$2.$ Keep Calm and Carry On $(5$ pt$)$ Calmodulin is a monomeric protein that binds $2$ Calcium ions $\backslash (\backslash$left$(\backslash$mathrm$\{$Ca$\}^\{2+\}\backslash$right$)\backslash ).$ Calmodulin can adopt $2$ conformations: the "closed" conformation is favored when no Calcium is present, and the "open" conformation is favored when Calcium is bound. The picture at right shows calmodulin's structure in the absence $($closed$)$ and presence $($open$)$ of calcium $($yellow spheres$).$

$2\mathrm{.}1.$ Calculate approximately how many amino acids are found in the blue alpha helix noted with an arrow in the "open" structure.

$2\mathrm{.}2.$ Propose one specific way that calmodulin might bind to $\backslash (\backslash$mathrm$\{$Ca$\}^\{2+\}\backslash ),$ including the type of interactions and atoms involved.

$2\mathrm{.}3.$ In the absence of Calcium, the standard free energy difference between the open and closed states of calmodulin is $\backslash (-4\mathrm{.}4\backslash$mathrm$\{$~kJ$\}/\backslash$mathrm$\{$mol$\}\backslash ).$ Calculate the concentrations of closed and open forms of calmodulin under standard conditions in a $5$ mM solution: $[$open$]=[$closed$]\backslash (=\backslash )$

$2\mathrm{.}4.$ The graph at right shows data for calmodulin binding to Calcium.

Define $\backslash (\backslash$boldsymbol$\{\backslash$theta$\}\backslash )$ for this system:

Give the $\backslash (\backslash$mathrm$\{$K$\}\_\{\backslash$mathrm$\{$d$\}\}\backslash )$ value for calcium binding to calmodulin at pH $8$ :

$2\mathrm{.}5.$ Propose a model for calmodulin binding to $2$ calcium ions that accounts for all of the data given. You can use abbreviations or pictures; define your symbols.

$2\mathrm{.}6.$ How does increasing pH impact calmodulin binding to calcium? The affinity $($choose one$)$: increases $/$ decreases $/$ does not change. Propose a possible biochemical mechanism for this phenomenon.