LecturesPart15

LecturesPart15 - Computational Biology, Part 15 A Simple...

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Unformatted text preview: Computational Biology, Part 15 A Simple Ionization Model Robert F. Murphy Copyright © 1996, 1999-2006. Copyright All rights reserved. Simple model: Acid Dissociation s For the dissociation of a weak acid HB ↔ B + H HB B+ s + H HB is referred to as the conjugate acid and HB B- is referred to as the conjugate base Bs The equilibrium equations are Ionization equilibria for amino acids s Need to consider which groups on an amino Need acid can be protonated/unprotonated acid s The carboxyl and amino groups that are The involved in peptide bonds have relatively constant pKs of ~2 and ~9 constant s The side chain pKs vary considerably. s Illustrations for Arg and Tyr follow. Arg- + _ + + H2Arg+ _ HArg _ + + H3Arg++ Tyr-_ _ _ H2Tyr + HTyr- H3Tyr+ _ + Example: An Ionizable Group Task: Given a pKa and a pH calculate fraction of base in unprotonated form fraction s Step 1: Enter pKa and pH as constant values into two cells into s Example: An Ionizable Group s Step 2: Enter formula Step using references to constants constants Example: An Ionizable Group s Note: The formula was made visible in the Note: spreadsheet by clicking the Formulas box on the View tab after selecting on Preferences... under the Tools menu Preferences... Tools Example: An Ionizable Group s Step 3: Convert to fraction of B Example: An Ionizable Group s Switch to viewing results of formulas rather Switch than the formulas themselves than Example: An Ionizable Group s New Task: Calculate fraction of B for more New than one pH value than s Step 4: Rearrange cells so that each row can Step be devoted to one pH value be Example: An Ionizable Group s Step 5: Enter a formula to generate a series Step of increasing pH values of Example: An Ionizable Group s Step 6: Copy the formula from cell B7 Step B7 down to cell B8 B8 Example: An Ionizable Group s Note that the reference to the pH value (cell Note A7) changed to A8 (which we wanted to A7 changed A8 happen) but that the reference to the pKa (cell B4) changed to B5 (which we didn’t) B4 changed (which Relative References s “Normally” a formula containing the names Normally” of cells (called references to those cells) are references updated when that formula is copied to another cell another s The row number is incremented by the The difference in row numbers between the original location of the formula and the new location location s The column number is incremented by the The difference in column numbers difference Relative vs. Absolute References s Such a reference is termed a relative Such reference because the reference is reference implicitly relative to the current cell implicitly s We may want to “fix” or “hold” a reference We so that it doesn’t change during copying a formula formula s This is termed an absolute reference and in This absolute Excel is created by putting a dollar sign ($) in front of the row or column number, or both both Example: An Ionizable Group s Step 7: Change the reference to the pKa to an absolute reference absolute Example: An Ionizable Group s Step 8: Copy the formula in cell C7 down Step C7 (note that the reference to B7 updates to B8) B7 B8 Example: An Ionizable Group s Step 9: Copy the formulas in cells A8:C8 Step A8:C8 down (note that the references to A7, A8, A7 and B8 increment but $B$4 doesn’t) and $B$4 Example: An Ionizable Group s Step 10: Switch back to viewing values Step rather than formulas to see results rather Names s To make it easier to read formulas To containing many cell references, some spreadsheet programs allow the creation of names for cells (like variable names in names programs) programs) Example: An Ionizable Group s New Task: Define absolute name for cell New absolute containing pKa containing s Step 11: Select cell B4 then Define Name Step B4 Define Example: An Ionizable Group s Note Excel has chosen a name based on the Note label in the adjacent cell and that the default label is for the name to refer to the currently selected cell selected Example: An Ionizable Group s Step 12: Use Apply Name to replace all Step Apply references to B4 in the spreadsheet with the B4 new name new Example: An Ionizable Group s Note formulas now show the name Example: An Ionizable Group s New Task: Define relative name for pH New relative s Step 13: Select cell A7 and Define Name Step A7 Example: An Ionizable Group s Note name now chosen based on label Note above B7. Change reference from $A$7 above B7 Change $A$7 (default is absolute for names) to $A7 (row $A7 number is allow to be relative) number Example: An Ionizable Group s Step 14: Apply Name Complex Models and Graphing s Before creating complex models, it is Before important to think about what graphical or tabular output is desired from the model. The organization of the spreadsheet should be optimized for this output. For example, if graphing of [P] vs. t is desired, try to place all values for t and [P] in consecutive cells in adjacent rows or columns. cells A Model with a Single Output s (Demonstration D2) Expanding a model for graphing s A better approach to the same problem is to better make many copies of the original spreadsheet (using copy and paste) and enter a different value of the independent variable in each copy. The results can be collected for graphing using references. collected s (Demonstration D4) Grouping Constants s The best method for graphing results for The multiple values of an independent variable is to redesign the original sheet so that only one row (or column) is needed for each value of the independent variable. This allows using fill down for the subsequent rows of the sheet. rows ...
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