integrative biology dynamic article · pdf filewith the advent of high-throughput biology, ......

724 Integr. Biol., 2011, 3, 724–732 This journal is c The Royal Society of Chemistry 2011

Cite this: Integr. Biol., 2011, 3, 724–732

Dynamic modeling and analysis of cancer cellular network motifsw

Mathieu Cloutieraand Edwin Wang*

ab

Received 28th January 2011, Accepted 5th May 2011

DOI: 10.1039/c0ib00145g

With the advent of high-throughput biology, we now routinely scan cells and organisms at

practically all levels, from genome to protein, metabolism, signaling and other cellular functions.

This methodology allowed biological studies to move from a reductionist approach, such as

isolation of specific pathways and mechanisms, to a more integrative approach, where biological

systems are seen as a network of interconnected components that provide specific outputs and

functions in response to stimuli. Recent literature on biological networks demonstrates two

important concepts that we will consider in this review: (i) cellular pathways are highly

interconnected and should not be studied separately, but as a network; (ii) simple, recurrent

feedback motifs within the network can produce very specific functions that favor their modular

use. The first theme differs from the traditional approach in biology because it provides a

framework (i.e., the network view) in which large datasets are analyzed with an unbiased view.

The second theme (feedback motifs) shows the importance of locally analyzing the dynamic

properties of biological networks in order to better understand their functionality. We will review

these themes with examples from cell signaling networks, gene regulatory networks and metabolic

pathways. The deregulation of cellular networks (metabolism, signaling etc.) is involved in cancer,

but the size of the networks and resulting non-linear behavior do not allow for intuitive

reasoning. In that context, we argue that the qualitative classification of the ‘building blocs’ of

biological networks (i.e. the motifs) in terms of dynamics and functionality will be critical to

improve our understanding of cancer biology and rationalize the wealth of information from

high-throughput experiments. From the examples highlighted in this review, it is clear that

dynamic feedback motifs can be used to provide a unified view of various cellular processes

involved in cancer and this will be critical for future research on personalized and predictive

cancer therapies.

Introduction

Cancer is a complex and multifactorial disease in which gene

mutations in signaling,1–3 metabolic4–6 and gene regulation7,8

networks accumulate in a dynamic process, leading to

deregulation of cell death and/or proliferation. Most of the

components of the underlying biological networks have been

a Computational Chemistry and Bioinformatics Group,Biotechnology Research Institute, National Research CouncilCanada, 6100 Royalmount Avenue, Montreal, Quebec H4P 2R2,Canada. E-mail: [email protected];Tel: (514) 496-0914

bCenter for Bioinformatics, McGill University, Montreal, Canadaw Electronic supplementary information (ESI) available. See DOI:10.1039/c0ib00145g

Insight, innovation, integration

This article reviews feedback motifs, and their associated

dynamic properties, in the context of cancer research. Feedback

motifs provide a rational explanation to widespread concepts in

cancer biology such as homeostasis, adaptation or bistability.

However, we often observe a gap between the identification of a

specific biological mechanism and the rigorous explanation of

the underlying dynamical system. This review will thus provide

some examples where the mechanisms are specific to cancer

biological processes, but always keeping in mind that the

underlying dynamical systems are generic and can be analyzed

in order to retrieve their properties. We thus report that the

importance of feedback motifs applies to multiple levels of

biological organization, from gene expression to signalling and

metabolism.

Integrative Biology Dynamic Article Links

www.rsc.org/ibiology CRITICAL REVIEW

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http://dx.doi.org/10.1039/c0ib00145g



This journal is c The Royal Society of Chemistry 2011 Integr. Biol., 2011, 3, 724–732 725

studied for decades using traditional approaches in biology

such as reductionism, linear logic and conceptual models

(i.e., a drawing or qualitative representation of the biological

mechanism). For the most studied biological networks,

including metabolic pathways, we now have access to complete

mapping of the system in online databases such as KEGG

(Kyoto Encyclopedia of Genes and Genomes: www.kegg.jp).

Similarly, signaling pathways relevant to cancer are well

determined and publicly available. The information gathered

in KEGG mostly comes from traditional biology studies; the

pathways were studied separately, and their topologies were

determined through careful experimental investigation of the

biochemistry of cell extracts. The advent of high-throughput

biology, starting with the sequencing of the human genome,

showed that reductionism gives a far from complete picture.

Biological function, and thus dysfunction in cancer, is based

on networks, nonlinearities and dynamic processes.9 Within

this context, the traditional approach is still relevant because it

provides valuable information on the components of the

system (i.e., the bottom up approach). However, it is now

recognized that cancer biology must be complemented with

networks10,11 and systems thinking.12–15

We will briefly present the network and systems biology

framework with emphasis on dynamical analysis of the network

motifs. The mathematical frameworks for such studies will be

briefly presented with focus on Ordinary Differential Equation

(ODE) models. With this perspective in mind, we will then

review works on biological networks relevant to cancer,

showing that the local properties induced by network and

feedback motifs are critical for cancer development. The

relevance of the network and systems approach for predictive

and personalized medicine will also be highlighted.

Dynamic networks for cancer biology

From pathways to dynamic network motifs

As presented in Fig. 1, we will review recent works in network

and systems biology, with emphasis on the dynamic properties

of such networks, and the emergence of functional properties

from simple feedback motifs.16,17 Interestingly, emergent features,

such as adaptation, can be observed in many biological

networks, ranging from metabolism18 to signaling,19 gene

regulation20 and physiology.21 Even more interesting is the

fact that the underlying principles behind such properties are

strikingly similar, even though they cover the complete range

of biological organization from gene expression to organ

physiology. A better understanding of how these functional

properties emerge from dynamic interactions is at the core of

the systems biology approach and will provide essential tools

for predictive modeling in medicine.22,23 Fig. 1 highlights the

changes in thinking that recently occurred in biology, whereas

functional properties are not linked specifically to one pathway

or gene, but to a network of dynamically interacting components

(Fig. 1B). However, due to the complexity of these networks,

we argue that reductionism is still relevant, mostly because the

local properties of network motifs are responsible for the

emergence of functionality from simple biochemical interactions.

Thus, from a complex and large network, it is possible to

extract ‘functional units’ composed of just a few nodes and to

analyze their dynamical properties and relevance to the

biological problems under scrutiny. Fig. 1C shows a simple

3-node network motif19 and possible functions, including

adaptation16,19 or bistability.16

Mathematical modeling of dynamic biological networks

Biological networks, such as signaling networks, metabolic

networks and gene regulatory networks are generally too large

and complex for their dynamic behavior to be determined by

intuitive reasoning. The same can be said for disease-related

pathways (such as the ones found in KEGG), as these are

composed of parts from the aforementioned networks. This

implies that even if we have computational and experimental

tools to estimate the local properties of biological systems,

such as the binding affinity of a drug for a target, this does not

lead to a comprehensive understanding of the effects of the

drug at the systems level.24 The most well-known examples we

can relate to this problem come from the field of metabolic

engineering, where micro-organisms are genetically manipulated

in order to improve the productivity of a specific molecule.

Many studies report failures in which the overexpression of a

locally sensitive enzyme (i.e., phosphofructokinase in glycolysis)

did not lead to increased flux in the pathway,25 an observation

that is reproduced by dynamic modeling at the systems level.26

It is now recognized that modeling and systems analysis is

necessary for full appreciation of the sensitivity of biological

systems to perturbations27 and that this analysis relates well to

drug development and novel therapies for complex diseases

such as cancer.28 Thus, an important goal in future medical

research will be to understand how large-scale networks

dynamically respond to local perturbations induced by drugs

and treatments.

Our review of the dynamic modeling of biological networks

and its relevance to cancer systems biology will be principally

centered on the mathematical modeling by ODEs and further

functional analyses. ODEs represent the most common frame-

work for the modeling of physical systems in science and

engineering and are also used widely in biological sciences.29,30

Depending on the specifics of the biological problem, other

modeling frameworks can be used; for example, Boolean

networks31 and Bayesian networks32 are widely used for fast

computation and data analysis of gene regulatory networks.

The ODE approach, despite a few drawbacks such as the

identification of kinetic parameters and computing time, can

be applied and scaled to a wide range of problems. This

facilitates the drawing of general conclusions based on the

observation of biological function and organization at

different levels. The approach has been used for practically

all cellular processes, including gene regulation networks,8,33

cancer-related signaling pathways,34–37 energy metabolism in

cancer38,39 and tumor physiology.40 The ODE approach

can also be complemented in various ways to account for

stochasticity41 or discontinuities42 (i.e., hybrid systems) when

the system contains a small number of molecules or discrete

events. Moreover, the ODE framework is also amenable to

integration of cellular processes that are of different natures.

For example, Kelly et al. built an ODE model to link tumor

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glycolysis to HIF signaling;35 other modeling reports have also

linked metabolism to energy signaling.38 Some studies using

ODE models go even further and integrate cancer-related

processes at various levels, accounting for cell cycle, drug

penetration, tumor physiology and metabolism.41 As we want

to emphasize the recurrent dynamic properties in biological

networks of various scales (gene, signaling and metabolism) in

this review, we will concentrate on the ODE representations of

these network motifs.

Integrating networks and feedback motifs in cancer

cells

Biological features of cancer network motifs and their

implications

Cancer signaling network motifs have certain properties and

lead to implications in molecular mechanisms of tumorigenesis

and practical applications such as prediction of prognosis

and the clinical outcomes of cancer patients. A large-scale

characterization of network motifs in cancer signaling showed

that positive signaling regulatory network motifs are preferentially

used by cancer driving mutating oncogenes, in contrast,

negative signaling regulatory network motifs are preferentially

used by methylated genes and tumor suppressors in cancer

cells.1 These observations are in agreement with the fact that

oncogenes often get mutated and then increase their biochemical

activities. Such a mutated oncogene in a positive feedback loop

might amplify the output signal and therefore consistently trigger

the downstream signals in cancer cells. On the other hand,

methylated genes and tumor suppressor mutations cause the

genes to lose or decrease their biochemical activities. Such a

gene in a negative signaling regulatory loop might also amplify

the cellular signals and trigger the downstream cellular signals

in cancer cells.

Combining these insights with the features of the degradation

of mRNAs or proteins in network motifs led to more under-

standing of the molecular mechanisms of the tumorigenesis

and even practical applications in cancer. In general, in a gene

regulatory motif, the regulator has a short half-life.43 Such a

feature decreases the response time of the network motifs to

the signal cues from environment or neighbouring cells. This

insight triggered the further examination of mRNA or protein

degradation in these motifs. microRNA (miRNA), a short

RNA sequence, which binds to 30UTR region of the genes, has

a function of blocking mRNA transcription or inducing

mRNA/protein degradation. Interestingly, microRNAs are

preferentially regulating positive signaling regulatory network

motifs but avoid regulating negative signaling regulatory

network motifs.2 miRNA is processed by the miRNAmachinery.

Therefore, these observations suggest that low activity of

the miRNA machinery could produce less miRNAs, which

could reduce the degradation of the gene products in positive

regulatory network motifs, and finally make the corresponding

signals amplified. This result is similar to that of oncogene

mutations in the positive regulatory network motifs, and

then leads to cancer signal amplification. Low expression of

key genes of the miRNA processing machinery could thus

promote cancer progression and metastasis. By examining

the expression of Dicer, which is the key gene of the

miRNA processing machinery, in two breast cancer patient

cohorts containing 581 samples,44,45 we found that the

expression of Dicer is indeed lower in metastatic samples than

the non-metastatic samples. Moreover, low expression of

Dicer is able to predict poor outcomes for breast cancer

patients.

Fig. 1 Representations of cell signaling networks. (A) Traditional, pathway specific view with receptors activating linear signaling cascades

leading to TFs activation, gene expression and protein. (B) Network view where biological information from high-throughput experiments is used

to build an unbiased network where components are not necessarily linked to one pathway. Also shown in (B) is the possible feedback loops within

gene expression networks. C: Systems analysis of biological networks components. Here a 3 nodes network is analyzed with ODEs, showing

2 recurrent cases: adaptation and bistable switching (further analysis of these motifs is provided in Fig. 2).

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Protein ubiquitination preferentially occurs in positive

signaling regulatory network motifs, however, these motifs have

functions of predominately inducing or positively regulating

apoptosis, a major component in cancer signaling.46 Therefore,

higher activities of protein degradation in these network

motifs could block apoptosis in cells, and then promote cancer

progression and metastasis. Indeed, the high expression level of

the genes for the 26S proteasome is significantly correlated with

tumor progression and metastasis.46 Furthermore, the expression

of the 26S proteasome gene set predicts the clinical outcome of

breast cancer patients.46 These observations suggest that the

molecular mechanisms of mRNA or protein degradation are in

general highly active in cancer cells. This insight has implications

for the development of cancer treatments and prognostic markers

could focus on the machinery of the molecular mechanisms of

mRNA or protein degradation.

Cancer network motifs tend to form clusters as hotspots

in the human signaling network47 and even form a larger

sub-network or a cancer signaling map. A cancer signaling

map has been constructed by mapping the cancer mutation

data derived from large-scale cancer genome sequencing onto

a human signaling network.1 Further network analysis identified a

network module containing B50 genes which are highly

interconnected and enriched with tumor suppressors and cell

cycle genes. This network module (common cancer signaling

module) is frequently used by many cancer samples regardless

of cancer types such that at least one gene from this network

module gets mutated cross B600 cancer samples studied.1

This result highlights that the common cancer signaling

network module is critical to cancer signaling for many

different cancer types. Furthermore, this insight led to the

development of an algorithm for finding high-quality cancer

Fig. 2 Feedback principles and their application within biological network motifs. The network motifs are modeled by ODE according to

principles presented in recent works.18,19,59,74

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biomarkers, focusing on cancer hallmarks’ gene expression

profiles.48 Moreover, each identified network prognostic

module contains a set of cancer mutating genes and their

interacting protein partners, both of which represent the same

biological process for a cancer hallmark.48 These modules

have high predicting accuracy (B90%) and high robustness

as validated in more than 1300 breast cancer patients.

Taken together, cancer network motifs and modules exhibit

special network properties and have mechanistic and practical

implications in cancer. Therefore, it will be critical to further

investigate how functionality arises (and is lost) in these

cancer-related motifs and modules and the following text will

provide some thought on how to use ODE models to that end.

Importance of feedback interactions

As shown above, positive and negative network motifs are

prevalent in cancer cells. The notion that feedback is important in

biology has been put forward in control theory49 and can be

traced back to the origins of cybernetics.50 The two major

concepts in this regard are positive and negative feedback.

Positive feedback, in which a molecule, cell or organism

promotes its own production or replication, is a fundamental

principle of biological evolution and organization, i.e., all

forms of life are self-replicating systems. Positive feedback

principles have many implications for cancer, the first being

that cancer cells are better at self-replication and are thus

favored in a selective environment.51 However, positive feed-

back can also be traced to the internal functioning of cancer

networks,52,53 and we will return to this point later. Negative

feedback is an important mechanism to organize and control

biological processes so that exponential growth is avoided16,18

or noise is reduced.54 Feedback in biological systems is able to

induce complex, dynamic behavior;16,55,56 this will not be

observed from the static, steady-state response of the system,

but rather from the temporal response to a perturbation of the

system. This has implication for experimental design, as the

typical dose-response experiments in biology do not account

for the dynamical aspects of the problem, and so experiments

should be designed accordingly.29,36,37,53

Functionality arising from simple, recurrent motifs and feedback

rules

The analysis of feedback motifs in biology allows for

identification of simple, yet rigorous, explanations for complex

dynamic behavior. In this regard, many observations can be

drawn on the functional properties of these network motifs

and have been reviewed elsewhere.55–57,16,20,24 In this review,

we will touch upon some of the possible functional properties

that can arise from feedback interactions in a 3-node network

motif (see Fig. 2); these motifs were built with current

knowledge and frameworks.19,20 Previous studies have only

highlighted specific aspects of feedback motifs, such as

adaptation.19 In Fig. 2, we want to emphasize that 3-node

networks are able to summarize simple and recurrent feedback

concepts in biology. Some common topologies are shown and

the recurrent mechanisms we show can be summarized as

follows.

� Node A (blue) mediates the input signal (cyan) and

communicates information to the rest of the network, e.g., a

membrane receptor or signaling kinase.

� Node C (red) is the output node from which a certain

dynamic response is expected, e.g., a TF in gene regulation, a

specific gene expression level in signaling or the production of

a molecule in a metabolic pathway.

� Node B (green) is the ‘buffer node’,19,20 which, depending

on the topology, corrects, delays or amplifies the response of

node C.

From this perspective, the question we ask is how the

topology and dynamics of the 3-node motif produces a certain

shape in the output node (C) for a specific input signal (I). In

Fig. 2, we highlight some of most common examples drawn

from various cellular processes. Careful dynamical analysis of

these networks motifs will be extremely important if we are

interested in understanding the behavior of normal and cancer

cells at the systems level. Thus, we will review these network

motifs, their properties and their relevance to cancer biological

networks. Note that Fig. 2 shows generic examples of feedback

motifs while many specific examples will be slightly more

complicated. For example, we show negative and positive

feedback loops containing 3 nodes, while the actual feedback

loops in a specific cellular process might be hidden in more

complex cascades consisting of more than 3 nodes. Apart from

the obvious delay that would result from the longer paths, the

basic principles remain essentially the same. The following

subsections will concentrate on the 6 network motifs presented

in Fig. 2 and their implications for cancer biology at various

levels, including gene regulation, signaling and metabolic

networks. One recurring theme in the subsequent analysis will

be the response of the motifs after a certain input ‘I’ is applied.

In terms of experimental investigations, this input is generally

an extracellular molecule (ligand, drug etc.) for which we can

decide the concentration profile.

A complete description of the network motifs and

computational methods is presented in Supplementary

Material 1 (SM1). The objective of this review is not to

highlight all the available computational methods to build

and calibrate ODE models. The examples shown in Fig. 2 are

thus intentionally generic and will be analyzed with emphasis

on their recurrence (even if only qualitatively) at various

levels of biological organization. The issue of parameter

calibration and network determination is also briefly discussed

in SM1 and interesting examples can be found in the

literature.1,14,22,36,37,58,59 The ODEs models of the network

motifs were implemented in the Matlab computing environment

(The MathWorks Inc., Natick, MA, USA) using the Systems

Biology toolbox.60

Negative feedback: adaptive response

The first row in Fig. 2A shows the adaptive response that

occurs for the integral negative feedback motif. In this study,

the concept of ‘integral feedback’ refers to the well-known

control theory principle of integrating the output error over

time and using this information to correct the process. More

specifically in Fig. 2A, the output is the level of node C and its

‘error’ is the deviation from 0. As seen in Fig. 2A (and from

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the equations in SM1), node B accumulates at a rate propor-

tional to signal C, the result being that the level of B is,

mathematically speaking, the integral of C with respect to

time. The interested reader is referred to previous works

on the subject,18 where a more elaborate development on this

equivalence between control theory and biological regulation

was presented.

The concept of integral negative feedback is observed at

practically all levels of biological organization and is an important

part of the adaptive response in biological systems.16,18–21,57,61 As

shown in Fig. 2A, if the dynamic response of node B is slower than

A–C, some time is available for C to accumulate. However, any

change in C is eventually corrected by the accumulation of B, and

the system returns to its original value. The result is that a

continuous signal (I) is transformed to a transient signal (C),

which has been observed in signaling cascades57,61 and gene

regulation.20 Recently, this configuration has been studied

extensively and has been shown to be one of two possible

ways to achieve adaptation.19 As this sort of transient

behavior is observed in signaling cascades related to cancer,57,61

its deregulation would have oncogenic properties, especially if

a growth signal that should be temporal (i.e., shaped as the C

node response) instead became continuous. In that regard,

oncogenic potential might not lie within a specific gene, but

rather in the disruption of a negative feedback motif in the

network. Interestingly, it should be noted that integral feedback

by a buffer molecule has also been identified in glycolysis,18

which has implications for the adaptive response of glycolysis

to perturbations. Because glycolysis and energy metabolism

are deregulated in many cancers,4,5 a more complete under-

standing of the underlying regulation structures will be crucial

in establishing which enzymes are the most promising

therapeutic targets.

Negative feedforward loop motif: robust response

Recently, there has been substantial interest in the structure

and function of the ‘incoherent feedforward loop’ motif in

biological networks.20 The term ‘incoherent’ comes from the

fact that the buffer node B (Fig. 2A, second motif) seems to

work in opposition to the signal flow between A and C (i.e., it

tries to shut down the signal). However, as has been reported

in many studies, this motif is recurrent57 and produces specific

responses, such as fold-change detection62 and noise attenuation.63

If node B is relatively slow to accumulate, adaptation will be

observed19 in a similar vein as the negative feedback loop.

However, an interesting property of the negative feedforward

loop is its potential to act faster because the signal from A

arrives to B and C at the same time. Shown in Fig. 2A (second

motif) is a situation in which node B accumulates in the same

dynamic range as A. Thus, the changes in C, which are

induced by A, are rapidly compensated by B, and the output

node C is limited to a narrow range of values (i.e., the motif

filters out noise from the input).

Interestingly, because a rapid response and negative regulation

is required from node B, we can expect miRNAs to be good

candidates to perform such a function in gene regulation

networks; this has been verified.64 Considering that miRNAs

mutations are involved in many cancers2 we can safely assume

that a better delineation of the regulation motifs in which

these mutations occur will be critical. Additionally, a negative

feedforward mechanism has been reported in a modeling

study of brain energy regulation;18 energy demand in

neurons was signaled to nearby astrocytes, which reacted by

providing energy substrates to neurons, thereby potentially

reducing noise in energy levels. Mutation of enzymes involved

in energy metabolism are found in a significant proportion

of gliomas;4 thus, a good understanding of the underlying

regulation motifs in brain metabolism will be important,

especially as many drugs also target energy metabolism in

cancer.5,6

Positive feedback motifs: the robust switch

Fig. 2B shows the positive feedback motif in which node C,

once activated by A, can keep itself active through a loop with

node B. If the feedback is strong enough, the loop between B

and C can remain active even after the input signal is

completely removed, thus making the switch irreversible. This

will transform the transient input signal into a continuous one.

Based on the same principle, the switch can also be reversible,16

only operate for a specific input range and shut down when the

input is removed. Accordingly, it is important to distinguish

between exclusive and non-exclusive switches. The first case

presented in Fig. 2B is the non-exclusive loop, in which nodes

B and C are activated together. Replacing the double positive

feedback with double negative feedback (Fig. 2B, second

motif) produces exclusive switching. More specifically, the

motif shown here is the toggle switch,16 whereas the system

can be switched ‘on’ (i.e. higher concentration of C) or ‘off’

(lower concentration) by transient pulses of a signal around an

‘operating point’ (shown here with I = 0.5).

Many examples of such mechanism have been described for

cell signaling65,66 and gene regulation.67 Cell division and cell

cycle are also regulated by reversible positive feedback loops,68

which allow switching between critical steps with more

robustness (i.e. the ‘all-or-none’ response) compared to, for

example, a direct response to a growth signal.16,24 However,

this robust response from the positive feedback motif comes at

a price; a reversible switch for normal cellular growth might

become deregulated by oncogenic mutations and then easily

become irreversible, leading to continuous growth and

uncontrolled proliferation. Recent examples of uncontrolled

cell proliferation due to positive feedback gone wrong can be

found52,53 and it is clear that the concept of positive feedback

will become more important as we unravel the complexities of

cancer-related networks. The experimental and modeling

approaches used to identify such structures53,68 should thus

be carefully studied and applied to other cellular processes.

At the metabolic level, examples of positive feedback are

much less common, but some examples can be found in oxidative

metabolism, such as reactive oxygen species can increase their own

production in aging cells through positive feedback,69 which could

potentially have implications for cancer biology. Again, instead of

focusing on specific genes, the identification of positive feedback

loops and their components in biological networks will improve

the process of mining the wealth of experimental data on

cancer-related mutations.1,14,34,52,68

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Delays and cascades

Fig. 2C shows a slightly different case: reactions from A to C

now include a cascade. If the cascade is direct (A - B - C)

and the transition between states is sharp,16,20 the response

node C can be a temporal transition of the input, which has

implications mostly for differentiation and developmental

processes.56 If we add negative feedback in the cascade

(C - B - A - C, second motif in Fig. 2C), the structure

becomes prone to oscillations, although the parameters of the

system could be such that the loop is fast enough to be stable

(as shown in the first panel in Fig. 2). Oscillations caused by

negative feedback with delay are quite common in biological

systems and are observed in many processes, including cell

cycle,70 metabolism,18,71 signaling72 and gene expression.58

This seemingly unstable behavior might be seen as an undesirable

effect of a feedback loop gone wrong (i.e., we intuitively expect

the feedback to work as shown in first panel in Fig. 2).

However, the oscillations can be desirable for circadian

rhythms, the synchronization of populations or the transient

expression of certain genes. With regard to cancer, many

examples are found, with the most important being the

negative feedback regulation of p53 via Mdm2, which can

generate pulsed responses (i.e. damped oscillations) to radiation

stress.58,73,74 The advantage of generating oscillations in p53

concentration is not clear yet, but it could help to repair DNA

damage if there is not a continuous exposure of the cellular

environment to this protein. Again, a better understanding of

the dynamic regulation of p53 and its oscillations will be

crucial for cancer research.75 A very interesting observation

concerning p53 oscillations is that the system seems to be

tunable depending on the amount of damage imposed. Moreover,

in this system, cancer cells react differently compared to

normal cells,73–75 with a critical difference being the development

of continuous oscillations (as shown in Fig. 2) instead of

damped oscillations. Although p53 and its interacting neighbors

are well-known therapeutic targets in cancer therapy, it might

be impossible to design therapies without a better understanding

of the dynamics of the system, and, in that regard, it is clear

that the analysis of the underlying dynamic network motifs is

critical.75 Finally, it is also known that metabolic pathways

can oscillate due to negative feedback, with glycolysis (under

anaerobic conditions) being one of the many examples. The

implication of glycolytic deregulation in cancer has been

understood since the pioneering work of Warburg,76 and

many studies now integrate energy metabolism into the global

picture of cancer biology,77 which has direct consequences for

drug development.78 The analysis of energy metabolism in

terms of feedback motifs has been performed in a theoretical

study;16 it will be important to assess the stability of these

metabolic feedback motifs in the presence of cancer mutations.

Implications for future research

As we can see from these recent works on biological feedback

motifs and their implications for cancer, the ‘local’ dynamical

properties in networks are the functional units on which larger

networks are built. In that context, it is clear that systems

biology and network approaches are not just about large-scale

data, but also about careful integration of feedback functions.

For most biological processes involved in cancer, we now have

access to a wealth of data, to a point where it is hard to draw

clear conclusions. A major problem is that the data are

context-dependent22,36,53 and do not always take into account

the dynamic behavior of the system. Therefore, we emphasized

that dynamic network motifs analysis provides a framework,

with which it becomes possible to relate seemingly unrelated

observations. We thus emphasized the possible links between

signaling, gene regulation and metabolic networks in the sense

that they share common functional units that are deregulated

in various cancers.

Thus, a major endeavor for future research will be the

integration of ‘omics’ data within the framework of dynamical

systems.79 However, the size of biological networks, often in

the range of a few hundred to a few thousand components,

makes it difficult to rapidly identify interesting targets,

especially when experimental studies are required. Therefore,

when studying a certain biological process related to cancer, a

first step should be to look for specific functional motifs, such

as the ones highlighted in this review, and to determine if they

are significantly involved in the specific process that is under

scrutiny. From this basic, preliminary understanding of the

system, it becomes easier to develop a rigorous experimental

design.59,80 As a synthetic example of this, Fig. 3 shows how

time series data can be used to construct and analyze dynamic

network motifs. First, we consider a case where the dynamic

response of a system (i.e. node C in our example) is measured

in normal conditions (red dots in Fig. 3A) and in the presence

of an inhibitor (purple dots in Fig. 3A), whereas in this specific

case, we know that the inhibitor affects node B. The major

observation is a loss of adaptive capacity for node C in the

presence of the inhibitor. Even though the profile shown here

is a hypothetical example, it does follow along with known

examples of adaptive response in signaling pathways.34,81,82

From this information, we can hypothesize that a negative

feedback (H1 in Fig. 3B) or feedforward loop (H2) is present

in the system, with node B acting as the buffer.19 As shown in

Fig. 3B, models for both motifs can be calibrated to reproduce

the experimental data (see parameters values in SM1). At this

point, it would thus be impossible to further discriminate

between the two motifs. However, using the predictive capacity

of ODE models, we can simulate the effect of an inhibitor of

node C, which reveals different responses for the two feedback

motifs (see Fig. 3C). More specifically, the major difference to

be expected will be in the response of node B in the presence of

the inhibitor, whereas it is active in H2 and inactive in H1.

This type of approach, where models are constructed from

experimental results and then used for hypotheses generation,

will speed up the experimental investigations with minimal

assumptions. The analysis of an ‘atlas’ of feedback motifs was

recently shown to be very effective for the study of develop-

mental processes83 and we argue that cancer research will

benefit from the use of this framework as well. A recent study

also showed how Bayesian modeling can be used to infer

pathway topology from time profile data.84 In that context,

and as shown in Fig. 3, ODE modeling could produce

additional insights and predictions. It is thus important to

highlight that the study of the dynamics in network motifs as

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presented in this review should be seen as a complement to

current approaches, offering the possibility of improved data

analysis. However, as highlighted elsewhere,74,76 experimental

investigations should still rely on hypothesis driven approaches.

A wide assortment of models of cancer cellular networks

calibrated with experimental data are now available34,36,37,40,81,82,85

and should thus be used in similar fashion to identify new

targets and approaches for cancer therapy.86 This will be even

so more important in a context where medicine is moving

towards personalized and predictive treatments.

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