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A Structural Model of Polyglutamine Determined from a Host-Guest Method Combining Experiments and Landscape Theory

The Center for Theoretical Biological Physics and the Department of Physics, University of California, San Diego, La Jolla, California

Correspondence: Address reprint requests to José N. Onuchic, University of California at San Diego, Dept. of Physics, 9500 Gilman Drive, La Jolla, CA 92093. Tel.: 858-534-7067. E-mail: jonuchic{at}ucsd.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Modeling the structure of natively disordered peptides has proved difficult due to the lack of structural information on these peptides. In this work, we use a novel application of the host-guest method, combining folding theory with experiments, to model the structure of natively disordered polyglutamine peptides. Initially, a minimalist molecular model (CC_ß) of CI2 is developed with a structurally based potential and captures many of the folding properties of CI2 determined from experiments. Next, polyglutamine "guest" inserts of increasing length are introduced into the CI2 "host" model and the polyglutamine is modeled to match the resultant change in CI2 thermodynamic stability between simulations and experiments. The polyglutamine model that best mimics the experimental changes in CI2 thermodynamic stability has 1), a ß-strand dihedral preference and 2), an attractive energy between polyglutamine atoms 0.75-times the attractive energy between the CI2 host Go-contacts. When free-energy differences in the CI2 host-guest system are correctly modeled at varying lengths of polyglutamine guest inserts, the kinetic folding rates and structural perturbation of these CI2 insert mutants are also correctly captured in simulations without any additional parameter adjustment. In agreement with experiments, the residues showing structural perturbation are located in the immediate vicinity of the loop insert. The simulated polyglutamine loop insert predominantly adopts extended random coil conformations, a structural model consistent with low resolution experimental methods. The agreement between simulation and experimental CI2 folding rates, CI2 structural perturbation, and polyglutamine insert structure show that this host-guest method can select a physically realistic model for inserted polyglutamine. If other amyloid peptides can be inserted into stable protein hosts and the stabilities of these host-guest mutants determined, this novel host-guest method may prove useful to determine structural preferences of these intractable but biologically relevant protein fragments.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Understanding the fundamental physics of protein folding is a goal of both experimentalists and theoreticians. Guided by landscape theory (Onuchic et al., 1997), an understanding of the fundamental principles of protein folding has recently advanced due to the development of 1), small fast-folding peptide systems (Blanco et al., 1994; Krieger et al., 2003; Marqusee et al., 1989; Munoz et al., 1997; Neidigh et al., 2002; Thompson et al., 2000; Yang et al., 2004) which are tractable to study by all-atom simulation (Bursulaya and Brooks, 1999; Daggett and Levitt, 1992; Garcia and Sanbonmatsu, 2001, 2002; Hansmann et al., 1999; Okur et al., 2003; Pitera and Swope, 2003; Shirley and Brooks, 1997; Wang and Sung, 1999; Yeh and Hummer, 2002; Zagrovic and Pande, 2003) and 2), minimalist simulation models which can effectively sample the dynamics of larger protein systems (Chan and Dill, 1993; Cheung et al., 2003; Clementi et al., 2000a; Ding et al., 2002; Klimov and Thirumalai, 2000; Shea et al., 1999). Although these research efforts are increasing our understanding of protein folding, many challenges remain. One significant goal is connecting the physical principles learned from protein folding studies to multiprotein interactions, such as binding and aggregation. Developing a theory consistent with both folding and binding processes is particularly crucial in understanding natively unfolded proteins which fold upon binding to other molecules (Guo et al., 2002).

An important disease pathology which can be addressed with protein folding theory is the assembly of unfolded protein monomers into ß-sheet amyloid fibers. In many amyloid diseases, mutations in genes which enhance the disease symptoms also result in increased amyloid fiber formation from the gene's protein product, both in vivo and in vitro. One prominent example of this phenomenon is found in Huntington's Disease (HD), where aggregation of the protein huntingtin is dependent on the length of a polyglutamine region within the huntingtin protein sequence (Zoghbi and Orr, 2000). Patients with longer huntingtin polyglutamine regions (>35 glutamines) demonstrate increased huntingtin amyloid fiber formation as well as an increased risk of neuron death, cognitive dysfunction, and atrophy of motor functions (Zoghbi and Orr, 2000). One major difference between HD and other amyloid diseases is that polyglutamine length is the only genetic factor needed to determine a patient's risk of developing disease symptoms whereas other non-polyglutamine amyloid diseases involve multiple genetic and behavioral determinants (Hardy and Gwinn-Hardy, 1998). Polyglutamine length has also been shown to be the sole risk factor of developing symptoms in other diseases as well (Zoghbi and Orr, 2000).

In individuals whose huntingtin gene exceeds the polyglutamine threshold, the likelihood of acquiring HD each year does not increase with age, indicating that age-related impairment of aggregate clearance is not a cause of the disease (Perutz and Windle, 2001). A second inference of this work is that a nucleation-initiated process, such as protein aggregation, is responsible for the onset of the disease (Perutz and Windle, 2001). The polyglutamine aggregation-disease link is further supported by studies showing that simple polyglutamine peptides will assemble into amyloid fibers (Chen et al., 2002a) and are toxic to cells when delivered to the nucleus as aggregates, but not monomers (Yang et al., 2002). Polyglutamine, both as a monomer and aggregate, offers a simple molecular system to explore amyloid formation and its role in polyglutamine disease.

Although the correlation between polyglutamine length and disease is straightforward, understanding the molecular events involved in polyglutamine disease remains unclear (Temussi et al., 2003). An increase in detailed molecular information on polyglutamine has been limited by the fact that structural information on polyglutamine has been difficult to obtain (Temussi et al., 2003). A detailed structure of unaggregated polyglutamine has not been determined, possibly due to the fact that monomeric polyglutamine is natively disordered (Altschuler et al., 1997; Bennett et al., 2002; Chen et al., 2002a, 1999; Gordon-Smith et al., 2001; Masino et al., 2002). As polyglutamine aggregates, an increase in ß-sheet spectroscopic structural indicators is observed (Chen et al., 2002b). However, even these polyglutamine aggregates can only be probed with low-resolution structural methods, such as circular dichroism (Altschuler et al., 1997; Bennett et al., 2002; Chen et al., 2002a; Masino et al., 2002), Fourier-transform infrared, and x-ray diffraction (Perutz et al., 2002, 1994), such that detailed information on this ß-sheet structure is limited.

The present study combines molecular dynamics, energy landscape theory, and experimental protein stability information to determine structural parameters for a minimalist model of polyglutamine. Reminiscent of earlier host-guest studies (Lotan et al., 1966; Wojcik et al., 1990), increasing lengths of the inserted polyglutamine "guest" into the "host" chymotrypsin inhibitor 2 mutants show increasing destabilization to the host CI2 protein (Ladurner and Fersht, 1997). Unfortunately, crystal structures and NMR structures of polyglutamine inserts into CI2 are disordered and do not show a discrete structure such as polyglutamine adopts in the context of the CI2 host (Chen et al., 1999; Gordon-Smith et al., 2001). However, thermodynamic stability and kinetic folding rates of these polyglutamine insert mutants can be used to determine the structural preferences of the polyglutamine insert (Ladurner and Fersht, 1997).

First, a minimalist molecular model (CC_ß) of the CI2 host is developed with a Go-potential and is shown to capture many of the folding properties of CI2 determined from experiments. Second, polyglutamine guests are inserted into the CI2 Go-model host and polyglutamine parameters are selected which best agree with host-guest thermodynamic results: a ß-strand dihedral and an attractive energy between polyglutamine atoms equaling 0.75 the Go-contact energy. Third, using this potential in the polyglutamine guest, kinetic folding rates of the host-guest mutants, structural perturbation of the CI2 host by the polyglutamine guest, and the structure of the inserted polyglutamine guest are shown to agree well with experiments.

Despite the good agreement between experiments and simulations for the CI2-polyglutamine host-guest system, it is unclear whether the polyglutamine energy potential will also accurately characterize the polyglutamine guest in the absence of the CI2 host. Although minimalist models may capture the essential physics of funneled energy landscapes, such as those observed in protein folding (Onuchic et al., 2000), the frustrated energy landscapes of natively disordered proteins may require a more detailed molecular model. To validate the minimalist host-guest approach used in the present study, the polyglutamine parameters determined in the present study will used in future studies to directly simulate polyglutamine chains, either as isolated monomers or as an aggregating system of multiple chains.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Molecular dynamics
Molecular dynamics (MD) simulations were carried out using AMBER 6 software, compiled on a Linux platform, employing the sander_classic program as an integrator for initial energy minimization and subsequent molecular dynamics (Pearlman et al., 1995). Simulations were performed on the wild-type protein chymotrypsin inhibitor 2 as well as CI2 insert mutants with MG₃SG₄SG₃M, MGQ₄GM, and MGQ₁₀GM inserted in substitution for methionine 40 (Ladurner and Fersht, 1997). The initial structure used for MD was determined by simulated annealing which used the 2CI2.pdb coordinates as an initial structure. For each protein studied, six simulations were run for 120 ns at the folding temperature (350 K for wild-type, 333 K for mutants) and the first 30 ns of MD was discarded as equilibration.

The following describes the AMBER sander_classic molecular dynamics parameters used in this study. The specific parameter values are listed in parentheses. The time step was 0.001 ps (DT = 0.001). Translational and rotational motion was removed at the beginning of each run and every 1000 time steps thereafter (NTCM = 1, NSCM = 1000, NDFMIN = 0). Initial velocities were randomly selected (INIT = 3, IG = random). If the absolute value of the velocity of any atom exceeded 500 Å/timestep, velocities are scaled such that the absolute value of the velocity of that atom = 500 Å/timestep (VLIMIT = 500). Temperature was maintained with external bath using the method of Berendsen (1984) with a coupling constant of 0.2 ps (NTT = 5, TAUTP = 0.2, TAUTS = 0.2). If the simulation temperature T_sim exceeds the average temperature T by >10 K, velocities are scaled such that T_sim = T. SHAKE was not used. The particle-mesh Ewald method was not used (IEWALD = 0). During each integration step, interactions between all atom pairs were calculated and this contact pair-list only update once at the beginning of the simulation (CUT = 9999, NSNB = 9999). No periodic boundary and pressure regulation were used (NTB = 0, NTP = 0). Structures and energies were saved every 1.5 ps (NTPR = 1500, NTWR = 1500, NTWX = 1500, NTWV = 1500, NTWE = 1500).

Go-model of CI2 host
In minimalist MD simulations of the host CI2 protein, each amino acid in CI2 is reduced to the backbone C atom and a single C_ß atom located at each side chain's center of mass (Cheung et al., 2003; Ding et al., 2002; Irback et al., 2000; Klimov and Thirumalai, 2000; Liwo et al., 2002; Takada et al., 1999; Vieth et al., 1995). For wild-type CI2, the overall potential energy for a given protein conformation is given by Eq. 1 as

(1)

Consistent with the original Go-model (Go, 1983), the minimum energy of each energy term is obtained when the protein is in the native folded state. For covalent bond distance terms,

(2)

where _r = 100 kcal/mol is the bond energy, r is the bond distance in the simulation, and r₀ is the native bond distance, summed over all bonds in 2CI2.pdb.

For the bond-angle term,

(3)

where = 20 kcal/mol is the bond angle energy, is the bond angle in the simulation, and ₀ is the native bond angle, summed over all bond angles in 2CI2.pdb (CCC, C_ßCC, CCC_ß).

For dihedral energies,

(4)

where are the dihedral energies, is the dihedral angle in the simulation, and ₀ is the native dihedral angle, summed over all dihedral angles in 2CI2.pdb (CCCC, C_ßCCC_ß, CCCC_ß, C_ßCCC). For backbone dihedrals (CCCC) dihedrals, and for side-chain dihedrals (C_ßCCC_ß /CCCC_ß /C_ßCCC),

In the Go-model of the CI2 host, two C atoms were selected as attractive if they fall within 7.5 Å in the crystal structure 2CI2.pdb and within an angular definition described by Veith et al. (1995). A C_ß–C_ß pair was determined to be attractive if they are separated by three or more residues and are indicated to be in contact using CSU analysis on 2CI2.pdb (Sobolev et al., 1999). No attractive contacts are allowed between C and C_ß atoms. Each attractive C–C and C_ß–C_ß contact is described by an attractive Lennard-Jones potential as

(5)

where _LJ = 0.8 kcal/mol is the contact energy, _ij is the native distance between the two contact atoms, i and j, given from the crystal structure, and r_ij is the distance between the two contact atoms, i and j, determined for a given iteration of the simulation.

If any two atoms are not determined to be attractive or fall within two residues of each other (i, i + 2), then their interaction is defined by a repulsive term

(6)

where _rep = 0.8 kcal/mol is the repulsive energy, _ij is the hard-sphere distance between the two repulsive atoms, i and j, and r_ij is the distance between the two repulsive atoms, i and j, determined for a given iteration of the simulation. In the simulations, _ij = r_i + r_j, where r_i, r_j = 1.9 Å (if atom i,j is C) or native C–C_ß bond distance (if atom i,j is C_ß).

A list of the parameters used in the CI2 host Go-model is shown in Table 1.

For bond distance energies in polyglutamine, Eq. 2 is used. For polyglutamine, _r = 100 kcal/mol is the assumed bond energy, r is the bond distance in the simulation, and r₀ = 3.81 Å (assumed if C–C bond) or 3.45 Å (assumed if a glutamine C–C_ß bond), summed over all bonds in the polyglutamine guest.

For bond-angle energies in polyglutamine, Eq. 3 is used. For polyglutamine, = 20 kcal/mol is the bond energy, is the bond angle in the simulation, and ₀ = 109.5° (assumed preferred polyglutamine bond angle), summed over all bond angles in the polyglutamine guest (CCC, C_ßCC, CCC_ß).

For dihedral energies in polyglutamine, Eq. 4 is used. For polyglutamine, where are assumed dihedral energies, is the dihedral angle in the simulation, and is a varied parameter in the present study, summed over all dihedral angles in the polyglutamine guest (CCCC, C_ßCCC_ß, CCCC_ß, C_ßCCC). The values of are assumed to be similar to the CI2 host: for backbone dihedrals (CCCC), and ; and for side-chain dihedrals (C_ßCCC_ß/CCCC_ß/C_ßCCC), and

In the model of the polyglutamine guest, the interaction between all nonlocal (i, i + 3 or greater) C atoms in the guest polyglutamine is attractive to approximate a fundamental propensity for polyglutamine chains to form backbone hydrogen bonds (Chen et al., 2002a). Similarly, the interaction between all nonlocal (i, i + 3 or greater) C_ß atoms in the guest polyglutamine is attractive to approximate a fundamental propensity for polyglutamine side chains to form stable bonds (Chen et al., 2002a). As with the CI2 host, no attractive contacts were allowed between C and C_ß atoms and the energy of the C–C and C_ß–C_ß contacts were equal, for simplicity. Each attractive C–C and C_ß–C_ß contact between residues within the polyglutamine guest is described by Eq. 5 and the total attractive contact energy is the sum of all attractive contacts in the polyglutamine guest. To distinguish between the Lennard-Jones energy between contacts in the CI2 host, _LJ = 0.8 kcal/mol, the contact energies in the polyglutamine guest are denoted with polyglutamine contact energy, _QQ, which is a varied parameter in the present study. For attractive contacts between nonlocal atoms in the polyglutamine guest, _ij is assumed to be 4.6 Å for C–C contacts or 5.2 Å for C_ß–C_ß contacts, consistent with distances observed between hydrogen bonded glutamine residues in ß-sheets, and r_ij is the distance between the two contact atoms, i and j, in the simulation. Using these assumptions, the only contact parameter to determine is the attractive Lennard-Jones potential between the polyglutamine atoms, _QQ.

As with the CI2 host, it is assumed that all local (i, i + 2 or less) Lennard-Jones interactions in the polyglutamine guest are repulsive since their conformations are defined by the dihedral parameters. Furthermore, since the crystal structure and NMR studies of CI2-polyglutamine host-guest mutants shows the polyglutamine guest residues as disordered (Chen et al., 1999; Gordon-Smith et al., 2001), it is also assumed that the Lennard-Jones interactions between atoms in the polyglutamine guest and the CI2 host are repulsive. Eq. 6 is used to determine the total repulsive contact energy as the sum of all repulsive contacts in the polyglutamine guest. For repulsive contacts involving atoms in the polyglutamine guest, _rep = 0.8 kcal/mol is the assumed repulsive energy, r_ij is the distance between the two repulsive atoms (i and j) in the simulation, and _ij = r_i + r_j, where r_i, r_j = 1.9 Å (if atom i,j is C) or native C–C_ß bond distance (if atom i,j is C_ß).

A list of the parameters used in the polyglutamine guest model is shown in Table 1.

Analysis of simulations
Thermodynamic quantities, such as free energy (G), energy (E), and entropy (S), are determined using the weighted histogram analysis method (WHAM) (Ferrenberg and Swendsen, 1988; Kumar et al., 1992). For each reported CI2 free energy, six MD simulations are sampled for 120 ns, with 90 ns used for WHAM analysis and the initial 30 ns discarded. The free energies are reported as an average and standard deviation of the WHAM-calculated free energy of each of the six 90-ns trajectories.

For kinetic refolding studies of CI2, 60 kinetic trajectories are collected to obtain statistically significant reaction rate measurements. The initial unfolded coordinates of each refolding trajectory are obtained from the final structure of a short simulation at 999 K of a randomly determined length (500–1500 ps) and random initial velocities. For each refolding trajectory, these initial coordinates are subjected to 300 K and random initial velocities and followed for 9000 ps, a sufficient amount of computational steps to refold all CI2 trajectories. For each trajectory, the average value of Q, the number of native contacts formed is determined at each MD iteration. From the 60 trajectories, six groups of 10 trajectories are averaged together and each group fit using the Marquardt algorithm with in-house software to Eq. 7 (Marquardt, 1963),

(7)

In Eq. 7, Q(t) is the average number of native contacts Q at time t, k_obs is the observed kinetic rate, Q is the change in the number of native contacts Q between native and unfolded CI2, and Q() is the equilibrium average native value of Q. The average and standard deviation of the rate constants k_obs are calculated from the six groups for each value of k_obs.

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Wild-type CI2
Minimalist models of chymotrypsin inhibitor 2 were examined to determine whether a minimalist CI2 model can capture experimentally determined properties and therefore be suitable for use in this study. CI2, denoted "Wild-Type CI2" in Fig. 1, is a small protein but contains many different types of secondary structures:

1. Alpha-helix (residues 12–24).
   
2. Parallel ß-sheet between ß-strands: three (residues 28–34) and four (residues 45–52).
   
3. Antiparallel ß-sheets between ß-strands, one (residues 3–5) and six (residues 60–64); two (residues 5–8) and five (residues 55–58); four and six.
   
4. Extended loop (residues 35–44).
   

View larger version (23K): [in this window] [in a new window]   FIGURE 1  Schematic of polyglutamine residues MGQ10GM inserted into the CI2 host. Wild-type CI2 host residues are labeled in blue, the insertion residue site, Met-40, is labeled in red, and the 10Q polyglutamine guest insert is labeled in green.

View larger version (20K): [in this window] [in a new window]   FIGURE 2  Wild-type CI2 demonstrates two-state folding behavior. (A) The number of native contacts (Q) between 10 and 22 ns in a simulation of wild-type CI2 at Tf = 350 K predominantly samples native (Q 125) or unfolded (Q 20) conformations. (B) A single peak is observed in the plot of the specific heat (CV) versus temperature (T), indicating two-state folding behavior. A 1-SD error of CV is shown with dashed lines (- - -). (C) A plot of potential mean force (PMF) versus native contacts (Q) at the wild-type CI2 Tf = 350 K shows two free-energy minima at the native (Q 125) and unfolded (Q 20) ensembles and a single free-energy maxima at the transition state (Q 70). 1 SD of PMF is shown with dashed lines (- - -).

(8)

In Eq. 8, E_i is the potential energy of each conformation in the simulation, k_B is the Boltzmann constant, and n(E_i) is the density of states, or number of iterations, of the simulation. In Fig. 2 B, a single specific heat peak is observed in wild-type CI2 simulations, consistent with a two-state mechanism and no stable intermediates. The error boundary of one standard deviation for C_V(T), determined from six independent simulations, is indicated in Fig. 2 B by dashed lines above and below the C_V(T) trace. The specific heat plot in Fig. 2 B is consistent with previous simulations of both C and CC_ß representations of CI2 (Cheung et al., 2003; Clementi et al., 2000b).

In Fig. 2 C, only two free-energy minima, corresponding to native (Q 125) and unfolded (Q 20) ensembles, are in a WHAM calculation of the number of native contacts (Q) versus potential mean force (PMF) for a representative wild-type CI2 simulation at T_f = 350 K, where

(9)

In Eq. 9, k_B is the Boltzmann constant, n(E_i) is the density of states in the simulation with the indicated value of Q, Q = X denotes all simulation configurations with X native contacts, and Q = ALL denotes all simulation configurations. Although PMF is not a direct measure of free-energy, differences in PMF are equivalent to the difference in free energy (G). For example, the free-energy difference between a native (Q = 125) and unfolded (Q = 20) ensembles (G_NU) can be estimated by Eq. 10 as

(10)

The two free-energy minima observed in Fig. 2 C demonstrates the two-state folding of the CC_ß CI2 Go-model, in agreement with experimental results (Jackson and Fersht, 1991) as well as previous simulation studies (Cheung et al., 2003, 2000b). Also indicated in Fig. 2 C are boundaries inclusive of the unfolded, native, and transition state ensembles. The error boundary of 1 SD, determined from six independent simulations in the PMF shown in Fig. 2 C, is indicated by dashed lines above and below the PMF trace.

Confirming two-state folding is the first step toward a successful computational model of CI2. The second step is to ensure that the transition state in simulations is in agreement with experimental -values. In a typical -value measurement, a CI2 mutant is made which removes the wild-type side chain at a single residue site i (i.e., wild-type side chain to alanine). To determine the degree to which, between 0 and 1, a side chain is structured in the transition state, the -value is calculated using Eq. 11,

(11)

It is important to note that interpretation of -values is complicated by alterations in the folding mechanism from the mutation and sampling of non-native contacts in the transitions state ensemble, which can lead to -values <0 and >1. Furthermore, -values derived from a single-site mutation cannot distinguish which additional residue contacts are involved in the transition state structuring, although these interactions can be measured with double mutants (Itzhaki et al., 1995). Also, the correlation between free energy and the formation of native side-chain structure may not be straightforward in all proteins (Bulaj and Goldenberg, 2001).

Despite these caveats, -value analysis remains an invaluable method to study the transition state structure and compare experimental and simulation results. In the low-resolution CC_ß model employed in the present study, a residue-to-residue -value comparison between simulation and experiment is not used. Instead, the accuracy of the CI2 model is evaluated on whether it predicts the predominant CI2 secondary structure elements involved in the transition state. In simulations, the free-energy perturbation method is used to calculate the -value of each contact from the wild-type simulation without actually having to simulate each mutation separately or conduct kinetic simulations (Clementi et al., 2000b). Using free-energy perturbation, the -value of each contact, i, is calculated by removing the energy of each contact from the wild-type energy function, effectively producing a deletion mutant at that contact. The -value itself is calculated using the energy difference between the wild-type and mutant energies (E) of the unfolded, native, and transition state thermodynamic ensembles through Eq. 12,

(12)

As with experimental -values, the free-energy perturbation method assumes that the folding mechanism will be unchanged when each contact is removed. Fig. 3 A presents each residue-residue wild-type CI2 contact with the simulated transition state -value of each contact indicated by its color. The upper left corner of Fig. 3 A indicates C_ß–C_ß contacts and the lower right corner indicates C–C contacts. Both the C–C and C_ß–C_ß -values are high in the -helix (residues 12–24), ß-strand ß₃ (residues 28–34), and ß-strand ß₄ (residues 46–52). These results are consistent with earlier results on a C model of CI2 (Clementi et al., 2000b). Standard deviations of simulated -values are no greater than ±0.05, indicating a high degree of confidence in the magnitudes of the simulated -values.

View larger version (18K): [in this window] [in a new window]   FIGURE 3  Simulation -values agree with experimental -values. The magnitude of the -values is indicated by color: < 0.3 (black square), 0.3 < < 0.6 (light-blue square), and > 0.6 (red square). Secondary structure elements of CI2 are shown for reference: ß1, ß2, , ß3, ß4, ß5, and ß6. (A) A contact map showing the simulation -values of the wild-type CI2 transition state for Cß–Cß contacts (upper left) and C–C contacts (lower right). The maximum standard deviation error of any simulation -value listed is ±0.05. (B) Experimental -values are shown for each residue (Itzhaki et al., 1995).

Polyglutamine insertion mutants of CI2
Fig. 2, A–C, and Fig. 3, A and B, have indicated that the CC_ß Go-model of CI2 used in this study captures the observed properties measured with experiments. As such, further studies involving more complex mutations involving significant amino acid inserts can be conducted. The present study focuses on the insertion of polyglutamine residues into the CI2 loop at residue methionine 40, as in the experimental work (Ladurner and Fersht, 1997). A schematic for this mutational method is shown in Fig. 1. The rational for examining these mutants is to determine the preferred polyglutamine dihedral, and Lennard-Jones energetic parameters, _QQ, and to later use these parameters in the simulation of polyglutamine chains in the absence of the CI2 host protein.

The present study focuses on three loop insertion mutants of CI2: 1), MG₃SG₄SG₃M (G10); 2), MGQ₄GM (Q4); and 3), MGQ₁₀GM (Q10). A schematic of these insert mutations is shown in Fig. 4 A. The Q4 and Q10 mutants were selected since, of the mutants studied, the length difference and therefore free-energy difference were the largest and most statistically significant (Ladurner and Fersht, 1997). The G10 insert mutant is simulated for reference as a random coil insert. Different polyglutamine dihedral parameters, and Lennard-Jones energetic parameters, _QQ, are imposed upon the polyglutamine guest inserts within the CI2 host Go-model, and the best match with experimental results is tentatively proposed as the "correct" polyglutamine computational model. Comparison of this model with experiments on the CI2-polyglutamine host-guest mutants is conducted in the present study. Comparison of this model with experiments on isolated polyglutamine chains will be the subject of future studies.

View larger version (13K): [in this window] [in a new window]   FIGURE 4  Schematic of the computational host-guest method. (A) Guest inserts MG3SG4SG3M (G10), MGQ4GM(Q4), and MGQ10GM (Q10) are inserted into the CI2 host at residue Met-40. (B) The free-energy difference between host-guest mutants CI2–Q10 and CI2–G10, GQ10–G10, and between CI2–Q10 and CI2–Q4, GQ10–Q4, is calculated directly from differences in PMF at Q = 120.

(13)

It should be noted that, for the CI2-polyglutamine host-guest mutants shown in Fig. 4 B, the number of native contacts present in the native state (Q 120) is slightly less than the wild-type CI2 in Fig. 2 C (Q 125). Nonetheless, the structure of the transition state of the CI2-polyglutamine host-guest mutants is essentially the same as the wild-type CI2 transition state shown in Fig. 3 A (data not shown). Thus, as suggested from experiments (Ladurner and Fersht, 1997), the folding mechanism of CI2 host is relatively unchanged by insertion of polyglutamine guests.

To model the guest inserts in the CI2 host, it is important to consider the necessary parameters to modulate. For the CI2 host, the minimum energy bond lengths, angles, dihedrals, and pairwise contacts for the CI2 residues are parameters biased to the values obtained from the crystal structure 2CI2.pdb. For the inserted polyglutamine guest residues, bond length and angle parameters are assumed to be similar to the values observed in proteins (see Table 1); bond lengths are 3.81 Å for CC bonds, 3.45 Å for CC_ß bonds, and all bond angles are set to 109.5°. Due to their large energy (_r, ) constraints, bond lengths and angles largely remain constant between folded and unfolded conformations of CI2 and therefore do not affect protein stability. However, protein stability does depend on dihedrals and Lennard-Jones contacts which will adopt non-native conformations at higher temperatures due to their small energy constraints (, _LJ).

Initially, different dihedral parameters in the polyglutamine guest insert are examined. Dihedral angles are set to values biasing the insert to different secondary structures of random coil, -helix, polyproline helix (PPII), and ß-strand. A random coil dihedral is achieved by setting the dihedral energy within the loop insert at For -helix, polyproline II helix, and ß-strand dihedrals, the dihedral energies are equal to the CI2 host dihedral energies (see Table 1). The atoms in the polyglycine insert G10 (MG₃SG₄SG₃M) are modeled with random coil dihedrals and hard-sphere repulsive interactions with all other atoms in the protein.

Fig. 5 A shows the values of G_Q10–G10 and G_Q10–Q4 for polyglutamine models with random coil, -helix, PPII, and ß-strand dihedral preferences. The G_Q10–G10 value is the free-energy difference between the CI2 host with a random coil glycine insert and CI2 with a polyglutamine insert in a particular secondary structure. The value of G_Q10–Q4 is the difference between two CI2 hosts, each with a different length of polyglutamine insert in a particular secondary structure. In Fig. 5 A, no polyglutamine insert dihedral parameter destabilizes the CI2 host exactly at the experimental values of G_Q10–G10 = 0.72 kcal/mol and G_Q10–Q4 = 0.64 kcal/mol. However, the ß-strand parameters produce the only model resulting in destabilization larger than experimental values. The PPII parameters slightly destabilize G_Q10–G10 but not G_Q10–Q4. The random coil and -helix models do not destabilize either G_Q10–G10 or G_Q10–Q4. In Fig. 5 A, error bars show standard deviations determined from six independent simulations, indicating that simulated G_Q10–G10 and G_Q10–Q4 are statistically significant measurements.

View larger version (13K): [in this window] [in a new window]   FIGURE 5  Simulated free-energy differences match experimental host-guest free-energy differences when the polyglutamine guest favors a ß-strand dihedral and QQ = 0.6 kcal/mol. (A) The stability difference between CI2–G10 and CI2–Q10, GQ10–G10 (red open circle), and between CI2–Q4 and CI2–Q10, GQ10–Q4 (blue open circle), is shown for a random coil, -helical, PPII strand, and ß-strand dihedral preference in the polyglutamine guest. (B) The stability difference between CI2–G10 and CI2–Q10, GQ10–G10 (red open circle), and between CI2–Q4 and CI2–Q10, GQ10–Q4 (blue open circle), is shown for a ß-strand dihedral + increasing values of the attractive contact energy between guest polyglutamine atoms, QQ. The best match between simulation and experiment is shown for GQ10–G10 (red solid circle) and GQ10–Q4 (blue solid circle) when the dihedral is ß-strand and QQ = 0.6 kcal/mol. For comparison in A and B, the experimentally measured free-energy differences are shown between CI2–G10 and CI2–Q10, (red dashed line), and between CI2–Q4 and CI2–Q10, (blue dashed line). Error bars on simulated values of GQ10–G10 (O) and GQ10–Q4 (O) shown in A and B are standard deviations calculated from six independent simulations.

Kinetics
Having determined parameters which produce agreement between simulation and experimental thermodynamics, agreement is expected between simulation and experimental kinetic results with these parameters. Fig. 6 A shows two sample "Q versus time" trajectories for the CI2–10Q insert mutant, one indicating a fast refolding trajectory (yellow) and the second indicating a slower refolding trajectory (green). In agreement with experiments, the transitions from unfolded to native CI2 occur in a single discrete step and do not significantly populate kinetic intermediates (Jackson and Fersht, 1991; Ladurner and Fersht, 1997). Fig. 6 B shows "Q versus time" averaged over all 60 kinetic refolding trajectories for wild-type CI2 (black), the 10G insert mutant (red), the 4Q insert mutant (blue), and the 10Q insert mutant (green). For the 10G insert mutant, the insert dihedral is random coil and _QQ = 0. For the 4Q and 10Q insert mutants, the insert dihedral favors ß-strand and _QQ = 0.6 kcal/mol. All trajectories in Fig. 6 B are shown to fit successfully with a single exponential equation, consistent with experiments (Jackson and Fersht, 1991; Ladurner and Fersht, 1997). This is also evident in Fig. 6 C, which shows that residuals of the fit are randomly dispersed for all trajectories. It should be noted that the average value of Q for the native state of the CI2-polyglutamine mutants in Fig. 6 B (Q 120) is slightly lower than that observed for wild-type CI2 in Fig. 2 A (Q 125). Nonetheless, the single exponential kinetic fits of both wild-type CI2 and all host-guest mutants in Fig. 6 B demonstrate that the basic folding mechanism remains unchanged.

View larger version (24K): [in this window] [in a new window]   FIGURE 6  Simulated folding kinetics using the calibrated model parameters of a ß-strand dihedral and QQ = 0.6 kcal/mol agree with experiments. (A) Two representative kinetic "Q versus time" trajectories for the CI2–10Q insert mutant are shown for a fast refolding trajectory (yellow line) and a slower refolding trajectory (green line). (B) The average "Q versus time" for all 60 kinetic refolding trajectories for wild-type CI2 (black points), the random coil 10G insert mutant (red points), the model parameter 4Q insert mutant (blue points), and the model parameter 10Q insert mutant (green points). Lines through each trajectory show a single exponential fit of the data. (C) Residuals of the single exponential fit through each trajectory are randomly dispersed for wild-type CI2 (black points), the random coil 10G insert mutant (red points), the Model parameter 4Q insert mutant (blue points), and the Model parameter 10Q insert mutant (green points). (D) The transition state stability differences between CI2–G10 and CI2–Q10, GQ10–G10 (red open circle), and between CI2–Q4 and CI2–Q10, GQ10–Q4 (blue open circle), are shown when random coil, -helical, and model (red solid circle/blue solid circle) parameters, and ß-strand parameters are applied to the polyglutamine guest insert. For comparison, the experimentally measured transition state free-energy differences are shown between CI2–G10 and CI2–Q10, (red dashed line), and between CI2–Q4 and CI2–Q10, (blue dashed line). Error bars on simulated values of GQ10–G10 (red open circle) and GQ10–Q4 (blue open circle) are standard deviations calculated from six independent simulations.

(14)

where R = 0.002 kcal/(mol * K) and T = 300 K. Shown in Fig. 6 D is a comparison of and with the experimental values of and (Ladurner and Fersht, 1997). In Fig. 6 D, the x-axis labels stating "random coil," "-helix," and "ß-strand" denote a guest insert model with dihedral parameters only (_QQ = 0 kcal/mol) whereas the x-axis label stating "Model" denotes ß-strand dihedral parameters combined with _QQ = 0.6 kcal/mol. In Fig. 6 D, the random coil, -helix, and Model parameters result in and which agree with experimental and within the simulation error. The ß-strand parameters result in and significantly larger than experimental and In Fig. 6 D, error bars show the standard deviation of and as determined by six independent averages of 10 simulation traces.

Structural perturbation of CI2 host by polyglutamine guest inserts
In Fig. 5 A, ß-strand dihedral parameters for guest insert polyglutamine residues destabilize the CI2 host when the insert is lengthened (G_Q10–Q4 1.5 kcal/mol). Also in Fig. 5 A, random coil parameters for guest insert polyglutamine residues do not destabilize the CI2 host when the insert length is increased (G_Q10–Q4 0). This fact suggests that the increase in chain entropy between a 4Q and 10Q guest insert is negligible (S_Q10–Q4 0). Thus, the free-folding energy differences from lengthening the ß-strand guest insert (G_Q10–Q4 1.5 kcal/mol) result from changes in the host energy, not entropy, as the stiffness of the guest insert will compete with the native contacts of the CI2 host near the insertion site. This loss of native state energy of the CI2 host can be observed between Fig. 2 A, where native wild-type CI2 has Q 125, and Fig. 6 A, where the CI2–10Q host-guest mutant has Q 120. Thus, increasing the ß-strand dihedral energy parameters for the guest insert polyglutamine should highlight structural perturbations in the CI2 host which account for the loss in CI2 free energy.

As is increased in the 10Q guest insert, 4 of the 134 native contacts in the CI2 host are perturbed in the native ensemble: 1), 38–48 spanning the insert; 2), 39–48 spanning the insert; 3), 41–48 C-terminal of the insert; and 4), 41–46 C-terminal of the insert. All other contacts do not show significant perturbation at increasing ß-strand dihedral energies. Fig. 7 A shows, for each of these four contacts, the normalized contact distance, increases as ß-strand dihedral energy () is increased. The increase in accounts for the increase in CI2 host energy as is increased in the 10Q guest. It should be noted that the parameter refers to the first energy parameter of the CCCC dihedral in Eq. 4. The second dihedral energy parameter of the CCCC dihedral, scales at 0.5-times the CCCC value of The energies of the C_ßCCC_ß, C_ßCCC, CCCC_ß dihedral values of scale at 0.25 the CCCC value of In Fig. 7 A, error bars show the standard deviation of as determined by six independent simulations.

View larger version (16K): [in this window] [in a new window]   FIGURE 7  Native ensemble simulations (300 K) of the CI2-polyglutamine host-guest mutants, using the model parameters (ß-strand dihedral and QQ = 0.6 kcal/mol) for the polyglutamine guest, agree with experiments where insertion of the polyglutamine guest induces minor structural perturbations of the CI2 host located near the loop insert region. (A) A normalized plot of the distance increase in four CI2 host contacts involving residues 38–48 (light-blue solid circle), 39–48 (red solid circle), 41–46 (dark-blue solid circle), and 41–48 (green solid circle) as ß-strand dihedral energy () is increased in the polyglutamine guest region of the CI2–10Q host-guest mutant. (B) A contact map shows perturbed CI2 host contacts in the native ensemble between wild-type CI2 and the CI2–4Q host-guest mutant with Model parameters applied to the 4Q insert. Contacts perturbed >2 Å between wild-type CI2 and CI2–4Q in simulations are shown in color in the upper left corner, 38–48 (light-blue solid square), 39–48 (red solid square), 41–46 (dark-blue solid square), and 41–48 (green solid square), and unperturbed contacts (black solid square). Wild-type CI2 crystal structure (2CI2.pdb) contacts absent in the CI2–4Q insert mutant crystal structure (1CQ4.pdb) are shown in color in the lower right corner, 39–48 (red open circle), 41–46 (red open circle), and 41–48 (red open circle), whereas unperturbed contacts are black (red open circle). For reference, the 4Q insert region is indicated by "Q" on the diagonal, and secondary structure elements of CI2 are shown along the x and y axes: ß1, ß2, , ß3, ß4, ß5, and ß6. (C) The mobility difference between each CI2 host C atom in the Model 10Q host-guest mutant versus the wild-type CI2, MQ10–MWT. Error bars shown in A and C are standard deviations calculated from six independent simulations.