Macromolecular Crowding Effects on Coupled Folding and Binding

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Macromolecular Crowding Effects on Coupled Folding and Binding Young C. Kim, Apratim Battacharya, and Jeetain Mittal J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp508046y • Publication Date (Web): 10 Oct 2014 Downloaded from http://pubs.acs.org on October 13, 2014

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The Journal of Physical Chemistry

Macromolecular Crowding Effects on Coupled Folding and Binding Young C. Kim,∗,† Apratim Bhattacharya,‡ and Jeetain Mittal∗,‡ Center for Computational Materials Science, Naval Research Laboratory, Washington DC 20375, and Department of Chemical and Biomolecular Engineering, Lehigh University, Bethlehem, PA 18015

∗ To

whom correspondence should be addressed Research Laboratory ‡ Lehigh University † Naval

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Abstract Replica exchange molecular dynamics simulations are performed on the protein complex, pKID-KIX, to understand the effects of macromolecular crowding on coupled folding and binding events. A structure-based protein model at the residue level is adopted for the two proteins to include intramolecular conformational flexibility, while crowding macromolecules are represented as spherical particles. The interactions between crowders and protein residues can be either purely repulsive or a combination of short-range repulsion and intermediate-range attraction. Consistent with previous studies on rigid-body protein binding in the presence of spherical crowders, we find that the complex formation is stabilized by repulsive proteincrowder interactions and destabilized by sufficiently strong attractive protein-crowder interactions. Competition between stabilizing repulsive and destabilizing attractive interactions is quantitatively captured by a previous theoretical model developed for describing the change in the binding free energy of rigid proteins in a crowded environment. We find that protein flexibility has little effect on the thermodynamics of the pKID-KIX binding (with respect to bulk) for repulsive and weakly attractive protein-crowder interactions. For strong protein-crowder attractive interactions, the destabilizing effect due to crowding is attenuated by protein flexibility. Interestingly, the mechanism of coupled folding and binding observed in bulk remains unchanged under highly crowded conditions over a broad range of protein-crowder interaction strengths. Also, strong protein-crowder attractive interactions can significantly stabilize intermediate states involving partial contact between pKID and KIX domains.

Keywords: kinase-inducible domain, transcription factor, protein-protein interactions, flexible docking, association mechanism


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Introduction Physiological media inside a cell contains various macromolecules such as proteins, DNAs, RNAs, and ribosomes that can collectively occupy as much as 40% of the cell volume. 1 The presence of such a crowded environment restricts the motion of biomolecules, and thus can have significant impact on various biophysical processes inside a cell. These effects are now widely recognized to be important for interpreting in vitro data based on dilute-solution environment (devoid of large number of cellular components) and are generally referred to as “macromolecular crowding" effects. 2,3 Significant efforts are currently underway to understand the crowding-induced changes in thermodynamics and kinetics of protein folding, 4–14 protein-protein interactions, 15–24 protein disorder, 25–29 and protein mobility. 30,31 Large fraction of previous studies have focused on the so-called excluded-volume effects, 32 under the assumption that crowding macromolecules can be modeled as inert species. The primary influence in this case is to reduce the volume available to biomolecules under study with respect to the dilute solution. 33 The net effect is to shift the thermodynamic equilibria toward more compact protein conformations, e.g., folded state with respect to the unfolded state in case of protein folding, 7,13 or bound state with respect to an unbound state in case of protein-protein interactions. 21 More recent experimental and theoretical studies have highlighted the importance of often neglected attractive interactions between protein(s) and crowding macromolecules 34–36 in counter-balancing the effect of excluded volume by shifting the thermodynamic equilibria toward states with higher surface area. 24,37 Inclusion of these additional effects can explain experimentally observed destabilization of globular proteins 38–40 as well as small effect of commonly used crowding agents (polyethylene glycol, dextran) on protein-protein interactions. 18 In the context of protein-protein interactions, previous work on macromolecular crowding has been mostly focused on complex formation between stable globular proteins. 41 In molecular simulation models, folded proteins are commonly approximated as rigid bodies ignoring intramolecular distance fluctuations, 21,36 though some attempts have been made to include local protein flexibility. 42 For complex formation between folded proteins modeled as rigid bodies, 43 it was 3 ACS Paragon Plus Environment


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shown that the complex stabilization due to repulsive protein-crowder interactions and complex destabilization due to attractive protein-crowder interactions can be captured quantitatively with a simple statistical mechanical model 24 or semi-quantitatively with the scaled particle theory (SPT) augmented with a mean-field attraction term. 36 The role of intrinsically disordered proteins (IDPs) or proteins with disordered regions is becoming increasingly apparent in protein interaction networks. 44 It is expected that high intrinsic flexibility can allow an IDP to recognize variety of target proteins without sacrificing specificity. 45 In several cases, an IDP bound to another protein adopts some stable folded structure. Two limiting scenarios have been proposed for protein binding involving IDPs – conformational selection and induced fit. In the conformational selection mechanism, a folded protein binds to pre-formed structural elements in a partner IDP, whereas in the induced fit mechanism, a folded protein binds to a largely disordered protein and structural elements form as concomitants of the binding. Based on simple theoretical arguments regarding the expanded nature of unstructured proteins, macromolecular crowding effects are expected to be more important for protein-protein interactions involving IDPs. There are relatively little experimental or simulation data on how commonly-used crowding agents may modify the binding affinity and the mode of recognition in IDPs binding to their target proteins. To study these, we perform extensive molecular dynamics simulations of a protein complex between phosphorylated kinase-inducible domain (pKID) of transcription factor CREB to the KIX domain of a CREB binding protein in the presence of spherical particles representing crowding agents. We use a slightly modified version of the previously proposed Go-like model by Turjanski et al. 46 for the pKID-KIX complex that successfully predicted the coupled folding and binding involving one of the pKID domains and KIX in excellent agreement with the experimental data. 47 Crowding macromolecules represented as spherical particles in our simulation can interact with protein residues via purely repulsive or Lennard-Jones (LJ) type attractive interactions. We find that repulsive protein-crowder interactions stabilize complex formation whereas attractive protein-crowder interactions counter-balance such stabilization and can even destabilize complex formation for high enough attraction strengths with respect to dilute


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solution. Interestingly, previously developed theoretical model for binding between rigid proteins can predict simulation results quantitatively in most cases. Most surprisingly, the mechanism of binding observed under dilute-solution conditions remains unchanged in the presence of repulsive and attractive protein-crowder interactions, although strong attractive interactions stabilize transient intermediate states.

Models and Methods Protein and Crowder Models We use a minimalist representation of a protein to model pKID and KIX where each amino acid residue is described by a single bead located at the corresponding Cα position (see Figure 1). The mass of each bead is considered to be the mass of the entire amino acid residue. The beads are connected by a coarse-grained representation of the peptide bond by the so-called harmonic “virtual bonds" along the protein backbone. 48 Also a harmonic potential is used to represent the angle potential between three adjacent beads. A knowledge-based sequence specific, but topologyindependent torsional potential has been used to represent the torsional angles between four adjacent beads along the Cα chain. Such sequence specificity and native structure independence has been effective in capturing the subtle differences in folding mechanisms and kinetics arising from sequence differences in topologically similar peptides. 48 The non-bonded interaction terms include attractive interactions for residues that are in contact in the native state (i.e., folded and bound state) and repulsive interactions between all other pairs of residues. For residues involved in intra-molecular native contacts, separated in sequence by two or more bonds, the following potential form is used: 10 6 12 σi j σi j σi j − 18 +4 , Vi j (ri j ) = εi j 13 ri j ri j ri j

(1)

where ri j is the distance between residues i and j, and σi j is the distance between i and j in the



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αA

KIX KIX

Coarse Graining

pKID αB Cα-based A model

IX

B

Coarse Graining

A

B

Figure 1: (Top) Cartoon representation of pKID-KIX complex structure (PDB ID: 1KDX). KIX protein (81 residues) contains three α -helical domains as shown in blue color. pKID protein (28 residues) contains two helical domains which are labeled as αA (red color) and αB (green color). (Bottom) Coarse-grained representation of pKID-KIX complex with Cα -based model used in this work.

C

native state at which the interaction energy is a minimum (equal to −εi j ). Values of εi j have been derived from the native structure (PDB: 1KDX) according to the rules set by Karanicolas and Brooks. 48 For residues involved in the inter-molecular native contacts between pKID and KIX, a 12-6 Lennard-Jones (LJ) potential is used instead of eq. 1 as follows:

C

Vi j (ri j ) = εi j

σi j ri j

12

σi j −2 ri j

6 ,

(2)

where, ri j is the distance between residues i and j, and σi j is the distance in the native bound state for the corresponding pair, while εi j is obtained similarly as for the intra-molecular native


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contacts, but scaled properly to obtain the binding free energy close to the experimental value (KD = 1.5µM 47 ). Equation 2 is slightly different from the standard LJ potential so that the potential minimum appears at the distance σi j rather than at the distance 21/6 σi j . This form of the inter-molecular interactions showed a faster convergence of simulation data compared to eq. 1 owing to the absence of a barrier in the potential function. Such faster convergence is difficult to achieve in highly crowded environments unlike previous simulations of the same system in dilute solution 46,49 that used the same form of eq. 1 for the inter-molecular native contacts. Note, however, that this particular model (as shown later) reproduced the essential details of the binding mechanism in dilute solution in accordance with the previous studies. 46,49 For pairs of residues not involved in the native contacts, a small value of εi j = 0.0001 kcal/mol is used for both intra- and inter-molecular interactions to represent a repulsive potential. The interaction diameters, σi j , for these cases were set equal to the sum of van der Waals (vdW) radii of the residues involved. For repulsive protein-crowder interactions, the following potential form has been used: Vi j (ri j ) = εr

σre f ri j − σi j + σre f

12 ,

(3)

where εr = 1 kcal/mol was used, and σi j is the interaction diameter calculated by adding the crowder radius, rc , and the vdW radius for a given residue. Here σre f is a parameter that guarantees the same interaction range independent of the crowder size, and is set equal to 6 Å . On the other hand, for attractive protein-crowder interactions, the following potential form is used: " Vi j (ri j ) = 4εa

σre f ri j − σi j + σre f

12

σre f − ri j − σi j + σre f

6 # ,

(4)

where the attraction strength, εa , is varied between 0.15 and 0.9 kB T . For crowder-crowder interactions, we use the repulsive interaction form eq. 3 with σi j = 2rc .



Simulation Details To obtain the equilibrium ensemble of protein complexes, we performed replica exchange molecular dynamics (REMD) 50 simulations in the canonical (NVT) ensemble using the Langevin thermostat with a friction coefficient of 0.2 ps−1 , which is smaller than that used to mimic the dynamics of water molecules (50-100 ps−1 ). Cubic boxes of varying sizes were used with periodic boundary conditions. The box sizes were varied so as to change the concentration of proteins. Sufficiently long REMD simulations were run for each of the 16 replicas spanning 276 to 665 K with a timestep of 10 fs with an exchange attempt between adjacent replicas every 5 ps ensuring adequate sampling. The simulation times were varied between 4 to 6 µs. The cutoff distance of 30 Å was used for the non-bonded interactions. We discarded the first 500 ns of the simulated trajectories for data processing. All the simulations were performed using Gromacs 4.0.5, which was modified to incorporate the non-bonded interaction potentials used in this study. In order to demonstrate that the system reached thermal equilibrium, we present the timeaveraged total potential energy as a function of time at different temperatures in Figure 2 (left panel). It shows that the thermal equilibrium is reached quickly within first 500 ns. The simulated 20

kcal/mol

15

dRMS (Å)

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10

5

0 -25

-20

-15

-10

-5

0

Uinter (kcal/mol)

Figure 2: (Left) Time-averaged total interaction energy of the pKID-KIX complex as a function of time at different temperatures. (Right) Two-dimensional potential of mean force for the intermolecular energy (Uinter ) vs dRMS between pKID and KIX at T = 300K. The simulation was performed with the box size of 15 nm. Several representative structures are also shown.


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bound structures of the pKID-KIX complex are compared to the experimental one (see Figure 2, right panel) using the distance-root-mean-square (dRMS) defined by

dRMS =

1 exp |disim j − di j |, N∑ i, j

(5)

exp where N is the total number of pairs (i, j), while disim j and di j are the distance matrices from the

simulated and experimental structures, respectively. Some representative structures are also shown to highlight the variability in the bound structures.

Free Energy Calculations In order to determine the binding free energy ∆Fb of the pKID-KIX complex, we measured the dissociation constant KD of the complex which is related to the binding free energy via ∆Fb = kB T (ln KD /K0 ), where K0 = 1 M. The dissociation constant KD can be obtained by fitting the fraction of bound complexes as a function of the total concentraion, [P]= c/V with c = 1.661 × 109 µM·Å3 , via the titration formula,

pb =

[P] , [P] + KD

(6)

where pb is the fraction of bound complexes. Note that the above equation is derived by solving the chemical master equation, 51,52 which is more appropriate to describe the stochastic binding of a small system at the single-molecule level. A complex was defined as bound if the inter-molecular interaction energy between pKID and KIX is less than -1 kB T . The choice of the energy cutoff was based on the bimodal distribution of the interaction energies obtained from the simulations. The total protein concentration was varied by changing the dimensions of the simulation box. Figure 3 shows the resulting fraction of bound complexes as a function of the total protein concentration for various crowder packing fractions, φ = 4πrc3 Nc /L3 , where Nc is the number of crowders. The data show the titration behavior for the fraction of the bound complexes. The solid



Fraction Bound

1 0.8 0.6 0.4 0.2 0

0

100

200

300

400

500

Conc [µM] 1

Figure 3: Titration behavior. Fraction of bound complexes as a function of protein concentration are shown for crowder size 9 Å. Repulsive protein-crowder interaction data for crowder packing fractions 0.05, 0.15, and 0.25 are denoted by black circles, green up triangles and blue right 0.9 Magenta squares represent data for attractive protein-crowder interaction triangles, respectively. strength of 0.45 kB T for crowder packing fraction 0.15.

Fraction Bound

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0.8 fits to the titration expression eq. 6 using the total protein concentration curves are the least-square with corresponding binding constants, KD .

0.7 the mechanism of coupled folding and binding, we calculated the fracIn order to characterize tion of native contacts, Qs , for a given conformation s as an order parameter using

0.6

100

1 300 400 , 0 )) 1 + exp(γ(r − λ r i j (i, j) Conc [µM] i j

−1 Qs = N200 s ∑

500

(7)

where the sum runs over the Ns pairs (i, j) of native contacts between the Cα beads which are separated by distances ri j in the configuration s while ri0j is the distance in the native state. Here γ is a control parameter that determines steepness of the contact step function eq. 7, 53 while λ accounts for the fluctuations between residues in contact. We used γ = 5 Å−1 and λ = 1.2. We calculated the two dimensional potential of mean force as a function of two pertinent order 10 ACS Paragon Plus Environment

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parameters. The various order parameters chosen are: inter-molecular native contacts between the αA domain of pKID and KIX (QCA ), inter-molecular native contacts between the αB domain of pKID and KIX (QCB ), inter-molecular native contacts between pKID and KIX (QC ), and intramolecular native contacts within pKID (QKID ). The total number of contacts in the native state for various order parameters were found to be 6 (αA -KIX), 21 (αB -KIX), 32 (pKID-KIX) and 13 (KIX), respectively.

Results and Discussion Binding thermodynamics The effect of crowding on the binding of pKID to KIX is described by calculating the change in the binding free energy, ∆∆Fb = ∆Fb (φ ) − ∆Fb (0), as a function of the crowder packing fraction φ . Note that ∆Fb (0) refers to the binding free energy in bulk (i.e., φ = 0). The ∆∆Fb data as a function of crowder packing fraction φ for repulsive crowders are presented in Figure 4 (left) as filled symbols for three different crowder sizes, rc = 9, 12, and 15 Å. The ∆∆Fb data for attractive crowders are shown in the right column of the same figure for crowder size 9 Å and the attraction strength between residues and crowders, εa = 0.15, 0.45, and 0.9 kB T . As anticipated, the data show the enhanced stability for the bound complex (∆∆Fb < 0) in case of repulsive protein-crowder interactions owing to lesser volume accessible to proteins in the presence of crowders. The formation of the complex is stabilized further as the crowder packing fraction increases. As the crowder size decreases, the stability for the bound complex is further enhanced. On the other hand, strong attractive protein-crowder interactions (εa & 0.45kB T ) result in destabilizing the bound complex (∆∆Fb > 0). In order to see whether the flexibility of protein chains (pKID and KIX) has any effect on the binding thermodynamics of the pKID-KIX complex, we calculated the binding free energy for the complex where both proteins were assumed to be rigid with the coordinates taken from the native state. The results are shown in Figure 4 as open symbols. Surprisingly, the data show that in 11 ACS Paragon Plus Environment


0 Repulsive

4

15 Å

3

12 Å

−2

rc = 9 Å

∆∆F bind/ kBT

−1

∆∆F bind/ kBT

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−3

Attractive

0.9 kBT

2 1

0.45 kBT

0

−1 0

0.1

φ

0.2

0.3

εa = 0.15 kBT

0

0.1

φ

0.2

0.3

Figure 4: Binding free energy. The changes in the binding free energy ∆∆Fb (φ ) = ∆Fb (φ ) − ∆Fb (φ = 0) obtained from REMD simulations (symbols) are shown as a function of crowder packing fraction φ for various cases. Filled symbols are the simulation data incorporating the flexible protein chains, while the empty symbols are the rigid-body simulation data, for repulsive (left) and attractive (right) crowders. The solid (left and right) and dashed (right only) curves are the predictions of the theoretical model 24 for flexible and rigid-body cases, respectively. Note that for attractive crowders (right), the crowder radius of 9 Å was used. case of repulsive crowders there is no apparent effect on the binding thermodynamics resulting from the flexible motion of protein chains. However, for attractive protein-crowder interactions, the flexibility of two proteins has noticeable effects on the protein-binding free energy at larger attraction strength (εa > 0.45 kB T ) as seen in the right column of Figure 4 for the crowder size of 9 Å. For smaller εa , the effects are negligible as for the repulsive protein-crowder interactions. To explain our simulation results quantitatively, the theory previously developed for rigid-body binding is adopted. 21,24 According to the thermodynamic cycle of the binding of two proteins, A and B, in the crowded solution, the binding free energy difference, ∆∆Fb (φ ), for A + B AB, is given by: ∆∆Fb (φ ) = ∆FAB (φ ) − ∆FA (φ ) − ∆FB (φ ),

(8)

where ∆Fα (φ ) is the solvation free energy of a protein or complex α (= A, B, AB) in the crowded solution with the crowder packing fraction φ . The solvation free energy ∆Fα (φ ) of a protein can 12 ACS Paragon Plus Environment

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then be divided into two parts as:

∆Fα (φ ) = ∆Fα,rep (φ ) + ∆Fα,att (φ ),

(9)

where ∆Fα,rep(att) is the contribution from the repulsive (attractive) interaction, respectively. The contribution to the binding free energy from the repulsive protein-crowder interactions can be calculated by adopting the scaled particle theory (SPT) of hard-sphere fluids. 54 In this theory the free energy required to form a spherical cavity of radius R in a hard-sphere fluid with particle radius rc and the packing fraction φ is given by:

∆F

SPT

9 2 3 y + 3y ρ˜ 2 + 3y3 ρ˜ 3 − ln(1 − φ ) /kB T = (3y + 3y + y )ρ˜ + 2 2

3

(10)

where ρ˜ = φ /(1 − φ ) and y = R/rc . The underlying idea in our theoretical model 21,24 is that the anisometric proteins can be considered as spherical objects for calculating the solvation free energy using the SPT. This assumption appeared to work quite well for describing the simulation data for the changes in the binding free energies of two rigid proteins. A protein or complex was modeled as a spherical particle of radius R by equating the total volume occupied by a set of solvated spheres of radii σi + rc (σi being the radius of a residue i) to the volume of a sphere of radius R + rc . Although pKID exhibits greater flexibility where it is highly disordered in the unbound state, based on the observation that there is no apparent difference in the binding free energies between flexible and rigid binding simulations for repulsive crowders, we calculated the effective radii for the isolated pKID, KIX and the complex pKID/KIX using the native structure. The effective radii of the proteins and the complex are shown in Table 1 for three different crowder sizes. The Table 1: Effective radius (in Å) for pKID, KIX and pKID/KIX for different crowder sizes using the native structure (PDB: 1KDX). rc pKID 9 10.9 12 11.3 15 11.5

KIX 15.6 16.0 16.2

pKID/KIX 17.4 17.8 18.0



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binding free energies for the complex were then calculated using these values and were shown in the left column of Figure 4 as solid curves. The plot shows an excellent agreement between theory and simulation for different crowder sizes. Note, however, that even if the intra-molecular fluctuations are considered in calculating the effective radii by calculating the ensemble averages over simulated structures of pKID, KIX and the pKID-KIX complex, little change appears in the theoretical predictions. The contribution to the solvation free energy from the attractive part of the potential energy can be calculated using the thermodynamic perturbation theory and statistical mechanics of hardsphere fluid 24 as follows:

∆Fα,att = −ρ ε¯α Sα {δ r + (gmax 0 − 1)λ },

(11)

where ρ is the crowder number density related to φ via ρ = φ /(4πrc3 /3). Here ε¯α is the orientational average of the attractive interaction between a crowder and protein (or complex) α and is obtained as follows: (i) Calculate the potential energy, Uα (r, Ω), as a function of distance, r, between the center of mass of a protein (or complex) α and a crowder for a given orientation Ω. (ii) Find the minimum of the potential energy, εm,α (Ω). (iii) Continue (i) and (ii) for all possible orientations Ω. Here we have chosen 104 orientations randomly. (iv) Calculate the orientational average, ε¯α = hεm,α iΩ . Sα is the surface area around the protein drawn by crowders, and δ r is the attraction range set equal to 3 Å, λ = (21/6 − 1)rc ' 0.12rc , and gmax is the max0 imum value of the radial distribution function g(r) of hard-sphere fluid. For the φ -dependence of gmax 0 , we use the Carnahan-Starling equation of state for a hard-sphere fluid, which leads to 3 gmax 0 (φ ) = (1 − φ /2)/(1 − φ ) .

The dashed curves in the right column of Figure 4 are the predictions of the above theory for attractive crowders using the parameter values obtained from the native structure. They are in excellent agreement with the rigid-body simulation data (empty symbols). However, for higher attraction strengths (εa & 0.45kB T ), the theory based on the single native structure shows larger


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discrepancies with the flexible simulation data (filled symbols). The major contribution to such differences between rigid-body and flexible simulations stems from the fact that pKID is highly unstructured protein in isolation, thus exhibiting greater flexibility compared to KIX or the bound complex pKID-KIX. To accommodate this into the theory, an MD simulation was performed on an isolated pKID to extract an ensemble of equilibrium structures. Using these structures, the set of the parameters were then calculated and averaged as listed in the parentheses of Table 2. Note, Table 2: Effective radius Rα (in Å), normalized average attraction strength ε¯α , and the surface area Sα (in Å2 ) for pKID, KIX and the pKID/KIX complex for rc = 9 calculated from the native structure. The values in parentheses for pKID are the ensemble averages from simulated structures based on an MD trajectory of an isolated pKID.

Rα ε¯α Sα

pKID 10.9 (11.7) 3.90 (3.49) 5521 (6132)

KIX pKID/KIX 15.6 17.4 4.54 4.42 8491 9849

in particular, that the average of the surface area for flexible structures of pKID is larger than the surface area of the structured pKID (derived from the native structure), while the average of the attraction strength, ε¯α , for flexible pKID is smaller. The combination of these two parameters (see eq. 11) yields a smaller value for the flexible pKID, and consequently results in a smaller change in the binding free energy. Using these parameter values, the changes in the binding free energy for attractive crowders are calculated and shown as solid curves in the right column of Figure 4. A slight improvement in the comparison between the theory and the simulation data is observed. However, for strong attraction (εa = 0.9kB T ) the theory still shows greater changes in the binding free energy in comparison to the simulation data. This may be attributed to the observation that at strong attraction the ensemble of pKID structures in isolation is quite different from that in the crowded environment, and thus the theoretical model based on the linear perturbation theory fails in such cases.



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Mechanism of Coupled Folding and Binding of pKID-KIX NMR titration and relaxation dispersion experiments suggest that the pKID-KIX complex forms an ensemble of nonspecific encounter complexes en route to the formation of the specific complex. 47 It was found that the association rate constant for the binding of the αA domain of pKID to KIX was about four times smaller than that for the binding of the αB of pKID to KIX, suggesting that the αB domain of pKID first binds to KIX followed by the αA domain. At the same time, the folding rate for the αB domain was about four times faster than that for the αA domain. It was thus suggested that the binding of pKID to KIX follows the induced-fit mechanism in which the folding of pKID is initiated by the binding of pKID to KIX. 47 This binding-induced-folding mechanism was also shown by Turjanski et al. 46 using a similar coarse-grained model, and later by Ganguly et al. 49 In the model by Ganguly et al., the intermolecular and intra-molecular native contact energies were scaled to match the experimental binding affinity of pKID to KIX and to reproduce the intrinsic helicities of the two domains of pKID. Although the binding affinities obtained from the two studies differed by about three orders of magnitude, a similar mechanism was observed in both cases. These studies showed a dominant pathway in which the formation of the pKID-KIX complex is initiated first by the binding of the largely unfolded αB domain of pKID to KIX while the αA domain is free. This binding process then accelerates the folding of the αB domain while it is bound to KIX. Subsequently, this is followed by the cooperative binding and folding of the αA domain to KIX. Our coarse-grained model also reproduces the same mechanism of coupled folding and binding (namely, the induced-fit mechanism) as a dominant one. To characterize the binding mechanism, we calculate the free energy as a function of the inter-molecular native contacts between the αA domain of pKID and KIX (QCA ) and the inter-molecular native contacts between the αB domain of pKID and KIX (QCB ), as well as a function of the inter-molecular native contacts between pKID and KIX (QC ) and the intra-molecular native contacts of pKID (QKID ). As observed in Figure 5, the binding of pKID to KIX in bulk (left column) is initiated by the αB domain of pKID as characterized by lower free energies along the states with 0 < QCB < 1 and QCA ≈ 0. Once the 16 ACS Paragon Plus Environment

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Bulk%

Repulsive%

A-rac1ve%(εa = 0.45 kBT)%

kcal/mol%

Figure 5: Two dimensional free energy surfaces (2D FES). The first row shows the 2D FES at 300 K as a function of inter-molecular native contacts between the αA (QCA ) and αB (QCB ) domains of pKID and KIX. In the second-row, 2D FES is plotted as a function of inter-molecular native contacts between pKID and KIX (QC ), and intra-molecular native contacts in pKID (QKID ). From the left, the 2D FES in bulk, repulsive (rc = 15Å, φ = 0.25), and attractive crowding (rc = 9Å, φ = 0.25, εa = 0.45kB T ) are shown. The box sizes are chosen such that the bound and unbound conformations have similar populations. αB domain is bound to KIX (QCB ≈ 1), the αA domain then binds to KIX (characterized by lower free energies along the states with 0 < QCA < 1 and QCB > 0.75. This result is anticipated from the simulations, since the number of inter-molecular native contacts between the αB domain and KIX (= 21) is more than three times of the number of inter-molecular native contacts between the αA domain and KIX (= 6). Consequently, the inter-molecular interactions between the αB domain and KIX is much stronger than that between the αA domain and KIX, and thus the binding of the αB domain to KIX is preferred to that of the αA domain to KIX. The free energy landscape on the QC QKID plane (second row) suggests that the binding of pKID to KIX indeed closely resembles the induced-fit mechanism such that while pKID is partially unfolded in isolation with QKID ' 0.6, its folding is completed once it is bound to KIX. The transition state lies near QC ' 0.25 and 17 ACS Paragon Plus Environment


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QKID ' 0.6. One may then ask whether crowding particles (either repulsive or attractive) have any effect on the binding mechanism of the pKID-KIX complex. The middle column of Figure 5 shows the free energy landscapes for the pKID-KIX complex in the presence of repulsive crowders. Compared to bulk (left column), there is little change in the overall binding mechanism. However, due to the excluded-volume effect that favors compact structures, the major contribution from the repulsive interactions with crowders is to increase the population of the native complex relative to encounter complexes and narrow the transition path toward the native state. On the other hand, the attractive crowders (right column) destabilize the formation of the native complex by inhibiting the binding event of αA and KIX. At moderate strength (εa = 0.45kB T ), the two-dimensional free energy surface as a function of QC and QKID shows two local minima for bound states (QC > 0.4), one corresponding to the native state (QC ' 1 and QKID ' 1) and the other to the intermediate state (QC ' 0.7 and QKID ' 0.65). This intermediate state corresponds to the state in which the αB helix of pKID is still bound to KIX but the αA helix is unbound due to its favorable interactions with attractive crowders. The destabilization of the binding of αA to KIX is due to the fact that the αA -KIX interaction is much weaker than that of αB -KIX. At higher attraction strength (εa = 0.9kB T ), the crowders destabilize the binding of the αA helix to KIX completely, thus shifting the bound equilibrium towards the intermediate state (see Figure 6).

Conclusions To understand how macromolecular crowding affects coupled folding and binding events, we have performed extensive replica exchange molecular dynamics simulations on the pKID-KIX complex using a structure-based coarse-grained model. Incorporating the effects of volume exclusion by the crowders and possible non-specific attractive interactions, both repulsive and attractive proteincrowder interactions have been considered. First, our work agrees with the previous experimental and simulation studies in which the binding of pKID to KIX follows the induced-fit mechanism in


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A"rac&ve)(εa = 0.9 kBT))

kcal/mol)

Figure 6: 2DFES for attractive crowding with εa = 0.9kB T and rc = 9Å at the packing fraction φ = 0.25. bulk. We show that the repulsive interactions between proteins and crowders stabilize the native complex by decreasing the binding free energy by ∼ 2kB T at higher crowder packing fraction. But attractive protein-crowder interactions have the opposite effect as these destabilize the compact native complex while favoring the intermediate encounter complexes. At high protein-crowder attraction strengths, the formation of the pKID-KIX complex is less favored compared to that in bulk and the binding free energy increases by ∼ 1kB T . Although the flexibility of pKID has little effect on the change in the binding free energy of the pKID-KIX complex in case of repulsive crowders, significant changes of up to 2kB T in the binding free energy were observed for strong proteincrowder attractions between rigid-body and flexible binding simulations. It was demonstrated that



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the theory previously developed for rigid-body binding can also be applied to describe the flexible binding of pKID to KIX quantitatively. The binding mechanism is largely unaffected by the presence of either repulsive or attractive crowders, where the induced-fit mechanism still remains the dominant pathway for the complex formation. However, the attractive crowders stabilize the intermediate states in which the formation of a weaker domain interaction (i.e., the αA helix-KIX interaction) is broken due to the proteincrowder attraction while the αB helix of pKID is still bound to KIX. Our finding suggests that in real systems where the interactions between crowding macromolecules and proteins are highly nonuniform and complex unlike the cases of the current study, the binding events can become more complicated depending on the nature of the interactions between domains of participating proteins and crowding molecules. Thus more comprehensive studies are needed to fully understand the effects of crowding molecules on protein-protein interaction in the cell.

Acknowledgement Use of the high-performance computing capabilities of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by the National Science Foundation grant no. TG-MCB-120014, is gratefully acknowledged.

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