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Stochastic model of protein production with feedback
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00:05
time and again and again but all we want to thank you for only need to speak to unwilling to talk about my PhD walked with 1 out in the changing what is done in joint work with the loss of of and Filippo their phone from interior so I'm going to talk about it protein soul 1st of all I need to make small introduction of alters the biological contract context the biological acquistion will want to answer 2 and then I would explain how we put that into mathematics into probabilities of waged is state of then the main result mathematical result in his half time I will explain some of aspects with some simulations 1st the biological context so you all know that's the unit of flight itself in the particular case of bacteria and their goal is to grow in divided as possible and to do so they're using function normally ,comma scope proteins which basically do everything the sale volume of bringing bringing the energy that composing with the will of the cell there you used as enzymes etc. and then produce from information based on the small part of the DNA which is which of the gene and so it's
01:35
a big deal proteins are beginning to sell it to present a 50 per cent of the dry is their concert premium money coasts in the healthfood 2000 types and each type you can have a few dozen of 20 groups of money cruise up to 10 to qualify and everything has to divide 2 to double in size and irregularities in the short amount of time just say 30 minutes for all the fuss and there is the thing that bring guests bring the biologists say that 85 per cent of the sources of the protein I did you dedicate the resources of cell and indicated protein prediction so it's the main mechanism into the cell Seoul How do you do with this sell produce proteins sold the most classical where President idiots is the 1 I have learned in high school so it's in 3 steps 1st year of the gene regulation the gene can be either in active at state are enacted it's act if it is active then he can produce the transcription of an Emory named committed political and missing the irony an irony and the Maroney as the last time also a few minutes until it is degree dated and each in marinated translated into protein and the protein is a very long lifetime much longer than the subdivision sold all the more the result that just simply say that at some point the just go away in 1 of the 2 would also sell its just sink the deviation
03:16
so the problem is that some this way of producing protein that is subject to high diabetes why because the interior of the bacteria's the Londoners medium everything goes with the them diffusion and each mechanism to produce a protein is Dutroux of this property around on a collision between molecules so anything of that make a statistic courses with a large availability in the protein production and the parameters that Aziz said 85 per cent of the resources of the protein are impacted by large availability so it's a huge problem for the bacteria and so came up with the idea that but there might be some mechanism in order to reduce the viability of all summer of proteins that these for the most important 1 and so for the old there out there saying that's there's all the ways of policing procedures like this 1 with the feedback so is basically the same thing in prison before being differences that each protein here has a tendency to Bryant on its own gene enhance deactivate it so each putting here as opponents into buying and selling jeans and is staying here for the system of entitlement and its budgets but terminology education and the important thing to note here is that the more protein you have a fear the most of his this Pitocco type of protein you have the mortgages would be inactive and the other way around if you if you proteins that James would be tends to be more active so it's really a feedback process and said we came up with the idea that might be a way of reducing the liability of
04:59
the the conjecture there is less liability with this feedback mechanism than there is in that I was calling to the classical so on goal would be to put that into recreations and true prevented season equation of a into a mathematical models and to compare the 2 distribution and to see if there with the thing that level have less violated the law by and then in the classical models sold hoped to put that into equation so moldering and not Mother India protein production is not doing their best to 17 and they're all them although have basically the same assumption it is of a grievance and the conservative would accuse the irrigation of what it is that is that is to say that the protection of Amerindian encouragement proteins and the lifespan of the weaker is everything of that the following an explosion the distributed that valuables from valuables which rates depends on the current state of them all other With all for the current state of the moment Seoul for the portion of the cursor ,comma long so it can be active or inactive in the transition is in this special time of freight line 1 manners and when it's inactive when Isaac was to Zurich and active again at a rate on my 1 plus if it's actively so if Isaac was to 1 game produced a Marine is something that is the big and which is the number for an area be increased by 1 of them with a rate of 1 that and each Mary as a lifetime of rates Mutu's so the Grover Righter off Amerindian degradation is miniature times and where exactly the same with the protein she are each emirate has a tendency to produce a protein such rate than that 3 the Gober rate is among the 3 times and in the team will be the number of protein would increase by 1 that case and each protein a lifetime of ministry and it's just simply did you didn't it so the Gerber will be used the term speak OK so we have that's it said this model has been studied the incident sometimes as a said and you can have a clear before which is the mean and variance everything is that terminated so things grew at an NSO weeks tried to do the same with all feedback so what would change here the only thing is here and you have Tennessee 4 of New each protein dimension to bind on its own genes so I would say that in here the Woodbine and on gene at a rate lower 91 minutes hats would spend what ahead here so the Grover rate of VAT vision 191 members had 2 times the number of protein whenever that action means feedback so it shows you that it is that so why hats is just simply would compare the 2 moguls and what you have to do what you have to have in mind is that the at the age of anyone miners had tense Kiev will be in the same I'm order of managers is among many 1 man is known to have on the average the same and dictation of the gene please let me just what it could to hack his mother's parameter OK so we try to do the same as before we try to make it to Montreux and there is indeed a problem is that when you are trying to make it to search for them from the mean you will have to compute the average too so it's not it's Hughes from you as start of she Tennessee seats as so you want to produce a union do nor the average putting the gene activity which is the mean of life and you can find it because there is a corporation when you try to make that so we cannot say we have no way of knowing uh and no more than an expression of for the and furthermore for the variance so other tissues traditionally the win that's we introduced a scheme which I to simplify the 2 models in true have simply isn't fighting off of model mailed to me to be able to make some conversion between the 2 so he
09:19
can result solved we introduce caning which is to say that we're going to increase the speed of some parts of the of the mobile so he I'm just saying that the activation and deactivation energy would be very fast and the creation and degradation of an Iranian would be very fast also compared to the preceding timescale so how we do that so we introduce and which is gaining Paratore will be increased to infinity and we'll continue to bite each family to appear like an yeah so long as and when good infinity will you have acted to nutritional religion very fast and the creation degradation of the marine very fast compared to the spot which is the creation and degradation of parties so what would happen so you have states will buy and iron and wouldbe owners quicks kind scale compared to keep in fact we have it in changing key with a will you ever following creation of a protein and instantly you iron and we which then you can bring and deepening of occurrence and of proteins and so on and
10:33
try to put that in the more mathematical Woods and I so he few have the toll 1 which is the 1st jump of key and X would be the occurrence and want of proteins where he would you we have is that the average um the have a range of the gene activity will reach a instantly there kilograms With the stain which is depending on the current amount of protein Texas it will be exactly the same the either regiments of an irony and we reached before any change in the um indicated brand which is also pending an X the current among the protein and sold you will have a right of prediction of protein which we very clearly instantly depends on the current unknown of proteins salt that would be the
11:25
perseverance of the process P which is number pretty conversant sufficient to invest in that process with it if it's a number of parties that birth rates would be this 1 depends on X the current imam of proteins and death freight never changes all will always miss 310 member proteins change depending on the amount of is the more opportunity you have the less of buffer would be high and the other way around so that it is for the thing that mobile for the classical mobile and entered the same and the it's almost the same thing known differences here it's not depending on excess salt if X is high all role is a very high very low it doesn't change the of of the the birth rate on which time
12:14
on the minutes and news week so all you have equilibrium uh things the first one for the classical is just a person process it's a difficult question runnin distributions and the other 1 is a living complicated that's we can walk with it and especially we can at this result saw here it's fall the classical model he has fulfilled the feedback which is interesting here is that if you prove you have to wear producing the same protein 1 the classic mobile the other 1 of the few mobile if we pursuing his seeing the same amount on average of producing these 2 ways in the classic ,comma room you have a virus will be the same as the mean and the other way with the feedback no longer have vines which is lower than the mean so it tends to go in favor all the things would favor of the conjecture saying that the thing that we need to reduce the rights so since I don't have much time I was stupid and that's just is trying to explain that the spirit of its we try to know military it's you have a loss by instantly is all of feedback but there is until it is very low bond role bond and we would find its way asymptotic result I'm not explaining
13:29
why the gesture With the assessment that the results to the other and ratio between violence and mean we reach 1 onehalf that history that is to say that in the thing that model the UTS you have a really the and widescale version of the feedback mobile you have a valiant than the mean they cannot reach you can reach the lower half of the ranch which is not very high if you want to look at the distributions is like a crucial something like that and that its review reduced only by the body of 1 of the group's square root of true because it's the movements and allegations as do the square root of the various salt Though it is reduced but not that much so we can rap and soul it's a year would basically with extreme care so the reduction of the variances admitted that 1 of the feedback Muller really exist in nature so if it's not that useful what is useful for all the for the cell so we can up with another idea very quickly
14:32
we say OK everything we will into knowledge is a result is there something different beating the 2 malls for the Unocal reasons so here we have done some simulation we yet which one's going faster to reach the catering for example or you have a cell we have antibiotics Anderson used to produce the contour antibiotics very quickly into produce the unity the country to the taking of a running short of moment of time which 1 which way we go of faster to read to the the the the the new delivery so that's the biological example so we make assimilation was stopped at the rule of petition process you have to obtain a high production costs average prediction and you see which 1 is going faster so
15:18
here is the father of the result she Andrew you have the feedback mobile and red you have looked the classical mobile and indeed is going much faster all the things that look to reach their nuclear kilogram than the the classic on 1 is going 20 per cent faster for this set of pirated particularly and it's quite in that equation with the biological results with big did do the real experiments and can be 50 per cent faster than we are in the same range of a lot of things so basically is eroding after talks or Indian I'm going to be quick we have questionable that for interesting there is an article of all that performance on on archive material the British side pocket the this so on the last part of your told and you will concluded and analysts is always assimilation yes there any animated worry that not only we we try to have a look about him that is there an identical results we could not find a way to do it easily so we just make some nations fallout but because in a given is quite for Italy's each other into the results with in dynamically associated harder according to the questions that is not sense of knowing could hit new
00:00
State of matter
Multiplication sign
Kontraktion <Mathematik>
Mathematical model
Volume (thermodynamics)
Insertion loss
Euler angles
Mereology
Food energy
Functional (mathematics)
Mathematics
Stochastic
Lecture/Conference
Resultant
Units of measurement
01:33
Point (geometry)
Product (category theory)
Statistics
Collision
State of matter
Interior (topology)
Multiplication sign
Parameter (computer programming)
Mechanism design
Subtraction
Physical system
Standard deviation
Process (computing)
Product (category theory)
Statistical dispersion
Cycle (graph theory)
Prisoner's dilemma
Mass
Prediction
Translation (relic)
Local Group
Mechanism design
Field extension
Order (biology)
Resultant
Reduction of order
Directed graph
04:59
Group action
Distribution (mathematics)
State of matter
Scaling (geometry)
Multiplication sign
Distribution (mathematics)
Mathematical model
Thermodynamic equilibrium
Mereology
Food energy
Variance
Number
Arithmetic mean
Average
Term (mathematics)
Energy level
Equation
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Area
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Scaling (geometry)
Conservation of energy
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Classical physics
Moment (mathematics)
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Infinity
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Incidence algebra
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Family
10:31
Ocean current
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Process (computing)
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Multiplication sign
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Thermodynamic equilibrium
Prediction
Mortality rate
Mortality rate
Number
Maxima and minima
Number
Mathematics
Computer animation
Buffer solution
Theorem
Right angle
Hydraulic jump
Subtraction
Hydraulic jump
12:13
Distribution (mathematics)
Multiplication sign
Distribution (mathematics)
Mathematical model
Insertion loss
Thermodynamic equilibrium
Limit (category theory)
Asymptote
Variance
Root
Average
Natural number
Reduction of order
Square number
Pairwise comparison
Poisson process
Process (computing)
Distribution (mathematics)
Variance
Mathematical model
Thermodynamic equilibrium
Local Group
Arithmetic mean
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Theorem
Right angle
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Reduction of order
14:32
Classical physics
Standard deviation
Product (category theory)
Process (computing)
Line (geometry)
Multiplication sign
Moment (mathematics)
Range (statistics)
1 (number)
Mathematical model
Thermodynamic equilibrium
Prediction
Set (mathematics)
Mereology
Rule of inference
Trajectory
Computer animation
Average
Time evolution
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Metadata
Formal Metadata
Title  Stochastic model of protein production with feedback 
Title of Series  Les Probabilités de Demain 
Part Number  11 
Number of Parts  17 
Author 
Dessalles, Renaud

License 
CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/20273 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2016 
Language  English 
Content Metadata
Subject Area  Mathematics 