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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- Fall '10
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- Biology, Computational Biology, pH, buffer solution, ionizable group
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