--- trunk/mattDisertation/lipid.tex	2004/01/30 21:47:22	1000
+++ trunk/mattDisertation/lipid.tex	2004/01/31 22:10:21	1001
@@ -4,6 +4,64 @@
 
 \section{\label{lipidSec:Intro}Introduction}
 
+In the past 10 years, computer speeds have allowed for the atomistic
+simulation of phospholipid bilayers.  These simulations have ranged
+from simulation of the gel phase ($L_{\beta}$) of
+dipalmitoylphosphatidylcholine (DPPC), \cite{Lindahl:2000} to the
+spontaneous aggregation of DPPC molecules into fluid phase
+($L_{\alpha}$ bilayers. \cite{Marrinck:2001} With the exception of a
+few ambitious
+simulations,\cite{Marrinch:2001b,Marrinck:2002,Lindahl:2000} most
+investigations are limited to 64 to 256
+phospholipids.\cite{Lindal:2000,Sum:2003,Venable:2000,Gomez:2003,Smondyrev:1999,Marrinck:2001a}
+This is due to the expense of the computer calculations involved when
+performing these simulations.  To properly hydrate a bilayer, one
+typically needs 25 water molecules for every lipid, bringing the total
+number of atoms simulated to roughly 8,000 for a system of 64 DPPC
+molecules. Added to the difficluty is the electrostatic nature of the
+phospholipid head groups and water, requiring the computationally
+expensive Ewald sum or its slightly faster derivative particle mesh
+Ewald sum.\cite{Nina:2002,Norberg:2000,Patra:2003} These factors all
+limit the potential size and time lenghts of bilayer simulations.
+
+Unfortunately, much of biological interest happens on time and length
+scales unfeasible with current simulation. One such example is the
+observance of a ripple phase ($P_{\beta'}$) between the $L_{\beta}$
+and $L_{\alpha}$ phases of certain phospholipid
+bilayers.\cite{Katsaras:2000,Sengupta:2000} These ripples are shown to
+have periodicity on the order of 100-200~$\mbox{\AA}$. A simulation on
+this length scale would have approximately 1,300 lipid molecules with
+an additional 25 water molecules per lipid to fully solvate the
+bilayer. A simulation of this size is impractical with current
+atomistic models.
+
+Another class of simulations to consider, are those dealing with the
+diffusion of molecules through a bilayer.  Due to the fluid-like
+properties of a lipid membrane, not all diffusion across the membrane
+happens at pores.  Some molecules of interest may incorporate
+themselves directly into the membrane.  Once here, they may possess an
+appreciable waiting time (on the order of 10's to 100's of
+nanoseconds) within the bilayer.  Such long simulation times are
+difficulty to obtain when integrating the system with atomistic
+detail.
+
+Addressing these issues, several schemes have been proposed.  One
+approach by Goetz and Liposky\cite{Goetz:1998} is to model the entire
+system as Lennard-Jones spheres. Phospholipids are represented by
+chains of beads with the top most beads identified as the head
+atoms. Polar and non-polar interactions are mimicked through
+attractive and soft-repulsive potentials respectively.  A similar
+model proposed by Marrinck \emph{et. al.}\cite{Marrinck:2004}~ uses a
+similar technique for modeling polar and non-polar interactions with
+Lennard-Jones spheres. However, they also include charges on the head
+group spheres to mimic the electrostatic interactions of the
+bilayer. While the solvent spheres are kept charge-neutral and
+interact with the bilayer solely through an attractive Lennard-Jones
+potential.
+
+The model used in this investigation adds more information to the
+interactions than the previous two models,
+
 \section{\label{lipidSec:Methods}Methods}
 
 \subsection{\label{lipidSec:lipidMedel}The Lipid Model}