Journal of Cancer Therapy, 2009, 1, 36-46
Published Online September 2009 in SciRes (www.SciRP.org/journal/cancer)
The Role of Reaction Engineering in Cancer Biology:
Bio-Imaging Informatics Reveals Implications of the
Plasma Membrane Heterogeneities
ABSTRACT
Recent developments in microscopy have led to revolutionary advances in our knowledge of the spatiotemporal dynam-
ics of proteins in the plasma membrane of living cells and of heterogeneity of the plasma membrane. For example, spa-
tial heterogeneities in the epidermal growth factor (EGF) receptor (EGFR) distribution in different domains of the
plasma membrane are becoming increasingly evident. However, the influence of these heterogeneities on cellular sig-
naling remains elusive despite uncontrolled receptor signaling being implicated in various forms of cancer. Herein, we
suggest a reaction engineering, multiscale simulation framework, coined as model based bio-imaging informatics. This
framework can fill in the scales’ gap between various experimental methods and analyze the wealth of image informat-
ics to unravel the influence of plasma membrane heterogeneities on the early events of the EGFR signaling, namely
EGF binding and EGFR dimerization. An overarching conclusion arising from our work is that the plasma membrane
heterogeneities can strongly modulate the amount as well the mechanism of ligand–receptor binding.
Keywords: multiscale modeling, kinetic monte carlo, receptors, diffusion, imaging, informatics, cancer
1. Introduction
The ErbB family of receptors triggers a rich network of
signaling pathways and regulate cellular functions, such
as proliferation, differentiation, and migration (Holbro
and Hynes, 2004; Yarden and Sliwkowski, 2001). In
higher vertebrates, the ErbB family of receptors consists
of four members: epidermal growth factor (EGF) receptor
(EGFR)/ErbB1/HER1, ErbB2/Neu/HER2, ErbB3/HER3,
and ErbB4/HER4. A large number of studies have fo-
cused on the ErbB signaling network, not only because of
their involvement in a variety of cellular processes, but
also due to their role in a variety of human cancers
(Yarden and Sliwkowski, 2001). Cancer appears as a
tumor made up of a mass of cells as a result of uncon-
trolled signaling, in particular the signaling initiated by
the ErbB family of receptors (Herbst, 2004; Holbro and
Hynes, 2004; Normanno et al., 2006; Yarden and Sli-
wkowski, 2001).
Since EGF binding represents the initial step for acti-
vating EGFR, considerable work has been devoted to
elucidating the mechanisms of EGF binding and EGFR
dimerization (Jorissen et al., 2003; Klein etal., 2004;
Lemmon et al., 1997; Sako et al., 2000; Schlessinger,
1986;Wiley, 1988;Wiley et al., 2003). A part from in
vitro biochemical experiments to study the mechanisms
of the EGFR activation (Jorissen et al., 2003), recent de-
velopments in microscopy have made it possible to visu-
alize protein dynamics in living cells (Weijer, 2003).
These developments have led to revolutionary advances
in our knowledge of the spatiotemporal dynamics of pro-
teins in the plasma membrane (Kusumi et al., 2005; Par-
ton and Hancock, 2004).
Over 30 years ago, the two-dimensional continuum
fluid mosaic model of the plasma membrane was pro-
posed by Singer and Nicolson (1972). The model de-
scribed the plasma membrane as a two-dimensional ori-
ented solution of integral proteins in the viscous phos-
pholipid bilayer. However,recent experimental data using
fluorescence recovery after photobleaching (FRAP), sin-
gle particle tracking, and optical laser trap methods sug-
gest that the membrane proteins do not randomly diffuse
in the plasma membrane (Jacobson et al., 1995; Kusumi
et al., 2005) as thought previously. In contrast, a new
model suggesting a compartmental picture of the plasma
membrane is emerging. Several studies have indicated
inhomogeneities in the plasma membrane and excellent
reviews have been published on this topic including Ku- ∗ Corresponding author. Tel.: [phone]; fax: [phone].

The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma 37
Membrane Heterogeneities
sumi et al. (2005), Kusumi and Sako (1996), Laude and
Prior (2004), Parton and Hancock (2004), and Vereb et al.
(2003). These studies have suggested localization of re-
ceptors within small regions, called microdomains, of the
plasma membrane. In this picture, membrane proteins,
such as EGFR, are confined in these microdomains and
exhibit different spatial properties in terms of local EGFR
density and local EGFR diffusivity (Murakoshi et al.,
2004; Murase et al., 2004; Vereb et al., 2003; Wilson et
al., 2004). Several studies have indicated that the lipid
rafts and other cholesterol-rich regions of the plasma
membrane can provide a localization platform to EGFR
(Pike, 2003; Roy and Wrana, 2005).
While an increasing number of experimental studies
are providing evidence of spatial heterogeneities of the
plasma membrane itself and of the EGFR distribution
(Kusumi et al., 2005; Laude and Prior, 2004; Lommerse
et al., 2004; Maxfield, 2002; Pike, 2003; Wilson et al.,
2004), the influence of these heterogeneities on cellular
signaling remains elusive. Despite computational efforts
to model ligand dynamics, receptor dynamics, and re-
ceptor trafficking (see Goldstein et al., 2004; Haugh,
2002; Kholodenko, 2006; Lauffenburger and Linderman,
1993; Mayawala et al., 2006; Monine et al., 2005; Mon-
ine and Haugh, 2005; Pribyl et al., 2003; Shvartsman et
al., 2004; Woolf and Linderman, 2003 and references
therein), only a few efforts, to the best of our knowledge,
have considered the influence of plasma membrane het-
erogeneities on EGFR signaling; see Mayawala et al.
(2005a,b) and Mayawala et al. (2006) and references
therein. More importantly, the wealth of information pro-
vided from modern imaging techniques has not yet been
analyzed in a quantitative manner.
In this paper, we propose a reaction engineering based
computational framework for the integration of bio-
chemical and imaging experimental data. Our focus is to
analyze the influence of plasma membrane heterogenei-
ties on the early events of the EGFR signaling, namely
Figure 1. Reactions of EGF binding and EGFR dimerization.
Reprinted by permission of Federation of the European
Biochemical Societies from Mayawala et al. (2005a), copy-
right 2005.
EGF binding and EGFR dimerization, by providing an
overview of our recent work. The organization of this
paper is as follows. First, an equilibrium model is em-
ployed to examine the effect of plasma membrane etero-
geneity on the uptake data of the ligand on the receptor.
Next, dynamic models are discussed. A simple criterion
is proposed to delineate whether one should use
well-mixed vs. distributed models and continuum vs.
discrete models. The first comparison to single particle
experimental data is presented. Finally, conclusions are
drawn.
2. Model Based Bio-Imaging Informatics: A
Framework for Integrating and Analyzing
Experimental Data
The EGF–EGFR reaction network is shown in Figure 1.
The network entails (i) binding (adsorption) to and de-
tachment (desorption) of ligand (L) on free or unbound
receptors (R), and their dimers (RR and RRL), (ii)
dimerization reactions between receptors and their re-
ver-se, and (iii) diffusion of receptors and their dimers
within the plasma membrane. Note that part of the recep-
tor is in the extracellular medium, part in the intracellular
medium, and the rest within the membrane. These reac-
tion–diffusion processes are typical of catalytic reactions
and more generally of reaction engineering, and applica-
tion of such models to biological systems can be invalu-
able.
The reaction network involves processes occurring on
a wide range of time and length scales, as shown in Fig-
ure 2. The disparity in time scales is due to a wide range
of reaction rate constants and diffusion. For the latter,
there is a characteristic microscopic time scale for diffu-
sion from one site to the next (as the receptors exchange
positions with the lipids of the membrane, Eisinger et al.,
1986). This exchange process results in diffusivity values,
which are much lower than those encountered in solution
and are more reminiscent of the values of activated sur-
face diffusion on catalysts. Furthermore, there is a mac-
roscopic time scale determined from the distance between
receptors and the microscopic diffusion time scale. This
macroscopic time scale can be much larger than the mi-
croscopic one due to the very low density of receptors on
the plasma membrane. This point is further elaborated
below. The length scale disparity arises from the differ-
ence in the size of a receptor (～1-10 nm in diameter)
and the size of the cell (～10-50 μm in diameter). Such
disparity in length and time scales seriously plagues both
experimental and first-principles modeling efforts.
More traditional imaging methods, such as electron
microscopy (EM) experiments using immunogold label-
ing (Miller et al., 1986; Vanbelzen et al., 1988) and co-
valent linking to chemical conjugates like ferritin
(Haigler et al., 1979), have a high spatial resolution but

38 The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma
Membrane
Heterogeneities
Figure 2. Length and time scales involved in the cell surface events of the EGFR signaling. Multiple length and time scales of
the system make conventional Monte Carlo algorithms for spatiotemporal modeling highly inefficient.
Figure 3. A time-length scale graph of the proposed approach of bio-imaging informatics. Computational integration of low
spatial and temporal resolution biochemical data with high temporal resolution (single particle tracking e.g., Sako et al., 2000)
and high spatial resolution (electron microscopy, e.g., Vanbelzen et al., 1988) imaging data. The images of the single particle
tracking and electron microscopy have been reprinted by permission from the Macmillan Publishers Ltd: Nature Cell Biol-
ogy (Sako et al., 2000), copyright 2000, and the Rockefeller University Press: Journal of Cell Biology (Miller et al., 1986),
copyright 1986.
no dynamics information (see Figure 3). Recently intro-
duced imaging methods, such as fluorescence confocal
microscopy (Verveer et al., 2000), single particle track-
ing. (Sako et al., 2000), and quantum dot based ligands

The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma 39
Membrane Heterogeneities
(Lidke et al., 2004), have high temporal resolution but a
relatively low spatial resolution (of the order of ～ 0.2-
0.5μm), as shown in Figure 3, due to their optical nature.
These methods exhibit high sensitivity, i.e., one can vi-
sualize individual proteins in a spot, but it is not unam-
biguously clear when many proteins are nearby. As a
result, available imaging technologies do not allow si-
multaneous high temporal and spatial resolution of mul-
tiple receptors. Traditional in vitro experimental tech-
niques (see Figure 3) provide no spatial information (they
typically give spatial average and often population aver-
age, i.e., over multiple cells, coarse-grained data). At the
same time, such experiments are relatively easy to con-
duct, and have been and will continue to be the backbone
of biochemical experimentation.
The above comments underscore the fact that currently
there is not a single experimental technique that simulta-
neously spans all length and time scales. Yet, imaging
provides a wealth of spatial and/or temporal informatics
at intermediate or mesoscopic length and time scales.
Unfortunately, all this information is difficult to interpret
using Qualitative models. The application of chemical
engineering principles can be invaluable in extracting
quantitative information to better elucidate the mecha-
nisms by which plasma membranes behave.
While further advances in experimentation should be
expected in the future, the aforementioned experimental
limitation creates a true opportunity for the emerging
field of multiscale modeling that links models at various
scales (Vlachos, 2005). To integrate these imaging data
along with biochemical data, we propose an approach,
coined as model based bio-imaging informatics, which is
depicted in Figure 3. We propose that multiscale models
could be used to fill in the scales’ gap between the vari-
ous experimental methods and integrate multiple experi-
mental data with the objective of understanding signaling,
reconciling various experimental data, and eventually
proposing experiments and increasing our understanding
of cancer. Some of these efforts of our group are re-
viewed below.
A natural question raised is which are the suitable
scales and corresponding models of the multiscale ladder
for studying plasma membrane phenomena. In vivo mi-
croscopy emphasizes the need for computational tools
that at least consider spatial heterogeneity. A patch model
(reminiscent of adsorption in heterogeneous adsorbates
and catalysts) is the simplest approach that can account
for spatial heterogeneity and is discussed in the next sec-
tion. Single molecule imaging points to the need for dis-
crete rather than the traditional continuum and often
well-mixed representation. Furthermore, the spatial het-
erogeneity of the plasma membrane and of the proteins
(e.g., cluster formation at longer times, uphill diffusion,
etc., which are not further discussed here) underscores
the possible inability of continuum spatial models, such
as reaction–diffusion models, for quantitative modeling
of these phenomena. Therefore, the most suitable ap-
proach for modeling mesoscopic scale phenomena in the
plasma membrane is a kinetic Monte Carlo (KMC) tool
(Chatterjee et al., 2004). This method has successfully
been used in catalysis since the 1980s (Ziff et al., 1986)
and provided insights into spatial correlations, fluctua-
tions, and phase transitions. However, direct application
of KMC simulation to biological systems is impractical.
We elaborate on this important issue next. We return to
the suitability of various kinetics-transport models later.
Extension of mesoscale models to smaller and larger
scales is obviously very important and should be consid-
ered in future work.
2.1. Spatial KMC Mesoscopic Simulation
Stochastic simulation of reaction–diffusion systems is
one of the most detailed but also most expensive
mesoscopic tools for studying surface phenomena (Chat-
terjee et al., 2004). It can be computationally prohibitive
with biologically relevant parameters, as indicated in
Figure 2, due to the large disparity in length and time
scales. As a result, most biological simulations have em-
ployed only a very small number of reactions (this is in
contrast to the combinatorial explosion of actual prob-
lems) and parameters of comparable magnitude only.
One of the major factors contributing to the high compu-
tational cost arises from the low density of receptors
making the macroscopic time scale for diffusion long
(this is a relatively unique feature of biological systems).
Furthermore, the separation of reaction time scales, a
phenomenon known as stiffness, plagues traditional
KMC simulation. The execution of one event at a time
(instead of simultaneously advancing all species) is an-
other obstacle of KMC. Finally, efficient implementation
(search and update) strategies can substantially affect
computational speed and programming ease. Recent ap-
proaches on acceleratedKMC methods hold promise for
overcoming these challenges. These efforts, by our group
and others, are reviewed in Chatterjee and Vlachos (2007)
and Vlachos (2005) and will not be repeated here.
Some comments regarding algorithmic implementation
are worth discussing briefly. Two main approaches for
spatial KMC implementation are the null-event and the
rejection-free algorithms (Chatterjee and Vlachos, 2007;
Reese et al., 2001). In this work, we selected the
null-event KMC algorithm mainly due to its implementa-
tion ease, and devised an improvement to handle the low
density of receptors (a hybrid null-event algorithm). In
the traditional null-event algorithm (e.g., Reese et al.,
2001; Ziff et al., 1986), a site is randomly picked. If the
selected site is occupied, then the transition rates of all
the microprocesses that can occur on the selected site are
computed. The transition rates are normalized with a
predefined maximum transition rate to calculate prob-
abilities. Based on these probabilities, a microprocess
may or may not (null-event) be selected to occur. At low
receptor densities, the null-event algorithm is computa-
tionally intensive because low density implies a large

The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma 40
Membrane Heterogeneities
probability of null events by mostly picking empty sites
of the lattice.
In our hybrid null-event algorithm, instead of ran-
domly picking lattice sites, we randomly pick only
among the occupied sites by simply tracking the occupied
sites. This is then a hybrid approach that combines the
ease of implementation of a null-event algorithm with the
success rate of a rejection-free algorithm. Corresponding
to typical densities encountered for receptors in the
plasma membrane, Figure 4 shows that this modification
can lead to over four orders of magnitude speed
up,depending on receptor density, over the conventional
null-event KMC method. This point illustrates that even
small algorithmic improvements can have a tremendous
impact on our ability to model biological systems.
3. An Equilibrium Model to Integrate Bio-
chemical and Electron Microscopy Data
Recently, we analyzed the influence of the plasma mem-
brane heterogeneities on the EGF binding to EGFR by a
loose integration of electron microscopy data and bio-
chemical data using a very simple equilibrium model
(Mayawala et al., 2005a). The Scatchard method (briefly
mentioned in Appendix A) has extensively been used to
analyze the experimental data of equilibrium EGF bind-
ing to EGFR (Klein et al., 2004;Wofsy and Goldstein,
1992; Wofsy et al., 1992; Zidovetzki et al., 1991). In a
simplistic way, the Scatchard equation, similar to the
well-known Langmuir isotherm for adsorption of species
on solid catalysts, describes the isotherm of ligand bind-
ing to receptors by appropriately linearizing the equation.
The data show a concaveup shape, as shown in Figure 5,
in contrast to the concave-down shape predicted using
typical equilibrium constants (Wofsy et al., 1992). While
several studies have provided arguments to explain the
concave-up shape, the mechanism responsible for the
concave-up nature has been a controversial issue for over
a decade (Chamberlin and Davies, 1998; Holbrook et al.,
2000; Klein et al., 2004; Wofsy and Goldstein, 1992).
Motivated by electron microscopy and biochemical data,
we hypothesized that heterogeneity in the local density of
the EGFR, due to localization in certain regions of the
plasma membrane, can lead to a concave-up Scatchard
plot of the EGF/EGFR system. In general, there can be
multiple domains with multiple receptor densities. Our
model assumed a simplified representation of the receptor
density heterogeneity by dividing the plasma membrane
into two domains of different receptor densities (a simple
two patch model). The total binding was calculated as the
binding in low- and high-density regions.
We compared the heterogeneous receptor density
model with the experimental data of EGF binding to
EGFR in A-431 cells. Figure 5 compares the fitted het
erogeneous receptor density model with the experimental
data of Zidovetzki et al. (1991). Fairly good agreement is
seen. At low EGF concentrations, binding takes place
predominantly in the high EGFR density regions because
Figure 4. The Scatchard plot: comparison of the heteroge-
neous receptor density model against experimental data
(Zidovetzki et al., 1991). The equilibrium parameters are:
K1 = 2.19M−1, K2 =1.02×103 M−1,K3 =4.77×105 M−1,K4
=6×106 M−1,K5 =K6 = 2.8 × 109 M−1. Reprinted by permis-
sion of Federation of the European Biochemical Societies
from Mayawala et al. (2005a), copyright 2005.
Figure 5. Comparison of CPU (min) of null-event KMC and
hybrid null-event KMC algorithms on a 600 × 600 lattice at
five different low densities for executing 4×105 collisions.
Density indicates the surface coverage. The values for
null-event KMC were calculated for 400 collisions and then
scaled for 4×105 collisions. The top curve shows that simu-
lation of low receptor density systems is impractical using
the conventional null-event KMC algorithm. The curves
show CPU savings of ～ 30, 000 (at the lowest density of
0.004%) to 800 (at the highest density shown of 0.11%). For
each data point, 10 simulations with different seeds of the
random number generator were used to collect statistics.
Simulations were performed on an AMD_ 2000+ MP proc-
essor.
of the presence of more predimerized EGFR. As the
concentration of the EGF increases, the high-density re-

The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma 41
Membrane Heterogeneities
gions get saturated and binding takes place in low-density
regions, containing mainly EGFR monomers.
The data were fitted assuming a localization of ～14%
of the EGFR in 0.17% of the plasma membrane. These
numbers are not unique and depend on the equilibrium
constants (which have not been determined based on a
heterogeneous model). The suggested extent of localiza-
tion lies, at least qualitatively, in the range suggested by
biochemical and electron microscopy studies. More im-
portant than the specific numbers is that it was found that
the concave-up shape is preserved over a wide range of
localization as well as equilibrium parameters (Mayawala
et al., 2005a). In future work, we propose obtaining mi-
croscopy data to characterize the effect of heterogeneity
of the plasma membrane and receptor density in micro-
domains and extract equilibrium constants from the
Scatchard plot, i.e., to carry out the analysis in the reverse
way from what we have done so far to obtain intrinsic
equilibrium constants.
This first computational analysis highlights the influe-
nce of the plasma membrane heterogeneity on EGFR
signaling, and serves as a motivation for further kinet-
ics-transport analysis discussed next.
4. Dynamic Modeling
4.1. Choosing a Suitable Mesoscopic Model
As alluded to above and further discussed in Chatterjee et
al. (2004) and Vlachos (2007), at each scale there is a
hierarchy of models, which vary in complexity, computa-
tional cost, and accuracy. It is therefore important to de-
velop simple criteria that can guide model selection
within a scale to strike a balance between accuracy and
computational cost. With this as a motivation, in this sec-
tion first we assess the importance of spatial phenomena
and then we evaluate the accuracy of partial differential
equations (PDEs) in transient situations (e.g., upon an
extracellular stimulation via exposure of cells to ligand)
when spatial effects are important.
In order to evaluate the importance of spatial effects on
overall kinetics in two-dimensional bimolecular reactions
a priori (i.e., without performing spatial simulations), we
have assessed the applicability of the second Damkohler
number (D a), defined here as the ratio of time scales of
collision between receptors and reaction. For a bimol-
ecular (dimerization) reaction A + B → AB, using the
mean-field approximation, the Da number can be defined
as (Mayawala et al., 2006)
f
AB
k
sD
eventreactionofscaletime
eventcollisionofscaletime
Da /1
/4/1 2
 =
AB
Arealf
D
k
4
, (1)
Figure 6. (a) ABA /


VS. BA


for Da numbers in the
range of 0.025–25 and an initial receptor coverage of
02.0
00


BA


(subscript 0 denotes initial conditions).
ABA /


=BA


follows the diagonal. (b) Comparison of
effective rate constant vs. time, obtained using the spatial
KMC and two simple PDE models, for three different initial
coverages and Da = 2.5. Curves represent the mean of 30
concentration profiles obtained using different random
number seeds. Reprinted with permission from Elsevier
from Biophysical Chemistry (Mayawala et al., 2006).
where DAB = DA + DB, DA and DB are the diffusivities of A
and B, respectively, kf and kf,Areal are the intrinsic reaction
rate constants for a bimolecular reaction between A and B
in units of (receptors/site)-1 s-1 and (receptors/area)-1 s-1, a-
nd s is the encounter radius. kf and kf , Areal are related usi-
ng the encounter radius, as follows:
2
kskAreal  (2)
To test the Da number criterion and ensure the lack of

The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma 42
Membrane Heterogeneities
finite size effects, spatial KMC simulations were perfor-
med, described in Mayawala et al. (2005b, 2006).
Let i

be the coverage of species i and AB /

be the
conditional probability of picking B given that the first
chosen site is occupied by A. When spatial correlations
are unimportant, then BAABA





/, and the dynamics
can be described using a well-mixed model. Deviations
from BAABA





/ provide a measure of the impor-
tance of spatial correlation effects.
Figure 6(a) compares ABA /


VS. BA


for an initial
density of 0.02 for both A and B, and Da numbers in the
range of 0.025–25. For a low value of Da=0.025,
ABA /


=BA


is indicative of a well-mixed situation.
An increase in the Da number leads to inability of diffu-
sion to homogenize spatial correlations (Vlachos, 2005).
In the receptor density range of interest (102-105 receptors
per μm2), we have found that dimerization reactions in
the plasma membrane with Da >
～0.1 require spatial
modeling (Mayawala et al., 2006). This criterion, based
on a standard dimensionless group, indicates that the
separation of time scales between diffusion and reaction
can be an efficient means of deciding whether a
well-mixed or a spatially distributed model should be
chosen.
Since PDE models could be used for spatial modeling,
next we have investigated differences between PDE and
KMC predictions. Two simple analytical PDE models
were used. First a quasi-steady state model by Lauffen-
burger and Linderman (1993) and second a transient
model by Torney and McConnell (1983) (for details see
Mayawala et al., 2006). Fig. 6(b) shows up to two orders
of magnitude difference in the transient effective reaction
rate constant of a bimolecular activation between simple
PDEs and spatial KMC. Furthermore, this simulation
indicates that the effective reaction rate constant depends
on initial conditions (e.g., cluster density) and plasma
membrane heterogeneity (e.g., different density of recep-
tors in various microdomains). Thus, estimation of intrin-
sic parameters from experimental data should pay par-
ticular attention to these issues.
This comparison shows that a spatial KMC model is
needed to capture the creation of a spatially non-random
distribution of proteins due to bimolecular reactions.
Furthermore, a spatial KMC model can also easily con-
sider the spatial heterogeneity of the plasma membrane
due to microdomains, and the noise resulting from a
small number of copies of activated receptors. Thus, the
KMC method is a natural framework for mesoscopic
modeling of biological phenomena on the plasma mem-
brane when spatial effects are deduced to be important.
4.2. Kinetic Modeling of the EGFR Dimerization
and the EGF Binding
The EGF binding can take place with three different re-
action paths. Path 1 (reactions 1, 5, and 6; see Figure 1)
Figure 7. (a) Evolution of high intensity spots representing
(EGF.EGFR)2 and low intensity spots representing
EGF.EGFR+EGF. (EGFR)2 obtained using our simulations
along with the data of single particle tracking experiments
by Sako et al. The simulations were performed for a recep-
tor number density of 5500 per _m2 and 18% dimers ini-
tially. The simulation intensity has been normalized with the
experimental data. © 2005 from Mayawala et al.; licensee
BioMed Central Ltd. (b) Contributions of the different re-
action mechanisms at 60 s as a function of EGF concentra-
tion with a receptor number density of 5500 and 125 recep-
tors per _m2. The bars indicate the mean obtained from 10
independent KMC simulations.
entails dimerization of unbound receptors followed by
ligand binding. Path 2 (reactions 4, 2, and 6; see Figure 1)
entails dimerization of an unbound and a bound receptor
followed by ligand binding. Sequence 3 (reactions 4 and
3; see Figure 1) entails dimerization of bound receptors.
Recently, we analyzed the relative contribution of these
paths in EGFR dimerization (Mayawala et al., 2005b).
Details on simulation size and model parameters are
given in Appendix B. Corresponding to the EGFR
dimerization events, the Da number ranges between 10-4
and 1.

The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma 43
Membrane Heterogeneities
The dynamics of the ligand binding events were com-
pared with the single particle tracking experiment of
Sako et al. (2000) at a low EGF concentration of 0.16nM
in the 0.60 s time interval as shown in Figure 7(a). The
predicted increase of low intensity spots, representing
monomers plus dimers having one EGF bound, and high
intensity spots, representing EGFR dimer with two EGF
molecules, is qualitatively consistent with the experi-
mental data. In agreement with the experiments of Sako
et al. (2000), path 1 was found to be dominant, contrib-
uting 95–100% in the formation of the bound–unbound
receptor (EGF.EGFR)2. This comparison serves as a
model validation step.
Single particle tracking experiments are typically lim-
ited to low ligand concentrations (Sako et al., 2000).
High concentration of ligand would lead to fluorescence
of a large number of EGFRs making it impossible to
visualize individual particles. However, simulations can
be used to overcome the limitation. Our simulations in
dicate that the relative contributions of paths 1–3 at 60 s
change with ligand concentration (see Figure 7(b)). At
low ligand concentration, path 1 dominates, whereas at
higher ligand concentration, a significant fraction of
dimers form via path 2 as well as path 3. At low ligand
concentration, most of the ligand binds to predimerized
receptors with higher affinity; however, the extent to
which free EGFR dimerization can occur is limited due to
the low affinity of free EGFR dimerization. At higher
ligand concentration, at least one of the dimerization
partners is ligand bound.
The receptor density can also significantly influence
the mechanism of EGF binding as shown in Figure 7(b).
For a low receptor density of 125 receptors per μm2, at
lower EGF concentration path 2 is dominant, whereas at
higher EGF concentration, path 3 is dominant. Path 1 is
not important at low receptor density because of the low
or negligible amount of predimerized EGFR.
Next, we analyzed the influence of spatial inhomoge-
neitiesn on the dynamics of receptor dimerization as de-
scribed in Mayawala et al. (2006) using a reversible
dimerization reaction A + B → AB. This reaction can
represent EGFR dimerization between bound and un-
bound receptors or heterodimerization between two
members of the ErBb family. We considered changes in
EGFR density, due to different cell lines as well as due to
localization, and in EGFR diffusivity. The variations in
Da number in Figure 8 capture different reaction rate
constants of different dimerization reactions shown in
Figure 1, and different diffusivities, e.g., the highest Da
number corresponds to fast dimerization of ligand bound
monomer EGFR in the plasma membrane microdomains
with reduced mobility.
Figure 8 shows that the diffusion limitation can sig-
nificantly lower the dimerization rate in cell lines with a
normal density as well as higher density (e.g., human
A-431 epidermoid carcinoma cells) of EGFR. For normal
cells, even a 100-fold higher density results in only ～
2.3-fold increase in the diffusion limited dimerization
rates (compare bottom and middle curves in Figure 8).
This indicates that localization is unlikely to cause a sig-
nificant increase in diffusion limited EGFR dimerization
rates in normal cells. However, comparison of the middle
and top curves in Figure 8 shows that in A-431 cells, only
a 10-fold higher density leads to 1–2 orders of magnitude
increase in the dimerization rate, suggesting that the
dimerization rate is greatly enhanced due to localization.
Obviously, this is a simple reaction network but illus-
trates the potential effect of spatial heterogeneity on sig-
naling; more work is needed to exploit these effects in the
full reaction–diffusion network of EGF–EGFR and other
receptors. Future study is also needed to explicitly link
these observations to their effect on intracellular signal-
ing events.
5. Conclusions
This work proposes that multiscale modeling can be in-
dispensable in filling the gap between various imaging
and biochemical methods. Multiscale modeling can capi-
talize on the imaging informatics and provide unprece-
dented quantitative understanding of biological phenom-
ena. Our initial work, reviewed in this paper, has al-
readyunderscored the importance of plasma membrane
hetero geneities on the EGF binding and the EGFR
dimerization. Our work serves as a proof of concept of
the feasibility of such simulations despite the disparity in
scales and toreconcile apparent discrepancies between in
vitro and in vivo experiments (e.g., on the cooperativity
of the ligand binding). Obviously, the success of our
model does not prove its correctness. Rather, the conclu-
sions of this paper serve as hypotheses for future experi-
ments. Such iterative approaches have been discussed in
Aldridge et al. (2006) and Ma’ayan et al. (2005). For
example, based on our equilibrium calculations, a future
experiment could entail change of the cholesterol levels
in the plasma membrane to observe its effect on the
Scatchard plot. Experimental protocols for changing
cholesterol levels have previously been developed (Pike,
2003). If the plasma membrane heterogeneities influence
the EGF binding, then changing the cholesterol levels
should change the distribution of the EGFR, leading to a
possible shape change of the Scatchard plot. It is typi-
cally from a disagreement between model predictions and
ex perimental data where one learns the most. Work
along these lines is in progress.
6. Acknowledgments
This work was supported by grants from the US Depart-
ment of Energy (DE-FG02-05ER25702) and the National
Science Foundation (CTS-0343757).We are than- kful to
Bridget S. Wilson (Department of Pathology, University
of New Mexico, Albuquerque, NM, USA) for providing
us the unpublished electron microscopy image.

The Role of Reaction Engineering in Cancer Biology: Bio-Imaging Informatics Reveals Implications of the Plasma 44
Membrane Heterogeneities
Figure 8. Effectiveness factor as a function of Da number
calculated at 33% of the equilibrium concentration of the
dimer produced from the reversible dimerization reaction
between EGFR. Different dimerization events shown in
Figure 1(a) are described by different Da number. Different
diffusivities in different microdomains on the plasma mem-
brane also contribute to Da number variation. The densities
reported on the plot are the initial densities. The bottom
curve is representative of an average EGF receptor density
in typical normal cells, the middle curve of localization in
normal cells and of an average EGF receptor density in
cancer cells, and the top curve of localization in cancer cells.
The points represent the mean of 30 concentration profiles
obtained using different random number seeds and the lines
just connect the points. Reprinted with permission from
Elsevier from Biophysical Chemistry (Mayawala et al.,
2006).
7. Appendix A. The Scatchard Method
The Scatchard method involves a transformation of
ligand–receptor binding data (an isotherm) such that the
ratio of bound receptor (B) to free ligand (L) concentrate-
ion when plotted as a function of bound ligand concent-
ration gives a linear relation with a slope of .Ka (associa-
tion constant) and an intercept as the total density of sites
RT (in the same units as B) (Scatchard, 1949),
Taa RKBK
L
B (A.1)
8. Appendix B. Simulation Size and Model
Parameters for KMC Simulations
The cell surface was represented using a two-d imen-
sional square lattice with each pixel of 2 nm × 2 nm in
size. The number density of receptors ranges from ～102
receptors per μm2 on normal cells (Benveniste et al., 1988)
to ～103 receptors per μm2 on A-431 cells which over-
express EGFR (Wiley, 1988). However, the local density
of receptors can be much higher in vivo because of the
localization of receptors in certain regions of the plasma
membrane, such as in lipid rafts (Laude and Prior, 2004;
Pike, 2003; Simons and Toomre, 2000). To represent
normal cells with 125 receptors per μm2, we simulated a
low density of 31 receptors on a 500 nm × 500 nm mesh,
and to represent A-431 cells with 5500 receptors per μm2,
55 receptors were randomly placed on a 100 nm×100 nm
mesh. The diffusivity of monomer EGFR has been re-
ported to be around 2 × 10-14 m2 s-1 (Kusumi et al., 1993;
Rees et al., 1984). The model parameters are summarized
in Mayawala et al. (2005b). We assumed two types of
EGF binding on the cell surface: low affinity binding on
monomer EGFR and high affinity binding on dimerized
EGFR.
Based on experimental studies (Gadella and Jovin,
1995; Martin-Fernandez et al., 2002; Moriki et al., 2001;
Vanbelzen et al., 1988; Yu et al., 2002), a fraction (～
18%) of receptors was initially placed at random loca-
tions as dimers on simulated A-431 cells. Corresponding
to the dimerization equilibrium constant for these data,
there is a negligible number of dimers in the absence of
ligand at a density of 125 receptors per μm2. The receptor
dimerization constants vary with ligand occupancy. Sev-
eral experimental studies have shown that dimerization
occurs with higher affinity if at least one of the receptors
is ligand bound. Finally, the highest affinity has been
suggested for dimerization between two ligand bounded
receptors (Lemmon et al., 1997; Sherrill and Kyte, 1996).
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