X-Git-Url: https://git.donarmstrong.com/?a=blobdiff_plain;ds=inline;f=kinetic_formalism.Rnw;h=683f29f005d219f5b2ef1aefe360993ea98b0d42;hb=8bcb93ccb71a8a2f830c42cf1ae7408c42b5dc24;hp=018c44ee596c859699800a23997db37a72fb68bf;hpb=68e4c8689f9dbcf56ab9d6d0488c9a77e6df169d;p=ool%2Flipid_simulation_formalism.git diff --git a/kinetic_formalism.Rnw b/kinetic_formalism.Rnw index 018c44e..683f29f 100644 --- a/kinetic_formalism.Rnw +++ b/kinetic_formalism.Rnw @@ -62,16 +62,40 @@ <>= require(lattice) require(grid) +# R in cal / mol K +to.kcal <- function(k,temp=300) { + gasconst <- 1.985 + return(gasconst*temp*log(k)/1000) +} @ \section{State Equation} % double check this with the bits in the paper \begin{equation} - \frac{d C^{j}_{i_\mathrm{ves}}}{dt} = k_{fi}k_{fi\mathrm{adj}}\left[C^j_{i_\mathrm{monomer}}\right] - - k_{bi}k_{bi\mathrm{adj}}C^j_{i_\mathrm{ves}} + \frac{d C_{i_\mathrm{ves}}}{dt} = k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]S_\mathrm{ves} - + k_{bi}k_{bi\mathrm{adj}}C_{i_\mathrm{ves}} \label{eq:state} \end{equation} +For $k_{fi}k_{fi\mathrm{adj}}\left[C_{i_\mathrm{monomer}}\right]$, +$k_{fi}$ has units of $\frac{\mathrm{m}}{\mathrm{s}}$, +$k_{fi\mathrm{adj}}$ and $k_{bi\mathrm{adj}}$ are unitless, +concentration is in units of $\frac{\mathrm{n}}{\mathrm{L}}$, surface +area is in units of $\mathrm{m}^2$, $k_{bi}$ has units of +$\frac{1}{\mathrm{s}}$ and $C_{i_\mathrm{ves}}$ has units of +$\mathrm{n}$, Thus, we have + +\begin{equation} + \frac{\mathrm{n}}{\mathrm{s}} = \frac{\mathrm{m}}{\mathrm{s}} \frac{\mathrm{n}}{\mathrm{L}} \mathrm{m}^2 \frac{1000\mathrm{L}}{\mathrm{m}^3} - + \frac{1}{\mathrm{s}} \mathrm{n} + = + \frac{\mathrm{m^3}}{\mathrm{s}} \frac{\mathrm{n}}{\mathrm{L}} \frac{1000\mathrm{L}}{\mathrm{m}^3} - \frac{\mathrm{n}}{\mathrm{s}}= + \frac{\mathrm{n}}{\mathrm{s}} = 1000 \frac{\mathrm{n}}{\mathrm{s}} - \frac{\mathrm{n}}{\mathrm{s}} + \label{eq:state_units} +\end{equation} + +The 1000 isn't in \fref{eq:state} above, because it is unit-dependent. + \subsection{Forward adjustments ($k_{fi\mathrm{adj}}$)} \begin{equation} @@ -93,6 +117,14 @@ curve(2^x,from=0,to=sd(c(0,4)), ylab="Unsaturation Forward Adjustment") @ +<>= +curve(to.kcal(2^x),from=0,to=sd(c(0,4)), + main="Unsaturation forward", + xlab="Standard Deviation of Unsaturation of Vesicle", + ylab="Unsaturation Forward (k cal)") +@ + + \newpage \subsubsection{Charge Forward} \begin{equation} @@ -114,6 +146,21 @@ print(wireframe(z~x*y,grid,cuts=50, rm(x,y,grid) @ +<>= +x <- seq(-1,0,length.out=20) +y <- seq(-1,0,length.out=20) +grid <- expand.grid(x=x,y=y) +grid$z <- as.vector(to.kcal(60^(-outer(x,y)))) +print(wireframe(z~x*y,grid,cuts=50, + drape=TRUE, + scales=list(arrows=FALSE), + xlab=list("Average Vesicle Charge",rot=30), + ylab=list("Component Charge",rot=-35), + zlab=list("Charge Forward (k cal)",rot=93))) +rm(x,y,grid) +@ + + \newpage \subsubsection{Curvature Forward} \begin{equation} @@ -130,6 +177,16 @@ curve(10^x,from=0,to=max(c(sd(abs(log(c(0.8,1.33)))), ylab="Curvature Forward Adjustment") @ +<>= +curve(to.kcal(10^x),from=0,to=max(c(sd(abs(log(c(0.8,1.33)))), + sd(abs(log(c(1,1.33)))), + sd(abs(log(c(0.8,1)))))), + main="Curvature forward", + xlab="Standard Deviation of Absolute value of the Log of the Curvature of Vesicle", + ylab="Curvature Forward Adjustment (kcal)") +@ + + \newpage \subsubsection{Length Forward} \begin{equation} @@ -144,6 +201,14 @@ curve(3^x,from=0,to=sd(c(12,24)), ylab="Length Forward Adjustment") @ +<>= +curve(to.kcal(3^x),from=0,to=sd(c(12,24)), + main="Length forward", + xlab="Standard Deviation of Length of Vesicle", + ylab="Length Forward Adjustment (kcal)") +@ + + \subsubsection{Complex Formation} \begin{equation} CF1_f=1 @@ -160,7 +225,7 @@ curve(3^x,from=0,to=sd(c(12,24)), \newpage \subsubsection{Unsaturation Backward} \begin{equation} - un_b = 10^{\left|3.5^{-\left}-3.5^{-\left}\right|} + un_b = 10^{\left|3.5^{-\left}-3.5^{-un_\mathrm{monomer}}\right|} \label{eq:unsaturation_backward} \end{equation} @@ -177,6 +242,20 @@ print(wireframe(z~x*y,grid,cuts=50, rm(grid) @ +<>= +grid <- expand.grid(x=seq(0,4,length.out=20), + y=seq(0,4,length.out=20)) +grid$z <- to.kcal(10^(abs(3.5^-grid$x-3.5^-grid$y))) +print(wireframe(z~x*y,grid,cuts=50, + drape=TRUE, + scales=list(arrows=FALSE), + xlab=list("Average Vesicle Unsaturation",rot=30), + ylab=list("Monomer Unsaturation",rot=-35), + zlab=list("Unsaturation Backward (kcal)",rot=93))) +rm(grid) +@ + + \newpage \subsubsection{Charge Backwards} \begin{equation} @@ -198,10 +277,24 @@ print(wireframe(z~x*y,grid,cuts=50, rm(x,y,grid) @ +<>= +x <- seq(-1,0,length.out=20) +y <- seq(-1,0,length.out=20) +grid <- expand.grid(x=x,y=y) +grid$z <- to.kcal(as.vector(20^(outer(x,y)))) +print(wireframe(z~x*y,grid,cuts=50, + drape=TRUE, + scales=list(arrows=FALSE), + xlab=list("Average Vesicle Charge",rot=30), + ylab=list("Component Charge",rot=-35), + zlab=list("Charge Backwards (kcal)",rot=93))) +rm(x,y,grid) +@ + \newpage \subsubsection{Curvature Backwards} \begin{equation} - cu_f = 7^{1-\left(20\left(\log cu_\mathrm{vesicle}-\log cu_\mathrm{monomer}\right)^2+1\right)^{-1}} + cu_f = 7^{1-\left(20\left(\log_{e} cu_\mathrm{vesicle}-\log_{e} cu_\mathrm{monomer}\right)^2+1\right)^{-1}} \label{eq:curvature_backwards} \end{equation} @@ -218,6 +311,20 @@ print(wireframe(z~x*y,grid,cuts=50, rm(grid) @ +<>= +grid <- expand.grid(x=seq(0.8,1.33,length.out=20), + y=seq(0.8,1.33,length.out=20)) +grid$z <- to.kcal(7^(1-1/(20*(log(grid$x)-log(grid$y))^2+1))) +print(wireframe(z~x*y,grid,cuts=50, + drape=TRUE, + scales=list(arrows=FALSE), + xlab=list("Vesicle Curvature",rot=30), + ylab=list("Monomer Curvature",rot=-35), + zlab=list("Curvature Backward (kcal)",rot=93))) +rm(grid) +@ + + \newpage \subsubsection{Length Backwards} \begin{equation} @@ -238,6 +345,20 @@ print(wireframe(z~x*y,grid,cuts=50, rm(grid) @ +<>= +grid <- expand.grid(x=seq(12,24,length.out=20), + y=seq(12,24,length.out=20)) +grid$z <- to.kcal(3.2^(abs(grid$x-grid$y))) +print(wireframe(z~x*y,grid,cuts=50, + drape=TRUE, + scales=list(arrows=FALSE), + xlab=list("Average Vesicle Length",rot=30), + ylab=list("Monomer Length",rot=-35), + zlab=list("Length Backward (kcal)",rot=93))) +rm(grid) +@ + + \newpage \subsubsection{Complex Formation Backward} \begin{equation} @@ -258,6 +379,20 @@ print(wireframe(z~x*y,grid,cuts=50, rm(grid) @ +<>= +grid <- expand.grid(x=seq(-1,3,length.out=20), + y=seq(-1,3,length.out=20)) +grid$z <- to.kcal(3.2^(grid$x*grid$y-abs(grid$x*grid$y))) +print(wireframe(z~x*y,grid,cuts=50, + drape=TRUE, + scales=list(arrows=FALSE), + xlab=list("Vesicle Complex Formation",rot=30), + ylab=list("Monomer Complex Formation",rot=-35), + zlab=list("Complex Formation Backward (kcal)",rot=93))) +rm(grid) +@ + +