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
-$(_\mathrm{vesicle})$, 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:
 
@@ -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
-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
@@ -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
-a range of $\Delta \Delta G^\ddagger$ of
+a $\Delta \Delta G^\ddagger$ of
 $\Sexpr{format(digits=3,to.kcal(2^(3.4)))}
 \frac{\mathrm{kcal}}{\mathrm{mol}}$.
 
@@ -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
-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:
 
 
@@ -992,10 +992,11 @@ popViewport(2)
 \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}