Discovery of a low order drug-cell response surface for applications in personalized medicine

Abstract

The cell is a complex system involving numerous components, which may often interact in a non-linear dynamic manner. Diseases at the cellular level are thus likely to involve multiple cellular constituents and pathways. As some drugs, or drug combinations, may act synergistically on these multiple pathways, they might be more effective than the respective single target agents. Optimizing a drug mixture for a given disease in a particular patient is particularly challenging due to both the difficulty in the selection of the drug mixture components to start out with, and the all-important doses of these drugs to be applied. For n concentrations of m drugs, in principle, n(m) combinations will have to be tested. As this may lead to a costly and time-consuming investigation for each individual patient, we have developed a Feedback System Control (FSC) technique which can rapidly select the optimal drug-dose combination from the often millions of possible combinations. By testing this FSC technique in a number of experimental systems representing different disease states, we found that the response of cells to multiple drugs is well described by a low order, rather smooth, drug-mixture-input/drug-effect-output multidimensional surface. The main consequences of this are that optimal drug combinations can be found in a surprisingly small number of tests, and that translation from in vitro to in vivo is simplified. This points to the possibility of personalized optimal drug mixtures in the near future. This unexpectedly simple input-output relationship may also lead to a simple solution for handling the issue of human diversity in cancer therapeutics.

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Discovery of a low order drug-cell response surface for applications in personalized medicine
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2014 Phys. Biol. 11 065003
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Discovery of a low order drug-cell response
surface for applications in personalized
medicine
Xianting Ding
1
, Wenjia Liu
1
, Andrea Weiss
2,3
, Yiyang Li
1
, Ieong Wong
4
,
Arjan W Griffioen
3
, Hubert van den Bergh
2
, Hongquan Xu
5
,
Patrycja Nowak-Sliwinska
2
and Chih-Ming Ho
4
1
School of Biomedical Engineering, Med-X Research Institute, Shanghai Jiao Tong University (SJTU),
1954 Huashan Road, 200030, Shanghai, People’s Republic of China
2
Institute of Chemical Sciences and Engineering, Swiss Federal Institute of Technology (EPFL), 1015
Lausanne, Switzerland
3
Angiogenesis Laboratory, Department of Medical Oncology, VU Medical Center, 1081 HV Amsterdam,
The Netherlands
4
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles (UCLA),
90095 Los Angeles, CA, USA
5
Department of Statistics, University of California, Los Angeles (UCLA), 90095 Los Angeles, CA, USA
E-mail: dingxianting@sjtu.edu.cn and chihming@seas.ucla.edu
Received 19 June 2014, revised 10 September 2014
Accepted for publication 15 September 2014
Published 26 November 2014
Abstract
The cell is a complex system involving numerous components, which may often interact in a
non-linear dynamic manner. Diseases at the cellular level are thus likely to involve multiple
cellular constituents and pathways. As some drugs, or drug combinations, may act
synergistically on these multiple pathways, they might be more effective than the respective
single target agents. Optimizing a drug mixture for a given disease in a particular patient is
particularly challenging due to both the difficulty in the selection of the drug mixture
components to start out with, and the all-important doses of these drugs to be applied. For n
concentrations of m drugs, in principle, n
m
combinations will have to be tested. As this may lead
to a costly and time-consuming investigation for each individual patient, we have developed a
Feedback System Control (FSC) technique which can rapidly select the optimal drug–dose
combination from the often millions of possible combinations. By testing this FSC technique in a
number of experimental systems representing different disease states, we found that the response
of cells to multiple drugs is well described by a low order, rather smooth, drug-mixture-input/
drug-effect-output multidimensional surface. The main consequences of this are that optimal
drug combinations can be found in a surprisingly small number of tests, and that translation from
in vitro to in vivo is simplified. This points to the possibility of personalized optimal drug
mixtures in the near future. This unexpectedly simple input–output relationship may also lead to
a simple solution for handling the issue of human diversity in cancer therapeutics.
SOnline supplementary data available from stacks.iop.org/PB/11/065003/mmedia
Keywords: biological complex system, combinatorial drug, feedback system control (FSC),
personalized medicine, precision medicine, synergetic and antagonistic interactions
(Some figures may appear in colour only in the online journal)
Physical Biology
Phys. Biol. 11 (2014) 065003 (12pp) doi:10.1088/1478-3975/11/6/065003
1478-3975/14/065003+12$33.00 © 2014 IOP Publishing Ltd Printed in the UK1

1. Introduction
The perturbation of cell homeostasis due to genetic and/or
epigenetic changes can result in aberrant proteins or cell
organelles. These can lead to uncontrolled cell growth, pro-
viding the underlying basis for most morbid and mortal ill-
nesses. Modern drug discovery mainly aims to identify novel
drug molecules which directly bind and inhibit such aberrant
molecular cell targets [1,2]. One of the main challenges of
drug discovery, therefore, is to identify such drug targets in a
complex cellular system.
Biological systems, on a cellular, organ or body level,
can be considered as complex systems [3]. Complex biolo-
gical systems, however, are very different from other types of
systems, such as an engineering system. A complex system
consists of a large number of building blocks, e.g. proteins,
mRNA, organelles. In biological systems, some of these
functional molecules are self-organized into pathways [4,5].
In contrast, engineering systems are assembled with parts that
are manufactured by following the first principle [6]. The
system’s functionality is well defined according to the design
goal. On the other hand, cellular system level responses
emerge from a network of regulatory and signaling pathways
and are adaptive within a large dynamic range [7]. Obviously,
sorting out an aberrant cellular component for drug targeting
in the midst of a complex system is like finding a needle in a
haystack. Even if a target is identified and a drug is developed
to inhibit it, single drug treatment often leads to drug resis-
tance [8,9]. Furthermore, in many diseases it is common for
there to be more than one disease causing target due to non-
linear interactions between signaling pathways. Therefore
combinations of synergetic drugs targeted to several pathways
and administered at low dose could represent an efficacious
treatment strategy [10,11].
The efficacy of a drug combination not only depends on
the selection of the drugs, but also on the dose ratios among
the drugs [10]. M drugs with N dose levels will generate N
M
possible combinations. A brute force search for an optimal
drug combination in such a large parameter space is a pro-
hibitive task. The recently developed Feedback System
Control (FSC) technique [12] can direct biosystems toward a
desired phenotypic outcome-based combinatorial drug sti-
mulation. FSC can home in on an optimal drug combination
with several orders of magnitude less experimental efforts
than testing all of the N
M
possibilities. FSC takes a top-down
systems approach by focusing on improving a phenotype
based on varying the combinatorial input stimuli. This
method completely avoids the bottom-up approach frequently
used in biology, where one attempts to predict and control cell
behavior based on an understanding of how the different
signaling pathways and molecules interact. It is surprising that
typically less than 15 iteration loop tests, with a few tens of
tests per iteration, can identify the optimal combination from
millions or more alternatives. FSC is a platform technology
which has been demonstrated in the eradication of cancers
[13], inhibition of viral infection [10], the maintenance of
human embryonic stem cells (hESC) [11], the reformulation
of Chinese herbal medicine [14], and the differentiation of
mesenchymal stem cells [15].
Even though it took a long time and a lot of effort, many
new targeted drugs and their combinations have been intro-
duced to the clinic in the past three decades. Unfortunately, a
patient’s response to most targeted drugs remains fairly low in
cancer treatments. For example, the response for lung cancer
patients is about 25% and only 10% for hepatoma [16]. Many
reasons contribute to these unsatisfactory results. Patient
diversity and cancer heterogeneity are among some of the
factors influencing the efficacy of cancer therapies [17].
Genetic profiles of individual patients with the same disease
vary across gender, race, etc and causes diversities of pro-
teomic networks through transduction. The current clinical
practice for chemotherapy is to use the same regimen for
patients with the same type of disease [18,19], therefore, a
low response is observed.
With the rapid development of micro/nano technology
based diagnostic instruments, fast and affordable genetic
analyses have become available and this has enabled the
development of genotypic personalized medicine (GPM)
[20,21]. GPM is based on the principle of customizing single
targeted or combinatorial drugs for a group of patients with
similar gene profiles and can result in better therapeutic out-
comes. These strategies, however, disregard the fact that
disease can also be independently caused by epigenetic sti-
mulations [22,23]. Therapeutic procedures can obviously be
much more precise, if they include consideration of disease
phenotypes. However, phenotypic personalized medicine
(PPM) needs to have a quantitative efficacy–drug relationship
a priori.
In this paper, we will present the results from investi-
gations of four biological models, including non-small-cell
lung cancer (NSCLC) treatment, Herpes Simplex Virus type 1
(HSV-1) eradication, mesenchymal stem cell osteogenesis
induction, and cancer treatment by angiogenesis inhibition. In
these studies, we show that the efficacy–drug dose relation-
ships of each system are simple and smooth. This finding
comes from one of the fundamental characteristics of complex
systems. Due to the process of evolution, organisms have
developed in such a way that they are robust and adaptive to
environmental stimulations. That is, the bio-complex system
response surface to extracellular stimulations must be very
smooth. This is the reason why we can easily locate an
optimal drug combination in a biological system after
approximately 15 iterations of the FSC technique. By testing
a small group of subjects, the efficacy–drug surface can be
established. With this quantitatively defined relationship,
PPM can be practiced with great confidence.
2. Results
2.1. Non-small-cell lung cancer (NSCLC) reduction
The authors of this study [13] aimed to optimize the combi-
nation of three anti-cancer drugs: AG490, a Janus Kinase 2
inhibitor; U0126, a MEK1 and MEK2 inhibitor; and
2
Phys. Biol. 11 (2014) 065003 X Ding et al

Indirubin-3′-monoxime, which is an antimitotic CDK/GSU
inhibitor. Compounds like the latter are sometimes used as an
ingredient in Chinese medicine. As a measurement of the
efficacy of the combination treatment and its ‘selectivity’, the
ATP levels of both an NSCLC cell line (A549) and of a
normal primary lung fibroblast (AG02603), are measured
after exposure to a large number of combinations of the three
above-mentioned agents for 72 h. It is argued that the three
selected drugs target distinct but nevertheless somewhat
connected intracellular pathways related to cell survival and
proliferation. Eight doses were selected for each of the three
drugs resulting in 512 possible combinations. The authors test
all these combinations and report the results in this study.
We then further analyzed the 512 data points by building
a second order linear regression model. At first we looked at
the impact of the dose change of each individual drug on the
therapeutic output ‘y’which quantifies cancer cell survival.
These single drug effects, also known as ‘main effects’in
statistics are shown in figure 1. All three drugs demonstrate
significant main effects, as can be seen by the obvious
decrease of ‘y’with the increasing dose of each compound.
We then checked the fidelity of the linear regression
model built from the 512 data points and found R
2
= 0.96
which is indicative of the good correlation between the
regression model and the experimental observations. We then
plotted the model predictions and the experimental points side
by side in figure 2(a). The fact that all points fall on a line
again suggests that the regression model faithfully represents
the experimental data. In figure 2(b) we then generated a
residual plot to evaluate whether the model might be biased
for any particular fitted values. The residuals are all fairly
close to zero, indicating that the regression model used is not
biased. We then generated a ‘normal Q–Q plot’to see if the
residual data follow a normal Gaussian distribution. This is
shown in figure 2(c). If the residual data do follow a normal
distribution, the points on the Q–Q plot will fall approxi-
mately on a straight line. This normal Q–Q analysis is another
way of checking if the regression model used shows bias. If
the residual plot does not follow a normal distribution then we
will have to re-examine the data using another modeling
strategy. In this case however, the residual points fall close to
a straight line, suggesting that the assumption of a normal
distribution holds. Only a few points fall far from the straight
line. These few points are unlikely to significantly influence
the overall statistical analysis and can be treated as statistical
outliers. In order to tell which data points are likely to be
outliers (e.g. points that are due to errors in the experimental
measurements), we generated the Cook’s distance for each
data point as shown in figure 2(d). Cook’s distance is a well-
accepted way to tell whether any outliers exist in the data set.
Data point No. 337 clearly shows a Cook’s distance value
larger than any other data point. This indicates that this
Figure 1. Single drug effects for the three drugs used in Non-Small-Cell Lung Cancer (NSCLC) reduction study. Integers under each panel
represent the absolute doses (unit: μM). System readout ‘y’represents the cancer cell survival rate.
3
Phys. Biol. 11 (2014) 065003 X Ding et al

particular point should be analyzed carefully and possibly
repeated, as it is likely that a measurement or recording error
occurred.
One key characteristic of linear regression modeling,
especially lower order regression models, is that the response
surfaces can be depicted with smooth contours, at least in the
region of the experimental values reported. In figure 3, con-
tour plots of each of the two-drug pairs out of the three drugs
tested are generated while fixing the third drug’s dose to be
equal to zero. Thus, when I-3′-M is not added to the mixture,
AG490 and U0126 combine optimally when AG490’s dose is
between 200 and 250 μM, while U0126’s dose is between 80
and 100 μM, possibly indicating some degree of synergism.
On the other hand, when the concentration of U0126 is set to
zero, and AG490 and I-3′-M are applied together, the optimal
anti-cancer effect is obtained when both drugs are at the high
dose end, i.e. no synergy is observed between these two
drugs. Finally, when the concentration of AG490 is set to
Figure 2. Regression analysis of combinatorial data achieved from NSCLC reduction study. (a) The model predictions and the experimental
observations are plotted for comparison; (b) residual plot shows a mean (the red line in the figure) close to zero, meaning the model is not
biased at any particular drug doses; (c) Normal Q–Q plot; (d) Cook’s distance plot.
050
20 40 60 80 1000
20 40 60 80 1000
20 40 60 80 1000
100 150 200 250 300 0 50 100 150 200 250 300 0 50 100 150 200 250 300
AG490
AG490 U0126
U0126
abc
I-3י-M
I-3י-M
0.1
0.2
0.2
0.2
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.7
0.7
0.7
0.7
0.8
0.8
0.8
0.8
0.9
0.9
0.9
0.9
0.1
1
1.21.31.4
1.1
Figure 3. Smooth contour plots of any two pairs of the three drugs used in NSCLC reduction study. (a) AG490 versus U0126; (b) AG490
versus I-3′-M; (c) U0126 versus I-3′-M. The contour plots are continuous without any sudden breaks, confirming the smoothness of the drug
combination dose-efficacy relationship.
4
Phys. Biol. 11 (2014) 065003 X Ding et al

zero, and we look at U0126 and I-3′-M being used together,
the optimal anti-cancer effect occurs when the U0126 con-
centration is between 100 and 150 μM, and either higher or
lower doses of this compound lead to a less optimal readout.
The three contour plots generated all appear to be quite
smooth in the domain of the concentrations tested, confirming
that the relation between the three chosen anti-cancer drugs
can be expressed with a simple second order linear regression
model.
2.2. Herpes simplex Virus type 1 (HSV-1) infection
In the first example above, we examined a typical anti-cancer
system treated with combinations of three drugs. In this
second example we investigate viral infection, another kind of
complex biological system which is commonly treated with a
drug mixture. In these viral-based diseases the drugs can
interact with both the host cells and the virus itself, thus
increasing the complexity of the system. We were then
interested to see if in such a complex biological system the
relation between the drug doses on the one hand, and the ‘y’
readout, which is the percent of viral infection, on the other
hand, can still be described by a 2
nd
order linear regression
model. We thus analyzed the measured percentage of viral
infection after treatment with different drug combinations in a
Herpes Simplex Virus type 1 (HSV-1) infected system [10].
In this paper, Ding et al aimed to optimize combinations of
the following drugs at seven drug dose levels: Interferon-
alpha, Interferon-beta, Interferon-gamma, Ribavirin (a gua-
nosine analog which interferes with viral RNA synthesis),
Acyclovir (a drug which is converted in the body to a strong
inhibitor of viral DNA-polymerase), and TNF-alpha. The
drugs were tested as to their efficacy in eradicating an HSV-1
infection in NIH 3T3 fibroblasts. Six drugs applied at seven
dose levels leads to a total of 117 649 possible combinations.
With the help of the FSC technique described above, the
authors then attempted to identify the most effective drug
combinations for inhibiting the viral infection. In this case
only 192 drug combinations were tested through 12 rounds of
experimental measurements, and the FSC method permitted
us to find several drug combinations that effectively com-
pletely eradicate the signs of viral infection. Due to the fact
that Ribavirin has a large number of possible side effects
which include bone pain, increased stomach acid and blurred
vision, a second FSC search was undertaken without Riba-
virin. The latter permitted us to identify an effective Riba-
virin-free drug combination in only 20 rounds of otherwise
the same experimental tests.
In the current study, we further analyzed the drug com-
bination data resulting from the previous FSC search. To do
this we investigated how the change of the dose of each
individual drug would influence the percent of viral infection,
i.e. the influence of one particular selected drug on the overall
system output ‘y’(percentage of viral infection). In such
‘main effect plots’, obtained from the pooled output data, we
thus fix the doses of the other drugs, and vary only the dose of
the drug of interest. In most cases the increase in drug dose
led to a better output, meaning a lower value of the percentage
viral infection. The only exception was TNF-alpha, which
shows the opposite effect, i.e. where a dose increase led to a
higher percentage of viral infection (figure 4).
We then generated a 2
nd
order linear regression model for
‘y’with the six drugs as explaining variables. The model
yielded a value for R
2
= 0.7448. The fidelity is not as good as
that seen in the NSCLC case. However, for a biological
system as complex as a viral infection, where the internal
variances, such as experimental batch-to-batch variance can
be as large as 20%, this is not unreasonable. We then per-
formed a ‘boxcox’transformation on ‘y’. Boxcox transforms
non-normally distributed data to a set of data that has an
approximately normal distribution. After the boxcox trans-
formation, a fourth root transformation was made on the ‘y’,
and the regression analysis was repeated by regressing y
1/4
over the six drugs. This transformation resulted in an increase
of R
2
from 0.7448 to 0.8103. In figure 5(a), we show that the
‘model-fitted’values and the experimental values for ‘y’
agree quite well with one another. As in the case of NSCLC
above, we also examined the residual plot and the Normal Q–
Q plot for this model. These data are shown in figures 5(b)
and (c), and no clear indications were found, suggesting
failure or bias of the model. The Cook’s distance plot sug-
gested only several outliers, as can be seen in figure 5(d).
Therefore one may conclude that even in such a complex case
as viral infection, the effect of a drug mixture on the per-
centage viral infection can still be modeled with a 2
nd
order
linear regression, though with somewhat reduced confidence.
2.3. Mesenchymal stem cell osteogenesis induction
As a third example of a study of a biologically complex
system to optimize a treatment with drug mixtures, we chose
to investigate a case of chemical stem cell osteogenesis
induction. Chondrogenic differentiation of mesynchymal
stem cells from bone marrow into mature tissue cells has been
shown to normally be mainly sensitive to the intrinsic prop-
erties of the extracellular matrix, like its structure, elasticity
and composition. Yoshitomo et al however decided to study
the application of combinations of seven chemical com-
pounds which are, among others, known to promote the
induction of osteogenic differentiation of mesenchymal stems
cells (MSC) [15]. It might thus be expected that the relation
between the dose of these extrinsic chemicals and the system
readout ‘y’, which in this case is osteogenic cell differentia-
tion, might not follow a smooth relation as given by a simple
2nd order linear regression. The following seven compounds
were included in the investigation: AA2P (L-ascorbic acid 2-
phosphate), VD3 (Vitamin D3), BMP-2 (bone morphogenic
protein 2), RA (retinoic acid), Dex (dexamethasone) and beta-
GP (beta-glycerophosphate). The authors of this study applied
the FSC technique and tested 107 drug combinations
experimentally. This led to a unique combination of drugs
that robustly induces bone mineralization.
In the present study, we further analyzed the same data
set as was generated by the FSC search by applying second
order linear regression analysis. As in the previous cases, we
first looked at the influence of each individual drug on the
5
Phys. Biol. 11 (2014) 065003 X Ding et al

Figure 4. Single drug effects for the six drugs used in Herpes Simplex Virus type 1 (HSV-1) infection study. Integers under each panel
represent the concentration levels. System readout ‘y’represents the percentage of viral infection.
6
Phys. Biol. 11 (2014) 065003 X Ding et al

Figure 5. Regression analysis on HSV-1 infection study. System readout ‘y’(percentage of viral infection) was non-normally distributed
data. A ‘Boxcox’transformation on ‘y’was made to transform ‘y’to a set of data that has an approximately normal distribution before the
regression analysis was done. (a) The model fitted values and experimental observed values are plotted against each other for comparison; (b)
residual plot; (c) normal Q–Q plot; (d) Cook’s distance plot.
012345789101112 0123456789
10
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10 012345678910 012345678910
11
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10 0123456789
10
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
-0.2 0.0 0.2 0.4 0.6 0.8 1.0
mean of y
mean of y
mean of y
mean of y
mean of y
mean of y
mean of y
Main Effect AA2P Main Effect VD3 Main Effect BMP-2 Main Effect Hep
Main Effect RA Main Effect RA Main Effect beta-GP
Figure 6. Single drug effects for the seven drugs used in Mesenchymal Stem cell osteogenesis induction study. Integers under each panel
represent the concentration levels. System readout ‘y’represents the yielding rate of osteogenic differentiation.
7
Phys. Biol. 11 (2014) 065003 X Ding et al

output ‘y’. This is shown in figure 6. It is interesting to note
that in this particular example of a complex biological system,
when the concentrations of the other chemicals are fixed, the
influence of the individual concentrations of each single
compound on ‘y’appears to be quite diverse. No simple trend
can be observed for any of these individual compounds. This
observation led us to believe that the optimal chemical mix-
ture for osteogenesis would be a rather unique combination of
compounds, in other words that the relation between ‘y’and
the doses of the compounds would not follow a well-defined
2nd order linear regression model (i.e. the surface would not
be smooth but rather be characterized by a quite localized
extreme value).
Yet, to our surprise, the 2
nd
order linear regression model
generated based on the tested data points showed an R
2
value
of 0.7444, which was much higher than our expectation.
When we examined the residual plots and Normal Q–Q plots,
we observed a pattern in the residual plots, which indicated
the residuals did not obtain a mean of zero (supplementary
figure 1(b)). When we further looked at the Cook’s distance
plot (supplementary figure 1(d)), we found data point No. 45
was a clear outlier. We then repeated the whole analysis by
removing data point No. 45. Indeed, the experimental
observations and the model predictions basically agree with
one another, as can be seen from figure 7(a). Furthermore,
upon examination of the residual plots and the Normal Q–Q
plots (shown in figures 7(b) and (c)), we did not observe a
clear residual distribution, indicating that even though there
was only modest fidelity, the second order linear regression
model was an acceptable approximation to the experimental
data. Figure 7(d) shows that Cook’s distance analysis did not
indicate any new outliers either.
2.4. Cancer angiogenesis inhibition
After examining the input–output relation for the efficacy of
multiple drug treatments in vitro in the three different com-
plex biological systems described above, we found that the
Figure 7. Regression analsyis on mesenchymal stem cell osteogenesis induction study. (a) The model fitted values and experimental observed
values are plotted against each other for comparison; (b) residual plot; (c) normal Q–Q plot; (d) Cook’s distance plot.
Table 1. Single drug concentration table used in anti-angiogenesis study (unit in table: μM).
Anginex Avastin Axitinib Erlotinib
anti-
HMGB1 Sunitinib
anti-
vimentin RAPTA-C BEZ-235
000000000
1 0.05 0.3 0.5 1 0.4 1 100 0.1
5 0.5 1 1 5 1 5 300 0.5
10 1 10 2 10 2 10 500 1
50 5 50 5 20 4 20 1000 2
100 10 100 10 40 10 40 2000 4
8
Phys. Biol. 11 (2014) 065003 X Ding et al

system’s response can, in each case, be fairly well modeled
with a smooth second order equation. If this finding could be
universally true for other complex biological systems, it may
be possible to identify optimal drug combinations by testing a
limited number of data points, which are then fitted with a
second order response function. This function can then be
used to find the optimal drug combination.
In order to test this rather bold hypothesis, we tried to
find an optimal combination of a fairly small number of anti-
angiogenic drugs (if possible four or less), starting from nine
Figure 8. Regression analysis for the cancer angiogenesis inhibition system. (a) All the regression coefficients are presented to remove the
less significant drugs used in the final combination; (b) normal Q–Q plot is used to check residual normality.
9
Phys. Biol. 11 (2014) 065003 X Ding et al

such substances. The starting compounds were carefully
selected for their known or presumed complementary anti-
angiogenic activity. The drugs chosen were Anginex (1),
Avastin (2), Axitinib (3), Erlotinib (4), Anti-HMGB1 anti-
body (5), Sunitinib (6), Anti-Vimentin antibody (7), RAPTA-
C (8), and BEZ-235 (9). As, up to this date, such treatments
have been only partially successful with the single compo-
nents listed above, it is now hoped that by using the FSC
technique an effective angiostatic combination of some of the
above listed drugs might be found. If, furthermore, this
combination would benefit from a significant degree of
synergism, it cannot be excluded that the treatment would
also imply the use of much lower drug doses than are nor-
mally applied with the single compounds. Reduced drug
doses may also carry the potential for having fewer side
effects and reduced driving force for the development of drug
resistance. Four drug concentrations were assigned to each of
the nine starting compounds thus creating 4
9
= 262144 pos-
sible drug combinations (table 1).
Immortalized human macrovascular endothelial cells
(ECRF24) were used in this study. We first applied the FSC
technique to optimize these nine drugs over ten iterations. The
FSC search optimization will be published in a separate
paper, as the present article focuses mainly on the analysis of
the cell survival response to the different drug doses. In each
of the ten iteration steps, 19 drug combinations were tested,
giving a total of 190 data points. Like before, we used these
points to build a second order linear regression model. As
expected, the predictions from the regression model and the
data points showed a high correlation of 0.8642. The R
2
value
equals 0.7468.
Based on the regression model shown in equation (1)
below (see the method section), where the output y is a
function of k drugs, we then tried to find the optimal drug
combination by looking carefully at all the single drug
coefficients (βi), all the drug–drug interaction coefficients
(βij), and all the single drug quadratic regression coefficients
(βii) which are plotted in figure 8(a). Since the model and the
experimental data showed a very good correlation, we then
used figure 8(a) to help us eliminate less important drugs. We
also take into account that, as shown in figure 8(b), the normal
Q–Q plot shows that there seems to be no violation of the
normality hypothesis for the residuals distribution. The y-axis
of figure 8(a) is such that the more negative the values of the
coefficients plotted along the y-axis imply a better contribu-
tion to lowering endothelial cell replication, and thus a higher
angiostatic effect. Anginex (1) showed a relatively low single
drug effect (β1) but a much higher 2
nd
order effect (β11),
meaning Anginex (1) is not likely to be a highly effective
drug when used individually. Furthermore, Anginex (1) did
not show the desired very low values in figure 8(a) for the
interaction with the other drugs. These observations may be
interpreted as minimal ‘synergies’between Anginex and the
other drugs (i.e. low values of Beta ik). Based on these rea-
sons, we could confidently drop Anginex (1) from the drug
mixture. Moreover, Avastin (2) and Sunitinib (6) did have
slightly positive coefficients (β2 and β6) in figure 8(a)
(although this may not be statistically very significant), which
is indicative of their not very good single drug contributions
to the angiostatic effect. As the model is run with real con-
centrations of each drug, single drug effects are quite
important. We therefore dropped drugs (2) and (6). The Anti-
HMGB1 antibody (5) has a quite negative coefficient for its
single drug effect (β5). However, unfortunately this drug
showed mainly ‘antagonistic-like’effects (the β5k coeffi-
cients are largely positive or around zero in figure 8(a) with
other drugs, and it had a rather positive value for the quadratic
term (β55). Therefore, drug (5) was also dropped from the
drug combination. Finally, the Anti-Vimentin antibody (7)
also shows a good single drug effect, but a fairly positive 2
nd
order effect, as well as mainly small coefficients for the
interactions with other drugs, indicating slight ‘synergism’or
slight ‘antagonism’. We therefore also dropped drug (7) at
this point. These procedures lead us to the optimal combi-
nation including the following four drugs: Axitinib (3),
Erlotinib (4), RAPTA-C (8) and BEZ-235 (9). Axitinib was
eliminated from this mixture, for, among others, reasons of
toxicity.
Thus the final optimal drug combination consisted of
drug (4) (10 μM) + (8) (100 μM) + (9) (0.02 μM). This com-
bination, at these rather low concentrations was sufficiently
potent to inhibit more than 90% of the endothelial cell pro-
liferation. Note that the EC50 values (the values that gave
50% survival) of drug (4), (8), (9) are approximately 20 μM,
500 μM and 0.05 μM, respectively, while the drug doses used
in combination were much lower, being reduced by a factor of
2–5 from the EC50 values. This fact confirms the successful
application of 2
nd
order linear regression modeling in
selecting a small group of very well-interacting angiostatic
compounds from the original nine. It also points to the pos-
sibility of rapidly designing effective drug combinations, an
opportunity that will be further tested in vivo and in pre-
clinical models in the near future. One may speculate that
such a rapid and not excessively expensive method of indi-
vidual drug optimization may be quite useful in the case of
cancers which change rapidly as a function of time.
3. Discussion
The diseased state in a cell commonly involves a number of
abnormal signaling pathways. It is therefore unlikely that a
single drug could inhibit all of the aberrantly activated path-
ways involved in a disease and its progression. Although in
some cases, individual drugs can show satisfying efficacy in
the treatment of a disease, the toxicity induced when drugs are
used at high dose, and drug resistance accumulated from
long-term drug administration, still often limit single-drug
regimens as effective long-lasting treatment options. An
alternate approach is to use drug combinations that can target
multiple diseased cellular nodes simultaneously. The synergy
among drugs in an effective combination can lead to reduced
dose, relieved side-effects and increased efficacy. In all of the
cases we studied, optimized drug combinations were superior
to their single-drug counterparts.
10
Phys. Biol. 11 (2014) 065003 X Ding et al

The FSC approach usually identifies the optimal drug
combination in less than 15 rounds of experimental efforts, by
testing only 2% or less of the total possible search space. This
paper, by investigating four different biological systems,
demonstrates that although biological systems are internally
complex, the drug dose-efficacy relationships can frequently
be expressed by low order input–output multi-dimensional
surfaces. This finding not only explains the puzzle of why
FSC is effective in drug combination optimization, but also
serves as the foundation for the idea that a small number of
well-designed experimental tests are adequate to form a rea-
sonable response surface for predicting optimal drug combi-
nations and doses.
In a biological system with multiple factors, experimen-
tally testing all the possible drug combinations can be a very
laborious, time consuming and costly process. If the response
of a biological system can be described with a smooth
function, then we only need to perform a small number of
tests in order to build up a reliable model for this input–output
relationship. This will then allow the rapid examination of the
entire search space. This suggests that to optimize combina-
tions of multiple factors in a bio-complex system, we may
start with only a few tests and examine whether the bio-
system’s response is smooth or not. If so, the optimal com-
bination could be faithfully designed by building up the
smooth response surface of the system with relatively few test
data points.
Clinically, tumor progression at different time points and
at different locations may dictate the effectiveness of the same
therapy. Even within the same tumors, multiple subtypes
could also require distinct treatments. This fact emphasizes
the necessity of applying combinatorial drugs to treat the
lethal disease. Tumors, as well as the other complicated dis-
eases, often involve multiple subtypes/strains or pathogenesis
intracellular signaling pathways. This complexity varies with
time and location as well. It is extremely challenging for one
single compound to deal with such complexities. Drug
combinations often tackle the problem from different angles,
and therefore are believed to be a more universal and effective
solution. The aim of the paper is to reveal the fact that
although biological systems are internally complex, the rela-
tionships between drug doses and phenotypic system
responses often follow relatively simple patterns. Further-
more, these patterns can often be modeled faithfully using
second order regression analysis. In order to verify this con-
clusion, the authors have tested the hypothesis in four dif-
ferent biological systems. These biological systems were
selected to be ‘on purposely’different to cover a relatively
large area of interest for biological research.
Genotypic personalized medicine (GPM) has been
extensively discussed recently. GPM diagnoses and cate-
gorizes patients based on their genotypic traits, and then treats
them based on targeted strategies. GPM has greatly improved
response rates to treatment in cancer patients. Yet, epigenetic
stimulation can also independently lead to disease. Therefore,
genetic investigations only address part of the problem
underlying diseased states. For this reason, developing ther-
apeutic strategies based on phenotypic clues may in fact be a
more direct route to evaluating the efficacy of a treatment.
However, in order to practice phenotypic personalized med-
icine (PPM), quantitative efficacy-drug relationships need to
be understood a priori. The work presented here demonstrates
the fact that a low order drug–cell response surface may well
commonly exist in biological systems, indicating that the FSC
approach could be an invaluable route towards PPM
optimization.
4. Method
4.1. Regression modeling
Regression modeling is done with R
©
and MATLAB
©
pro-
gramming languages.
For a bio-complex system with k drugs, a standard form
of the linear regression model is as follows:
∑∑ ∑∑
ββ β β ε=+ + + +
== ==+
yxx xx(1)
i
k
ii
i
k
ii i
i
k
ji
k
ij ij
0
11
2
11
where
β
0,
βi
,
β
i
i
and
β
ij are the intercept, linear, quadratic and
bilinear (or interaction) terms [24,25]. In this study, a full
model with all the coefficients (including intercept, linear,
quadratic and interaction terms) in a 2nd order linear
regression model was built for each case.
A stepwised linear regression analysis was done in R
programming to remove those drugs that contributed the
statistically non-significant regression terms to form a cleaner
final regression model. Fitted values and experimentally
observed values are plotted side-by-side to evaluate the fitness
of the regression model. The residual plot was generated to
evaluate whether the regression model is biased for any par-
ticular fitted values. The Cook’s distance plot was generated
to reveal possible outliers in the experiment, if any. Finally, a
series of transformation (log/square-root/square transforma-
tion) on the system readout was made to increase the judging
efficiency (P-value) of the regression model.
4.2. Data sets
Three datasets were selected in this study based on previously
published literature [10,13,15]. In all of these three cases, the
FSC technique was applied to identify optimized drug cock-
tails to tackle different biological questions. This paper aimed
to study why the FSC technique could be implemented so
effectively to optimize drug combinations, so we elected to
only analyze data sets that were generated using the FSC drug
cocktail search practice. The data set in the anti-angiogenesis
study was generated by the authors in a separate experiment
to validate the findings from the study of the first three
data sets.
4.3. Drugs acquisition for anti-angiogenesis study
Anginex® was provided by Peptx (Excelsior, MN, USA).
Erlotinib and Axitinib were obtained from LC laboratories
(Woburn, MA, USA), Sunitinib was from Pfizer Inc. (New
11
Phys. Biol. 11 (2014) 065003 X Ding et al

York, NY, USA) and BEZ235 was from Chemdea LLC
(Ridgewood, USA). Anti-Vimentin monoclonal mouse anti-
body (clone V9) was purchased from Dako (Glostrup, Den-
mark) and anti-HMGB1 antibody was purchased from Santa
Cruz Biotechnology (Heidelberg, Germany). Avastin® was
purchased from Genentech (San Francisco, CA, USA).
RAPTA-C was synthesized and purified based on a previous
publication [26].
4.4. Cell culture and maintenance for the anti-angiogenesis
study
Immortalized human macrovascular endothelial cells
(ECRF24) were cultured in a cell culture medium containing
50% DMEM, 10% FBS and 50% RPMI 1640 supplemented
with an addition of 1% antibiotics (Life Technologies,
Carlsbad, California, USA).
4.5. Cell viability assay for anti-angiogenesis study
Cells were seeded at a density of 2.5 × 10
3
cells/well on a 96-
well culture plate. Cells were given a 72 h incubation time
with the drug combinations. Drugs were premixed in the
culture medium. Cell viability was calculated using the
CellTiter-Glo luminescent cell viability assay (Promega,
Madison, WI, USA).
Acknowledgment
This work was supported by the National Natural Science
Foundation of China (81301293) and National Science and
Technology Major Projects for ‘Major New Drugs Innovation
and Development’(2014ZX09507008). The authors would
like to acknowledge the Institute of Chemical Sciences and
Engineering at EPFL for providing the design of experiment
as well as the experimental data for the cancer angiogenesis
inhibition project.
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