuracy. The glasslike states found in our bulk simulations correspond to an irreversible amorphous aggregation of the proteins. Table 3 presents the free energies for eight states of chains in simulations with an oil-water interface. All simulation were started from a thermalized configuration with the chains adsorbed at the interface. Because in a MC simulation only free-energy differences between states observed during the simulation can be calculated, it is possible to shift the free-energy scale to a convenient reference point by adding a constant value to every free energy. In our previous studies, we set the free energy of the single folded bulk chain equal to zero. We employed the same definition here for the two-chain simulations. The bulk free energies in Table 3 have been taken from ref 13, and the interface free energies have been computed by biased MC runs in this work. Because it is difficult to obtain accurate free energies for the four bulk states in simulations with more than two chains,
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we report only free energies for the adsorbed states for these systems. For the same reason, we have to choose a different reference state for the three- and four-chain simulations. We elected to set the free energy of the single folded adsorbed chain equal to the same value as in the two-chain simulation to make comparison of the results most convenient. A comparison of the three- and four-chain free energies with two-chain bulk free energies is not possible, however. We can make two comparisons using the data in Table 3. For the two-chain simulations, we can compare bulk states with adsorbed states. We see immediately that the free energy of all adsorbed states is much lower than that of the corresponding bulk states. This is especially true for the unfolded states, in agreement with our above findings that adorption is irreversible and that the interface strongly unfolds the proteins. The free-energy difference between all adsorbed states and all bulk states is -12.1kBT, which is 1.1kBT less than the difference for a single chain (-13.2kBT). One would expect such a difference from the fact that the chains tend to aggregate in the bulk, which lowers the bulk free energy. A more detailed analysis supports this expectation in part but shows additionally that one adsorbed chain is stabilized by a second one, too. The stabilization of a bulk chain by adding a second one is 1.7kBT, whereas the stabilization of an adsorbed chain by adding a second one is 0.6kBT. We expect the following properties of our system to be responsible for this behavior: Amino acid residues, on average, dislike water to some extent. This is necessary for the proteins to fold. Folding, however, comes with an entropy penalty. Adding a second chain allows the system to reduce the number of unfavorable amino acid-water contacts compared to the number for two separated folded chains even more and at a much lower entropy penalty. This explains why small chains tend to be prone to aggregation. When the chains are sufficently large, the effect of eliminating amino acid-water contacts is less pronounced, and the chains are less prone to aggregation.13 At the interface, the very unfavorable oil-water interaction creates a strong driving force for the protein to the interface. Here, the effect of adding a second chain is less pronounced because creating a new amino acid-amino acid contact is favorable only when no oil-water contact is created by this process. When we compare the two-, three-, and four-chain simulations of adsorbed chains, we realize some differences compared to bulk simulations. Although we observed that aggregation increases strongly with the number of chains in bulk water and becomes essentially irreversible for four chains, there is only a weak effect of the number of adsorbed chains on the aggregation strength. Also, the aggregation of adsorbed chains was always reversible under the conditions studied. One 64-mer at the Interface. We found previously that 27mers and 64-mers exhibit considerable differences in their aggregation behaviors.13 The main difference is that 64-mers are much more stable against aggregation than 27-mers because in the 64-mer a larger part of the chain belongs to the hydrophobic core than in the 27-mer and there are more specific strongly attractive pairs of amino acids possible in the long chain. Such specific and attractive contacts are not neccessarily hydrophobic contacts, but pairs of hydrophilic amino acids are possible (e.g., a positively and a negatively charged amino acid attract each other strongly). To invesigate whether 64-mers are more stable against adsorption or maintain their native structure to a larger extent than 27-mers, we performed some simulations with 64-mers. However, the result is different from the aggregation studies: For the parameters that correspond best to real water and oil, the chain adsorbs quickly and irreversibly and loses its native structure
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to a great extent. For example, at T ) 0.9Tm, Cs,water ) 0.2, ω j water ) 0.16, Cs,oil ) -0.1, ω j oil ) 0.16, and Eoil-water ) 0.3, the 64mer has 10.9 native and 23.79 total contacts, compared to Nnat ) 66 and Ntot ) 70 for a chain in bulk water at the same temperature. This means that, in terms of the fraction of native contacts that are kept at the interface, the 64-mer unravels even more than the 27-mer. We conclude from these findings that the stability of the native state of a lattice protein is only of minor importance for its adsorption characteristics. The main driving force is the oil-water dislike that forces the protein to be a mediator between the oil and the water beads. Because this force is much stronger than differences in the stability of the native structure, it is the factor that mainly determines adsorption behavior.
Conclusions We have applied our new interaction energy scale toward the simulation of an oil-water interface. We find from these simulations that it is mainly the balance of unfavorable interactions that drives the chain to the interface. The amino acid-water interaction needs to be repulsive, on average, to promote compact protein structures and to facilitate protein folding. The oilwater interaction is repulsive because oil and water do not mix. And finally, the amino acid-oil interaction should be modeled as being unfavorable because the solubility of normal proteins in water is better than in oil (with membrane proteins being an exception, but these proteins have a different sequence and are designed for oil). We find that for a given oil-water interaction the adsorption is strongest when the average interaction of an amino acid bead with water is slightly more repulsive than with oil. When the amino acid-oil interaction is very unfavorable, adsorption is very weak. These effects suggest an additional way to prevent adsorption in real systems. Whereas the standard way is to reduce the free energy of the folded chain in bulk water (e.g., by adding sugars that act as excipients), one could add an oil-soluble component that makes amino acid-oil interactions unfavorable to reduce adsorption. For the first time, to our knowledge, we studied the effect of interface softness for several interaction parameter sets. It turns out that the characteristics of a fluid interface (i.e., the possibilities for oil beads to move into the water and into the core of the protein) are very important to the adsorption and denaturation properties of the interface when the oil-water repulsion is not too strong. When this repulsion becomes stronger, the effect diminishes because local mixing rarely takes place any more. In our study, aggregation at the interface during multichain simulations was always reversible. This might be due to the short chains employed and the relatively low surface concentrations. To provide reliable data that can be generated in a reasonable time, we report only results for systems where we were able to reach equilibrium in our simulations. Therefore, we cannot provide any information on slow kinetic effects of protein adsorption from our simulations, though such effects are very important in real systems (aging of adsorbed proteins). We found that it makes qualitatively no difference whether a 27-mer or a 64-mer is used to study adsorption, similar to protein folding but in contrast to bulk aggregation. Acknowledgment. We thank Dusan Bratko for helpful discussions and Alexandra Eck for coding an interface between our simulation program and the ray-tracing software Povgen. For financial support, we are grateful to DAAD (German Academic Exchange Service) for a fellowship to K.L. and to the Office for Basic Sciences of the U.S. Department of Energy. LA052535H
