We propose a methodology to capture short-lived but biophysically important contacts of biomacromolecules using the biomolecule-water nuclear Overhauser effect as an indirect microscope. Thus, instead of probing the direct correlation with the foreign biomolecule, we detect its presence by the disturbance it causes in the surrounding water. In addition, this information obtained is spatially resolved and can thus be attributed to specific sites. We extend this approach to the influence of more than one change in chemical environment and show a methodological way of resolution. This is achieved by taking double differences of corresponding σNOE/σROE ratios of the systems studied and separating specific, unspecific, and intermediate influence. While applied to crowding and encapsulation in this study, this method is generally suitable for any combination of changes in chemical environment.

Water is the only natural solvent of biomolecules and is vital to understand protein structure, dynamics, and function.1,2 Water molecules control the hydrogen-bonding framework of proteins and can be structural components in pockets and clefts.3,4 Biomolecular reaction equilibria and kinetics differ significantly in confined, living-matter like environments compared to the usual diluted buffer samples studied in labs.5,6 Site-selective desolvation plays a major role in fields such as molecular docking7 and enzymatic catalysis.8 

Likewise, protein-protein interactions are profoundly important in molecular recognition.9 For instance, the protein ubiquitin (UBQ) controls many protein degradation pathways10 by forming specific complexes with partner molecules.11–14 Beyond stable protein-protein complexes, more recent studies emphasize the importance of less specific interactions between proteins encountered in cytosol, which may contain up to 400 g/l of organic matter.15 On the one hand, protein mobility is lowered drastically by confinement between different macromolecules and the thus reduced volume (excluded volume effects). However, the influence of crowding goes beyond matter transport effects. Havenith et al. showed that using biochemically plausible cosolutes stabilizes ubiquitin (UBQ) structure by direct interaction, which is of enthalpic nature. In contrast, they found that polyethylene glycol (PEG), a popular voluminous cosolute in crowding studies lacking specific interactions with the protein, leads to destabilization instead due to the excluded volume effects of entropic nature.16 Candotti et al. discouraged the usage of unspecific voluminous crowders such as PEG altogether in favor of realistic bio-organic matter.17 

Both biomolecule and water properties are further altered by encapsulation in a cell; encapsulation encourages protein-protein aggregation and affects folding rates, preferred conformations, and biomolecule structure stability,6,18–20 the latter either positively21–23 or adversely24 depending on the system studied. Encapsulated water exhibits a smaller dielectric constant,25 greater viscosity, slowed down molecular rotation26 but normal27 to elevated28,29 collective rotation. Both macromolecular crowding and encapsulation form the condition known as confinement, one of the key characteristics of living matter. In fact, both of these affect the confined molecules similarly.30 For example, both encourage compact conformations and increase folding rates.31 

Thus, we see a need for a measurement methodology able to (1) capture short-lived protein-protein interactions and (2) distinguish these crowding effects from encapsulation effects and to do so on a spatially resolved scale to study the effects on different protein domains.

Intermolecular protein-protein interactions can be studied by transient intermolecular Nuclear Overhauser effects (NOEs), which measure cross-peaks, e.g., of hydrogen atoms bound to different proteins. While this method is very selective as it measures the direct interaction of two selected atoms, it comes with the trade-off that the supermolecular aggregate needs to survive at least on the NMR time scale32 [at least (1000 MHz)−1 = 1 ns]. Figure 1 shows double-logarithmic histograms of protein-protein contact times obtained from molecular dynamics (MD) simulations both for 5 ubiquitin (UBQ) molecules in solution33 as well as 5 UBQ molecules encapsulated in a cellular mimic.34 While the absolute frequency of these contacts differs slightly, the distribution in time is linear,

logN(t)=klog(t)+d,
(1)

and equal for all systems despite their structural diversity, corresponding to a polynomial

N(t)=d*tk
(2)

in double-linear space with k ≈ −2. Given a certain duration of the protein-protein contact, the probability of finding a contact lasting doubly as long is four times less. This distribution means that only a minority of all protein-protein contacts will last on the NMR-time scale (about 1% of all contacts at 1 ns), all other 99% thus invisible to the transient NOE.

FIG. 1.

Double-logarithmic histogram of the absolute (left-hand side) and relative (right-hand side) abundance of a protein-protein contact over contact duration time. These times were evaluated by Voronoi nearest-neighbor contacts of residues belonging to different protein molecules. The level of scaling refers to force field modifications detailed in Sec. II. We found more contacts for the unscaled systems as opposed to the scaled ones, analogous to Zagrovic’s findings.35 

FIG. 1.

Double-logarithmic histogram of the absolute (left-hand side) and relative (right-hand side) abundance of a protein-protein contact over contact duration time. These times were evaluated by Voronoi nearest-neighbor contacts of residues belonging to different protein molecules. The level of scaling refers to force field modifications detailed in Sec. II. We found more contacts for the unscaled systems as opposed to the scaled ones, analogous to Zagrovic’s findings.35 

Close modal

Recently, we have shown that long-lived interaction patterns of proteins, e.g., with a cell wall or a complex partner, can be mapped and spatially resolved onto the surface of the said protein via protein-water cross-peaks.36–38 In this method, we locate the presence of other interfaces indirectly by disturbances (retardations) in the surrounding water body. While we lose the specificity of direct protein-protein spin pairs, the proposed methodology offers some benefits:

  • Aggregates do not need to associate long enough to be captured by NMR since we only measure average water dynamics around the site of interest, affected by aggregate partners.

  • The indirect NOE does not depend on the specific occurrence of an isolated pair NOE (which often leads to unsatisfactory “absence of proof is not proof of absence” scenarios). Rather, the measurement is deferred to one protein hydrogen interacting with many water hydrogen atoms.

  • The identity of the aggregate partner or its specific hydrogen atoms needs not to be known, only the hydrogen atoms of the proteins of interest.

  • In addition to structural information, protein-water NOEs inherently contain hydration dynamics information.39 

Our four systems used in the frame of this study were previously featured in published works (bulk dilution,40 crowded system,33 encapsulated reverse micelle system,27 and the crowded and encapsulated system34), which focused on the dielectric properties of H2O/protein systems. Refer to the corresponding articles for more details about the methods employed. Gruebele pointed out the benefits of using the same trajectory to calculate different properties in terms of comparability.41 

We chose ubiquitin (UBQ) as a representative protein. It is an integral component in many protein degradation pathways10 and interacts with multiple other proteins. It is small (76 amino acids), spherical, and compact. At physiological conditions, it is net neutral; thus, we do not need to consider alternative tautomers nor the choice of proper counterions and its dipole is well-defined. The structure of UBQ was taken from the wwPDB database,42 entry 1UBQ,3 and parameterized with appropriate CHARMM36 atom types.43–46 

We chose the SPC/E water model47 to represent the aqueous solvent since it reproduces spectroscopic observables such as dielectric loss,48 terahertz bands,49 NMR,50 and neutron scattering51 better than the TIP water models. It was demonstrated to combine well with the CHARMM protein force field.52 

As for the reverse micelle systems, the dielectrically inert immersion medium isooctane was modeled with united atoms representing CH, CH2, and CH3 atom groups in order to save computational resources. For this reverse micelle exterior, we chose the GROMOS 45A3 force field,53 which was designed specifically for supermolecular hydrophobic structures such as lipid aggregates and micelles. The atomic charges were set to zero. In practice, it combines well with the CHARMM force field and accurately reproduces experimental dielectric absorption,54 nuclear quadrupole resonance,26 and terahertz bands.55 

We chose the mixed zwitterionic/neutral lauryldimethyamine-N-oxide (LDAO)/1-decanoyl-rac-glycerol (DMAG) surfactant, a 35/65 mixture empirically discovered by the group of Wand using screening experiments.56,57 This surfactant was demonstrated to safely encapsulate a variety of diverse proteins and even t-RNA in reverse micelles as opposed to the more popular anionic sodium bis(2-ethylhexyl) sulfosuccinate (aerosol-OT, AOT) surfactant, which degrades most proteins with only few exceptions such as UBQ.57 The polar head group was modeled atomistically with appropriate CHARMM36 atom types except for the charge, which was obtained from quantum-chemical calculations. The tails were modeled analogously to isooctane with united atoms, parameterized using the GROMOS 45A3 force field except for the charge, which was set to zero. We refer the reader to Ref. 29 for more details regarding the surfactant model and force field.

The water loading of the reverse micelle

w0=[H2O][surfactant]=NH2ONsurfactant=10
(3)

was chosen in analogy to Wand’s finding stable UBQ-loaded LDAO/DMAG reverse micelles at this water loading.56,58 The reverse micelle size was chosen according to preceding studies54 for the reverse micelle carrying 1 UBQ and linearly scaled up for the reverse micelle carrying 5 UBQ molecules.

Table I summarizes the compositions of all the simulated systems. λprotein and λsurfactant refer to the level of λ-scaling, which is explained in more detail below.

TABLE I.

Overview of the MD simulations used in the frame of this project.

λproteinλsurfactantNH2ONUBQNNa+NClNisooctaneNLDAONDMAG
1 UBQ/H2O (bulk)40  
   45.000 150 150 
5 UBQ/H2O (crowded)33  
1.0 1.0 Unscaled 17.369 58 58 
1.1 1.0 Scaled … … … … … … … 
1 UBQ/H2O/LDAO/DMAG/isooctane (encapsulated)27  
1.0 1.0 Unscaled 1.500 9000 50 100 
1.1 1.0 Half-scaled … … … … … … … 
1.1 1.1 Fully scaled … … … … … … … 
5 UBQ/H2O/LDAO/DMAG/isooctane (crowded and encapsulated)34  
1.0 1.0 Unscaled 7.500 9000 250 500 
1.1 1.0 Half-scaled … … … … … … … 
1.1 1.1 Fully scaled … … … … … … … 
λproteinλsurfactantNH2ONUBQNNa+NClNisooctaneNLDAONDMAG
1 UBQ/H2O (bulk)40  
   45.000 150 150 
5 UBQ/H2O (crowded)33  
1.0 1.0 Unscaled 17.369 58 58 
1.1 1.0 Scaled … … … … … … … 
1 UBQ/H2O/LDAO/DMAG/isooctane (encapsulated)27  
1.0 1.0 Unscaled 1.500 9000 50 100 
1.1 1.0 Half-scaled … … … … … … … 
1.1 1.1 Fully scaled … … … … … … … 
5 UBQ/H2O/LDAO/DMAG/isooctane (crowded and encapsulated)34  
1.0 1.0 Unscaled 7.500 9000 250 500 
1.1 1.0 Half-scaled … … … … … … … 
1.1 1.1 Fully scaled … … … … … … … 

Recently, both the groups of Zagrovic35 and Mittal59 pointed out that current force fields yield simulation artifacts for MD simulations including more than one protein in solution. This leads to, e.g., erroneous solvation energies and unnaturally strong protein-protein associations. This defective behavior is due to force fields being calibrated and optimized for a single solvated biomacromolecule. Thus, by extension, this also concerns reverse micelles loaded with a protein. In order to account for these well-known force-field defects, we employed the λ-scaling approach proposed by Best and Mittal to correct these behaviors. It consists of deepening the Lennard-Jones potential well depth ϵ by a multiplicative factor λ,

ULJ(r)=4ϵλσr12σr6.
(4)

It has been found that setting λ = 1.1 yields the desired simulation behavior in accordance with the empirical findings.59 Technically, CHARMM does not store pair interaction parameters σ and ϵ persistently but creates them from atomic ones upon simulation initialization in transient memory. The new, scaled parameters then overwrite the standard CHARMM ones by using NBFIX commands, which are summarized in the supplementary material of Refs. 33 (crowded system), 27 (encapsulated system), and 34 (crowded, encapsulated system).

For the crowded bulk system, we created simulations both with the standard force field parameters as they are (unscaled system) and corrected according to Best and Mittal (scaled system). For the encapsulated single protein system and the encapsulated crowded system, we devised simulations using standard force field parameters (unscaled system), scaled protein-water interactions as proposed by Mittal (half-scaled system), and both protein-water and surfactant-water interactions corrected (fully scaled system). Overall, we used five independent replicas for each level of λ-scaling to exclude statistical force field artifacts as well.

In order to detect the influence of possible force field defects, Fig. 2 correlates σNOE/σROE values of the same protons, but at different levels of λ-scaling.

FIG. 2.

Effect of the λ-scaling on the experimental observable Δ(σNOE/σROE) showing the NOE to ROE ratio differences between the diluted bulk system to the crowded system (top row), encapsulated system (middle row), and the combined crowded and encapsulated system (bottom row). The black line marks equality.

FIG. 2.

Effect of the λ-scaling on the experimental observable Δ(σNOE/σROE) showing the NOE to ROE ratio differences between the diluted bulk system to the crowded system (top row), encapsulated system (middle row), and the combined crowded and encapsulated system (bottom row). The black line marks equality.

Close modal

The Δ(σNOE/σROE) values of pure encapsulation (middle row) seem to be barely affected by any level of λ-scaling. However, multiprotein systems in solution do show systematic differences as previously pointed out by Zagrovic35 and Mittal.59 Quite generally, the scaled system exhibits faster hydration dynamics (higher NOE to ROE ratios). For the combined crowded and encapsulated system, we again see little differences when just altering the level of surfactant scaling (bottom row, central diagram). However, when increasing the level of protein-water scaling, the hydration dynamics increase for most protein hydrogens.

Based on this analysis, we decided to select the level of scaling according to Best and Mittal and used the scaled crowded system, as well as the half-scaled encapsulated and combined protein systems in the discussion of the remaining of this article.

The molecular structures were inserted into the initial cubic simulation box with the software PACKMOL60 using numerical seeds. In the case of the nonmicellar systems (bulk dilution and crowded), the protein molecule(s) were randomly positioned and then surrounded with the appropriate amount of water molecules. In the case of the reverse micelles, the protein was either set into the box center (encapsulated system, 1 UBQ) or distributed closely around it (crowded and encapsulated system, 5 UBQ) and then surrounded by a sphere of the specified amount of water molecules. This aqueous core was then surrounded by a layer of properly oriented surfactants with the polar head groups facing the water nanopool. This protomicelle was then surrounded by a cubic box of isooctane molecules as the immersion medium. For reasons of statistical stability, five independent replicas of each system and each level of λ-scaling were constructed.

All subsequent simulation steps were performed by DOMDEC CHARMM.61,62 The initial intermolecular geometry was energetically minimized by 2000 steps of steepest descent and then equilibrated as a periodic isobaric-isothermal (NpT) ensemble at T = 300 K until the box length converged. The actual trajectory was then produced as a periodic isochoric-isothermal (NVT) ensemble at T = 300 K. The equations of motion were integrated with a leap-frog scheme63 using the Nosè-Hoover thermostat.64,65 High-frequency vibrations of covalent bonds including hydrogen atoms were constrained with the SHAKE algorithm.66 In all systems, a time step of 2 fs and a write frequency of 1 ps were chosen. In all complex (nonbulk) systems, at least 100 ns of the initial trajectory was discarded to avoid slow equilibration artifacts often found in reverse micelles, particularly systematic protein motion.54 Electrostatic interactions were treated with the Particle-Mesh Ewald (PME) method67,68 on a 64 × 64 × 64 grid (bulk system) or else a 128 × 128 × 128 grid using cubic splines of order 6 and κ = 0.41 Å−1 (tinfoil boundary conditions).

The atomic coordinates comprising the trajectory were read into a Python program using the MDAnalysis module.69,70 Voronoi tessellation was performed using the Voro++ implementation.71 A Python/Cython hybrid program employed in previous NOE studies36,39 was used to track the temporal evolution of the protein hydrogen-water hydrogen connecting vectors. The time series were stored and resolved by the protein hydrogen identity and by the initial spin-spin distance (resolution 1 Å). The correlation was calculated without using the convolution theorem. At each starting point, the protein was centered in the simulation box to ensure a minimum distance to each interacting solvent spin. The coordinates were then individually unfolded for each correlation to allow for a natural diffusive motion of the water molecules without coordinate jumps caused by periodic boundary conditions.

The persistently saved correlation decays were then loaded into a Python program, real-part Fourier-transformed using the numpy.fft library and the NOE/ROE values calculated as described in Sec. III.

In order to test our hypothesis whether indirect NOE measurements can capture macromolecular crowding, we repurposed molecular dynamics (MD) simulations featured in previous articles:

  • one molecule of UBQ diluted in bulk water40 as the unaffected solvated reference (bulk system);

  • five molecules of UBQ in bulk water33 (crowded system);

  • one molecule of UBQ encapsulated in a reverse micelle27 (encapsulated system);

  • five molecules of UBQ encapsulated in a reverse micelle34 (crowded and encapsulated system).

The systems employed in the frame of this study are summarized in Fig. 3. This study focuses on changes in NOE observables upon introducing a new chemical influence. Thus, we need to measure the difference between a test sample of interest, e.g., a protein in complex with another protein and a reference sample lacking this influence, e.g., the same protein, but without partners. None of these changes should alter the conformation of the protein in question significantly; otherwise, one has to disentangle the desired hydrogen changes originating from foreign interface presence from those caused by the conformational change.

FIG. 3.

Schematic overview of the chemical environments of UBQ considered in the frame of this study. The direction of the connecting arrows indicates an increase in environment complexity with red standing for crowding by more UBQ molecules and yellow standing for encapsulation in the LDAO/DMAG reverse micelles.

FIG. 3.

Schematic overview of the chemical environments of UBQ considered in the frame of this study. The direction of the connecting arrows indicates an increase in environment complexity with red standing for crowding by more UBQ molecules and yellow standing for encapsulation in the LDAO/DMAG reverse micelles.

Close modal

In this study, we selected a diluted bulk-liquid solution of UBQ as the reference system due to the lack of any other chemical influence. In practice, it may be not advisable to use bulk-liquid dilutions as reference systems since protein hydration dynamics in dilution are fast72 and necessitate specialized technology to measure NOEs, such as hyperpolarized solvent NMR.73 Instead, one could also perform protein complexation experiments confined in reverse micelles, where hydration dynamics and hydrogen exchange reactions are drastically slowed down.74,75 In this case, the isolated confined proteins would be the reference system and the confined complex would be the test system. While this experimental setup may be tempting, perturbing protein-surfactant interactions have to be accounted for, as we will demonstrate later.

Due to computational feasibility, encapsulation in a cell is mimicked by encapsulation in a reverse micelle. A biological cell has a different size, and its membrane has a different curvature and composition compared to these reverse micelles. However, reverse micelles are able to mimic some aspects of biological matter, such as the presence of a volume limiting interface. From these trajectories, we extracted the protein and water hydrogen atom positions and their temporal evolution. We evaluated time correlation functions (TCFs) tracking the temporal behavior of the protein-water hydrogen connecting vectors rIS(t), each representing an interacting spin pair,

gIS(t)=1rIS(0)31rIS(t)332cos2(θIS(t))12,
(5)

where θIS(t) describes the angle swept by the spin-joining vector rIS during time t. The real-part Fourier transform of this TCF yields the spectral density function (SDF) J(ν), which contains all information about the dipole-dipole interactions,

JIS(ν)=0gIS(t)cos(2πνt)dt.
(6)

For the protein-water NOE, we need to consider one spin I located on the protein interacting with many spins S at the water hydrogen atoms,

J(ν)=SJIS(ν).
(7)

The experimentally observable relaxation rates σNOE and σROE are simple linear combinations of the SDF,

σNOE(ν)=0.6J(2ν)0.1J(0),
(8)
σROE(ν)=0.3J(ν)+0.2J(0).
(9)

While calculating NOE observables this way from a trajectory is far more expensive computationally than to use analytical models, we thus avoid assumptions intrinsic to these models, which may not hold up in reality. For instance, NOE models often assume a strictly exponential correlation decay, yet experimentally, nonexponential TCFs have been determined for some liquids.76,77

Experimentally, exact NOE cross-relaxation rates of 2D NMR spectra can be obtained from the NOE buildup,78,79 in particular, if taking the diagonal peaks into consideration.80 The exact measurement of these rates is difficult due to a normalization problem, particularly in 2D NOESY spectra. Riek et al. have shown that the problem of determining NOE cross-relaxation rates can be simplified by obtaining NOE cross intensities, normalized to the diagonal cross-peak.81 

The measurement of protein-water NOE cross peaks as a means of studying hydration dynamics was pioneered by Wüthrich and Otting,82–86 tacitly assuming that they are short-ranged (1/r6) like the intramolecular NOEs commonly used in molecular structure elucidation. However, theoretical model studies by Halle revealed the long-range nature (up to 1/r) of the intermolecular NOE,87 mainly owing to the interaction with many spin partners instead of just one and the increasingly slow pair diffusion with the growing distance of the interacting particles. Subsequent model studies88–90 and MD simulations90,91 confirmed that while short-ranged, site-specific information is present, it is buried by a multitude of long-ranged, unspecific contributing signals.

Later, it has been claimed39 that the NOE is, in fact, short-ranged and that the unspecific long-ranged part merely adds a constant to all protein-water σNOE, thus not altering the sequence of NOE signals, merely the absolute value. This assumption is problematic for two reasons:

  1. An additional unspecific offset to σNOE makes it experimentally impossible to estimate protein-water correlation times from relaxation rates. Usually, for near-exponential TCFs, it holds that

J(ν)=μ04π22γH41r6τ1+(2πντ)2.
(10)

However, a typical relaxation rate of 0.01 ms−1 measured for a surface proton-water cross-peak would yield a pair correlation time of 3 ns. This is the P2 tumbling time of ubiquitin itself and would relate to the unrealistic case of water tightly bound to the surface. Only when using an experimentally barely determinable rn with n ranging from 1 to 3,89,91 one obtains a more realistic water residence time of a few picoseconds.92 

  1. The offset addition holds only for strongly diluted bulk solutions, since it takes a regular, uniform water body to contribute equal signals to the total NOE. For confined systems, this is not true due to the excluded water volumes brought about by other macromolecules and biological interfaces. See the supplementary material for more information on inhomogeneous water bodies in confinement.

Experimental studies by Wand et al. measured the hydration dynamics maps of the protein ubiquitin (UBQ) by not taking the raw NOESY signal, but the fraction σNOE/σROE74,75 relating the cross-relaxation rate of the laboratory frame (NOE) and the rotating frame (ROE). We confirmed that this ratio correlates with water translational dynamics represented by residence times at the specific protein surface proton. Nonsurface protons lacking water contacts do not correlate meaningfully.39 Absolute entities (NOESY and ROESY) are, in fact, long-ranged due to the nature of the SDF. However, relative entities (i.e., fractions of the SDF) eliminate the long-ranged unspecific contributions due to error compensation laws, thus rendering the NOE short-ranged.36 

Forming the difference between these ratios of the same protein hydrogen atoms in two different chemical environments yields structural information,

ΔxσNOEσROE=σNOEσROExσNOEσROEref,
(11)

where the reference ratio would typically refer to a diluted bulk solution (hydrated biomolecule without further influences). By forming the difference, we obtain the changes in hydration specifically brought about by chemical influence x, e.g., the additional presence of a different protein as opposed to its absence. The ratios σNOE/σROE represent absolute time scales, which allow for the detection of heterogeneous biomolecule features such as pockets holding slow structural water.39 Differences represent ratios of time scales due to their logarithmic context with the water residence time τr at the studied site,39 

σNOEσROElog(τr),
(12)
ΔxσNOEσROE=σNOEσROExσNOEσROEreflogτr,xτr,ref.
(13)

On this relative scale, only differences of chemical environments matter. That is, both a very fast hydration site (e.g., an exposed surface proton) and a very slow site (e.g., a protein proton inside a water cleft) will appear equal if they are slowed down by the same factor, even though their absolute time scales differ drastically.

The computational results are shown for the encapsulated, crowded, and combined system in Fig. 4. As pointed out previously,36–38 the encapsulated system is divided into two major regions: The α-helix site is barely affected by encapsulation, but the opposite β-sheet region shows strongly retarded hydration dynamics. Experimental studies by the group of Wand have reported a similar NOE/ROE pattern for encapsulated UBQ.74,75 We found that in all independent replicas, at all levels of force field scaling, the UBQ molecule diffuses to the reverse micelle wall and stays there for the remaining simulation time with its β-sheets facing the capsule wall. This region contains the hydrophobic patch (Leu-8, Ile-44, and Val-70),93 which is involved in most UBQ-protein binding processes (e.g., Refs. 11–14). The slowed down hydration and thus the noticeable presence of the foreign interface is brought about by a thin interstitial layer of water exhibiting extremely retarded molecular dynamics36 while retaining its bulk solution structure as confirmed by experiments.94 The problem of biomolecule-wall association when loading reverse micelles with biomolecules has previously been pointed out.95,96 For instance, this phenomenon is responsible for the deactivation of the enzyme cutinase upon encapsulation.97 In the specific instance of encapsulated UBQ, the same behavior was also reported in a MD simulation using a vastly different force field93 and was found in NMR experiments by Simorellis and co-workers reporting on enhanced Lipari-Szabo order parameters of the UBQ β-sheet, indicative of rigidification by interaction with the surfactants.30,98,99

FIG. 4.

Relative hydration dynamics differences for the encapsulated system [Δencap(σNOE/σROE), top panels], the crowded system [Δcrowd(σNOE/σROE), central panels], and the combined crowded and encapsulated system [Δcrowd,encap(σNOE/σROE), bottom panels]. Hydrogen atoms picking up slower hydration dynamics than in the reference bulk system are colored blue, neutral influences white, and accelerations (physically unlikely) are shown in red.

FIG. 4.

Relative hydration dynamics differences for the encapsulated system [Δencap(σNOE/σROE), top panels], the crowded system [Δcrowd(σNOE/σROE), central panels], and the combined crowded and encapsulated system [Δcrowd,encap(σNOE/σROE), bottom panels]. Hydrogen atoms picking up slower hydration dynamics than in the reference bulk system are colored blue, neutral influences white, and accelerations (physically unlikely) are shown in red.

Close modal

In addition to protein-wall interactions, we are now able to report on short-lived protein-protein contacts seen in the middle panel of Fig. 4. Note how the hydration retardation patterns differ from those of the encapsulation case. First, the retardations are moderate in comparison, probably owing to the short-lived nature of protein-protein contacts introducing less hydration perturbation than long-lasting protein-wall associations. Second, other regions are affected in this case. While both encapsulation and crowding slow down the hydration of the floppy C-terminus (Arg-72–Gly-76), other proteins prefer contact via the α-helix site while leaving out large parts of the β-sheet.

The system, both encapsulated and crowded, resembles the cellular situation most closely. Note how almost every hydrogen reports on slowed down hydration dynamics with respect to the infinite-dilution bulk system. This is to be expected considering the complicated chemical environment, but it lacks the informative quality of the above two cases: What parts of UBQ face other proteins and what other parts face the reverse micelle wall, if any? While one may try to interpret this case based on the results of the above two less complicated cases, a simple 1:1 transfer of observations is not possible as we will show.

Instead, we approach the distinction of the two chemical influences in a mathematically proper way. Consider the paths of increasing environmental complexity implied in Fig. 3: We can first crowd UBQ with other UBQ molecules, then encapsulate the aggregate system, or else we first encapsulate one UBQ molecule, then crowd it in the capsule with other UBQ molecules. The double differences of these two paths are defined as

ΔΔxxyσNOEσROE=ΔyσNOEσROExΔxσNOEσROE=σNOEσROEx,yσNOEσROExσNOEσROExσNOEσROEref=σNOEσROEx,y2σNOEσROEx+σNOEσROEref.
(14)

Here, Δy(σNOE/σROE)x describes the hydration changes caused by a chemical influence y imposed on a protein already under a different influence x. Δx(σNOE/σROE) describes the hydration changes brought about by the first change in chemical environment, x. In the frame of this study, x and y stand for encapsulation in a reverse micelle and crowding with other UBQ molecules. (σNOE/σROE)x,y represents the measured NOE to ROE ratio of the protein with both chemical influences x and y imposed, (σNOE/σROE)x stands for the protein under the influence of x (but not y), and (σNOE/σROE)ref stands for the reference state, in our case bulk solution.

By forming a double difference of chemical influences x and y, we are studying the ratio of their relative time scales. Again, this entity is irrespective of absolute dynamics time scales but reports solely on the relative effects of compared chemical influences. Retardations brought about primarily by the chosen intermediate state (just one of the two influences imposed, in this case x) will be positive, and retardations primarily caused by the follow-up transition will be negative.

The situation becomes more complicated when considering that there could also be accelerations, which would invert the sign. However, introducing more interfaces to the chemical environment as we do here slows down hydration dynamics;4,100,101 thus, we rule out this case. Also, note that these two double differences are not equal; path independence is true for sums of differences, not differences of differences. Instead, the double differences will depend strongly on the NOE/ROE values of the intermediate states. From these two double differences ΔΔxxy and ΔΔyxy, we can extract information on which of the two chemical circumstances caused a certain effect. For this end, we distinguish four cases occurring for two arbitrary chemical influences x and y (in our specific case crowding and encapsulation) on an arbitrary protein hydrogen atom. For the sake of clarity, these cases are also demonstrated on a purely hypothetical protein depicted in Fig. 5.

FIG. 5.

Hypothetical example of some protein, where σNOE and σROE of seven residues (A-G) were measured in four different systems. The numbers were deliberately chosen to be simple. (Top left panel) The protein in the reference system, in this case bulk-liquid solution. For each of the seven residues, a NOE/ROE value of 1 was measured, representative of the fast hydration dynamics on the surface of bulk-liquid dissolved proteins.39 The only exception is the buried residue B, which only sees a slow water molecule captured in a cleft. (Top right panel) The same protein, encapsulated in a reverse micelle with the surfactant head groups being drawn as yellow spheres. The residues C, E, and F are in close proximity to the surfactant wall and perceive slow interstitial water dynamics, leading to a drop in NOE/ROE. The other four residues do not perceive changes in hydration dynamics; thus, their relative time scales remain unchanged. (Bottom left panel) In this case, we crowded the protein with some other biomacromolecule (pictured in bright blue), which preferentially interacts with the protein at its southern part containing residues D, E, and G. (Bottom right panel) The model protein experiencing both encapsulation and crowding. Note how the double differences are not state functions, i.e., the values differ depending on the chosen path. Residue A still does not interact with either surface, residue B does not interact with any surface due to its position in a cleft, residue C selectively interacts with the wall, residues D and E are proximate to the other biomacromolecules, and residues F and G are liberated and fully hydrated.

FIG. 5.

Hypothetical example of some protein, where σNOE and σROE of seven residues (A-G) were measured in four different systems. The numbers were deliberately chosen to be simple. (Top left panel) The protein in the reference system, in this case bulk-liquid solution. For each of the seven residues, a NOE/ROE value of 1 was measured, representative of the fast hydration dynamics on the surface of bulk-liquid dissolved proteins.39 The only exception is the buried residue B, which only sees a slow water molecule captured in a cleft. (Top right panel) The same protein, encapsulated in a reverse micelle with the surfactant head groups being drawn as yellow spheres. The residues C, E, and F are in close proximity to the surfactant wall and perceive slow interstitial water dynamics, leading to a drop in NOE/ROE. The other four residues do not perceive changes in hydration dynamics; thus, their relative time scales remain unchanged. (Bottom left panel) In this case, we crowded the protein with some other biomacromolecule (pictured in bright blue), which preferentially interacts with the protein at its southern part containing residues D, E, and G. (Bottom right panel) The model protein experiencing both encapsulation and crowding. Note how the double differences are not state functions, i.e., the values differ depending on the chosen path. Residue A still does not interact with either surface, residue B does not interact with any surface due to its position in a cleft, residue C selectively interacts with the wall, residues D and E are proximate to the other biomacromolecules, and residues F and G are liberated and fully hydrated.

Close modal

Case 1: ΔΔxxy = 0 and ΔΔyxy = 0. This refers to the cases of either no effect of either chemical environment (Δx = 0 and Δy = 0) or, more generally, an equal effect of either (Δx = Δy). The site of interest is not dominantly influenced by either x or y. In Fig. 5, this is the case for residue A, which never faces either interface and residue B, which is buried and thus unaffected by changes in surface hydration.

Case 2: ΔΔxxy = −ΔΔyxy. This antisymmetric case means that one of the relative retardations is greater than the other (Δx > Δy or Δy > Δx). This is the desired case where we can say which chemical influence (e.g., crowding or encapsulation) dominates one of the protein sites. For instance, a residue may only interact with other proteins, but not with the surfactants. This case will be referred to as the selectivity case. The sign of the double difference will indicate which chemical environments affect the studied site:In the case of the exemplary protein shown in Fig. 5, residue C always interacts with the reverse micelle wall, while residue D always interacts with the other biomacromolecules, which is reflected in their respective double differences.

Dominant influencexy
ΔΔxxy Positive Negative 
ΔΔyxy Negative Positive 
Dominant influencexy
ΔΔxxy Positive Negative 
ΔΔyxy Negative Positive 

Case 3: ΔΔxxy = ΔΔyxy. This symmetric case is more complicated. It means that we cannot discern which of the two chemical environments is dominant in one site as both selectively interact with this part of the protein. Take, for instance, a cationic amino acid that will always interact with a surfactant of opposite charge but does also form salt bridges to anionic amino acids of other proteins if no such surfactant is available. Naive interpretation of the observables according to case 2 would yield in this case:Thus, interpretation would depend on the chosen observable. Without knowing the actual atomistic events, it is impossible to tell in the crowded and confined environment which influence is dominant because the said amino acid will, upon encapsulation, interact with the wall instead of its previous protein partner, but this is not noticeable using this methodology, henceforth referred to as a silent change. Taking the protein in Fig. 5 as an example, residue E interacts with both the surfactants and the other biomacromolecules. For the combined-influence case, we cannot tell its primary influence by taking double differences; by naive analysis, the positive sign of ΔΔeec implies interaction with the surfactants, while the positive sign of ΔΔcec implies interaction with the other biomacromolecule. From NOE data alone, we cannot distinguish these two cases. The interaction of residue E with the surfactant wall silently changes upon crowding with the other biomacromolecules.

Sign observedPositiveNegative
ΔΔencapcrowd,encap Surfactant Protein 
ΔΔcrowdcrowd,encap Protein Surfactant 
Sign observedPositiveNegative
ΔΔencapcrowd,encap Surfactant Protein 
ΔΔcrowdcrowd,encap Protein Surfactant 

Case 4: ΔΔxxy = 0 and ΔΔyxy ≠ 0. In this case, the combined influence of x and y has no effect on the chosen site, but one of the intermediates does. For example, one amino acid side chain may interact with the reverse micelle membrane in the simple encapsulation case, but in the encapsulation-crowding case, the formation of aggregates may move this residue away from the membrane due to geometrical reasons. This is the case of the reversible intermediates. The sign interpretation in terms of hydration dynamics is straightforward. A positive sign indicates that the intermediate state (in this case x) has retarded sites compared to the state of both influences, a negative sign means a relative acceleration.Residues F and G in the protein shown in Fig. 5 exhibit this behavior. Upon encapsulation, residue F is proximate to the surfactant wall, experiencing slow hydration dynamics. Introducing other biomacromolecules alters the geometry of the protein-surfactant complex and residue F is moved away from the surfactant wall, experiencing bulklike dynamics. This is reflected in its NOE double differences: The occurrence of the nonzero entry indicates the encapsulation-only state, and the positive sign indicates a retardation. Likewise, terminal residue G detects the proximity of other biomacromolecules upon crowding, but under both chemical influences, the resulting average geometry points this residue into the bulk-liquid phase.

Sign observedPositiveNegative
ΔΔxxy x site retarded x site accelerated 
ΔΔyxy y site retarded y site accelerated 
Sign observedPositiveNegative
ΔΔxxy x site retarded x site accelerated 
ΔΔyxy y site retarded y site accelerated 

Naturally, all protons will exhibit convolutions of these four basic cases. Ignoring the nonmeasurable first one, we disentangled all protein double differences. First, we removed the maximum common double difference values

ifΔΔxxy>0ΔΔyxy>0ΔΔxxy*=ΔΔxxymin(ΔΔxxy,ΔΔyxy)ΔΔyxy*=ΔΔyxymin(ΔΔxxy,ΔΔyxy),
ifΔΔxxy<0ΔΔyxy<0ΔΔxxy*=ΔΔxxymax(ΔΔxxy,ΔΔyxy)ΔΔyxy*=ΔΔxxymax(ΔΔxxy,ΔΔyxy)

such that for all points in the remaining curves, it either holds that ΔΔxxy*=0  and  ΔΔyxy*0 or ΔΔxxy*=ΔΔyxy*. The term removed represents the silent changes. We then separated the remaining curves by removing antisymmetrical contributions, forming the selective signal. The remaining terms ΔΔxxy* and ΔΔyxy* contain the reversible intermediate signals. Note, however, that due to mathematical reasons, this residual term also includes contributions from the intermediate differences not relevant to our analysis. We thus accept these values in the case of seeming retardations only if (σNOE/σROE)(x,y)>(σNOE/σROE)(x) and in the case of suspected accelerations only if (σNOE/σROE)(x)>(σNOE/σROE)ref.

Figure 6 presents both the double differences and the distinctions described above.

FIG. 6.

(Gray panel) Double differences ΔΔencapcrowd,encap(σNOE/σROE) (top row) and ΔΔcrowdcrowd,encap (σNOE/σROE) (bottom row). Note how the two double differences are different and thus not path-independent. Red areas mean that the first influence dominates, whereas blue indicates the second influence being the dominant one (excluding the possibility of hydration dynamics accelerations). (Green panel) Selectivity of a given protein hydrogen. Green protons mean that the site can be sorted clearly and distinctly to one of the two chemical influences. (Blue panel) The red color marks silent changes, i.e., sites where both crowding and encapsulation retard hydration dynamics, but it cannot be said which influence of the two is the deciding one, that is, is the side rather coordinated by other proteins or by the capsule membrane? Red protons mean that influence assignment is ambiguous. (Red panel) Intermediate states of the monoencapsulated state. Red color means that this site is more strongly retarded in the intermediate than in the final combined state, while blue color indicates faster dynamics in the intermediate state than in the reference or the combined state.

FIG. 6.

(Gray panel) Double differences ΔΔencapcrowd,encap(σNOE/σROE) (top row) and ΔΔcrowdcrowd,encap (σNOE/σROE) (bottom row). Note how the two double differences are different and thus not path-independent. Red areas mean that the first influence dominates, whereas blue indicates the second influence being the dominant one (excluding the possibility of hydration dynamics accelerations). (Green panel) Selectivity of a given protein hydrogen. Green protons mean that the site can be sorted clearly and distinctly to one of the two chemical influences. (Blue panel) The red color marks silent changes, i.e., sites where both crowding and encapsulation retard hydration dynamics, but it cannot be said which influence of the two is the deciding one, that is, is the side rather coordinated by other proteins or by the capsule membrane? Red protons mean that influence assignment is ambiguous. (Red panel) Intermediate states of the monoencapsulated state. Red color means that this site is more strongly retarded in the intermediate than in the final combined state, while blue color indicates faster dynamics in the intermediate state than in the reference or the combined state.

Close modal

ΔΔencap, crowd refers to first encapsulating one protein, then crowding it in the reverse micelle. This observable shows extensive positive contributions pictured in red. These differences consist of the β-sheet and the C-terminus, the encapsulation interaction domains. On the other hand, we see negative contributions involving parts of the α-helix and the 310 helix involving the residues Glu-18, Ser-20, Asp-21, Thr-22, Asn-25, Ala-28, Lys-29, and Tyr-59. While negative contributions may refer to hydration accelerations upon introducing a foreign interface in vicinity, this is physically unlikely. Rather, this region is probably dominated by protein-protein contacts, as we will show below. The alternative observable ΔΔcrowd, encap reveals a somewhat similar pattern, but in reverse.

The selectivity panel shows protons where the influence can be clearly identified in green and the ambiguous ones in red. For instance, the C-terminus consisting of Arg-72 to Gly-76 interacts both with other proteins and with the reverse micelle wall, and thus, it is not known which influence is more prominent. We note two major selective regions: On the one hand, the α-helix and the 310 helix mentioned above. As we have seen in Fig. 4, this region interacts with other UBQ proteins but not with the wall; thus, it is selectively affected by crowding. This is particularly interesting since Lys-29 is part of a slow water pocket39 barely affected by encapsulation. Yet, protein-protein contacts appear to affect this structural feature. On the other hand, the central part of the β-sheets consisting of residues Asn-60, Ile-61, Glu-64, Ser-65, and Leu-67 is selective. As we have seen above, this site is dominated by encapsulation interactions. The surrounding parts of the β-sheet are unselective, however, and may be in contact with either capsule wall or other UBQ molecules.

The panel below summarizes the silent changes, where a protein site is affected by either influence without being able to tell which one is dominant in this part. In essence, they agree with the nonselective protons shown in the selectivity panel. Note, however, that protons subject to silent changes are not in contradiction to, e.g., selective reversible intermediates. All it means is that not every dynamic influence on this site can be explained by either one chemical environment as we saw, for example, for the C-terminus.

The bottom panel illustrates the influence of intermediates not seen in the combined environment. The intermediates encountered in free-solution crowding are not depicted since our mathematical filtering described above indicated that most of the signal is without meaning, except for retardations found in Thr-14, Val-26, and Lys-33. These residues are involved in protein-protein contacts, yet to a lesser extend when encapsulated in a reverse micelle. The row in this panel shows the intermediates occurring in the single-UBQ reverse micelles. Note how both the C-terminus and the β-sheets, the two major regions in contact with the reverse micelle wall, exhibit retarded hydration dynamics, despite the crowded reverse micelles already showing retardation in this region. This means that while the same regions are affected, they are affected more strongly in the 1-UBQ reverse micelle compared to the 5-UBQ one. This proves that the UBQ-surfactant wall contact is more strict in the single-UBQ reverse micelle, while in the crowded, cell-like reverse micelle, the proteins also explore the capsule phase space. This is why the combined influence of two chemical environments cannot always be explained by either isolated one. See the supplementary material for more information on the protein position in a reverse micelle. Figure 7 summarizes the findings for UBQ.

FIG. 7.

Summary of the presence of foreign interfaces on the UBQ surface detected by protein-water NOEs: The floppy C-terminus interacting with both reverse micelle wall and other UBQ molecules (purple), the β-sheet favoring proximity to the reverse micelle wall (red), and the parts of the α-helix and the 310-helix interacting with other UBQ molecules (blue). The three residues depicted in cyan interact with UBQ molecules more strongly in unconfined solution than encapsulated.

FIG. 7.

Summary of the presence of foreign interfaces on the UBQ surface detected by protein-water NOEs: The floppy C-terminus interacting with both reverse micelle wall and other UBQ molecules (purple), the β-sheet favoring proximity to the reverse micelle wall (red), and the parts of the α-helix and the 310-helix interacting with other UBQ molecules (blue). The three residues depicted in cyan interact with UBQ molecules more strongly in unconfined solution than encapsulated.

Close modal

The physicochemical properties of biomolecules in living matter are strongly impacted by both encapsulation and the concentrated presence of organic matter, e.g., other biomacromolecules. Yet, particularly, the latter is difficult to detect in a site-resolved way due to their short contact times.

Intermolecular protein-water NOEs contain the desired spatial and dynamical information necessary. We reaffirm the notion that pure intermolecular NOESY or ROESY signals cannot be used for this task as both are long-ranged and confined water bodies are inhomogeneous. Their fraction, however, can.

It is possible to detect the presence of other proteins in proximity to the reference protein via disturbances (retardations) of water dynamics reported by NOE/ROE.

For more complicated, living-matter like environments where a protein is exposed to both confinement and macromolecular crowding, it is possible to detect the presence of foreign interface contacts too, but hard to tell them apart. We offer a mathematical way to discern the dominant influence of either, requiring the NOE measurement of four samples: The protein under both influences (crowding and encapsulation), under either one and the reference system.

Based on this analysis, we found that UBQ is located at the surfactant wall in a reverse micelle holding just one protein, whereas five UBQ in a reverse micelle behave more dynamically and explore the reverse micelle phase space. See the supplementary material for more details.

We have thus demonstrated the indirect protein-water NOE as a microscope into the protein-water and protein-protein dynamics in cell-like environments. While this article dealt with the specific case of UBQ crowding and encapsulation in a reverse micelle, all of the above can be expected to hold for any biomacromolecule exposed to any two different chemical influences. For instance, it might also be able to distinguish the favored interaction sites of two different crowders while carrying out the system in encapsulation. This setup may be more beneficial experimentally as it allows us to avoid fast hydration dynamics of the bulk system as well as to compare influences from fast exchange dynamics in diluted systems to the slow ones found in reverse micelles.

See the supplementary material for a discussion of the inhomogeneity of confined water phases and its impact on interpreting σNOE, a discussion of the position of proteins confined in a reverse micelle, and a comprehensive table of NOE observables calculated for the protein protons in all chemical systems.

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