Computer Engineering

Bogazici University

Bebek,Istanbul 34342 Turkey

Submitted to

CMPE 58B Final Project

by

Melih Sozdinler

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Digital Organism Simulates Life and

Cancer Evolution

Haluk Bingol, Melih Sozdinler

January 15, 2010

Abstract

From just two cells somehow, human being emerges. During this de-

velopment, cells form some structures called tissues. Tissues form organs.

Organs form Systems. This is basic knowledge to form simple human be-

ing. With this project, we are going to try to simulate this development

as a digital organism. We will try to understand which model could be

used and what parameters are needed for this kind of organism. It is

interesting to represent some illnesses such as cancer. Cancer is due to

the malfunction of one or several cells [1]. We can add some parameters

into the digital living systems to see in what ways the malfunction of one

digital cell causes cancer. With this perspective, we can have a detailed

investigation over cancer cell evolution.

1 Introduction

We motivated to simulate the living organism in digital environment. Our main

concern is to show that during the evolution of cells to organs in what ways

some illnesses may occur. For instance, Cancer is one of the serious illnesses

that human being encountered recently. We can understand some mechanisms

behind Cancer, and early detection is vital part to become cured.

In our case, we model a digital organism with cells and corresponding organs.

Organism is dynamic, meanly, new cells can be formed and older cells may

die. To this environment, we add some specific parameters such as mutation to

constitute and simulate digital organism and which factors lead to the emergence

of cancer or other diseases due to mutation.

In the literature, there are some efforts to form digital organisms [4]. In [9]

they found that the organism size promotes multi cellular structures in digital

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organisms. In [7], they called a space for replication as soup and each cell

chooses one random option for itself. They claim that random mutations derived

more complex and more efficient organism. In [2], they are trying to determine

the critical mutation rate for digital organism. Also, in [3] they investigated the

evolution in robust environment and how they can adopt to harsh environment.

Moreover, in [5] they argue the relations and interactions in digital organism

and they conclude that compex organisms are more robust to single mutation

and multiple mutation rates. In [8] and [10], they arguee the multicellular lives

and how it can be multicellular organism evolves from a single cell. In [6], they

are also trying to convey the origin of complex feature using digital organisms.

During this project paper, we will mainly concern to experiment the model

with different effecting parameters by tuning these parameters. Our digital

organism consist of imitated cells with gene sequences rather than having an

instruction set. We called as digital organism since we imitate the functions of an

organism with digital cells and their gene sequence. Indeed, we try to come up

with some important results. Paper outline is; we first give the model definition

and then we show some experimental results, finally, we make a conclusion.

2 Methods

The digital organism that we model have specific parameters. In order to define

an organ from cells, first we need to define an organ cell. In our setup, organ

cell constitutes a digital binary gene sequences with length lsequence. Binary

genes mean that organ cells have specific genes plus some other genes at a given

specific intervals. The first constraint is minimum number of genes parameter

that is needed by a organ for the specific gene interval over digital gene se-

quences referred as αmin. If this constraint is not maintained by any cell of

organ, this cell is considered as out of organ and forms unmaintained structure.

These structures are all called Cancer Cell in our assumption. In real organism,

forming Cancer Cell can occur for several reasons. We notice that one of the

main reason is malfunctioning replication. This means that, new born cell have

its roots from the parent cells and if there is a disorder during the replication,

cell may completely differ from its parent cell and neighbor cells as well. At

this time, the living body should respond these cells since when they replicate,

they will maintain another copy. So the living organism should defeat these

cells before they maintain sufficient number of cells in group. This assumption

realistic since our body have many malfunctioning cells even when we are read-

ing these sentences. We are also fighting against these cells to avoid from rapid

replication of these cells. Indeed, our digital organism does not like these cells.

We called these cells as alone cells after first formation. At each time step, digi-

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Figure 1: Digital Organism with several digital organs and its topology

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tal organism handles each cells with some probability pdie−alone. pdie−alone can

hold for any cell and when it holds, organism checks the neighborhood whether

or not the cell is rare in its neighborhood. If it is rare organism feels that it is

enemy. Then, it absorbs the cell.

We also, another probability called pdie−rate. When pdie−rate holds for any

cell, it dies. Then, new cell introduced into organism for the randomly selected

organ. The new formed cell is also connected to some neighbors from the same

organ.

The topology of our organism consist of cells and interactions among these

cells. Each cell connected to the other cells of the same organ with size αconnectivity

parameter. It is usually defined before the simulation. Furthermore, we have

also selected cells among the set of cells of each organs as a boundary cells whom

are connected to the other organs with the sum of the total size αconnectivityout.

We mention about organ interval and genes sequence. Each digital cells

have a sequence of genes. If it belongs to specific organ, then it should have

unique interval that contains a sequence of genes specified by the organ. The

organ interval has specific length parameter called as linterval where lsequence >

linterval.

We have also one more parameter, to specify number of organs as αtypes.

Finally, crucial part of our simulation is mutation parameter referred as

pmutate. When mutation occurs with the probability pmutate, the inverse subset

of genes are selected and the cell of an specific organ turns into unmaintained

structure or Cancer Cell.

We believe that all these parameters are sufficient enough to form real or-

ganism and imitate the artificial life of this organism. We have two showcase,

in Figure 2 and 3. In these two figures, αtypes = 5, αconnectivityout= 10,

αconnectivity = 10, pdying = 0.001, linterval = 20 and lsequence = 100. In Figure

2, you will see four subfigures, each of them have different pmutate and constant

pdie−alone = 0.001. As mutation probability increases, organism can not main-

tain its self structure and gradually from a to d, digital organism is mutated

and indeed have serious cancer problem at each organ. In Figure 3, you will

see three subfigures again with different pmutate and constant pdie−alone = 0.01.

This time pdie−alone = 0.01 is helpful to the organism and somehow digital

organism resist to cancer cells although it has lost some organ cells. We can

directly relate pdie−alone to some drugs and treatment. In this figure, treatment

and drugs responded well against mutation and can stop the diffusion.

At the next section, we will discover how mutation rate and other param-

eters are effective over the organism when they are manipulated. We have

sophisticated evaluations and then we will have a conclusion section.

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Figure 2: Network status after 1000 iterations with die alone rate 0.001mutation rate (a)0.02;(b)0.05;(c)0.10;(d)0.50

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Figure 3: Network status after 1000 iterations with die alone rate 0.01mutation rate (a)0.02;(b)0.05;(c)0.10

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Figure 4: Experiment 1.1 Histograms

3 Results and Discussions

Our digital organism consists of several parameters. Each parameters have

different contribution and loss. Since we are interested with the ratio of the

cancer cells at specific time instances, we will mainly try to in what way digital

organism can cure the cancer cells.

We have several comparison issues. The first one is considering the effect of

changes in pdie−alone rate. Next, we will check how pmutate effects the organism.

Then, we will have an experiment to see the results of different αconnectivity

values.

3.1 Die Alone Probability vs Ratio of Cancer Cells

In Figure 4, histograms are given to the corresponding pdie−alone probability.

When pdie−alone rate is 0, we have the highest Ratio of Cancer Cells. This is

expected since no stopping mechanism is proposed for the replication of cancer

cells. If we increase the pdie−alone probability rate, each cell who are alone in the

neighborhood will be handled with pdie−alone. Indeed, the continuous increase

helps us to decrease the Ratio of Cancer Cells at all tested size of organisms.

For each case, we iterate 1000 time iterations to mature the digital organism

and then it is repeated 10 times due to computation constraints. As a result, we

obtained exponential decrease for each pdie−alone rate. This experiment gives

us a clue about the treatment technique. When the organism size is small, we

need a cure technique that is more fatal than compared to larger organisms.

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Figure 5: Experiment 1.2 Plots

Large organisms could have more chance to deal with the mutated cells.

In Figure 5, we give 3D plots of the network size between 500 and 600, the

mutation probability and probability of die alone between 0.10 to 0.50. The

implication of these plots are die alone rate works for the sake of mutation

probability due to the high mutation probability and normal cell begins to die.

3.2 Mutation Probability vs Ratio of Cancer Cells

In Figure 6, we have several plots corresponding to different mutation prob-

ability. pdie−alone probability is constant, 0.005. Interestingly, plots reach to

the top for all pmutate values at smaller organism sizes. Each plots are like a

logarithmic distribution. The trend of plots are decreasing, and when we in-

crease the mutation rate, Ratio of Cancer Cells decreases more aggressively at

a given increasing networks size. Indeed, all the plots converges to the some

points closer to 0.

It is relevant for cancer cells that increasing the size of the organism makes

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Figure 6: Experiment 2 Plots

the mutated cells alone and although we increase mutate probability, digital

organism can deal with this increase using the experimented pmutate. We can

make a conclusion that larger organisms can resist the mutation rate with the

help of cell population in both organs and immune system. We do not implement

the immune mechanism but the size of organism forms a natural immunity

against the mutated cells.

3.3 Connectivity vs Ratio of Cancer Cells

The connectivity between digital organ cells maintain the crowd behavior. Each

connected other organ types and cancer cells can not interrupt this behavior eas-

ily as shown in Figures 2, 3 and 1. In Figure 7, we tested different connectivity

values and according to the results we can detect that connectivity likes low ”Ra-

tio of Cancer Cells”. During the experiment, we tested 20 times 1000 time step

for specific organism size and αconnectivity value. pmutate is 0.02 and pdie−alone

is 0.005. When we increase the size of connectivity values, we lower the Ratio

of Cancer Cells for the specific size of organism. We will see that result from

the histogram plots. The trend is downward for the histograms. Furthermore,

the effect of an increase is less effective for larger organism sizes. Indeed, this

experiment shows us to maintain more concrete body we need to have more

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Figure 7: Experiment 3 (a)Plots;(b)histograms

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Figure 8: Experiment 4 Plots

connected digital cells.

3.4 Treatments vs Ratio of Cancer Cells

In this subsection, we consider the three defined parameter in methods sections.

These are mutate probability, die alone probability, and connectivity increases at

each treatment. We give plots for treatment versus cancer cell ratio in Figure 8.

Connectivity increases by 1 from 10 to 20, mutate probability increases from

0 to 0.50 and die alone probability increases from 0 to 0.25. Die rate is very

small. Plots are interesting. The case of increase in each parameter is accepted

as treatment. There are 11 treatment with the one that we start. Each plot is

the plot of network size from 100 to 1000. The highest cancer cell rates are still

relevant for low sized organisms. The interesting point is that the exponential

trend changes to logarithmic and eventually to linear trend when we increase the

size of organisms. This implies that organism responds both with connectivity

and die alone probability in more steady fashion that forms linear trend with

increasing treatments.

3.5 Die Rate vs Ratio of Cancer Cells

We mention about the die rate of our digital organism. The die rate is also

effecting factor since it is the probability of die of each cells in our network.

Furthermore, it is possible that all cells have an equal chance to die. This leads

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Figure 9: Experiment 5 Plots

to die of normal cells too. When we increase the die rate of the organisms with

steady parameters and size 500, the organism corresponds the a semi logarithmic

increase in cancer cell in Figure 9 and logarithmic regressing is the best fit for

the plot. This is related to die rate since it hits the normal cells generally

and effects the organ whole structure. Then eventually, the number of cancer

cells and normal cells are stabilized in terms of size. The die rate actually

regenerates the system but when it is high, the organism regenerates too much

and the evolution is in the sake of cancer cells.

4 Future Work

We propose well experimented digital organism and we followed in what ways

the ratio of cancer cells or mutated cells are effected. As a future work, we also

propose some other ideas. Real organism have millions of cells and this makes

the simulation harder. Since we made some abstractions due to the limited

time experimental repetition, some of the plots have some variations. We also

limited the number of cells to 1000. When we increase the organism size, we

need initially implanted cancer cells since their evolution would not be possible

in million of cells. This leads us to infer the effect of network size in our plots.

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Assumption of zero cancer cell or mutated cell may be too optimistic for a real

organism.

Furthermore, rather than two types of cells, we can add one more cell type

which is called immune cells. Immune cells are healing cells and they have an

ability, cure other cells. Two approach is possible, they can be mobile or stable.

Mobile ones can have ability to have neighbors from selected cells from some

area. This assumption, force us to locate the cells at the beginning and each

new born cell have a location closer to its neighbors. If immune cells connected

to some area, it will ability to heal cancer cells and return them to normal

functionality. On the other hand, stable ones do not need location, they need

neighborhood information. If cancer cell is connected to immune cell, this will

lead to healing process. During healing, cancer cell will have a chance to escape

with some probability. In real life, cells responds to heal methods different ways.

In some cases, cells may resist to treatment and that makes the patient worse.

This probability may correspond to this resistance.

We will also need to differ random mutation. As in [7]’s case, mutation are

helpful for the emergence of complex and efficient organism. Also adaptation

may be due to mutation, since organism may lose some organs but maintains

better organs instead or organ efficiency or specialization may change. We added

some parameters to the implementation but these are not completely tested in

experimental section. The mutation part may be extended in the future.

These modifications on model could be interesting and we can imitate the

real organism precisely.

5 Conclusion

In a conclusion, we provide a basic model corresponding to real organism as

we simulate digital organism. Our main concern is in what ways unusual cell

structures are formed these are also assumed as cancer cells. We accept the

cancer has unique type and then we make several concluding remarks,

• Mutated cells can be cured by increasing network size and probability die

alone rate

• High die rates can result with the case of spread in mutation

• Increasing connectivity, decreases the number of cancer cells

• Smaller organism are more vulnerable to mutation as we see in digital life

and know from real life

• Probability of die alone can work against the normal cells when the mu-

tation probability is high

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We also give some future work for this research at the previous section that

would be precise additions for our digital organism and better way to simulate

the evolution of cancer.

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