Assignment A08: Semi-empirical Methods (SEM) and Layer Methods (LM)

Transcription

1 Assignment A08: Semi-empirical Methods (SEM) and Layer Methods (LM) Many reactions occur in highly anisotropic environments, which are persistent over time. This is very different from the effects of solvation, which are moderated by the fluxional nature of solvation and the consequential averaging over many random orientations of solvent molecules. What happens to molecular structure and molecular properties when the molecule is placed in a polar and persistent environment? This question is of central relevance in all of biology because polysaccharides, proteins, RNA and DNA all are highly polar and anisotropic environments. We will explore this question for double-stranded DNA as an example. It is the primary purpose of Assignment A08 to Characterize the Bonding of an Adenine-Thymine Base Pair Inside of one Specific Double-Stranded DNA Structure. You will be working with the crystal structure of ds-dna in the file IRx0.pdb provided on the course website. You will have to find a 3-base pair model with the sequence AAT (A = adenine, T = thymine), and we will compare the properties of the central AT base pair of that 3-base pair model to a free AT base pair. This ambitious assignment requires a combination of several previously learned skills with a number of new skills. You will be working with an experimental ds-dna structure and you need to edit this structure to obtain the 3-base pair model. You will learn various methods for the application of geometry constraints, and you will employ semi-empirical methods (SEM) and layer methods (LM, e.g., ONIOM). The various tasks are broken down into several steps to facilitate and guide your work. 1

2 (a) Optimized Structure of Free AT Base Pair at B3LYP/6-311G**. Perform a complete optimization and compute vibrational frequencies of the AT base pair at the B3LYP/6-311G** level. The AT base pair is the hydrogen-bonded Watson-Crick aggregate of adenine and thymine; no sugar (R = H in the insert on p. 1) and no phosphate, just the nucleobases. You may compute frequencies if you like. This is your reference for the discussion of the anisotropic effects of the ds-dna environment. You will need the optimized structure of the free AT base pair and the Mulliken charges of the atoms of the free AT base pair. (b) Setup of 3-Base Pair ds-dna Model. Go to the course website and download IRx0.pdb. Find a 3-base pair AAT sequence (A = adenine, T = thymine). Using the methods learned in A02, edit the ds-dna structure following these considerations: (1) The backbone should terminate at one end with a CH 2 OH group at C4 of the deoxyribose and at the other end with an OH group at C3 of the deoxyribose. There should only by two phosphate diester moieties in the backbone of each strand. (2) DNA contains mono-anions of a diester of H 3 PO 4. Hence, the 3- base pair fragment would be a tetra-anion and there would be some cations associated with the tetra-anion to give charge neutrality. For simplicity, add one H-atom to each phosphate unit so that the model contains neutral diesters of H 3 PO 4. (3) Check the hydrogen-count on each nucleobase. Adenine should have an exocyclic amino-group. One of the N-atoms in the imidazole ring of adenine is attached to the sugar and the other imidazole N-atom does not carry an H-atom. Thymine should have an NH group between the carbonyls. Add any missing H- atoms and delete any excessive H-atoms to obtain a complete and overall neutral model of a closed-shell system (singlet). Save this model in a GJF file. (c) Optimized Structures of 3-Base Pair ds-dna Model at AM1. Perform a complete optimization of the model generated in (b) using the semi-empirical theory AM1. (d) Partially Optimized AM1 Structure of 3-Base Pair ds-dna Model with Frozen Backbones. You will find that the stacking of the base pairs in the optimized structure of (c) has little resemblance to the crystal structure. One needs to apply constraints to obtain a model of 2

3 the electronic structure of the geometry that actually occurs in the crystal structure. It is one option to freeze all C, O, and P atoms in both backbones. This freezing includes atoms C3 and C4 of every sugar. For this purpose, we need to learn about the command option opt=readoptimize ( Add opt=readoptimize to the command line of the GJF file of (b) and add a section similar to the following lines after the geometry section to the GJF file. [The numbers are from the model defined by REG while preparing the present assignment. The numbers will be different depending on your work in (b).] [last line of geometry section] (empty line) atoms=h, N (optimize all H- and N-atoms) atoms=c notatoms=50,39,38,32,20,19,13,1,89,90,102,83,72,71,53,65 (don t opt. Cs listed) atoms=o notatoms=15,18,34,37,88,85,70,67 (don t optimize O-atoms listed) atoms=p notatoms=16,37,86,68 (list the numbers of the P-atoms in your structure) (empty line) (e) AM1 Optimization of Hydrogen Positions of 3-Base Pair ds-dna Model. Even with the constraints of (d), the stacking of the base pairs in the partially optimized structure still differs markedly from the crystal structure. The situation could be improved by using a larger 5-Base Pair model or a 7-Base Pair model with a central AT unit. On the other hand, one could assume that the positions of all non-hydrogen atoms are measured quite precisely by X-ray crystallography and that we only need to determine the best positions of the hydrogen atoms. We will take the latter perspective and, thus, freeze all C, N, O, and P atoms. This can be accomplished easily with the opt=readoptimize command and the addition of the line noatoms atoms=h after the geometry section to the GJF file. [Note: One could freeze one atom at a time with the Redundant Coordinates facility by selection of Cartesian Coordinate and Freeze and specification of the atom. But the ReadOptimize option is so much faster, and it is well worthwhile spending the time to learn about.] 3

4 (f) ONIOM(B3LYP/6-311G**:AM1) of 3-Base Pair ds-dna Model with Central AT in High Layer. Starting with the structure obtained in (e), you need to (1) define which atoms are to be optimized and (b) define which atoms belong to which theoretical level. Optimize the positions of all atoms of the central AT base pair while keeping everything else frozen. This can be accomplished relatively easily with the opt=readoptimize command and the addition of the line noatoms atoms={list atom numbers of atoms in central AT pair here} in the input section after the geometry section to the GJF file. Use the Select Layers facility in GaussView and define all atoms as belonging to the LOW layer. Then define the central A and T moieties as belonging to the HIGH layer. Use the expansion method described in lecture and start from the atom in each nucleobase, which is most removed from the attached sugar. Select the job type Optimization and define the theoretical levels for both layers. Save the GJF file. Run the ONIOM job. (g) Components of Write-Up. Submit one Word file A08_ your_last_name(s).docx (doublespaced or 24 pt, 12 pt Times New Roman, with page numbers) to the instructor and for peer review. The Word file must contain a discussion followed by three Figures, one Scheme, and one Table (see below for details). Each Scheme, Figure, and Table with its legend on a separate page and in that order; Scheme legend above in Title format; Figure legend below in sentence format; Table title above in Title format. Use page breaks and section breaks as needed. Use ChemDraw to generate the Scheme and insert the Scheme as enhanced metafile. Figure 1: Top: B3LYP/6-311G** optimized structure of free AT base pair from part (a) with direction of electrical dipole moment shown as vector. In the legend, provide the molecular dipole moment and the total energy. Bottom: B3LYP/6-311G** optimized structure of free AT 4

5 base pair with atoms color-coded according to their Mulliken charges. In the legend, provide the most important structural parameters that characterize the hydrogen-bonding of the AT base pair. Scheme 1: Show the AT base pair and show the IUPAC atom numbering. Table 1: This table will have three columns. Column 1: fragment (= atom with attached H) using the numbering of Scheme 1. Adenine fragments first, then thymine fragments. Column 2: B3LYP/6-311G** Mulliken charge in free AT base pair from part (a). Column 3: B3LYP/6-311G** Mulliken charge of central AT base pair in 3-base pair model of part (f). Figure 2: Top: Optimized structure from (c). Center: Partially optimized structure from (d). Bottom: Partially optimized structure from (e). Show backbones on left and right. This Figure with its legend must fit on one page. Figure 3: Partially optimized structure from (f). This is the star figure of A08. Make it a winner! Show backbones on left and right. This Figure must fit on one page; use landscape mode. (h) Content of Discussion. Very briefly describe what you did and refer to Figures 1 3, Scheme 1, and Table 1 in the discussion at the most appropriate location. One possible organization is as follows: First paragraph: Talk about free AT base pair of part (a) using Scheme 1, Figure 1, and Table 1. Then define the research problem, that is, formulate the question as to what happens to the electronic structure of AT inside of ds-dna. Second paragraph: Discuss the model formations of parts (c) - (e) with the AM1 method and various constraints using Figure 2. Third paragraph: Discuss the model formation of part (f) with the ONIOM(B3LYP:AM1) layer method using Figure 3. Compare columns 2 and 3 of Table 1 and formulate a conclusion. Submission & Deadlines: Submit the A08_ your_last_name(s).docx file as attachment to on Tuesday, 11/01/16 by midnight. For peer review, bring one stapled hardcopy (in color) of the file A08_ your_last_name(s).docx to class on Wednesday, 11/02/16. 5