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MODELING AND VISUALIZING SELECTED MOLECULAR COMMUNICATION

PROCESSES IN BIOLOGICAL ORGANISMS: A MULTI-LAYER PERSPECTIVE

by

Aditya Immaneni

A THESIS

Presented to the Faculty of

The Graduate College at the University of Nebraska

In Partial Fulfilment of Requirements

For the Degree of Master of Science

Major: Computer Science

Under the Supervision of Professor Massimiliano Pierobon

Lincoln, Nebraska

April, 2018

MODELING AND VISUALIZING SELECTED MOLECULAR COMMUNICATION

PROCESSES IN BIOLOGICAL ORGANISMS: A MULTI-LAYER PERSPECTIVE

Aditya Immaneni, M.S.

University of Nebraska, 2018

Adviser: Massimiliano Pierobon

The future pervasive communication and computing devices are envisioned to be tightly

integrated with biological systems, i.e., the Internet of Bio-Nano Things. In particular,

the study and exploitation of existing processes for the biochemical information exchange

and elaboration in biological systems are currently at the forefront of this research direction.

Molecular Communication (MC), which studies biochemical information systems with theory

and tools from computer communication engineering, has been recently proposed to model

and characterize the aforementioned processes. Combined with the rapidly growing field

of bio-informatics, which creates a rich profusion of biological data and tools to mine the

underlying information, this investigation direction is set to produce interesting results and

methodologies not only for systems engineering but also for novel scientific discovery. The

multidisciplinary nature of this work presents an interesting challenge in terms of creating a

structured approach to combine the aforementioned disciplines for the study of information

propagation processes in biological organisms, and their relationship with information for

their control, optimization, and exploitation. In this thesis, we study a selection of these

processes, through different and independent contributions, at the system layer, cellular

layer and pathway layer. First, we model the overall functionality of a multicellular metabolic

system, the human digestion, in terms of energy production from major nutrients in the food.

Second, we analyze metabolic processes in a single cell and their adaptability to incoming

nutrient availability information from the environment. Third, we model and characterize

the processes that enable information to propagate from the external environment and be

processed by the cell. Numerical results are presented to provide a first proof-of-concept

characterization of all these processes in terms of communication theory. While it may be

possible to connect each of these layers in future work, this goes beyond the scope of the

work reported in this thesis.

iv

DEDICATION

This thesis is dedicated to my parents Sudhaker and Vani Immaneni

v

ACKNOWLEDGMENTS

I thank my adviser Dr. Massimiliano Pierobon for his continued support and guidance. His

enthusiasm has always motivated me to work harder. I would also like to thank my commit-

tee members: Dr. Juan Cui and Dr. Tomas Helikar for their effort in reviewing my thesis

and their interest in my work.

Moreover, I want to thank all the members of the MBiTe Lab, including Zahmeeth Sakaff

who collaborated with me in studying the cell metabolism and the JAK-STAT pathways. I

also want to thank Ravi, Natalie, Karthik, Colton and Francesca for supporting and helping

me when I needed it the most. I acknowledge Natasha’s help with accessing the computing

resources of the Holland Computing Center and the Open Science Grid. Further I acknowl-

edge Jiang’s help for accessing the TCGA data and for helping me get started with the Open

Science Grid.

Finally, I thank all my family members and friends for their support and inspiration. My

parents, who drive me to be the best version of myself. My sister Maithreyi, for proof reading

my thesis and providing timely feedback.

vi

Table of Contents

1 Introduction 1

2 Bio-System Layer 7

2.1 Simulation of Glucose Metabolism in Cells . . . . . . . . . . . . . . . . . . . 8

2.2 Controlling the Direction of ODE Equations . . . . . . . . . . . . . . . . . . 9

2.3 Result: Glucose and ATP Graphs . . . . . . . . . . . . . . . . . . . . . . . . 11

2.4 Computational Tools for Bio-System Layer . . . . . . . . . . . . . . . . . . . 12

3 Cell Layer 13

3.1 Metabolic Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2 Available Biological Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.3 Result: Visualization of Large Scale Chemical Data . . . . . . . . . . . . . . 16

3.4 Computational Tools for Cell Layer Simulation . . . . . . . . . . . . . . . . . 19

4 Pathway Layer 23

4.1 JAK-STAT Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.2 ODE and Gillespie Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.3 Mutual Information Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.4 Result: Mutual Information Flow Graph . . . . . . . . . . . . . . . . . . . . 39

4.5 MAPK Pathway . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

4.6 Result: Mutual Information Change Due to Mutation . . . . . . . . . . . . . 43

vii

4.7 Computational Tools: Pathway Layer . . . . . . . . . . . . . . . . . . . . . . 46

5 Future Work 47

5.1 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

5.2 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

6 Conclusion 52

Bibliography 53

1

Chapter 1

Introduction

Computer engineering research is experiencing an increasing interest in studying the commu-

nication features of biological processes and organisms, motivated by the recently proposed

Internet of Bio-Nano Things paradigm [1]. At the basis of this research, Molecular Commu-

nication (MC) theory is an emerging branch of communication engineering that studies the

propagation of information through molecule exchange and chemical reactions. Future MC-

enabled devices are envisioned to perform functions such as the detection of heart disease [2],

regulation of insulin levels in the body and to serve as an interface for external devices [3].

The principles of MC can be applied to the design systems that interact with biochemical

processes such as a diagnostic drug delivery system [4] or to code information [5]. It can also

be applied to develop communication systems that interconnect nano-scale devices(nano-

machines) with inorganic machines enabled by nano-technology [6] or with organic machines

enabled by synthetic bilogy [7]. In this thesis, through three different studies we look at MC

in biological organisms.

Among the biological processes that can be studied through MC, metabolism is of particular

interest given its fundamental role of processing nutrients to extract energy in biological

organisms [8]. The metabolic system in the human body is responsible for the production

of energy for various functions performed by the cell. Within the cell, a complex system of

reactions, the metabolic network , is responsible for this energy production as well as cell

2

growth and reproduction. This network can be classified into chains of pathways that utilize

the compound present in the environment to produce energy, biomass and other cellular

compounds. Moreover, metabolic processes are continuously regulated and optimized on the

basis of information on nutrient availability, chemical, and physical condition of the envi-

ronment inside and outside biological organisms. This tight connection of metabolism and

its regulation with information processing and communication makes it a suitable ground to

apply MC theory for its modeling, characterization and model-driven discovery of emergent

behaviors [9], and for its future utilization and engineering into the pervasive computation

and communication substrate of the aforementioned future Internet of Bio-Nano Things.

For this thesis, three different layers are independently studied where a selection of processes

are characterized on their MC performance. In the bio-system layer we look at how complex

multicellular bio-systems react to new information. At the cell layer, we look at how avail-

ability of new information, modifies the processes in a single cell organism. In the pathway

layer we look at how biochemical processes can propagate information within the cell.

Recently developed techniques in image processing combined with the increasing availability

of food data provide tools to estimate the nutrients provided by different kinds of food [10].

When this food is ingested, it is processed by the digestive system to provide glucose that

is then transferred by the blood stream to various cells in the body [11]. The glucose in the

blood is then taken by individual cells for the production of energy [12].

In the bio-system layer by available information on food intake, circulation of glucose

through blood and metabolism of glucose by the cell, a computational model is built for

the analysis of the human digestive system. Metabolism on a large scale is observed in the

digestive system of multicellular organisms, termed in this thesis as the bio-system layer of

metabolism.

At the cell layer, drawing inspiration from [13], the changes in the processes internal to the

cell of single celled microbes are studied. By applying FBA, the steady-state fluxes of the

3

metabolic processes in the human gut microbes Bacteroides thetaiotaomicron (B.theta) and

Methanobrevibacter smithii (M.smithii) are obtained. For these microbes, we considered

seven of the major nutrients in the external environment of the cell as inputs to the network.

The activation and deactivation of these processes is then visualized. Human gut microbes

were studied since they are simple and more treatable.

Next, we looked at the signal transduction network which is a complex communication

channel due to the presence of non-linear behavior, stochasticity, feedback and feed-forward

loops. By studying the signal transduction pathway we understand how information from

the external environment of the cell propagates to the internal structure of the cell to control

cell responses such as metabolism. In the pathway layer, we characterize the performance

of the signal transduction pathway in propagating information external to the cell to the

nucleus of the cell and we also quantify the information handled by each process of the cell.

We then propose a computational method which utilizes stochastic chemical reactions and

estimation of MI from multidimensional data.

The rest of this thesis describes the work done at each of the layers and discusses the results

and computational tools applied. The system layer, cell layer and pathway layer are studied

in Chapters 2, 3 and 4 respectively. As we probe deeper into the layers, the complexity

increases due to increase in information availability. This wealth of information provides an

excellent opportunity to apply various tools and techniques of visualization. Visualization

tools Gephi, D3.js and JHive are studied. Further hive plot visualization is applied in order

to present a complex network in a more compact and informative fashion. Also, as proof of

concept, we characterize the changes in the signal transduction pathways due to mutation.

Through the comparison of the MI between a normal and a mutated signal transduction

pathway, the information loss is quantified. Finally, a proof of concept for a self visualizing

bacterial colony is described.

4

Figure 1.1: Summary of study in bio-system layer

Figure 1.2: Summary of study in cell layer

5

Figure 1.3: Summary of study in pathway layer

Motivation

In my first semester at UNL I took a class in Genetic Engineering. As I learned about the

various mechanisms that govern biological systems, I was fascinated by their similarity to

electronic circuits. The possibility of treating biological systems as a computational and

communication system drew me further into the field. While it was a daunting task, a

layered approach helped me understand the required concepts better.

Contribution

Bio-System Layer: A computational model to estimate the production of glucose and

Adenosine TriPhosphate was developed. The model was then ported to the Open Science

Grid to obtain higher throughput.

6

Cell Layer: For a cells’ metabolism, Mutual Information is calculated with lab data, to

assess the cells’ real world performance as a communication system. The large scale network

of reactions in the cell is visualized with hive plots.

Figure 1.4: Overview of contributions in each individual layer

Pathway Layer: For the JAK-STAT pathway, Mutual Information flow is visualized as

a network. The change in Mutual Information due to mutations in MAPK Pathway is

calculated as well.

7

Chapter 2

Bio-System Layer

When studying a Bio-system layer process, complex sub-processes are treated as black boxes.

This means that we start by understanding the relationship between input and output instead

of the processes that control them. This level of abstraction reduces the complexities of the

underlying system making it easier to study the system as a whole.

In this chapter we study the digestive system. As per the CDC there are 30.3 Million (9.4%

of US population) cases of diabetes. The production of Adenosine TriPhosphate(ATP) is

affected by diabetes [14, 15]. ATP is the energy currency of the cell. ATP is obtained

by processing of glucose by the metabolic pathway of the cell. Since diabetes affects the

processing of glucose by the body, ATP production is affected by diabetes. With increased

availability of food data, including applications that determine the major nutrients in food,

it becomes easier to estimate nutrients in the food intake. In order to study diabetes better,

we built a kinetic model of the metabolic system. By studying the processes involved in the

digestive system a better understanding of diabetes can be obtained. The end goal of the

study here is to integrate the application developed in [10] with a glucose model [8] to give

the ATP produced by the cell. The application in [10] takes an image of a plate of food and

estimates the amount of calories in a plate of food. Further the nutrition information, viz.

the amount of Carbohydrates, Proteins and Fats is provided. This information is utilized by

our model to provide the ATP produced by the cell for the intake of food.

8

Figure 2.1: Overview of the System,background source: [16]

Figure 2.1 gives the overview of the system under study. At the input end, food intake can

be broken down into various nutrients according to its composition. The digestive system

processes nutrients in the system and provides cells with glucose via the blood stream. The

cells uptake glucose available in the blood stream and process it to form ATP. Here, food

intake can be considered as input to the system. Depending on what is measured, cell glucose

or ATP can be considered as the output. Since a large part of the blood glucose comes from

the carbohydrates [17], carbohydrates in the food are the primary focus in food input. As

the output concentration of glucose and ATP produced is received. This can be visualized

as a line graph showing the concentration in time.

2.1 Simulation of Glucose Metabolism in Cells

This section summarizes the contribution by Rad in [8]. The process of cell glucose uptake

and its conversion to glucose is simulated by this model. The model simulates the glucose

metabolism by taking into account the reactions that take place in the glucose metabolism

9

pathway. Reactions in the glucose metabolism pathway are simulated as Ordinary Differen-

tial Equations(ODE). A first order Taylor series expansion is used to find the concentration of

all the species in the reactions. This method was chosen to give a good initial approximation

of the system.

2.2 Controlling the Direction of ODE Equations

In order to connect the input(food intake) to the measured output(ATP), relationship of cell

glucose uptake with food intake is to be understood. As described in [11], insulin levels in

the blood follow the blood glucose levels closely. Figure 2.2 shows this relationship. The

parameters for the graph is obtained by fitting the model described in [11] with the human

blood glucose insulin levels described in [18].

At the initial step of the simulation, a food input is simulated by setting the ingested glucose.

At each step of the simulation the blood glucose and insulin levels are calculated as described

in [11]. From the blood glucose levels the cell glucose levels can be determined by applying

Hills function. The minimum and maximum uptake values can be obtained as described

in [12,19]. At each step the cell ATP levels are calculated by the ODE model.

10

0 50 100 150 200 250 300 350Time is seconds

-50

0

50

100

150

200

Bloo

d G

luco

se m

g/dl

Bloo

d In

sulin

pm

ol/l

GlucoseInsulin

Figure 2.2: Glucose Insulin Graph

Figure 2.3: Model Overview

11

Figure 3.1 gives the overview of the system. SBML (Systems Biology Markup Language) [20]

is a an XML file standard for specifying biochemical reaction data. In our model we take all

the reactions and constants for the metabolic pathway. JSBML (Java SBML) [21] is a Java

library to parse SBML files. Since our model was developed using Java we use JSBML.

2.3 Result: Glucose and ATP Graphs

Figure 2.4: Glucose and ATP Production

Figure 2.4 shows the production of ATP of Glucose and ATP in nMol/L for a simulation

of 10 hours. For this simulation we provided a glucose input at two time steps t=0h and

t=6.5h. These times were chosen to make sure the system reaches a steady state. We see

that the ATP follows the levels of cell glucose. Once glucose levels reach a stable state its

response is seen to be lower than the previous glucose input.

12

2.4 Computational Tools for Bio-System Layer

Many computational tools are available to simplify the process of studying system level inter-

actions. The software MATLAB [22] provides a number of toolboxes to make mathematical

computation easier. In the study described in this chapter, the curve fitting toolbox was

used to fit the data based on the equations in [11].

The Open Science Grid (OSG) [23, 24] is a a great tool for running a large number of sim-

ulations. Each of the simulations are run on their own node, so they all essentially run at

the same time without waiting for the previous one to finish. The challenge here is to make

the simulation portable enough to work independently on any platform. In order to test our

model for various initial concentrations we utilize the OSG. On the OSG, for 100 different

initial concentrations, we obtained a runtime of 1.2 minutes. In contrast, the runtime was 80

minutes for a system with an i7 5700HQ(2.7 Ghz) and 12GB RAM. From the simulations we

obtain a large dataset. The data processing and graph generation becomes a tedious task.

The macros option in MS Excel was used to process the simulation data and to automate

the generation of graphs.

13

Chapter 3

Cell Layer

Moving on to the next layer, we focus on the processes that happen in the cell. Within a cell

there are a lot of reactions that occur at any given time. Hence, we treat the cell as a bag

of reactions that are constantly processing information in the form of external compounds.

Once this information is processed by the cell, the output can be seen as the compounds

released by the cell and sometimes by the physical changes to the cell. At this layer, to

maintain simplicity, the interaction between one cell with another is not studied. Only the

processes and interactions that occur within the cell are considered. Studying the behavior

of a single cell helps with developing a simple model that can be further developed to include

the interactions with other cells.

In this chapter we look at metabolic pathways in a human gut microbes. Since these microbes

are unicellular they are perfect for studying the behavior of a single cell. In particular,

the metabolic pathways of Bacteroides thetaiotaomicron(B.theta) and Methanobrevibacter

smithii(M.smithii) are studied. These were chosen due to the availability of the lab data.

The role of the metabolic pathway is to convert the Input (Growth Medium) to Output

(Biomass). The growth medium is analogous to food intake in the previous chapter as the

growth medium consists of nutrients vital to the growth of the bacteria. We start by looking

at all the processes that go on in the pathway. Once the pathway is well defined, we see the

challenges faced in processing and visualizing the data.

14

3.1 Metabolic Pathway

This section describes the work done by Sakaff in [25].

ZS 2016

Abstraction of Our Binary Encoder (Stage I)

10

cN

c1

c3

c2

Transmitter

Receiver

Channel

Metabolic Network State

Environment Chemical

CompositionEnzyme

ExpressionRegulation

c1 c2 c3 cN. . .

Transmitted Signal Channel Received Signal

r1 r2 r3 rM. . .Enzyme Expression Regulation

JN

J1

J3

J2

Chemical compound 1Chemical compound 2Chemical compound 3Chemical compound 4…

r1=1

r3=1

r2=1r4=1

r5=0

rM=0

r7=1

r8=1

rN=1

Figure 3.1: Abstraction of the Metabolic Communication System

The metabolic pathway contributes to the physical growth of the cell. The input to the

metabolic pathway comes from external compounds present around the cell. Therefore, the

environment that the cell grows in is vital to the metabolic pathway. As discussed earlier,

we treat the metabolic pathway as a channel that transmits the input(Growth Medium) to

output(Biomass and other compounds released by the cell). In order to characterize the

system we need to observe the output for various values of the input. In the case of B.theta

we have 7 compounds that comprise the input which control the reactions that occur within

the cell. Biomass is estimated by taking into account the reactions that contribute to its

formation.

Once this input-output relationship is characterized, the variation of the output to each

value of input is calculated. Mutual Information gives the correlation between two random

variables. Hence, the predictability of the output with respect to an input can be obtained

15

by calculating the Mutual Information of the system. The calculation of Mutual Information

is discussed in a later chapter. The value of Mutual Information can be used to determine

the ideal environmental conditions for the growth of a cell with a focus on the cell providing

more information of its environmental conditions. This means that we can determine the

most optimal environment to use the cell as a transmitter.

For B.theta the Mutual Information upper bound for the lab data was found to be 3.3068

bits. Similarly, for M.Smithii the Mutual Information upper bound is found to be 4.5222

bits.

3.2 Available Biological Data

There are a lot of processes that take place in the cell. These processes are classified into

pathways based on their functions. In order to simplify the calculations we only consider

the metabolic pathway. The other pathways cannot be ignored as these do interact with the

metabolic pathway, controlling the reactions that occur in the pathway. To account for these

interactions we use Flux Balance Analysis(FBA). FBA estimates the reaction fluxes based

on the input. These flux values can be used to simulate the metabolic pathway independent

of the signaling pathways that control it. FBA is run for various growth media. The Growth

media represent the various input combinations possible.

Once the FBA is run, the reaction fluxes for each of the growth media are obtained. This

can be used to simulate the pathway as an ODE model. As described in [26], when FBA

is used, the differential equations can be modeled using Michaelis-Menten rate equations.

This essentially fixes the direction of reversible reactions by treating the enzymes as always

present. From the FBA we obtain the chemical reactions that take part in the metabolic

network, the data is extracted for each of the growth media. It is now possible to obtain the

biomass values for different growth media, enabling the calculation of Mutual Information.

16

3.3 Result: Visualization of Large Scale Chemical Data

Figure 3.2: Network representing active chemical reactions in metabolic pathway

Figure 3.2 shows the chemical reactions that occur in the cell represented as a network. There

are approximately 1000 compounds with 900 reactions happening between them. There are

1000 compounds with the 900 reactions. It is seen that the network representation is complex

and not easy to follow. The nodes are arranged using the Force Atlas 2 [27], which arranges

the nodes so that they don’t overlap and are placed close to the nodes that they share edges

17

with. This results in having the nodes with higher degree (both in and out degree) placed

in the center. The size of the nodes have been made proportional to the degree, making it

easier to identify the compounds which are the most active.

A cleaner way to represent this data is to use hive plots [28]. By prefixing the location of

each node in the network, it becomes easier to study each node. This consistency of location

provides familiarity so that a comparative study can be easily performed. In hive plots nodes

are placed along predetermined axis. The hierarchy of the nodes on the axis is kept constant,

so that the nodes do not vary across different networks.

Figure 3.3 shows the hive plot for a growth medium labeled ’Group F’. Group F represents

a configuration of the input. In order to classify the nodes into reactants, reactions and

products 3 axes are used. The compounds external to the cell are given a higher position in

the hierarchy. This makes it easier to identify the external compounds in network. Although

the nodes and edges have increased, hive plots simplifies the network visualization in the

following way. Consider H2O, an external compound to the cell. Assign it the highest level

in the hierarchy, so that it is always at the top of its axis in the products and reactants.

When comparing two growth media it becomes easy to observe what are the changes to H2O.

Further, differential hive plots can be generated to compare different graphs easily.

18

Figure 3.3: Hive Plots

Figure 3.4 shows two differential hive plots comparing the growth media ’Group F’ with

’Group G’ and ’Group Z’ respectively. Group F and Group G have the same output value

in terms of biomass value and produce the highest in all of the media available. In contrast

Group Z produces the least biomass. In the hive plot we see that Group F and G differ by

a few reactions, while Group F and Z have a larger variation.

19

Media F vs G

Media F vs Z

Figure 3.4

3.4 Computational Tools for Cell Layer Simulation

In this section we look at the tools that can be used for processing the data at cell layer

simulation. Python was used to process the input file obtained after FBA. Python allows for

developing quick prototypes. The libraries available for Python enable easy development of

applications. Pythons’ JSON library was used to extract the data from the input file. The

files required for visualization are generated using Python as well. Following subsections

discuss the visualizations tools used.

Gephi

Gephi [29] is a GUI application for visualizing networks. The nodes can be manually created

or can be imported as a file. For this project we generated the network as a .csv file. Once

20

the network is visualized, a better understanding of the system is obtained. This helps in

deciding the direction of further processing and visualization of the data.

Jhive

Jhive [30] is a java based application used to create hive plots. The software takes files in

the dot format and visualizes them as hive plot. The dot format contains the list of nodes

and the list edges. The algorithm HivePlotGenerator takes a JSON file and converts it to a

dot file for Jhive. The advantage of using Jhive is the inbuilt option to use the differential

hive plot generator.

Algorithm 1: HivePlotGenerator(File)

1 Extract all the compounds(nodes) from the input file

2 The for loop in lines 3-6 sets the nodes for all compounds in different media

3 for each compound extracted do

4 set the position of the compound in the hierarchy

5 set the node labels as compound names and set the relevant data

6 end

7 Create a template graph file with all the node data set

8 for each growth media do

9 for each reaction in the growth media do

10 Set each reaction as a node Set the edges from reactants to the reaction node

Set the edges from reactions to the products

11 end

12 Create the Hive plot file from the Nodes template and the reactions data

extracted.

13 end

21

D3.jS

D3.js [31] is a JavaScript library for most types visualization. It is a very powerful for

visualization, however it required good understanding of JavaScript and other web technolo-

gies. [32] is a good example of a hive plot implementation in D3.js.The advantage here is

that the hive chart can be mode more interactive. Figure 3.5 shows a bar chart developed

using D3.js. Some of the starter code is borrowed from the tutorials [cite links]. The chart

shows the mutual information values obtained for different growth media.

22

Figure 3.5: Chart showing the mutual information values for various input combinations

23

Chapter 4

Pathway Layer

In the previous chapter we looked at the cell as a whole. In this chapter we start looking at

the inner workings of the cell. Specifically, signaling pathways which control the reactions

that occur in the cell. As described in the previous chapter, the signal transduction pathways

control the fluxes of the metabolic pathways. While FBA does gives us the optimal values

of the fluxes, being able to obtain real time fluxes of the reactions in the metabolic pathway

helps us study the cell better.

In this chapter we perform a study in the JAK-STAT pathway, Again, the interactions

between the compounds are modeled as a network. In addition to calculating the Mutual-

Information(MI) between the input to output, the MI value is calculated between the input

and all other modes of the network. We also look at ODE and Gillespie simulations for

studying the JAK-STAT pathway. Next, we look at characterizing the changes due to mu-

tation in the signal transduction pathway. Particularly, we look at the MAPK pathway and

the gene expression data available in TCGA.

Signal Transduction Pathways

Signal transduction pathways are series of chained biochemical processes where molecules

interact with each other to propagate physical or chemical signals through biological cells [9].

24

Figure 4.1: Overview of a signal Network

25

In particular, with reference to Fig. 4.1a, they most commonly propagate extracellular sig-

nals (embedded in physical or chemical parameters in the extracellular environment) into the

cell, where the information they carry is utilized to accordingly regulate major cellular func-

tionalities, such as the cell growth rate and cell division (proliferation), cell differentiation,

cell death (apoptosis, anti-apoptosis), and cell physiological stability (homeostasis). This

propagation is most commonly initiated at the cell membrane by special proteins (biological

macromolecules with specific functions), called receptors, which are sensitive to extracellu-

lar signals by binding to information-bearing molecules from the extracellular environment.

Upon this binding reactions, the receptors undergo a conformational change in the intracel-

lular space, and initiate cascades of chemical reactions, i.e., protein-to-protein interactions,

where specific proteins, the kinases, get activated through the addition of a phosphate group

(phosphorylation), and subsequently, possibly after binding to other protein into complexes,

activate other proteins downstream of the cascade. Other specific proteins, the phosphatases,

“reset” the activated proteins along the cascade by removing the aforementioned phosphate

group (dephosphorylation). These cascaded reactions triggered by the initial extracellular

signal result in the overall propagation of the information through reaction chains, which

ultimately results into the activation of transcription factors, which are other proteins that,

when active, are able to regulate the aforementioned cellular functionalities by increasing

(induced) or decreasing (repressed) the expression of one or more downstream DNA genes

inside the cell nucleus [33]. Through these biochemical processes, the initial information con-

tained in the concentration of extracellular molecules is transduced into the concentration of

bound receptors, which is in turn transduced into the concentration of activated kinases and

protein complexes along the reaction cascade, and finally into the concentration of activated

transcription factors.

26

Molecular Information Abstraction

In this chapter, we abstract the aforementioned biochemical processes underlying cell sig-

nal transduction pathways as communication channels that propagate the input information

from extracellular signals to each protein of the pathway, which ultimately relay this infor-

mation as output information to the transcription factors in the cell nucleus, as sketched

in Fig. 4.1b. Our aim is to provide a quantitative characterization of this information as

it flows through the signal transduction pathway, and we rely on the following assumptions

commonly accepted in computational biology literature:

• The concentrations of all the aforementioned molecular species are considered homoge-

neous at any time instant outside the cell membrane (information-bearing molecules), at

the cell membrane (receptors), inside the cell membrane (phosphorylating proteins), and

inside the cell nucleus (possibly other phosphorylating proteins, transcription factors), re-

spectively. This assumption corresponds to a compartmentalized well-stirred system in

chemical system modeling [34].

• Each chemical reaction in the pathway, expressed in general as AC Bkf

��*)��kr

CCD, where

A;B are the reactant molecule species, C;D are the product molecule species, and kf and

kr and the forward and reverse reaction rates, respectively (for irreversible reactions kr D 0

and the backward arrow is omitted, and B and/or D can be omitted depending on the

reaction), is modeled mathematically through mass action kinetics as follows [34]: dŒC �.t/

dtD

kf ŒA�.t/ŒB�.t/ � kr ŒC �.t/ŒD�.t/, where Œ:�.t/ denotes the concentration of the molecule

species as function of the time t . The same expression is valid by substituting ŒD�.t/ in

place of ŒC �.t/. In the pathway picture of Fig. 4.1b, each circle represents a reactant or

product molecule specie, and each arrow corresponds the molecule specie participation to

a chemical reaction. These molecule species might be subject to degradation reactions,

expressed as Akd

��! 0, where kd is the degradation rate, and action kinetics formulation as

27

dŒA�.t/

dtD �kd ŒA�.t/. Chemical reactions are affected by noise according to the Chemical

Master Equation (CME) [34], which can be computationally implemented through the

Gillespie’s Stochastic Simulation Algorithm (SSA) [35].

• The input concentration of information-bearing molecules in the extracellular environment

Xs.t/, where s is a molecular species out of S extracellular signals, is the result of a

molecule source in the extracellular environment (another cell or a dose provided to the cell

culture during an experiment), which consequently varies the concentration Xs.t0/, where

t0 corresponds to an initial state of the system, by an amount X s, whose value corresponds

to the input information, which is kept constant during the propagation of this information

through the pathway. This models the situation where in a lab experiment a chemical

reagent is added to a cell culture in a determinate quantity [36]. The output concentration

of transcription factors Youtk.t/, as well as the concentration of all the proteins involved

in the aforementioned cascaded reactions of the pathway Yj .t/, are in general functions

of the time t . We define T as the time interval necessary for all these concentrations to

reach a steady-state regime (constant or periodic).

In agreement with the aforementioned assumptions, Fig. 4.1b captures the abstraction of the

information flow in a typical cell signaling pathway, as we propose in this paper. In particular,

the Input Information is carried by a change at time t0 in the extracellular concentrations

of information-bearing molecules at the input of the signal transduction pathway, quantified

through the entropy expression H�fXsg

SsD1

�. This information is propagated through the

signal transduction pathway by the modulation of the interactions between the pathway

proteins, which result into a time evolution of the concentration of each of these proteins

within the aforementioned time interval T . Biological noise and other effects [37] tend to

decrease the information content in the protein interaction modulation by randomization

or equivocation [38] during its propagation in the signaling pathway, resulting in a residual

28

information at each pathway protein, quantified through the Mutual Information (MI) Ij D

I�fXsg

SsD1 I

˚Yj .t/; t0 � t � t0 C T

�at protein j . Finally, the protein-protein interaction

modulation through the pathway is transduced into the modulation of the concentration of

each downstream transcription factor k, k D 1; : : : ; K, which is the Output Information of

the pathway, quantified through the MI Ik D I�fXsg

SsD1 I fYoutk

.t/; t0 � t � t0 C T g�

. In

Fig. 4.1b, and in the rest of the paper, this information flow is graphically depicted for each

pathway protein as a circle with area proportional to the corresponding MI.

4.1 JAK-STAT Pathway

The JAK-STAT pathway is a signal transduction pathway that controls various functions

of the cell including proliferation. Changes in JAK-STAT pathway play significant role in

diabetes [39–41] and plays a part in cancer [42]. In JAK-STAT pathway, the receptors form

a complex with external compounds such as Cytokines. Jak then forms a complex with the

Receptor-Cytokine complex. This complex then recruits STAT, which acts as a transcrip-

tion factor which controls gene regulation. Figure 4.2 shows the JAK-STAT pathway as a

network of chemical reactions. This network is later used to represent the flow of information.

In order to perform a study on the JAK-STAT pathway, a robust model of the pathway is

required. [43] summarizes the available models. Since we are studying the information flow

of the pathway we require data on the chemical reactions that take place in the JAK-STAT

pathway. Therefore we look for kinetic models. Finally, the model by Yamada et al [44] was

chosen because it is a well studied ODE model of the JAK-STAT pathway. The final model

is obtained from the biomodels database [45] as it guarantees that the model is as close as

possible to the the work done in [44]. It is better to use the readily available model rather

than re-invent the wheel. In the previous chapter we had looked at applying flux balance

29

analysis(FBA) to the metabolic pathway. However, a similar approach with Signal Trans-

duction pathways is not possible. For the metabolic pathway it can be assumed that when

an enzyme is available it is always present in high enough quantities to constantly enable the

reaction. Hence Micahelis-Menten kinetics can be applied for the metabolic pathways. How-

ever in the case of signal transduction pathways the concentration of enzymes may or may

not be enough to sustain the reactions. In this case the rate equations need to be modeled

using the mass action kinetics. As a consequence of not being able to use Michaelis-Menten

kinetics, FBA cannot be applied to the signal transduction pathways.

4.2 ODE and Gillespie Simulation

ODE

The JAK-STAT model obtained from biomodels website is used to run ODE simulation.

In the ODE model, the chemical reactions modeled as differential reactions are available.

The concentration of each species can then be found by forming the differential equations

that find the change in species concentration. The model from biomodels is available as

an SBML file. Three tools(MATLAB, Python and COPASI) were tested to run an ODE

simulation. In the end MATLAB was chosen for reasons later discussed when we look at

Gillespie simulation. Utilizing ODE simulation the input sensitivity of the JAK-STAT model

is determined. At this point I would like to acknowledge Zahmeeth Sakaff’s contribution in

determining the input sensitivity. This work was done as a collaboration for [46] . Figure

4.3 visualizes the input sensitivity of the model. Here the input is the concentration of the

Cytokine Interferon, the output is the value of activated Stat1n Dimer(since it controls DNA

transcription). It was found that the pathway is most sensitive to Interferon(IFN) values of

0-20 nMol/litre .

30

End-to-end Molecular Communication Channels in Cell Metabolism: an Information Theoretic Study 0

R

JAK

Receptor-JAK

IFN-Receptor-JAK

IFNRJ2

IFN-R-J2*

STAT1c

IFNRJ2*-STAT1c

STAT1c*

IFNRJ2*-STAT1c*

STAT1c*-STAT1c*

SHP2

IFNRJ2*-SHP2

PPX

STAT1c*-PPX

STAT1c-STAT1c*

STAT1n*-STAT1n*

STAT1n*

PPN

STAT1n*-PPNSTAT1n

STAT1n-STAT1n*

mRNAnmRNAc

SOCS1IFNRJ2*-SOCS1

IFNRJ2*-SHP2-SOCS1-STAT1c

STAT1c*-STAT1c*-PPX

STAT1n*-STAT1n*-PPN

IFNRJ2*-SOCS1-STAT1c

IFN

IFNRJ2*-SHP2-STAT1c

IFNRJ2*-SHP2-SOCS1

IFNR

Nucleus

aCell

Figure 4.2: Jak STAT pathway visualized as a network

31

0

50

100

150

200

250

300#

Tim

e

14

40

36

00

57

60

79

20

10

08

0

12

24

0

14

40

0

16

56

0

18

72

0

20

88

0

23

04

0

25

20

0

27

36

0

29

52

0

31

68

0

33

84

0

[STA

T1n

*-ST

AT1

n*]

(n

M/L

)

Time (seconds)

Figure 4.3: Sensitivity of JAK-STAT to input Interferon

Gillespie Simulation

In an ODE simulation, for each time step it is assumed that all possible reactions occur at

each time step. Therefore, the order in which the reactions are processed is not important.

However, when we consider the way reactions occur, a stochastic order of the reactions is

more realistic. Since chemical reactions are basically interactions of molecules, the order of

chemical reaction is more like a spatiotemporal function. The Gillespie algorithm solves this

by treating the order of reactions as a random event.

Both Copasi and MATLAB have algorithms for Gillespie simulation. MATLAB provides

32

stochastic simulation under the Sim biology toolbox. The SBML file was imported into

MATLAB and the custom rate equations were modified into mass action law equations.

This allowed for Gillespie simulation in MATLAB. Once a valid setup for Gillespie was

obtained, we require a large number of simulations within the input range of IFN pre-

viously calculated. Between the input range of 0-20 nMol/litre with a step of 0.4, we

simulate each concentration 100 times. Although each simulation is not computationally

intensive, calling each of the simulation with a for loop is not as efficient. MATLAB has

a built in for loop called parfor that executes the loop iterations parallely. This signifi-

cantly reduces the computation time as we obtain a better resource utilization. The algo-

rithm ParallelStochasticSimulation(File) shows the Gillespie simulation using the parallel

for. For each of the simulations we store the values of concentration for all time steps.

Algorithm 2: ParallelStochasticSimulation(File)

1 load the sim biology model from the file

2 set the simulation options: Time Steps, Solver, etc.

3 for each concentration between 0 to 20 at 0.4 steps do

4 Set the initial concentration value

5 parfor 100 values do

6 Simulate the model using sim biology Generate the plots Save the data

7 end

8 end

33

Figure 4.4: Plot from Gillespie Simulation

Figure 4.4 shows the plot from the Gillespie simulation. Compared to the ODE simulation

we see that the curves in the plot are not that smooth. This is expected for the stochastic

simulation.

4.3 Mutual Information Calculation

The calculation of mutual information helps quantify the loss of information in the JAK-

STAT pathway. By calculating the Mutual information between the input(Interferon for the

JAK-STAT pathway) and each of the nodes present in the pathway we observe the flow of

information through the pathway. In this section we look at calculating Mutual Information

34

for multi-dimensional data.

The relationship between the various entropies can be seen as:

I. NXsourcej NXdest/ D H. NXsource/ �H. NXsourcej NXdest/ D H. NXdest/ �H. NXdest j NXsource/

H. NXsource/ D

ˇ x maxsource

x minsource

P NXsource.xsource/ log2.P NXsource

.xsource//:dxsource

H. NXsourcej NXdest/ D

ˇ xmaxdest

x mindest

P NXdest.xdest/:

ˇ x maxsource

x minsource

P NXsource j NXdest.xsourcejxdest/:

log2.P NXsource j NXdest.xsourcejxdest//:dxsourcedxdest

Calculation

As per [46], we detail a methodology to estimate the aforementioned molecular information

flow parameters starting from the knowledge of the chemical reactions of the pathway, and

their kinetic rates, as expressed in Sec. 4. For this, we take into account that in general

the signaling pathway communication channels as defined above are characterized by the

non-linearity of chemical reactions, and the effect of feed-forward, and feedback loops in the

pathway reaction cascade [47], which, together with the aforementioned CME noise [34], do

no allow for a closed-form analytical expression of the MI parameters. As a consequence,

in this paper we devise a computational approach based on the stochastic simulation of

chemical reaction kinetics through the aforementioned SSA [35]. Based on this simulation

methodology, we estimate the MI by collecting and analyzing data, inspired by the procedure

in [36,47] with the following three main differences: i) we are based on a computational sim-

ulation rather than expensive wet lab experiments, which does not pose stringent constraints

on the size of the data set that can be collected; ii) we estimate the MI taking into account

35

the complete time evolution of the output, instead of only accounting for a single value of

the output in a dose-response characterization, often made in experimental studies, such as

in [36]; iii) we perform the MI estimation not only at the pathway output, but also at each

protein and protein complex.

For simplicity of notation, in the following we will consider a pathway having only one

species of information-bearing molecules at the input (S D 1), and only one type of output

transcription factors (K D 1). All the following expressions can be generalized to signal

transduction pathways with multiple inputs and outputs.

Computational Approach

Goal

The final goal of our computational approach is the estimation of the MI QIj at each pathway

protein j , expressed as

QIj D QH.X/ � QH.X j˚Yj .t/; t0 � t � t0 C T

/ ; (4.1)

where H.:/ and H.:j:/ denote the estimated entropy and conditional entropy, respectively, X

is the input concentration of information-bearing molecules, and˚Yj .t/; t0 � t � t0 C T

is

the time evolution of the concentration of the pathway protein Yj .t/ within a time interval T

from t0. The estimation of the output MI QIout is expressed as in (4.1) and in the subsequent

equations by substituting out in place of j .

Details

The necessary data for the MI estimations is obtained through SSA simulations of the chem-

ical reactions of the pathway [35]. In particular, for each value xi , i D 0; : : : ; I , of the input

concentration X sampled from the range between xmin and xmax, defined here as the value

below which the concentrations of any pathway protein do not significantly change, and the

36

value above which the same concentrations do not show noticeable changes in their time

evolution, we run a total of R simulations. Each SSA simulation is run independently, and

starts in the same steady state that the system reaches with an input concentration value

X D 0.

The estimated input entropy QH.X/ is computed through the histogram approach [48] as

QH.X/ D �

IXiD1

pX.xi/ log2

�pX.xi/

wX

�; (4.2)

where pX.xi/ D 1=I , according to the simplifying assumption of having a uniformly dis-

tributed input, in agreement with [36], and wX is the sampling interval .xmax � xmin/=I .

The estimated conditional entropy QH.X j˚Yj .t/; t0 � t � t0 C T g/ of the input concentration

X given the time evolution of the concentration of the pathway protein j is computed as

QH.X j˚Yj .t/; t0 � t � t0 C T

/ D

�

XNj;t0

XNj;t1

� � �

XNj;tN

pYj

�˚yj;tn

N

nD0

�Sfyj;tng

N

nD0XsD1

pX jfyj;tng

N

nD0

.xs/

log2

0@pX jfyj;tngN

nD0

.xs/

wX;fyj;tng

N

nD0

1A ; (4.3)

where tN D t0C T , N being the number of time samples considered when discretizing Yj .t/

within the interval T (for computational processing),˚yj;tn

N

nD0is a set of values of the

protein concentration Yj .t/ at time instants t0; t1; : : : ; tN , Nj;tnis the number of histogram

bins considered for the protein concentration value Yj .tn/ to compute the multidimensional

histogram pYj, Sfyj;tng

N

nD0

and wX;fyj;tng

N

nD0

are the number and the size of histogram bins

considered for the input concentration X to compute the histogram pX jfyj;tng

N

nD0

.xs/, where

37

wX;fyj;tng

N

nD0

D .xmax � xmin/=Sfyj;tng

N

nD0

and xs is a value from the concentration input

fxigIiD0 sampled according to the histogram. The numbers of histogram bins Nj;tn

are com-

puted from the aforementioned simulation data according to the Doane’s formula [48] as

follows:

Nj;tnD 1C log2.C /C log2

1C

gYj .tn/

�gYj .tn/

!: (4.4)

where C D I �R is the total number of simulation runs, gYj .tn/ is the estimated 3rd-moment-

skewness of the distribution pYj .tn/ from the simulation data, and �gYj .tn/D

q6.C�2/

.CC1/.CC3/.

The number of histogram bins Sfyj;tng

N

nD0

is computed with a similar expression as in (4.4) by

substituting Yj .tn/ (and C ) with the set of xi values (number of xi values) that resulted in a

concentration evolution for protein j equal to˚yj;tn

N

nD0. Finally, the probabilities pYj

, for

all the J pathway proteins, and pX jfyj;tng

N

nD0

, for all the combination of values yj;tnat each

time instant tn of each of the J pathway proteins, are computed as histogram distributions of

the aforementioned data according to Algorithm 3. In Fig. 4.5 we show a graphical example

of the computation of�fZi;rgtn

; btn

�as per Algorithm 3 for a protein in the case study

pathway detailed in Sec. 4.1, where we consider the results of multiple simulation runs for

different input concentrations, and overlay at tn the Nj;tnequally-spaced bins between min

and max values.

38

!",$%

tn

[STA

T1n*

-STA

T1n*

] (nM

/L)

Time (seconds)

Extracellular Environment

Intracellular Environment

Cell Membrane

Extracellular

Signals

Transcription Factor

InputConcentration

max

min

# '( )*%+

Figure 4.5: Graphical sketch of the computation of Steps 1-4 of Algorithm 3 for the phos-phorylated and dimerized output transcription factor STAT1n*-STAT1n* of the JAK-STATpathway.

39

Algorithm 3: Probability Histograms for Equation (4.3)

Data: R simulation runs for each of I input concentrations containing values for all

N simulation steps

Result: For each protein j , pYjand p

X jfyj;tngN

nD0

1 for each simulation time step tn do

2 Create fZi;rgtnby extracting protein j concentration for each simulation run r

and input concentration i

3 Map each value of fZi;rgtnin Nj;tn

equally-spaced bins (with index btn) between

min and max values, expressed as�fZi;rgtn

; btn

�4 end

5 Obtain matrix M of size C by N by combining all the mapped bin indices btnfor each

simulation run .i; r/ and each time step tn

6 Compute the multidimensional histogram considering each row of M as a datapoint:

pYj

�˚yj;tn

N

nD0

�7 for each bin in the multidimensional histogram do

8 Take all the input values corresponding to the values˚yj;tn

N

nD0that define the

current multidimensional bin

9 Compute the histogram pX jfyj;tng

N

nD0

by mapping the input values found at Step 8

into Sfyj;tng

N

nD0

equally space bins between min and max values

10 If no input value from Step 8, set pX jfyj;tng

N

nD0

D 0

11 end

4.4 Result: Mutual Information Flow Graph

As shown in Fig. 4.6, the JAK-STAT kinetic model that we utilize to compute the numerical

results of this paper consists of J D 34 chemical species (proteins) and 46 reactions, and

40

its complete description and parameter values can be found in [44] and in the Biomodels

database [45], respectively. In this model, the input is the concentration of a small signaling

protein called interferon gamma (IFN- /IFN-green node) while the output is the phosphory-

lated transcription factor STAT1n*-STAT1n* (blue node). In Fig. 4.6 we show the complete

interconnections between different protein species, and proteins at different phosphorylation

(denoted with a * when phosphorylated) or binding (dashed or denoted by their initials)

states involved in reactions.

To obtain the data necessary for our computational approach, we utilized the implementa-

tion of the SSA algorithm in MATLAB Simbiology. Through these simulations, the values

of xmin and xmax, defined in Sec. 4.3, were found to be 0 and 20 nmol/litre, respectively.

For simplicity, we considered a number I D 51 different input concentrations, resulting in

a sampling interval wX D 0:4 nmol/litre. For each input concentration, we arbitrarily run

R D 100 independent simulations for a time interval T D 10; 000 seconds, estimated as

defined in Sec. 4. The time step of each simulation is set to tn � tn�1 D 1 second (N =

10,000). In Fig. 4.5 we show the simulation results for the phosphorylated and dimerized

output transcription factor STAT1n*-STAT1n* at each time step for only one of the R runs

for a restricted number of input concentrations out of I .

The MI values for each pathway protein estimated from the simulation data through the

computational approach in Sec 4.3 is reported in Fig. 4.6, and graphically shown in a cor-

responding proportional size of each graph node (protein). As expected, the value of MI

is decreasing as the information propagates through the reaction cascades, accumulating

chemical noise at each reaction (data processing inequality), from an estimated input en-

tropy QH.X/ D 4:35 bits to an estimated output MI QIout D 1:65 bits.

41

In Fig. 4.7 we show a comparison bar chart between the MI of Fig. 4.6 estimated by taking

into account the time evolution˚Yj .t/; t0 � t � t0 C T

of each protein concentration, and an

MI similarly estimated, but only taking into account the maximum value maxt0�t�t0CT Yj .t/.

As expected, the latter generally underestimates the MI of the pathway proteins.

End-to-end Molecular Communication Channels in Cell Metabolism: an Information Theoretic Study

R(3.69)

JAK(0.56)

Receptor-JAK(4.34)

IFN-Receptor-JAK(4.35)

IFNRJ2(4.35)

IFN-R-J2*(4.03)STAT1c(3.92)

IFNRJ2*-STAT1c(3.86)

STAT1c*(3.98)

IFNRJ2*-STAT1c*(0.61)

STAT1c*-STAT1c*(3.82)

SHP2(3.9)

IFNRJ2*-SHP2(2.03)

PPX(3.88)

STAT1c*-PPX(3.86)

STAT1c-STAT1c*(0.73)

STAT1n*-STAT1n*(1.65)

STAT1n*(1.31)

PPN(1.3)

STAT1n*-PPN(1.06)

STAT1n(0.57)

STAT1n-STAT1n*(0.56)

mRNAn(0.56)mRNAc(0.56)

SOCS1(0.56)IFNRJ2*-SOCS1(0.56)

IFNRJ2*-SHP2-SOCS1-STAT1c(0.56)

STAT1c*-STAT1c*-PPX(3.45)

STAT1n*-STAT1n*-PPN(1)

IFNRJ2*-SOCS1-STAT1c(0.56)

IFN(4.35)

IFNRJ2*-SHP2-STAT1c(3.84)

IFNRJ2*-SHP2-SOCS1(0.56)

IFNR(4.35)

0

Nucleus

aCell

Figure 4.6: Estimated MI of the JAK-STAT pathway (node size proportional to MI value in[bits]).

42

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Mutua

lInformation(in

bits)

Max_Value_Dependent_MI Time_Evolution_Dependent_MI

Figure 4.7: Comp. MI with time evol. Vs. MI with max values.

4.5 MAPK Pathway

The MAPK(Mitogen Activated Protein Kinase) is a signal transduction pathway that has

been shown to be significant in Cancer Research [49–51]. Mutations in the genes of the

MAPK may lead to a cancerous state in the cell. By computing the Mutual Information for

the MAPK pathway as a network we hope to understand how the mutations modify the flow

of information. Similar to the JAK-STAT pathway, the receptor in the MAPK pathway is

EGFR(Epidermal Growth Factor). For transcription factor(output) c-Fos is chosen from the

pathway. In this section we look at applying gene expression data from the TCGA database

to obtain Mutual Information of the MAPK network.

43

TCGA Data

TCGA(The Cancer Genome Atlas) [52] is a database for Genomic data. The database

contains gene data from tumor and non tumor cells for 33 cancer types. For this study we

consider the mutations in the MAPK pathway that lead to colon cancer. Access to cancer

data was ensured by the local copy of the TCGA database hosted by the UNL Systems

Biology and Biomedical Informatics, managed by Dr.Cui. From the database we utilized the

gene expression data. The method utilized to obtain the genomic data is RNA-Seq, which

gives the value of mRNA expression for each gene. The expression is obtained in Fragments

Per Kilobase of transcript per Million mapped reads(FPKM). Since mRNA is responsible

for generating information in the biological cell network, utilizing the gene expression data

should provide us with an estimation of the information flow.

4.6 Result: Mutual Information Change Due to Mutation

In Fig. 4.8 we show data points extracted from TCGA colon cancer data. In the following,

we demonstrate our approach for calculating the communication performance of a signaling

pathway from high-throughput genomic data, and compare them in healthy and cancer cells.

For each sample, we extracted the expression of EGFR and the corresponding expression of

the immediate early gene c-Fos [53]. Although cell signaling pathways are dynamic, and their

input-output behavior is in general a function of the time, we can consider these data points

as steady-state average samples from an ensemble of non-synchronized signaling pathway

states.

44

0

50

100

150

200

250

300

350

400

0 2 4 6 8 1 0 1 2 1 4 1 6

C-FO

S [F

PKM

]

EGFR [FPKM]

mRNA Expression EGFR vs C-FOS

Tumor

Healthy

Poly. (Tumor)

Poly. (Healthy)

Figure 4.8: Egfr vs Fos fpkm

By observing the polynomial trend lines [54] of the healthy samples Vs the tumor sample, it

is clear that in healthy cells the expression of c-Fos can be controlled more precisely and over

a larger range than in tumor cells, where c-Fos is mostly around a stable (and low, as also

confirmed in [55]) value for almost all range of observed EGFR expression. Inspired by the

methods in [13], we can quantify these two cases of controllability in terms of communication

performance of the pathway, i.e., Mutual Information (MI) from information theory [38],

which is expressed as follows: I .EGFRI cFos/ D H .EGFR/ �H .EGFR jcFos /,

where EGFR and cFos represent values of the expression of EGFR and c-Fos observed in

the aforementioned data. The input entropy:

H .EGFR/ D �PK�1

kD1 P .Ak � EGFR < AkC1/ log2 P .Ak � EGFR < AkC1/

is computed from the probability histogram of EGFR values in the data [56] with bin num-

ber K and size AkC1 � Ak chosen according to the Doane’s formula [48]. The conditional

45

entropy of the input given the output H.EGFRjcFos/ is computed as follows:

H.EGFRjcFos/ D �PN�1

nD1 P.Bn � cFos < BnC1/PM�1

mD1 P.Cm � EGFR < �

� CmC1jBn � cFos < BnC1/� log2 P .Cm � EGFR < CmC1 jBn � cFos < BnC1 /

where P .Bn � cFos < BnC1/ and P .Cm � EGFR < CmC1

jBn � cFos < BnC1 / are the probability histogram of cFos values, and EGFR values corre-

sponding to cFos within a determinate histogram bin, computed from values in the data [56]

as mentioned above.

We compute two mutual information values, namely, Ihealthy .EGFRI cFos/ � 0:73 bits

(41 samples) and Itumor .EGFRI cFos/ � 0:27 bits (470 samples) considering in each case

only the data from the healthy samples and tumor samples, respectively. As in communica-

tion theory mutual information expresses how much information at the input of the channel

is contained at its output, or in other words, the controllability of the channel output by

modulating the input, similarly we have quantified the controllability of the c-Fos expres-

sion by modulating the input of the pathways, represented by the EGFR expression. Since

Itumor .EGFRI cFos/ < Ihealthy .EGFRI cFos/, as expected, their difference of 0.46 bits

quantifies the information loss suffered by tumor tissue cells in colorectal cancer through

the mechanism of regulation of the c-Fos gene by the EGF signal. This result demonstrates

that it is possible to infer the communication performance of a signaling pathway from high-

throughput genomic data, and at the same time quantitatively characterize a cancer by a

decrease in these performance. In this project, we will extend this approach to quantita-

tively characterize the communication performance at each reaction in the pathway, and the

performance loss associated to each single genetic change leading to disease. The MI value

for healthy cells was found to be 0.73 bits while for the tumor case it was found to be 0.27

bits.

46

4.7 Computational Tools: Pathway Layer

Some of the tools used in the previous layers are used in the Pathway Layer as well. As de-

scribed earlier MATLAB was used for Gillespie Simulations. Additionally COPASI(COmplex

PAthway SImulator) [57] is provides a convenient way of creating,editing, and simulating

pathway models. SBML files can be imported/exported to/from COPASI allowing for porta-

bility of model.

In section 4.3 we saw the mutual information calculation. For this calculation, based on the

number of simulations and time duration of simulation, we generate a 5000 by 10000 matrix,

for each of the 33 compounds. On a system with an i7 5700HQ(2.7 Ghz) and 12GB RAM

a run time was 14 hours was required for the computation. Further the calculation is IO

intensive as all the data has to be loaded from the disk and cannot be stored in the memory

due to large size. In order to speed up the calculations we used the Holland Computing

Center at UNL. By dividing the task load between 8 nodes of the HCC we were able to

reduce the computation time to 4 hours.

47

Chapter 5

Future Work

For future work we hope to add another layer to this layered perspective. Abstracting a

system even further, we consider the interaction between two organisms or more specifically

a colony of single celled organisms that interact with each other. We propose to control these

interactions to the effect of obtaining a system that can visualize itself or its surroundings.

We hope to provide a way to effectively communicate the state of our system which can

be perceived instead of being interpreted. We take the example of a bacterial colony that

can sense the toxicity of water. The toxicity of the colony can be effectively communicated

through self visualization. Once a toxicity is sensed, this would be converted to a meaningful

number which can be displayed by the colony. Further we divide the tasks into sensing and

visualization by introducing a second colony. The introduction of the second colony provides

modularity, simplicity, and standardizes the system. The second colony could display the

result of any function performed by the first colony so long as its output matches the input

to the second colony. A membrane can be used to separate the colonies, such that only the

input signal of the second colony can pass through the membrane.

48

Figure 5.1: System Block Diagram

5.1 Design

We base our design on a simple seven segment display. A seven segment display utilizes 4

horizontal and 3 vertical segments to form a display. A light emitting diode illuminates each

of the segment; the illumination of a segment is based on the number being displayed. The

light emitting diodes would be replaced by bacteria with Green Florescence Protein (GFP),

whose production of GFP is based on the number being displayed and their location with

respect to the segment markers. GFP is a protein that reflects ultra violet light. Therefore

the bacteria glows under ultra violet light when GFP is present.

49

Figure 5.2: Segment Markers

Figure 5.2 shows the layout of the segments labeled from one to seven. in order to display

the number 3, the segments one and six would be off and the segments two,three, four, five

and seven would be on. We can utilize the below truth table to form the necessary equations

for each of the segments.

Table 5.1: Truth Table for 7 segment display

Number D C B A 1 2 3 4 5 6 7

0 0 0 0 0 1 1 1 1 1 1 01 0 0 0 1 0 0 1 1 0 0 02 0 0 1 0 0 1 1 0 1 1 13 0 0 1 1 0 1 1 1 1 0 14 0 1 0 0 1 0 1 1 1 0 15 0 1 0 1 1 1 0 1 1 0 16 0 1 1 0 1 1 0 1 1 1 17 0 1 1 1 0 1 1 1 0 0 08 1 0 0 0 1 1 1 1 1 1 19 1 0 0 1 1 1 1 1 0 0 1

By using Karnaugh maps we obtain the following equations:

one = D+C*B’+B’.A’+C.A’

50

two=D+B+CA+C’A’

three= D+C’+B’A’+BA

four=D+C+B’+A

five= D+C’B+C’A’+BA’+CB’A

six=C’A’+BA’

seven=D+CB’+BA’+C’B

where A’ represents the compliment of A.

The values derived from the above equations are boolean values which can be used to control

the production of GFP.

5.2 Simulation

Gro is used to simulate bacterial colonies. It is helps prototype the logic for a genetically

engineered cell. It was developed by the Klavins Lab for Synthetic Biology at the University

of Washington. [58]

We simulate the system by hard-coding the number to display in binary format. Using 4

boolean variables bit0 to bit4 we specify the numbers from 0-9. The bacterial colony is then

allowed to grow for 26 seconds of simulation time and the growth rate is then set to zero.

This prevents the bacteria from moving. As the simulation time reaches 30 seconds, we

enable the display function which makes the bacteria produce GFP based on the equations

for the segments. If the bacteria senses the chemical signal for a segment and if the segment

equation is true, the bacteria produces GFP.

51

Figure 5.3: GRO Screenshot

Figure 5.3 shows the number 6 displayed using the GRO simulator.

52

Chapter 6

Conclusion

We observed the various types of data available at each layer of the system. Further, some

of the tools available to a Bioinformatician are studied. With more and more discoveries in

the field of biology, it will become essential to keep track of all the resources available. For

data sources we have; TCGA for Genomic and Cancer Data and The Biomodels repository

for pathway data. While for Computation we have

• Python for data processing

• MATLAB for metamathematical studies

• HCC and OSG for large scale computation

For visualization we demonstrate the capabilities of Excel, D3.js, Gephi and Jhive. In the

context of communication we show how Mutual Information calculations can be applied at

the cell and pathway layers to quantify the communications that happen within the system.

We also briefly look at building biological systems that can communicate their internal state.

53

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