Computer Engineering Bogazi¸ ci University Bebek,Istanbul 34342 Turkey
Submitted to CMPE 58B Final Project
by Melih S¨ ozdinler
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Digital Organism Simulates Life and Cancer Evolution Haluk Bing¨ol, Melih S¨ozdinler January 15, 2010 Abstract From just two cells somehow, human being emerges. During this development, cells form some structures called tissues. Tissues form organs. Organs form Systems. This is basic knowledge to form simple human being. 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.
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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.
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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 sequences referred as Îąmin . 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 reading 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, digi3
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 organism 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 maintain 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 parameters 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 0.001 mutation 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 0.01 mutation rate (a)0.02;(b)0.05;(c)0.10
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Figure 4: Experiment 1.1 Histograms
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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.
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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. 8
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.
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Mutation Probability vs Ratio of Cancer Cells
In Figure 6, we have several plots corresponding to different mutation probability. 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 increase 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.
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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 easily 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 ”Ratio 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.
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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.
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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 12
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.
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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.
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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 mutation probability is high 14
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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plexity, robustness and genetic interactions in digital organisms. Nature, 400(6745):661–664, August 1999. [5] R. E. Lenski, C. Ofria, T. C. Collier, and C. Adami. Genome complexity, robustness and genetic interactions in digital organisms. Nature, 400:661– 664, 1999. [6] R. E. Lenski, C. Ofria, R. T. Pennock, and C. Adami. The evolutionary origin of complex features. Nature, 423:139–144. [7] A. N. Pargellis. The spontaneous generation of digital “life”. Phys. D, 91(1-2):86–96, 1996. [8] K. Thearling and T. S. Ray. Evolving multi-cellular artificial life. In In, pages 283–288. MIT Press, 1994. [9] M. Willensdorfer. Organism size promotes the evolution of specialized cells in multicellular digital organisms. Journal of evolutionary biology, 21(1):104–110, January 2008. [10] Y.-G. Zhang, M. Sugisaka, and X. Wu. Bottom-up development of multicellular digital organisms. Artificial Life and Robotics, 4:143–147.
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