add start of raphael changes

diff --git a/kinetic_formalism_competition.Rnw b/kinetic_formalism_competition.Rnw
index fbc030795ea1dc436e18fdd9777778c6b67a956d..2a47cf45e9154e5c6ea02824029f3d195a925c38 100644 (file)
--- a/kinetic_formalism_competition.Rnw
+++ b/kinetic_formalism_competition.Rnw
@@ -120,7 +120,7 @@ to.kcal <- function(k,temp=300) {
 % double check this with the bits in the paper
 
 For a system with monomers $(_\mathrm{monomer})$ and a vesicle
 % double check this with the bits in the paper
 
 For a system with monomers $(_\mathrm{monomer})$ and a vesicle

-$(_\mathrm{vesicle})$, the change in composition of the $i$th component of
+$(_\mathrm{vesicle})$, the change in concentration of the $i$th component of

 a lipid vesicle per change in time ($d \left[C_{i_\mathrm{vesicle}}\right]/dt$)
 can be described by a modification of the basic mass action law:
 
 a lipid vesicle per change in time ($d \left[C_{i_\mathrm{vesicle}}\right]/dt$)
 can be described by a modification of the basic mass action law:
 


@@ -541,7 +541,7 @@ unsaturated and saturated lipids forming heterogeneous domains. Void
 formation is increased when the unsaturation of lipids in the vesicle
 is widely distributed; in other words, the insertion of lipids into
 the membrane is greater when the standard deviation of the
 formation is increased when the unsaturation of lipids in the vesicle
 is widely distributed; in other words, the insertion of lipids into
 the membrane is greater when the standard deviation of the

-unsaturation is larger %
+unsaturation is larger. %

 %%% \RZ{May need to site (at least for us) works showing
 %%%   mismatch-dependent ``defects''}. %
 Assuming that an increase in width of the distribution linearly
 %%% \RZ{May need to site (at least for us) works showing
 %%%   mismatch-dependent ``defects''}. %
 Assuming that an increase in width of the distribution linearly


@@ -808,7 +808,7 @@ reasonable base for $x$ is 2, leading to:
 \end{equation}
 
 The most common $\mathrm{stdev} l_\mathrm{vesicle}$ is around $3.4$, which leads to
 \end{equation}
 
 The most common $\mathrm{stdev} l_\mathrm{vesicle}$ is around $3.4$, which leads to

-a range of $\Delta \Delta G^\ddagger$ of
+a $\Delta \Delta G^\ddagger$ of

 $\Sexpr{format(digits=3,to.kcal(2^(3.4)))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$.
 
 $\Sexpr{format(digits=3,to.kcal(2^(3.4)))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$.
 


@@ -896,7 +896,7 @@ Just as the forward rate constant adjustment $k_{\mathrm{f}i\mathrm{adj}}$
 does, the backwards rate constant adjustment $k_{\mathrm{b}i\mathrm{adj}}$
 takes into account unsaturation ($un_\mathrm{b}$), charge ($ch_\mathrm{b}$), curvature
 ($cu_\mathrm{b}$), length ($l_\mathrm{b}$), and complex formation ($CF1_\mathrm{b}$), each of
 does, the backwards rate constant adjustment $k_{\mathrm{b}i\mathrm{adj}}$
 takes into account unsaturation ($un_\mathrm{b}$), charge ($ch_\mathrm{b}$), curvature
 ($cu_\mathrm{b}$), length ($l_\mathrm{b}$), and complex formation ($CF1_\mathrm{b}$), each of

-which are modified depending on the specific component and the vesicle
+which is modified depending on the specific component and the vesicle

 from which the component is exiting:
 
 
 from which the component is exiting:
 
 


@@ -992,10 +992,11 @@ popViewport(2)
 \end{figure}
 
 \subsubsection{Charge Backwards}
 \end{figure}
 
 \subsubsection{Charge Backwards}

-As in the case of monomers entering a vesicle, monomers leaving a
-vesicle leave faster if their charge has the same sign as the average
-charge vesicle. An equation of the form $ch_\mathrm{b} = a^{\left<ch_v\right>
-  ch_m}$ is then appropriate, and using a base of $a=20$ yields:
+As in the case of monomers entering a vesicle, opposites attract.
+Monomers leaving a vesicle leave faster if their charge has the same
+sign as the average charge vesicle. An equation of the form
+$ch_\mathrm{b} = a^{\left<ch_v\right> ch_m}$ is then appropriate, and
+using a base of $a=20$ yields:

 
 \begin{equation}
   ch_\mathrm{b} = 20^{\left<{ch}_v\right> {ch}_m}
 
 \begin{equation}
   ch_\mathrm{b} = 20^{\left<{ch}_v\right> {ch}_m}