Emergence Using Reinforcing Feedback: Quorum Sensing Bacteria

Model Overview:

This model introduces the concept of emergence and reinforcing feedback by using simulated bacteria as a platform. Using two types of agent-sets; bacteria and autoinducers, this model works as a proof of concept that demonstrates how individual bacteria (agents) may rely on reinforcing-feedback to work collectively in order to produce an emergent phenomena.

What is Emergence?

“Emergence may seem mysterious, but it is actually something that we experience every day. For example, a single water molecule of two hydrogen atoms and an oxygen atom does not feel wet (assuming you could feel a single molecule). But a few billion water molecules in a cup feel wet. That is because wetness is a collective property of the slippery interactions between water molecules in a particular temperature range… Similarly, what we call a symphony is a pattern of sound that emerges out of the playing of individual instruments, and what we call a kidney is a pattern of cells working together to provide a higher level function that none of the cells could do on its own.”

Eric Beinhocker- Origin of Wealth1

Take a puzzle down from a dusty shelf and shake the contents onto a table. Now take a piece of the puzzle at random and inspect it. Note the color, shape, and presence of patterns on the piece. Now take another, and do the same. After awhile you may begin have some semblance of what certain differences there are between certain pieces, and you might notice certain trends in patterns. Now consider doing this process until you’ve looked at every single piece in the puzzle. Having considered each piece, would you have a clear understanding as to what the completed puzzle looked like? Perhaps, but certainly not as clearly as you would if you were to put all the pieces on the table, assemble them together, and see what as a whole they revealed.

Like the picture of the completed puzzle, there are certain things that only become apparent or real to us when many other things interact with one another to form them. There appear to be many things that make a qualitative change or shift once a certain

1 Beinhocker, E. D. (2007). The origin of wealth: Evolution, complexity, and the radical remaking of economics. Century. quantitative boundary is crossed. Traffic jams2, flocking birds3, and even our own consciousness4 are examples of emergent properties that we experience in our day to day life. However, our understanding of exactly how these phenomena occur, and how to understand the significance of emergent properties is a challenging facet to the study of complex systems5.

What is feedback?

“All dynamics arise from the interaction of just two types of feedback loops, positive (or self-reinforcing) and negative (self-correcting) loops. Positive loops tend to reinforce or amplify whatever is happening in the system: The more nuclear weapons NATO deployed during the Cold War, the more the Soviet Union built, leading NATO to build still more....Negative loops counteract and oppose change... The larger the market share of dominant firms, the more likely is government antitrust action to limit their monopoly power. These loops all all describe processes that tend to be self-limiting, processes that seek balance and equilibrium.”

John D. Sterman6

Feedback can be seen as the process by which an output is ‘fed’ ‘back’ into the initial input that created it. This can either be negative ( self-correcting) or positive ( self- reinforcing). These processes can be used as a tool to describe complex systems where a great many loops of reinforcement and correction work together to compose the dynamic behavior of a system. In the instance of quorum-sensing bacteria we see that the presence of autoinducers, which are produced by individual bacteria, encourages bacteria to produce even more autoinducers. Here we have a system that is composed of at least one self-reinforcing ( positive ) feedback loop; as more autoinducers are made, the higher the

2 Resnick, M. (1997). Turtles, termites, and traffic jams: Explorations in massively parallel microworlds. Mit Press.

3 Cavagna, A., Cimarelli, A., Giardina, I., Parisi, G., Santagati, R., Stefanini, F., & Viale, M. (2010). Scale-free correlations in starling flocks. Proceedings of the National Academy of Sciences, 107(26), 11865-11870.

4 Baas, N. A., & Emmeche, C. (1997, February). On emergence and explanation. Santa Fe, NM: Santa Fe Institute.

5 Anderson, P. W. (1972). More is different. Science, 177(4047), 393-396.

6 Sterman, J. D. (2000). Business dynamics: systems thinking and modeling for a complex world (Vol. 19). New York: Irwin/McGraw-Hill. chance there will be to make even more, creating a higher chance that even more will be made!

What is Quorum Sensing?

The word quorum, having its etymological roots in Latin ( the genitive plural of qui meaning; of whom ) means in the larger sense; a particular group’s minimum amount individuals needed to make a decision. In regards to this model, our quorum is a group of bacteria. This raises the question; how do bacteria know there are enough individuals in their group (a quorum) to make a decision? And, what is the decision that they are making?

In the late 60’s microbiologists observing bioluminescent bacteria7 surmised that there was some amount of collective effort done by individual bacteria that resulted in a bunch of bacteria lighting up all at once. The concept of a decentralized process guiding the group activity was expanded upon in the 70’s by another group of microbiologists8 showing that the bacteria were in fact inducing bioluminescence by means of a molecule called an autoinducer. Bacteria were sending out these autoinducers into their environment, and other bacteria of the same species were able to detect the presence of these molecules. In a sense, bacteria were communicating to each other by producing these little molecules. By being able to detect autoinducers bacteria were able to answer the question; how many other bacteria are around me right now?

The purpose of answering the question of how many, has to do with the reaction a bacteria has when a certain number (threshold) of these autoinducer molecules are encountered. When a particular threshold of ‘how many’ is breached, bacteria begin transcribing genes that synthesize chemicals that, depending on the bacteria transcribing them, have a wide range of outcomes,

“Quorum sensing is the regulation of gene expression in response to fluctuations in cell- population density. Quorum sensing bacteria produce and release chemical signal molecules called autoinducers that increase in concentrationas a function of cell density. The detection of a minimal threshold stimulatory concentration of an autoinducer leads to an alteration in gene expression....These processes include symbiosis, virulence,

7 Kempner, E.S. and Hanson, F.E. (1968) Aspects of light production by Photobacterium fischeri. J. Bacteriol. 95, 975-979.

8 Nealson, K.H., Platt, T. and Hastings, J.W. (1970) Cellular control of the synthesis and activity of the bacterial luminescence system. J. Bacteriol. 104, 313-322. competence, conjugation, antibiotic production, motility, sporulation, and biofilm formation.” 9

Consider this strange situation:

Imagine yourself in a perfectly dark room. You stumble around the room looking for a light switch, but find there are none. Alas you take inventory of your situation. You hold in your hand an empty flashlight that seems to require an usual amount of batteries to turn on. You also have a bunch batteries filling all of your pockets. You try and fit each of the batteries you have in your flashlight, and find that for some reason they just don’t fit inside. Wandering around aimlessly you step on something strange and reach down to find that you’ve discovered a battery on the floor. You try this new battery and low and behold; it fits! You decide it would be a good idea to start getting rid of your other batteries, as they are of no obvious use to you, and you’re finding ones that seem to work a lot better anyway. As you walk around, each new battery you find encourages you to drop more and more of your batteries that you can’t use. Finally it seems, that every where you turn is a new battery that works with your light and you are dropping batteries left and right. Finally; you find the last battery you need to turn your light on, and just before you do so you notice all around this dark room other flash lights are lighting up, you turn yours on, and before you know it, the whole room is awash in the individual flashlights.

Here you are the bacteria, the batteries are the autoinducers, and the light from the flashlight is the product of you transcribing genes. What is interesting about quorum- sensing and the dark room full of people walking around aimlessly with cumbersome flashlights, is that the collective action of bacteria, and the flashlight-holders isn’t regulated by any central figure; there is no master bacteria and there is no king of the flashlight holders. Nothing is telling each group to act all at once, it is only by means of using a shared environment, having a shared threshold and having a shared method of communication that allows each group of individuals to act collectively. It is this collective response that we describe as being an emergent property of the system.

How the Model Works:

The world is populated with a set number of bacteria that randomly wander around both reproducing and creating autoinducers. Each bacteria has a random chance of dying, and will never exceed the population size set by the carrying capacity in the model. Autoinducers bounce around randomly in the model as well, and have a random chance of dying. When an autoinducer and a bacteria meet, the autoinducer ‘nests’ inside the bacteria. Once a bacteria has a certain number of autoinducers ‘nested’ inside of it, the bacteria begins to change the color of the patchers surrounding it, simulating the diffusion of a generic chemical. This chemical dissipates at a set rate specified by the model. A plot

9 Miller, M. B., Bassler, B. L. (2001) Quorum Sensing in Bacteria. Annu. Rev. Microbiol. 55, 165-199 graphically shows the change in population of bacteria and autoinducers over time, as well as the amount of patches that have present a partial amount of the chemical diffused by the bacteria.

Buttons/Sliders/Switches:

Buttons:

Setup: Clears all agents from the world and clears all plots.

Go: Toggles between iterating the model, and stopping the model.

Organize: Allows the user to position the bacteria how they choose.

Sliders:

Set-Population: Sets the initial starting population of bacteria.

Carrying-Capacity: Sets the maximum number of bacteria that are allowed to be present in the model at any given iteration.

Switches:

Reinforcing-Feedback: Toggles between the bacteria responding to the presence of autoinducers as a source of positive feedback.

Model Key:

This agent-set represents generic bacteria.

This agent set represents autoinducers produced by bacteria agents.

These patches colored with a gradient of red indicate the presences of a generic chemical produced by the simulated bacteria.

Exercises:

1) Play with the set-population slider. See what effect different initial populations have on the emergent behavior of the bacteria. Does it speed up the process? Slow it down? If so, why?

2) Play with the carrying-capacity slider. Does the maximum amount of bacteria change the ability for them to have emergent behavior? Why do you think this is?

3) Do some outside research and find what naturally occurring biological behaviors that bacteria engage in would inform you of you answer to Exercise 2.

4) What are some things in your day to day life that could be described as being emergent? Explain why you think so.

5) Using the organize button, try different organizations of bacteria. Do you notice any difference in clumping bunches of them together?

6) Turn reinforcing-feedback switch to the ON position and run the model. Now, turn the reinforcing-feedback switch to the OFF position and run the model again. What differences do you see? If any, explain in your own words why this is. What role does reinforcing-feedback play in quorum-sensing?

7) What processes around in the world can you describe as having reinforcing feedback?

8) Go into the code of the emergencebacteria.nlogo model. Find the procedure labeled feedback:

to feedback

if reinforcing-feedback = true [ ask bacterias [ let see count autoinducers in-radius .5 if see > 3 [ hatch-autoinducers 1 [ set color blue set size 1 jump 3 ] ] ] ] end

8a.) What changes could you make to this code that would hasten emergent behavior in the mode? 8b.) What changes would lessen it? References:

Beinhocker, E. D. (2007). The origin of wealth: Evolution, complexity, and the radical remaking of economics. Century.

Resnick, M. (1997). Turtles, termites, and traffic jams: Explorations in massively parallel microworlds. Mit Press.

Cavagna, A., Cimarelli, A., Giardina, I., Parisi, G., Santagati, R., Stefanini, F., & Viale, M. (2010). Scale-free correlations in starling flocks. Proceedings of the National Academy of Sciences, 107(26), 11865-11870.

Baas, N. A., & Emmeche, C. (1997, February). On emergence and explanation. Santa Fe, NM: Santa Fe Institute.

Anderson, P. W. (1972). More is different. Science, 177(4047), 393-396.

Sterman, J. D. (2000). Business dynamics: systems thinking and modeling for a complex world (Vol. 19). New York: Irwin/McGraw-Hill.

Kempner, E.S. and Hanson, F.E. (1968) Aspects of light production by Photobacterium fischeri. J. Bacteriol. 95, 975-979.

Nealson, K.H., Platt, T. and Hastings, J.W. (1970) Cellular control of the synthesis and activity of the bacterial luminescence system. J. Bacteriol. 104, 313-322.

Miller, M. B., Bassler, B. L. (2001) Quorum Sensing in Bacteria. Annu. Rev. Microbiol. 55, 165-199