Biophysics Rotation Data Report Denise M Kilburg Winter 2015

1

Introduction

Retroviruses are (+)-strand RNA viruses that share the same basic genomic organization and mode of replication.[1] HIV-1, like all retroviruses, must integrate a reversed transcribed copy of its RNA genome into host DNA to form an infected cell.[2, 1] Essential viral catalytic enzymes include reverse transcriptase (RT) and integrase (IN). The former copies the RNA genome into the dsDNA form and the latter catalyzes both the 3’-processing and integration of the double-stranded viral DNA into the host chromosomal DNA.[1, 3] HIV-IN, Figure 1, has been shown to be a viable drug target but resisitence to inhibition is large even combined with highly active antiviral therapy.[3] Therefore, other means of inhibition, such as targeting essential cofactors has been explored.[3]

Figure 1: A depiction of HIV-1 Integrase(PBD: 3AVB).[3]

Due to the fact that small perturbations of the structure around the LEDGF binding site produce lethal viral phenotypes, small molecule HIV-1 IN associates with chromatin and inhibitors of this binding site might also disrupt forms a tighly bound complex with host tran- HIV pathogenesis[1, 2, 3]. scriptional coactivator p75 (Figure 2), also known as lens epithelium-derived growth factor In 2011, Rhodes et al. made a series of (LEDGF).[2] Previous experiments have shown peptides consisting of the amino acid sequence that LEDGF mediates the nuclear localization SLKIDNLD from the loop of LEDGF that is of HIV-1 IN as well as prevents proteosome known to bind the IBD of HIV-1 Integrase. Two degradation.[2] LEDGF binds to a small, peptides of note were the linear SLKIDNLD seapproximately 80 residue IN binding domain quence and a cyclic version of the same amino (IBD) within the integrase C-terminal region.[2] acid sequence. They reported the difference in 1

2

Cyclic SLKIDNLD peptide structure was taken from the crystal structure of HIV-1 Integrase to which it was bound (PDB ID: 3AVB). Schr¨odinger’s Maestro program was used to isolate and prepare the cyclic peptide structure. The linear peptide was prepared by breaking the bond between the S-D amino acids of the cyclic peptide. The resulting structure was modified to resemble the zwitterionic form. The IMPACT program[5, 6] (Schr¨odinger, LLC) was then utilized to perform an energy minimization of the two peptide structures. Once the structures were energy minimized, temperature replica exchange simulations were used to obtain peptide conformations. Temperature replica exchange is a technique that samples a rough energy landscape of the biomolecules, rapidly converting between conformations that are separated by high energy barriers.[5] Eight replicas of the system were run over a series of temperatures, 300 to 400K, using constant temperature molecular dynamics.[5] The simulations were 25 ns in length. Once completed, VMD was used to ascertain the peptide RMSD from the original crystal structure peptide. Only the collected ensembles at a temperature of 300K were used.

Figure 2: Depiction of LEDGF/p75 (PDB: 2B4J). The region that interacts with HIV-1 IN is the loop on the top left. This region of p75 contains the amino acid sequence SLKIDNLD.

IC50 values of a linear peptide sequence compared to a cyclic version. The linear peptide gave an IC50 > 500 µM while the cyclic was found to have an IC50 ' 85.2 µM. Here we try to account for these differences by examining the free energy of reorganization and binding energy[4]. 2/19/2015

Methods

PRD_000819_620.gif (880×880)

Energy minimization steps were then performed on the cyclic and linear peptide structures in complex with the binding site of HIV-IN that had been prepared previously. Molecular Dynamics simulations, using IMPACT, were then run at 300K, λ = 1 for 48 hours. The energy of binding was collected from these simuFigure 3: Depiction of SLKIDNLD cyclic peplations. The structure of the peptides were then tide taken from PDB:3AVB.[3] loaded into VMD and the backbone positions were compared to the crystal cyclic structure http://www.rcsb.org/pdb/images/PRD_000819_620.gif

1/1

2

peptide with the RMSD Trajectory Tool. This was used to find a cutoff RMSD for calculations regarding the energy of reorganization.

s ux¯ = √ N

The energy of reorganization, ∆Greorg , was calculated using the probabilities of the structures being within a certain RMSD from the crystal structure peptide. The amount of structures within this cutoff RMSD were counted. The probability was then calculated by dividing the frequency by the total number of structures. This was done for both the cyclic and the linear peptide. The ∆Greorg was then calculated using Equation (1), ∆Grorg = −RT ln P

N 1 X (xi − x ¯ )2 N − 1 i=1

s2 =

(5) (6)

x¯1 − x¯2 t= r s21 s22 N1 + N2

(7)

where t is the Welch’s t-statistic. 

ν '  2 2 s 1 N1

s21 N1

1 N1 −1

+ +

 s22 2 N2 

 s22 2 1 N2 N2 −1

(8)

where ν is an estimate of the degrees of freedom.

(1)

where R is the Univeral Gas Constant and P is the probability of being within the RMSD cut3 Results off. The ∆∆Greorg between the cyclic and linear peptide was calculated using Equation (2). Table 3 and 4 give a description of the state history of the eight replicas during the initial linear ∆∆Greorg = ∆Gcyclic (2) temperature replica exchange simulations. The reorg − ∆Greorg tables show that the most replicas for the cyclic The difference in binding free energy between peptide sampled a variety of temperatures in an the cyclic and linear peptides is defined by equaunbiased way, resultiing in a good experimental tion (3), sampling of conformations. The linear peptide replicas had a more biased sampling, however ∆∆Gb = ∆∆Eb + ∆∆Greorg (3) the averaging of these states should suppress where ∆∆Eb is the difference in the average these differences. Table 5 and 6 show the RMSD binding energy of the cyclic and linear com- for the original crystal structure bound peptide of the structures taken from the temperature plexes. replica exchange simulations. The figures from For the purposes of statistical analysis the fol- Table 5 are sorted by replica and show that the for the linear peptide, once equalibrated, lowing formulas were used: never had a RMSD values less that 2.0 ˚ A. The N cyclic peptide data, shown in Table 6, however, 1 X x ¯= xi (4) consistantly had RMSD values less that 2.0 ˚ A N i=1 for all replicas. The RMSD values of only the where N is the number of steps. replica structures at 300K are shown in Figure 3

4. Figure 6 presents the data shown in Figure 1 as a histogram to give a better picture of the spread and frequency of the RMSD from the crystal structure peptide.

peptide. Using these values as the cutoff RMSD for the original temperature replica exchange structures, it was found that the energy of reorganization for the cyclic peptide is 0.70 kcal/mol. As noted previously, there were no linear structures that had a RMSD value less that 2.0 ˚ A. Therefore, one can only say that the energy of reorganization for the linear peptide is at least 4.0 kcal/mol. Accordingly, using Equation (2), the ∆∆Greorg < -3.3 kcal/mol. These results are summarized in Table 1.

Linear: RMSD per Cycle at 300K "300_25_85trajrmsd.dat" 6

RMSD

5

4

3

Table 1: Results summary for the free energy of reorganization calculations

2

1

0

200

400

600

800

1000

1200

Cycle

Linear Cyclic

Cyclopeptide: RMSD per cycle at 300K 4

"300_1_8trajrmsd.dat"

Cutoff RMSD [˚ A] 1.8 1.6

# of Total # structures ≤ RMSD of structures 0 1142 472 1526 ∆∆Greorg = -3.3 kcal/mol

P <8.8×10−4 0.309

∆Greorg [kcal/mol] > 4.0 0.7

3.5

Figure 7 shows a histogram of the binding energy obtained from the IMPACT MD simulations. The average energy of binding for the cyclic peptide and linear peptide were found to be -50.0 ± 0.4 kcal/mol and -53.0 ± 0.5 kcal/mol respectively. Using these values, the ∆∆Eb is 3.0 ± 0.6 kcal/mol. Using Equation (3), the difference between the binding free energy for the cyclic and linear peptide is at least -0.3 kcal/mol. Figure 4: RMSD values for cycles at 300K for all This result is in agreement with the experimental results of Rhodes et al.[3]. According to their replicas experimental results the the difference in binding free energy is ' -1.0 kcal/mol. A summary of Once the RMSD data was ascertained for the results for the energy of binding MD simulations peptide alone, MD simulations were run with are given in Table 2. IMPACT to find the binding energy between the peptide and HIV-1 IN for both the cyclic and linear structures. Figure 5 shows the RMSD 4 Discussion data taken from the MD simulation. From this data the maximum binding distance for the The results of the single peptide temperature linear peptide is 1.8 ˚ A and 1.6 ˚ A for the cyclic replica exchange experiments showed that the 3

RMSD

2.5

2

1.5

1

0.5

0

200

400

600

800 Cycle

1000

1200

1400

1600

4

Table 2: Results summary for the energy of binding simulations

RMSD values of ligand 1.6

"trajrmsd.dat"

1.5 1.4

E¯b s2 s uE¯b Linear -53.0 44.7 6.69 0.5 Cyclic -50.0 38.0 6.16 0.4 ∆∆Eb = 3.0 ± 0.6 kcal/mol ∆∆Gb < -0.3 kcal/mol

RMSD [Angstroms]

1.3 1.2 1.1 1 0.9 0.8 0.7 0.6 0

50

100

150

200

250

Cycle Linear Peptide Ebind RMSD

cyclic peptide structure did not, in general, deviate more than 2.0 ˚ A from it’s original crystal structure position. On the otherhand, the RMSD fluctuations of the linear peptide were much more pronounced with an average RMSD of 3.4 ˚ A. This result was not unexpected as a more linear structure is more entropically favored than a cyclic structure. Therefore a much higher reorganization energy for the linear peptide was expected. The reorganization energy of the linear peptide was found to be at least 4.0 kcal/mol, which is larger than that of the cyclic Figure 5: RMSD from the MD simulations for the Cyclic and Linear peptides. peptide by a factor of 5.7. 1.8

’lin_ebindtrajrmsd.dat’

1.7

RMSD [Angstroms]

1.6

1.5

1.4

1.3

1.2

1.1

1

0

50

100

150

200

250

Cycle

It was then decided to further the experiment by running MD simulations to find the binding energy between HIV-1 IN and the cyclic and linear peptides. According to the results, the linear peptide once bound to HIV-1 IN, has a stronger interaction than that of the cyclic peptide by about 3.0kcal/mol. When combining the data from the two experiments, the resulting change in the free energy of binding, -0.3 kcal/mol in favor of the cyclic peptide, is in accordance with the experiments by Rhodes et at.

formed, Equations (7) and (8), on the energy of binding data, it was found that the average binding energy of the cyclic and linear peptides were statistically the same. Therefore it is incorrect to state that there is a difference in binding energy of the two peptides. If this is actually the case, than the free energy of binding is at least -3.3 kcal/mol in favor of the cyclic peptide.

In this study, we determined the relative binding free energy without utilizing direct evaluaHowever, when the Welch’s t-test was per- tion using alchemical calculations. The bind5

[5] Banks,J.L.; Beard, Y; Cao, A.E.; Damm, R. et al. (2005) Integrated Modeling Program, Applied Chemical Theory (IMPACT). J. Comp. Chem., 26, 1752

ing free energy is actually defined as the the free energy difference between the λ = 0 state (uncoupled) and λ = 1 state (coupled).[7] Here, we only used the coupled state in our calculations. This may be the cause of the uncertainity/inaccuracy of our estimate of the binding free energy. Further studies employing BEDAM (Binding Energy Distribution Analysis Method), where a Hamiltonian replica exchange λ-hoping strategy is used to sample canonical distributions of structures in each λ state,[7] are needed to determine a more accurate binding free energy.

[6] Gallicchio, E.; Paris, K. and Levy, R.M. (2009) The AGBNP2 Implicit Solvent Model. J. Chem. Theory Comput., 5, 25442564 [7] Wickstrom, L.; He, P.; Gallicchio, E. and Levy, R.M. (2013) Large Scale Affinity Calculations of Cyclodextrin Host-Guest Complexes: Understanding the Role of Reorganization in the Molecular Recognition Process.J. Chem. Theory. Comput.,9, 31363150

References [1] Pedersen,F; Skou,P; Pyrz,M; and Duch,M. (2011) Retroviral Replication. In:Encylopedia of Life Sciences (ELS). John Wiley & Sons, Ltd: Chichester. DOI: 10.1002/9780470015902.a0000430.pub3 [2] Cherepanov,P; Ambrosio,S; Ellenberger,T; and Engelman, A. (2005) Structural basis for the recognition between HIV-1 integrase and transcriptional coactivator p75. PNAS, 102:48, 17308-17313 [3] Rhodes,D; Peat,T; Vandergraff,N; et al. (2011) Crystal Structures of Novel Allosteric Peptide Inhibitors of HIV Integrase Identify New Interactions at the LEDGF Binding Site. ChemBioChem, 12, 23112315 [4] Gallicchio, E. and Levy, R. (2011) Recent Theoretical and Computational Advances for Modeling Protein-Ligand Binding Affinities.Adv. Protein Chem. Struct. Biol., 85, 27-80 6

Table 3: Linear peptide state history data Replica r0 r1 r2 r3 r4 r5 r6 r7

state.history description dispersed most at 300K most low temp dispersed high/low most above 360K most below 380K most above 360K

mean RMSD [˚ A]

# of structures

min RMSD [˚ A]

max RMSD [˚ A]

2.74 2.74 4.47 4.67

802 848 866 877 906 871 905

1.57

3.52

1.44 1.19 1.64 1.19 1.49

7.36 7.56 7.56 6.35 7.64

3.76 5.32

Table 4: Cyclic peptide state history data Replica r0 r1 r2 r3 r4 r5 r6 r7

state.history description dispersed dispersed dispersed low/high dispersed dispersed dispersed dispersed

mean RMSD [˚ A] 1.58 1.69 2.02 2.95 1.63 2.52 1.61 1.65

# of structures 833 805 784 768 799 810 810 831

min RMSD [˚ A] 0.94 1.01 0.97 1.03 0.82 0.96 0.91 0.95

max RMSD [˚ A] 2.68 3.50 3.07 4.08 2.91 4.25 2.23 2.34

Linear: cycles 250-850 at 300K

Cyclo: cycles 1-800 at 300K 1200

"output_freq.dat" using 1:3

500

1000

400

800 Frequency

Frequency

600

300

600

200

400

100

200

0 0

1

2

3 RMSD

4

5

0

6

"output_freq.dat" using 1:3

0

1

2

3 RMSD

4

5

6

Figure 6: Frequency of binned RMSD values. Bin 1 includes Rmsd values of 0-1, bin 2 includes values from 1-2, etc.,

7

Figure 7: Frequency histogram showing Ebind data from MD simulations for the Cyclic and Linear peptides.

8

Table 5: RMSD as a function of Cycle for the Linear Peptide Linear Peptide: Replica r1 RMSD per Cycle

Linear Peptide: Replica r0 RMSD per Cycle 8

3.6

"lin_r0_cycletrajrmsd.dat"

Linear Peptide: Replica r2 RMSD per Cycle 3.4

"lin_r1_cyctrajrmsd.dat"

"lin_r2_cyctrajrmsd.dat"

3.4 7

3.2 3.2 3

5

4

3

2.8

RMSD [Angstroms]

RMSD [Angstroms]

RMSD [Angstroms]

6

2.6 2.4 2.2

3

2.8

2.6

2.4

2 1.8

2

2.2 1.6

1

1.4 0

100

200

300

400

500 Cycle

600

700

800

900

1000

0

100

200

400

600

700

800

2

900

0

8

6

6

4

RMSD [Angstroms]

6 RMSD [Angstroms]

7

5

5

4

3

2

2

2

1

1 500

600

700

800

900

0

100

200

300

400

500

600

700

800

900

Cycle

Linear Replica r3

Linear Replica r4

Linear Peptide: Replica r6 RMSD per Cycle 7

8

"lin_r6_cyctrajrmsd.dat"

"lin_r7_cyctrajrmsd.dat"

7

6 RMSD [Angstroms]

5

4

3

5

4

3 2 2

1 0

100

200

300

400

500

600

700

Cycle

Linear Replica r6

800

900

1 0

100

200

300

400

500 Cycle

600

700

Linear Replica r7

9

800

900

"lin_r5_cyctrajrmsd.dat"

1 0

100

200

300

400

500 Cycle

600

700

Linear Replica r5

Linear Peptide: Replica r7 RMSD per Cycle

6

700

4

3

Cycle

600

5

3

400

500

Linear Peptide: Replica r5 RMSD per Cycle

"lin_r4_cyctrajrmsd.dat"

7

300

400

8

7

200

300

Linear Replica r2

Linear Peptide: Replica r4 RMSD per Cycle

"lin_r3_cyctrajrmsd.dat"

100

200

Cycle

8

0

100

Linear Replica r1

Linear Peptide: Replica r3 RMSD per Cycle

RMSD [Angstroms]

500 Cycle

Linear Replica r0

RMSD [Angstroms]

300

800

900

1000

800

900

1000

Table 6: RMSD as a function of cycle for the cyclic peptide Cyclic Peptide: Replica r0 RMSD per Cycle 2.8

Cyclic Peptide: Replica r2 RMSD per Cycle

Cyclic Peptide: Replica r1 RMSD per Cycle 3.5

4

"r0_cyctrajrmsd.dat"

"r2_cyctrajrmsd.dat"

"r1_cyctrajrmsd.dat"

2.6 2.4

3.5

3

3

2.5

2 1.8 1.6 1.4

RMSD [Angstroms]

RMSD [Angstroms]

RMSD [Angstroms]

2.2

2.5

2

2

1.5

1.5

1

1.2 1 0.8 0

100

200

300

400

500

600

700

800

0.5

1

900

0

100

200

300

400

Cycle

500

600

700

800

900

0

100

200

300

400 Cycle

Cycle

Cyclic Replica r0

Cyclic Replica r1

Cyclic Peptide: Replica r3 RMSD per Cycle 4.5

3

600

700

800

Cyclic Replica r2

Cyclic Peptide: Replica r4 RMSD per Cycle

"r3_cyctrajrmsd.dat"

500

Cyclic Peptide: Replica r5 RMSD per Cycle 4.5

"r4_cyctrajrmsd.dat"

"r5_cyctrajrmsd.dat"

4

4 2.5

3.5

3

2.5

RMSD [Angstroms]

RMSD [Angstroms]

RMSD [Angstroms]

3.5 2

1.5

3

2.5

2

2 1.5 1 1.5

1

1

0

100

200

300

400 Cycle

500

600

700

0.5

800

0

100

Cyclic Replica r3

200

400 Cycle

500

600

800

"r7_cyctrajrmsd.dat"

"r6_cyctrajrmsd.dat" 2.2

2

RMSD [Angstroms]

2

1.8

1.6

1.4

1.8

1.6

1.4

1.2

1.2

1

1

0.8

0.8 0

100

200

300

400

500

600

700

800

900

0

100

200

300

Cyclic Replica r6

400

500

600

Cycle

Cycle

Cyclic Replica r7

10

0

100

200

300

400

500

600

700

Cyclic Replica r5

Cyclic Peptide: Replica r7 RMSD per Cycle

2.2

0.5 Cycle

2.4

2.4

700

Cyclic Replica r4

Cyclic Peptide: Replica r6 RMSD per Cycle

RMSD [Angstroms]

300

700

800

900

800

900