Microbial Compounds and Organelles

~sciocont wrote:

That protocell list is going to disappear soon, I think,

What do you mean?

Also, in terms of propulsion, how do cilia and flagella move the cell differently? Or do they?

NickTheNick wrote:

~sciocont wrote:

That protocell list is going to disappear soon, I think,

What do you mean?

Ok, here's my promised bigpost.

The current protocell list is woefully unscientific, and, though endocytosis is a good method (most likely the only method) for getting things like chloroplasts, mitochondria, and our thermoplasts, it doesn't really work for things like Cilia, lamellipodes, etc. Thus we need to structure microbe stage more like multicellular stage where mutation, not endocytosis, drives evolution. The current protocell list details almost all of the parts we would need in a cell editor to design a vast array of functioning protists, so we shouldn't ditch it. It's just that an individual flagellum cannot function without a cell to support it, so it shouldn't be swimming around in the world alone.
I'm going to rewrite the current protocell list here and reclassify protocells into traditional organelles and assimilated organelles, and things that we can ditch altogether.

Spoiler:

Orange numbers are now organelles that can be gained through mutation and not through endocytosis. Their new names and any new notes on them are given here.
1)flagellum- can evolve from cilia or vice versa
2)cilia- can evolve from flagellum or vice versa
3)lamellipodes- these are rigid exoskeletal extensions that act like legs
4)pseudopodic movement- this will be available to a player whenever their cell membrane is loose enough around the central cytoskeleton to allow it, and will not involve a specific visible organelle, but will require a mutation giving it the ability to coordinate large membrane movements.
6)Conjugal Nuclei- extra nuclei within the cell used for sexual reproduction; if you reproduce sexually, your population can grow more rapidly and you can evolve more rapidly as well. There will probably be many ways to sexually reproduce, and asexual reproduction is an option as well.
7)Predatory Pilus- the description there seems great to me
8 )Slime Gland- vacuole that fills with antiphagocytic slime and can be released upon contact with another cell.
16)Cell Wall- can be added to outside of membrane and attached to cytoskeleton. this protects you from the elements and other cells to a certain extent, depending on its thickness. However, it does restrict your motile and feeding abilities somewhat, which we can detail at some later point.
17)Communal Membrane Proteins- these are membrane proteins that can evolve that allow you to attach to other members of your species.

Green numbers can be achieved through mutation or engulfment.
5)Bioluminescence can be achieved through the assimilation of luminescent bacteria, or by the development of a luminescent organelle.

Blue numbers can be gained exclusively through endocytosis.
11)Mitochondria begin as free-living aerobically respirating bacteria engulfing them has a 1 in 1000 chance of symbiosis, which will dramatically increase the efficiency of your cell. It will be virtually impossible to survive without gaining them fairly early in the game.
12)Chloroplasts begin as free-living sessile cyanobacteria. Engulfing them has a 1 in 2000 chance of symbiosis. They will need mitochondria to function, and can only function, and are only found, in well-lit environments. They won't be around in the initial ocean vent biome.
13)Thermoplasts will be found as free living sessile bacteria in the initial biome. They have a 1 in 2000 chance of becoming symbiotic. They will only work in very hot areas, but can work without mitochondria, albeit not very efficiently.

Any numbers not listed above will either be standard organelles (vacuoles, lysosomes) or not included (producers, dissolvers)

Many of the organelles will have several different stages of efficiency, such as the lysosomes, mitochondria, chloroplasts, and thermoplasts. This list is not final: it is my attemt to make cell stage organelles sensible and scientific. Please add your thoughts.

So when the player first starts, do they start with a cell that has a membrane loose enough to allow for pseudopodic movement?

How will quantities of compounds that are stored by the cell be measured? What units?

What do you mean by a chance of symbiosis?

Also, I think we should list what organelles and abilities the cell starts with, along with what compounds it can consume, for reference.

And what are the instincts for a cell at this stage? This is what I got.

-Nourishment
-Energy

NickTheNick wrote:

So when the player first starts, do they start with a cell that has a membrane loose enough to allow for pseudopodic movement?

How will quantities of compounds that are stored by the cell be measured? What units?

What do you mean by a chance of symbiosis?

Also, I think we should list what organelles and abilities the cell starts with, along with what compounds it can consume, for reference.

And what are the instincts for a cell at this stage? This is what I got.

-Nourishment
-Energy

I think we should start them out with a flagellum, but it doesn't really matter. Quantities of compounds-I'm not sure. I want to say that Seregon and I decided on moles, but I'm not sure, since we're dealing with very small amounts, and a mole is way larger than anything we'll be stuffing into the cell, no matter the material.
When you engulf things, you eat them. However, there is a small chance that you will not successfully digest them, and they will become part of your cell (endosymbiosis)
The cell should start out with a nucleus, simple cytoskeleton, and a basic golgi apparatus and ER. Finally, they get a flagellum or some cilia.

What do you mean by instincts?

For the organism editor UI, there are some tabs called "Instincts", with Nourishment, Energy, and Health being among them. Kind of like stats for an MMORPG. I thought they would be called the same for the microbe stage, because it is still organism mode.

NickTheNick wrote:

For the organism editor UI, there are some tabs called "Instincts", with Nourishment, Energy, and Health being among them. Kind of like stats for an MMORPG. I thought they would be called the same for the microbe stage, because it is still organism mode.

Ah. Ok, nourishment and energy are good, and we may want to have a growth progress bar as well.

Okay, so your bigpost was hugely useful. I think that now that we have that, I'd like to create a list specifically outlining all of the organelles for the first stage, outlining what processes they undergo with specific numbers and equations, outlining what abilities they unlock, and outlining any other significant details.

Also, before I start, how does ATP translate into energy? Or are they synonymous?

So for the below, whenever I highlight something in red that means I don't know what to put there, so please fill me in on the red spots. Also, please fill me in on significant details that I forget to mention.

- Organelles -

Flagellum:
Provides boost to movement speed in a direction opposite (180 degrees) from position of placement. Speed boost of X-Y*(I was thinking we make speed just be a value, no units).
*X-Y being the range of speed that is provided

Cilia:
Provides boost to movement speed in a direction perpendicular (90 degrees) from position of placement. Speed boost of X-Y* (Same as above).
*Of course, since adding one cilium to a cell with a small mass has greater effect than adding one cilium to a cell with a large mass, so we need to model effective speed as a function of mass and speed (I'm highlighting this red because I don't know what the equation should look like, please help me out with this). Note that speed and effective speed are two different variables; speed is an absolute value, while effective speed is relative to the mass of the cell in question. Please, if you can think of something simpler for calculating speed, please say so.

Chloroplast:
Allows Photosynthesis --- 6 Carbon Dioxide + 6 Water = 1 Sugar + (6 Oxygen) --- Compounds inside the brackets are released as waste.
The entire process is dependent on light. Light increases or decreases the reaction rate, or frequency, based on its intensity. Areas with 100% light concentration react at full speed, while areas with 50% react with half speed.
Therefore, --- Reaction rate = Space in organelles x Basal
reaction rate x Product (input compound concentrations) x Product (1 -
output compound concentrations) ---

Mitochondria:
Allows Aerobic Respiration --- 1 Sugar + 6 Oxygen = 38 ATP + X Nourishment + (6 Water + 6 Carbon Dioxide) --- Compounds inside the brackets are released as waste. Remember, that since, I am going to stop pointing that out.
*Should energy even be included. Will ATP just translate into energy?



I will edit this list as I go. Please, feel free to contribute, as I am no biologist.

NickTheNick wrote:

How will quantities of compounds that are stored by the cell be measured? What units?

~sciocont wrote:

Quantities of compounds-I'm not sure. I want to say that Seregon and I decided on moles, but I'm not sure, since we're dealing with very small amounts, and a mole is way larger than anything we'll be stuffing into the cell, no matter the material.

I did suggest basing the compound units on moles in our pm discussion. In that PM (which I've now lost) I worked out roughly how many moles you could fit into a cell, and used that as the basis for the unit. A quick rehash now suggests that an average human cell has a mass similair to 1 nano-mole of hydrogen, or ~5.6 pico-moles of glucose. A nice unit for giving us round numbers would then be the femto-mole (1/1000 nano-moles), so that a typical cell would weigh around the same as 5600 units of glucose, but could feasibly *contain* perhaps 1-200. Note that a typical prokaryote is around ~1000 times smaller than a human cell, and a typical virus around ~100-1000 times smaller than that.

Also, instincts sound like they should describe behaviours, so perhaps the examples given where default behaviours (seek energy, seek nutrients), rather than attributes?

To all intents and purposes, ATP = energy. It is the most commonly used temporary/short-term energy storage 'device' in most life I know of. For the purpose of creating the game, that's all you need to know. For curiosities sake I'll mention that ATP (adenosine-TRI-phosphate) is created from ADP (adenosine-DI-phosphate) and phosphate whenever energy is produced in a cell (e.g.: respiration). When energy is used ATP is converted back to ADP - think of ADP being an empty rechargable battery, and ATP a full one, except that you have millions of them, and you can't partially charge one.

Almost all number we use will need a unit. We don't have to show it to the player, or mention it anywhere, but we should know what it is. Not knowing that unit will drive any mathematicians among us (myself included) nuts, and make doing various calculations more hit and miss than they should be. If you don't know what the unit should be, take the SI unit (for speed, meters per second) and scale it down till it fits, so something along the lines of nanometers per second.

With relative and absolute speed, what I think your getting at is the energy expended moving the cell, and the result of that expenditure. It's been too long since I studied physics to remember the equations involved, though most of those I can think of deal with acceleration rather than speed.

Photosynthesis does not produce nourishment, more on that in a second. It also does not directly produce energy (it can, by short-circuiting glucose production, and several variants on photosynthesis produce energy as a byproduct, but I'm not sure we should go into that). The energy captured by photosynthesis is used to produce glucose, which is the long-term energy storage unit, and can be converted back into energy via respiration.

Reaction rates should also be dependant on the concentrations of required, and produced, compounds. Halving the CO2 or water concentration, should also halve the reaction rate. More chloroplasts means more potential 'space' for the reaction. The equation for all this I used in my prototype was this, with light being treated as an input compound:

Reaction rate = Space in organelles * Basal reaction rate * Product (input compound concentrations) * Product (1 - output compound concentrations)

Again, respiration does not produce nourishment. Noutrition isn't an arbitrary measure of health, but rather a measure of whether a lifeform has sufficient access to nutrients. Nutrients again are a fairly well defined list of compounds a lifeform needs, in the case of our cells that might be nitrogen, phosphorous, iron, etc. I'm not sure how we'll represent these nutrient compounds, as we can't really justify including all of them in the compound system, so we might have nitrogen come from ammonia (which is used in so many different places it's worth included), and clump most of the others together in a nutrient compound, which all life needs in relatively small quantities to survive.


...that's all I can think of at 7 in the morning, will have another look at this tonight.

Propulsion? I believe that is physics. Lets see what can i do about that formula. Sorry about any unit name i get wrong, i didnt study this in english.

We want to go from ATP to movement, that is, change in speed.

Lets start at a femto-mole, wich acording to Seregon is a good unit. That is 10^-15 moles. Acording to wikipedia, ATP is worth about 30 kJ/mol, so one unit of ATP would exchange into 3*10^-14 kJ, that is, 30 picoJoules.

However, not all energy in transformed into movement. I dont have any idea about how efficient a cell is, but from what i supose i would say that it is from 25% to 50%. We can tweak this value to balance things out. Some propulsions will be more eficient than others, too. Now we have an energy of 15 picoJoules

Joules are a unit of work, wich can be expressed as a difference in kinetic energy.Then, the formula we have will be like so: W=Δ KE = (1/2)*m*Δv². Here i am assuming the force is being made is paralel to the gain in speed, wich should always be. We now have that our energy of 15 picoJoules, aplied to a cell that probably weights from 2*10^-14 to 10^-12 Kg. Lets assume 10 ^-13 Kg. The gain in speed will be of 0.54 m/s.*

So the final equation is Δv = sqrt(0.5*mass*efficiency*energy rate of ATP*amount of ATP). The mass is cubically proportional to the size, the efficiency depends on the way of propulsion and the energy from ATP is related to some biochemistry formula i dont understaund.

* This is WAY too big. either i screwed up with the numbers, the efficiency is way lower, a femptomole is not good for measuring ATP or it is really not that hard to move as a cell.

Daniferrito wrote:

Propulsion? I believe that is physics. Lets see what can i do about that formula. Sorry about any unit name i get wrong, i didnt study this in english.

We want to go from ATP to movement, that is, change in speed.

Lets start at a femto-mole, wich acording to Seregon is a good unit. That is 10^-15 moles. Acording to wikipedia, ATP is worth about 30 kJ/mol, so one unit of ATP would exchange into 3*10^-14 kJ, that is, 30 picoJoules.

However, not all energy in transformed into movement. I dont have any idea about how efficient a cell is, but from what i supose i would say that it is from 25% to 50%. We can tweak this value to balance things out. Some propulsions will be more eficient than others, too. Now we have an energy of 15 picoJoules

Joules are a unit of work, wich can be expressed as a difference in kinetic energy.Then, the formula we have will be like so: W=Δ KE = (1/2)*m*Δv². Here i am assuming the force is being made is paralel to the gain in speed, wich should always be. We now have that our energy of 15 picoJoules, aplied to a cell that probably weights from 2*10^-14 to 10^-12 Kg. Lets assume 10 ^-13 Kg. The gain in speed will be of 0.54 m/s.*

So the final equation is Δv = sqrt(0.5*mass*efficiency*energy rate of ATP*amount of ATP). The mass is cubically proportional to the size, the efficiency depends on the way of propulsion and the energy from ATP is related to some biochemistry formula i dont understaund.

* This is WAY too big. either i screwed up with the numbers, the efficiency is way lower, a femptomole is not good for measuring ATP or it is really not that hard to move as a cell.

Great post. There is good reason for that number being much too big.

Ok, so according to this paper the top speed of a euglena (simple flagellate protist) is about 100 micrometers/second I think this is a good top speed for us to shoot for. This is .0001 meters/second, much slower than your quoted figure. This is because the energy in the ATP is not going straight out the back of the cell. It's being used to power proteins that twirl the flagellum. The individual filaments making up a flagellum all use ATP in order to flex their dyeinin proteins, causing the filaments to slide against each other and thus making the entire flagellum flex. This means that a lot of energy coming in from ATP creates very little backwards thrust, the force that it is supposed to be exerting. By my estimate, the flagellum is about 1/900th as efficient (9 strands to create1/100th of the force) at creating forwards force as would be desirable.
That still gives a speed of .0006 m/s with your estimates, but is a lot closer than .54 m/s

Wow, i didnt know that was so inefficient. However, the increase of speed i calculated doesent have to match with the max speed for a cell. This is a totally different number. Let me explain:

There are two ways to go from energy to movement. Either the energy is instantly transformed into kinetic energy, wich translates into speed, or it is aplied during some distance as a force, wich translates into speed too.

With the second method, you can add that applied force plus the resistance force together, wich will result in net speed gain. As resistance (in a fluid) is proportional to speed (higher speed means more resistance), there will be a speed at wich both forces will be equal and so they will cancel each other out and the cell will keep its speed.

With the first method, you cannot do that, you will have to add resistance at other place. However, it is closer to how a computer works, at cycles. Each cycle, some energy in transformed into speed, and resistance can easily be defined as a percentage of the actual speed lost each cycle.

On top of that, the unit i started out was quite arbitrary. The mass of the cell i estimated was of 10^-13, wich is 10 times smaller than a human cell, wich makes my cell 3.16 times faster than a human one.

@Seregon: The instincts are meant to be somewhat abstract and simplified representations to the stats of an organism/cell, think mana or health in any RPG. I think it would be better to differentiate early on between ATP and energy, even if one just directly translates into the other, simply because later on in the Aware stage energy won't be simply from ATP, so it keeps some consistency between the stages. The bars just indicate how much energy it has and how much it has fed or needs to feed.

Nanometers/second sounds good.

My apologies, I meant to clarify that as maximum potential speed. Then acceleration would have to be calculated within that. More on this in my response to Daniferrito.

So do chloroplasts require mitochondria or some means of anaerobic respiration to benefit the cell?

What do you mean by more "space"? Do you mean multiple cases of the reaction can be taking place at a time?

What would determine the basal reaction rate of cells and/or organelles?

Nutrients as a compound sounds better, I think, than multiple ones. However, I worry that if we replace a single nourishment/hunger bar with multiple bars that require multiple compounds we will be overwhelming the player.

@Daniferrito:Will we be measuring the mass of the cell? If so then we can you the standard 1/2mv^2, but if it would be too much effort I think we could even just replace mass with area of the cell. Also, with this equation would it be force or energy that is increased by adding more flagella or cilia? I was thinking that the flagella and the cilia are the means by which they move, and the ATP is the resource they expend to move.

@sciocont: Wow, so an efficiency rate of 1/900? That does help solve the problem. So then the equation would look like

Max Speed = (1/2 x mass* x 1/900 x energy rate of ATP x amount of ATP in femto-moles)

By the way, could someone clarify what the energy rate of ATP means? Is that just how much energy each femto-mole of ATP creates?

*Or area, whichever we agree upon

NickTheNick wrote:

@Seregon: The instincts are meant to be somewhat abstract and simplified representations to the stats of an organism/cell, think mana or health in any RPG. I think it would be better to differentiate early on between ATP and energy, even if one just directly translates into the other, simply because later on in the Aware stage energy won't be simply from ATP, so it keeps some consistency between the stages. The bars just indicate how much energy it has and how much it has fed or needs to feed.

Nanometers/second sounds good.
Micrometers/second is better for our scale, as I posted above

So do chloroplasts require mitochondria or some means of anaerobic respiration to benefit the cell?
All cells can anaerobically respire, it's how they get energy. Chloroplasts essentially run the reaction of aerobic respiration in reverse, but can do it with a net gain in energy because they use light. They produce glucose, which is then broken down to yield ATP in regular aerobic respiration, which requires Mitochondria

Nutrients as a compound sounds better, I think, than multiple ones. However, I worry that if we replace a single nourishment/hunger bar with multiple bars that require multiple compounds we will be overwhelming the player.
If we must represent multiple compounds at once, i'm in favor of using a radar chart

@Daniferrito:Will we be measuring the mass of the cell? If so then we can you the standard 1/2mv^2, but if it would be too much effort I think we could even just replace mass with area of the cell. Also, with this equation would it be force or energy that is increased by adding more flagella or cilia? I was thinking that the flagella and the cilia are the means by which they move, and the ATP is the resource they expend to move.

@sciocont: Wow, so an efficiency rate of 1/900? That does help solve the problem. So then the equation would look like

Max Speed = (1/2 x mass* x 1/900 x energy rate of ATP x amount of ATP in femto-moles)

Cellular processes are often highly inefficient. Aerobic respiration is absolutely disgusting in that regard. It has a relatively high ATP yield, but the metabolic pathways in it are immensely circuitous.

@daniferrito- good thinking, I hadn't taken into account the fluid resistance.

Okay, so micrometers/second.

Those radar charts look very nice. It would be much better than multiple bars if it comes to that.

Okay, thanks for clearing that up. I'll try and edit my list once I get more time later today, but with admin powers you are free to go and edit it for me if you want.

@Dani: I think the second method sounds good, as long as it is code-able, because from what I know it sounds pretty similar to Newton's laws.

I understand your point about energy being different for different stages. For a cell energy is ATP, it doesn't 'exist' in any other form, though it is stored in many forms:
- ATP very short term (minutes), immediately usable by almost any function in the cell (this includes functions performed by cells in larger organisms, our muscles use ATP to function in the same way a cells flagellum does)
- Sugars are long term energy storage molecules (hours-days), they cannot be used for energy, but can be process to produce energy (in ATP form) via respiration. In the absence of mitochondiria (or oxygen) anaerobic respiration (glycolysis) takes place, though this produces far less ATP per glucose (about 12 I think... can't remember the exact number). 6 ATP/glucose ~scio
- Fat is a more space efficient energy storage molecule, and is very long term (weeks-years), which can be converted to sugars for transportation, or indirectly into ATP via the krebs cycle.

To put it another way, energy cannot exist freely in a cell, it is either stored in one of the above compounds, or being used immediately (or wasted). In conclusion, ATP = energy, for aware stage organisms energy probably = sugar. The question is whether we want to let the player know this, or whether we simply label the relevant compound as 'energy'? For the purpose of the compound system, there is effectively no such thing as energy, either ATP or sugar is used to do 'stuff'.

Space was a bad word, perhaps 'capacity' fits better, but basically yes, more reactions at the same time. Basal reaction rate is a constant we define for balance, some reactions should be faster or slower than others, though for now we can assume most basal reaction rates will be 1. I agree that we can't show the player everything, or it would be overwhelming (though we may want the option to see all compound levels in a seperate screen), they should be able to survive using just a few basic bars (e.g.: energy/ATP, nutrition, sugar/fat/energy storage etc.).

As you say, energy rate is the energy (measured in joules, or similair unit) per unit of ATP. It is primarely useful to help use work out the ratio of ATP used to work done for all the processes we'll need (such as Dani's speed example).

Ok, let me clarify some things, you are getting some things wrong.

To start of, my formula doesent calculate max speed, but ATP to kinetic energy. For max speed we will need to take into acount friction.

Secondly, it has a square root at the start. That means that in order to double the speed gain, you need to provide 4 times more energy. This balances out because a cell double the size, would be able to store 8 times more energy (because it ocupies a volume)

Thirdly: Althrough i posted two methods, they are exactly the same. At the end, they get the exact same output. However, the second one would require triple the calculations, and friction would be much harder to calculate too. The first one, i got working in a four-lines long python script

Yes, the mass can be calculated from the size, if we asume all cells have the same density. However, it isnt surface, but volume. I believe the dinsity of the cells is equal to water's so it looks like this:
mass=(4/3)*pi*(0.1*r)³
Where mass is the mass in kilograms and r is the cell's radius in meters.

Fore someone interested in how computer code looks like when doing this calculations here it is:

Spoiler:

It is python instead of c++, c++ doesent look like this.

You can see the right formula there too.

Wait, so the equation calculates the amount of kinetic energy gained per unit (in this case femto-moles) of ATP used? We would also need an equation then for max speed, as a function of variables such as the cell's mass/volume, and the number of propulsion organelles placed on the cell applying force parallel to the direction of movement.

Right, I meant to include that but forgot. I'll fix that now.

Oh, I'm sorry, I thought those were two different methods of coding this type of a propulsion system into the game.

Great! That looks like a much simpler way of calculating the mass of a cell, as opposed to what I was imagining.

So Dani, once we iron out the propulsion algorithms, would you or Andrew be able to make a prototype simply to test out the movement? All you would need are circles for the cells, one of the backgrounds made so far tiled across the environment, and simple triangles or other shapes to represent each flagellum or cilium. Then you would just have multiple cells of different mass and different numbers of flagella and cilia to test out the propulsion. Plus, it would be a nice thing to doodle around with once its done.

We dont actually need max speed. Resistance (AKA speed loss) will keep total speed under a maximum. The easiest thing is to multiply the actual speed by some factor (in my example 0.95) every timestep*, wich will slow down the cell eventually. This doesent really relate to any phisical formula, as i dont the one that defines friction in a fluid.

Well, you are right, we could really code it both ways, but the second one is a pain to code, its only better if you are doing the calculations on paper.

Ah okay perfect! So that will cover max speed.

Sorry to repeat myself, but would you be able to make a prototype?

Daniferrito wrote:

We dont actually need max speed. Resistance (AKA speed loss) will keep total speed under a maximum. The easiest thing is to multiply the actual speed by some factor (in my example 0.95) every timestep*, wich will slow down the cell eventually. This doesent really relate to any phisical formula, as i dont the one that defines friction in a fluid.

Well, you are right, we could really code it both ways, but the second one is a pain to code, its only better if you are doing the calculations on paper.

No way in hell I would want to calculate fluid resistance on a complex shape in realtime, that's just silly. Excellent work.

Well, it isnt a complex shape, they are cells, so they are mostly spheres.

A quick look at the wikipedia page for it (here) shows the formula:

F = 0.5*1*v²*0.47*pi*r²

This formula only applies to spheres (0.47*pi*r²) moving through water (1), but i think asuming everything is spherical is nearly right. For coeficients for other shapes, you can look here.

About the prototype, i'll look into it, but i can guarantee nothing.

Double post

I did a fast prototype in python. It is in the thrive dropbox, inside the folder called prototypes. Just double-click movement.py.

You can also download it through the link

https://www.dropbox.com/sh/j0piz7hy3i777zf/I8vvsjbEEX

In order for it to work, you must have installed python 2.7 in your system and added it to the path (it does it automatically)

How does this look for movement? It doesent use any of the physical formulas, and there is still some things to iron out. At least it shows the maximum speed thing. I'll see if i can make it so you can edit the cell parameters, to see how each variable affects movement.

Daniferrito wrote:

Well, it isnt a complex shape, they are cells, so they are mostly spheres.

A quick look at the wikipedia page for it (here) shows the formula:

F = 0.5*1*v²*0.47*pi*r²

This formula only applies to spheres (0.47*pi*r²) moving through water (1), but i think asuming everything is spherical is nearly right. For coeficients for other shapes, you can look here.

About the prototype, i'll look into it, but i can guarantee nothing.

Realize, however, that evolved and constructed cell shapes will become much more complex. The sphere approximation will probably do though.

Great work Dani! The next step would be, like you said, to add cells of differing mass and numbers of cilia/flagella to see if they all move realistically.

So, correct me if I'm mistaken, but we've covered basic propulsion then. What's next, collision? I would imagine that to be very simple, and not even based on organelles like propulsion is. All we need is:

P_Before = P_After

With P representing momentum. The above equation only works in a closed system however. So basically, we just substitute mass*velocity for one of the P's on either side to calculate the other. So:

P = mv

And, in case it is needed, but I don't think we will be needing to go this deep, we could also include the:

ΔP = FΔt

With F being force and t being time.

You're on the right track. Collisions come in a few different forms: elastic, inelastic, and perfectly inelastic.

In perfectly inelastic, the two entities stick together after collision so mv(obj1)+mv(obj2)=(m(1)+m(2))v(final)

In inelastic, they bounce together, but some energy is absorbed by either shape. This is what we'll be simulating for collision, but i don't have an equation for it off of my recent physics notes.

In elastic, they bounce apart and no energy is lost. initial[mv(obj1)+mv(obj2)]=final[mv(obj1)+mv(obj2)]

Realise though, that we most likely needn't worry about this, since I'm sure we'll have any requisite equations for this in the various libraries we will use. (Seregon, dani, confirm?)