Information Biology - Investigating the information flow in living systems

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Information Biology - Investigating the information flow in living systems
From cells to dynamic models of biochemical pathways and information theory, and back.
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How to apply Shannon's information theory to biology.
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[Music] what happens if you mix Shannon's information theory and biological systems a dish better served hot please welcome our computational systems biology chef who will guide you through investigating the information flow in living systems please welcome with a very warm round of applause Juergen Paula [Applause] thanks a lot and thanks for having me
it's it's great that so many of you are interested in that topic which is not about technical systems but actually biological cells so I'm leading a group
in Heidelberg at the University there and we are mostly interested in how
information is processed sensed start communicated between biological cells and we are interested in that because
it's not obvious that they actually manage to do that in a really reliable fashion they don't have transistors they only can use their molecules mostly proteins big molecules that are little engines or little motors in the cell that allow them to fulfill their biological functions if information processing fails in cells you get diseases like epilepsy cancer and of course others now cellular signaling pathways have been studied in some detail mostly single pathways more and
more also networks of pathways but surprisingly little deep surprisingly little conceptual little conceptual work have been done on them so you so we know the molecules that are involved - if we know how they react how they combine to freedom - to build these pathways but we don't know how actually information is transferred or communicated across these pathways and we intend to fill that gap in in our group and of course first we
have to we have to model these networks we have to model these chemical
biochemical pathways and this is how we proceed so you have a you have a cell you can't see that here but on the upper left corner you have that scheme of a cell with all the different components you have in the in this cell where chemical reactions happen so chemical reactions take by chemical species ions proteins what-have-you and they convert them into other chemical species and these reactions happen in the different compartments now it's very important to assign speeds or velocities to these reactions because these speeds determine
how fast the reactions happen and how the dynamic behavior then results and once you have done that you can translate all of that into a mathematical model like the one shown here on the right this is an ordinary
differential equation system I don't want to go into detail I only have like two or three formulas that that might be interesting for you so this is just any mathematical model you have of these of these systems and then you can start analyzing them you can ask questions like how does the system change over time that's simulation which parts influence the behavior most what are the stable States to give oscillations there steady state and so on now you don't have to do that by hand because we're actually also developing a software
that's just another thing I guess you know that all models are wrong we try to build useful ones so I said you you
don't have to do this by hand because we are also into method development and we are building scientific software one of the software's we build is called capacity complex pathway simulator it's free and open-source you can all go to that website download it play around with it if you want because we also use more demanding computations which we sent to compute clusters we also developed a scripting interface for
capacity which is called cork the capacity connector and this allows you to use the capacity back-end with all the different tools that are in capacity from you our programming environment and then you can build workflows and sent them to compute cluster we think it's easy to use if if you play around with it you get stuck then just let me know so this is software you can use you can play around with and where do we get the models well there is a model database and that is
called bio models dotnet also free to use you can go there download models at the moment they have almost 800 different manually curated models and almost ten times of that that are built automatically you can just download them in the so called SB ml format which is the systems biology markup language that then import it into capacity or other software and play around with them ok so coming back to biology one of our favorite systems is calcium signaling
and calcium signaling works roughly like this you have these little I mean the the oval thing is the cell then you have these red cones there are hormones and other substances that you have in your bloodstream or somewhere out outside the cell they bind to these black things which are receptors on the cell membrane and then the cascade of processes happen that in the end lead to an in stream of calcium ions these blue balls from the ER which is not emergency room but in a
plasmatic ridiculous which is one of the compartments in the cell into the the main compartment the cytosol of the cell and also calcium streams in to the cell from outside the cell and this leads to a sharp increase of the concentration of calcium until it's pumped out again there are pumps that take calcium ions and remove them from the cytosol and pump them out of the cell and back into the ER this is very important because calcium is a very versatile second messenger that's what they what they call it it regulates a number of very important cellular processes if you move your muscles your muscle contraction is regulated by calcium learning secretion of neurotransmitters transmitters in your brain fertilization a lot of different things are regulated by calcium and if you simulate the dynamic processes you get behavior like that here you can see it
oscillates it shows these regular spikes so this is the calcium concentration over time now if you actually measure this in real cells and this is data
measured by a collaboration partners of mine in England you see it's not it's not that smooth you get these differences in amplitude of the peaks you get secondary spikes you get fluctuations around the basal level and this is because you have random fluctuations in your system intrinsic random fluctuations that are just due to random fluctuations in the timings of singly reactive events single reactions by chemical reactions that happen and in order to in order to capture this behavior because this behavior is important that can hamper reliable information transfer we have to resort to special simulation algorithms for
example the so called Gillespie algorithm and if you do that and apply to the calcium system you can see you can actually capture the secondary peaks and all the different other fluctuations you have in there now this is just a Monte Carlo simulation I say just it's really time-consuming and demanding because you have to calculate each and every single reactive event in the cell
and that takes a lot of time that's why we do that on a computer I told you already that calcium is a very versatile
second messenger so you have very many different triggers of calcium response in the cell things that lead to a certain calcium dynamics and on the other hand downstream calcium regulates many different things and so you have these our class or bowtie structure and that's why people have speculated about
the calcium code how can it be that the proteins should go back that actually do all these cellular functions
sorry these green cylinders that bind
calcium and are then activated or inhibited by it how can it be that they
know which stimulus or which hormone is outside of the cell they don't see them
because there was a cell membrane and around the cell around the cytosol so people have speculated is is there an information encoded in the specific calcium waveform is their calcium code and how can it be that the proteins actually decode that that code it's fairly established that calcium has shows amplitude modulation so the higher the amplitude of calcium the more active get some proteins it also shows frequency modulation
meaning the higher the frequency of the calcium oscillations the more active gets some proteins but maybe there are other information carrying features in the in the waveform like duration waveform timing and so on now a doctoral student in my group on
Asha has looked into frequency modulation and he actually showed that there are proteins in that case in fat which is the nuclear factor of activated T cells which are important in your immune system they only react to calcium oscillations of a certain frequency so they they get activated in a very narrow frequency band and that's why we call it band pass activation okay so you I guess
you all know signaling speeds of technical systems their value fast by
now one of our results because we quantify actually information transfer is that calcium signaling operates at roughly 0.4 bit per second if you compare that to technical systems that seems very low but maybe that's enough for all the functions that the cell has to fulfill so how did we arrive at this result well we used information theory classical information theory pioneered by people like Claude Shannon in the 40s
also by Hartley Chucky and a few other
people so they looked at technical systems and they have this prototypical communication system where there is an information source on the left side and then this information is somehow encoded it's transmitted over a noisy channel where this where the message is scrambled when it's received by receiver decoded and then hopefully you get the same message at the destination that was chosen at the at the information source and in our case we look at calcium as an information source and we study how much information is actually transferred to downstream proteins how do you do that
well information theory 101 information
theory primer in statistical information theory of the Shannon type you look at random variables you look at events that have a certain probability of happening so let's say you have an event that has a probability of happening and then Shannon said that the information content of this event should be the negative logarithm which is shown here the the curve on the right right hand side should be the negative logarithm of the probability meaning that if if an event happens all the time and I will show you an example later there is no information content the information content is zero there is no surprise if that event happens because it happens
all the time it's like a sunny day in somewhere in the desert however if you go to lower probabilities then the surprise becomes bigger and the information content rises now in a system you have several events that are possible and if you take the average uncertainty of all possible events you get something the channel called entropy this is still not information because information is a difference in entropy so you have to calculate the entropy for system and then you calculate the entropy that is remaining after an observation say and this difference is the information gained by the observation now coming to a simple example let's say we have a very simple weather system where you can only have rainy and sunny days and let's say they are equally likely so you have a probability of 1/2 for each of them the average is is the average of the of the negative logarithm is 1 so we gain when you observe the weather in this system you gain one bit per day ok you can also think of bits as the information you need or a cell needs to answer or decide on one yes-or-no question now if it's always sunny and no rain then you get zero information content or uncertainty the average is zero so you don't get any information if you observe the weather in the desert to say 80 20 you get a certain bit number per day in that case point sixty four-bit per day and you can do that for light say in that case Leipzig has 99 rainy days per year according to the deutsche vetted inst and this gives you an information of 0.8 for a bit per day you can do it in in general way so let's say you have one event with the probability of P and another event with a probability of one minus P and then you get this curve which shows you that the information content is actually maximal if you have maximal uncertainty okay if you have equally likely events if you have more possible events in that case four different ones sunny cloudy rainy and thunderstorm you get two bit and this is because of the logarithm so if you have double the amount of events and they're equally likely you get one bit more okay hope I didn't lose anyone okay now we are always looking at processes dynamic things things that change over time and if we look at processes we have to look at transition probabilities so we have to change probabilities to transition probabilities and and you can summarize them in a matrix so let's say if we have a sunny day today it's more likely that
it's also sunny tomorrow and less likely that it's raining maybe only 25% and if it's rainy today you can't tell it's equally likely and these processes are also called Markov process Markov was a
russian mathematician and you have them everywhere these Markovian processes are used in your cell phones in your hard drives they used for error correction the PageRank algorithm of Google is one big Markov process okay so you're using you're using them all the time nothing technological would work nowadays without them now because we have we have
knowledge about today's weather the uncertainty about tomorrow's weather decreases so now we have an entropy rate instead of an entropy and the difference is again the information you gain by today's weather so in you can do the maths in our example the entropy would be point nine two bit per day and the entropy rate given that you know today's weather is less it's a ten point eight seven bit per day now to complicate
things a bit more and maybe we also look at a second process in that case air pressure and you can measure air pressure with with these little devices
the barometers and maybe if it's sunny today and the air pressure is high you get in 90% you get a sunny day tomorrow and only in 10% of the cases you get a rainy day and so on you can go through the table in our case I looked it up yesterday we had high air pressure and it was raining so in our little model system it would mean that it's sunny today now I told you information is a decrease in uncertainty now how much information do we get by the barometer by knowing the air pressure and this is the difference in uncertainty without barometer and with the barometer and in our case we have to assume that the probability of high and low air pressure is the same and we get 0.39 bit per day that we gain by looking at the air pressure now what does that have to do with biological systems well we have two processes we have a calcium process that shows some dynamics and we have the process of an activated protein that does something in the cell so we can look at both of these and then calculate how much information is actually transferred from calcium to the protein how much inform how much uncertainty do we lose about the protein dynamics if we know the calcium dynamics and this is mathematically exactly what what we are doing and this is called transfer entropy it's an information theoretically measure developed by
Thomas Reiber in 2000 there are some practical complications that that we are working on and this is what we are using actually for the calculations so in our
case we have data from experiments or we use models of calcium oscillations and and then we couple a model of a protein to these calcium dynamics this gives us time causes both of calcium and protein stochastic time causes in including the random fluctuations and then we use the information theoretic machinery to to study them and some of our results I
want to show you for example if you increase the system size if you increase the particle numbers if you if you make the cell bigger then the information that you can transfer is higher meaning if the cell invests more energy and produces more proteins it can actually achieve a more reliable information transfer which comes of course with costs for the cell also it seems and that if you use more complicated dynamics meaning not only spiking but maybe bursting behavior where you have secondary spikes then you can transmit more information because the input signal carries more information or can carry more information in its different features another result is that proteins
are very interesting result I think is that protein proteins can actually be tuned to certain characteristics of the calcium input meaning with all the different calcium sensitive proteins in the cell they are tuned to a specific signal so they only get activated or they only these pathways only allow information transmission if a certain signal is observed in the cell by these proteins so in a way the 3d structure of the protein defines how it behaves dynamically how quickly it binds and so on how many binding sites it sites it have it has and then this dynamic
behavior determines to what input signals that protein is actually sensitive and on the right hand side you can see some regulations we did and the Peaks actually show where this specific protein which is calmodulin light protein you don't have to memorize that it's a very important calcium sensitive protein where these differently parameterised models actually get activated and allow information transfer and this allows differential regulation because you have all the different proteins you have only one calcium concentration and only the proteins that are sensitive to a specific input get activated or do their things in the cell now if you look at more complicated
protein so calmodulin the one i just showed you was only activated by calcium more complicated proteins like protein kinase c for example they are both activated and inhibited so they show biphasic behavior where in an intermediate range of calcium concentration they get activated with very high or very low concentrations they are inactivated and you can actually see that these more complicated proteins allow a higher information transfer and again producing these more complicated proteins might be more costly for the cell but it can can be valuable because they allow more information to be transferred and this
you can see in this plot where we actually scanned over the activation and
the inhibition constant of these model proteins and you can see that you have these sweet spots where you get a very high information transfer so color coded is transfer entropy now coming to a
different system just quickly we also looked at other systems of course calcium is calcium signaling is just one of our favorite one we also looked at bacteria and this is e coli and a very famous model system for biologists and these are cells that can it can actually move around because they have little propellers at the end and so they want
to they want to find sources of nutrients for example to to get food so they they swim into a direction and then they decide whether to swim whether to keep swimming in the direction or whether to tumble reorient randomly and swim in some other direction the problem for them is they are too small they they can't detect a concentration gradient of nutrients of food between the front and the back of the cell so they have to swim in one direction and then they have to remember some nutrient concentration of some time back and then they have they have to compare is the nutrient constant concentration actually increasing then I should continue swimming if it's decreasing I should reorient and swim in some other
direction and this allows them to on average swim towards sources of food now in order to compare over time the nutrient concentrations they have to memorize they have to know how much nutrients we're there some time ago and for that they have a little memory and the memory is actually in the you can see on the left-hand side the receptor that actually senses these nutrients they can be modified these
receptors we call that methylated so they get a methylation group attached and they have different states of methylation five different ones in that model we are looking at and this builds a memory and we looked into that we quantified that with with information theory this is a measure this is called mutual information it's not transfer entropy it's another measure of in that case aesthetical information you can see this is the amount of information that is actually thought about the nutrient concentration that is outside of the cell and this is it nuts it's not in bits it's just a different you can translate them it's just a different unit for information and you can also see how the different methylation States so these are the colored curves how they go through how they are active with different nutrient concentrations and this is ongoing research so maybe next time hopefully next time I can show you much more and just to finish this we also look at time scales because the time scale have to be they have to be right okay the system adapts so if you keep that cell in a certain nutrient concentration it adapts to that nutrient concentration and goes back to its normal operating level now if you increase the nutrient concentration again it shows some swimming behavior so
if the depth but it also has to decide it also has to to compare the different nutrients at different positions and that's how they have to manage the different time scales of decision-making and memory or adaptation and we are looking into that as well coming to the
conclusions I hope I could convince you that information theory can be applied to biology that it's a very interesting topic that's a it's a fascinating area and we are just at the beginning to do that I also showed you that it's such that in signaling pathways the the components can be tuned to their input which allows differential regulation so even though you don't have wires you can still specifically activate different proteins with one signal or multiplex if you want we are of course in the process of studying what features of the input signal lie to the information carrying so we are looking into things like waveform and timing and we want to look into how these things change in the deceased case so if you have things like cancer where certain signaling pathways are perturbed or fail we want to exactly find out what does that do to the information processing capabilities of the cell we also found out that estimation estimating these information theoretically and quantities it can be a very tricky business and another project we are doing at the moment is actually only on how to interpret these in a reliable manner how to estimate this
from sparse and noisy data so that's also ongoing work I would like to thank some of my collaborators of course my
own group but but also some others particularly in particular the capacity team that is spread all over the world and with that I would like to thank you
for your attention and I would be happy to answer any question you might have thank you [Applause]
[Music] if you have questions there are two microphones microphone number one microphone number two and please speak loud the individual microphone and I think the first one is microphone number two your question please has there been any work done on computational modeling of g-protein coupled receptors and the second messenger Cascades there can you repeat
that sorry as which one it worked on on computational modeling of g-protein coupled receptors g-protein yeah oh yes I mean we are doing that because calcium is actually I mean the calcium signal is actually triggered by a cascade that includes the g-protein most of these receptors are actually G coupled or Chi protein coupled receptors so that's what we are doing thank you microphone number two again first of all thanks for the
talk and I want to ask you to talk a little bit about how different proteins get activated by different signals and could you go a bit into detail about
what kind of signal qualities the proteins can detect so are they like are they triggered by specific frequencies or specific decays like which characteristics of the signals can be picked up by the different proteins well that's that's actually what we study I mean we have another package that is linked here is the last one the oscillator generator this is a package in our that allows you to create artificial inputs where you have complete control over all the parameters like amplitude duration of the peak duration of the secondary peaks frequencies of the primary peaks of the secondary peaks we fraction period and so on you have complete control and we do at the moment we are also running scans and want to find out what proteins are actually sensitive to what parameters in the input signal what we know from calcium is that for example calcium calmodulin kinase 2 also very important protein in the nervous system and that shows frequency modulation and this is also it has also been experimentally where they put that protein on the surface they immobilized it on a surface and then they super fused it with calcium concentrations or with solutions of different calcium concentration in a pulsed manner and they measured the activity of the protein and they showed that with increasing frequency the activation gets bigger it at the same time it also shows amplitude modulation okay it's also sensitive to the amplitude meaning the absolute height of the concentration of calcium Thanks thank you and again
number two please I so you talked about a lot of on and off kinetics and I wonder if you think about neurons which
not only having on and off but also many amplitudes that have take a big role in development of cells and synapses how do you measure that so how do you measure like baseline sporadic activity of calcium well in our case there are different ways of measuring calcium but that's not what we are doing we are measuring sorry but more like how do you integrate it in your system because it's not really an on/off reaction but it's more like sporadic ministry yeah I mean in in the case of calcium you have these these time causes okay and we look at the two complete cut time costs so we have the calcium concentration sampled at every second or half second in the cell by different methods so our collaboration partners they use different dyes that show fluorescence say when they bind calcium some others show bioluminescence and then we use these time causes in the neural system it's a bit different there you also get the analog mode where neurons are directly connected and they they exchange and substances but most of the case you have action potentials and they didn't go into neural systems at all because things they are totally different you get these action potentials that are uniform mostly so they they all have the same duration they all have the same dude and then people in neuroscience or computational neuroscience mostly they boil the information down to adjust the timings of these Peaks and they use this information and mathematically this is a point process and and you can use different mathematical tools to study that we are not really looking into neurons we are mostly interested in non excitable cells like liver cells pancreatic cells and and so on cells that are not activated they don't show a massive depolarization like in neurons thank you thank you and obviously again number two hi so you mentioned cam kinases too and I got you don't work on your science specifically but I'm pretty sure you had a quite extensive knowledge in the subject what do you think about this I would say hypothesis that were quite popular a few years ago I think in the u.s. mainly about the fact that the Zetas Skeletron of neurons can actually encode and decode through kinases in the sky in the city Skeletron memories like bits in a you know in a hard drive well III is your feeling I'm not going to speculate on that specific hypothesis because I'm not really into that but I know that many people are also looking into spatially effects which I didn't mention here I mean the model I showed you is a spatially homogeneous model we don't we don't look at concentration gradients within the within the cell our cells are homogeneous at the moment but people do that and of course then you can look into things for example like a new topic is morphological computation meaning that especially you can also perform computations but if if you're interested in that I mean we can talk offline do you buy it I can because I can give you some pointers there yeah but do you have a good feeling about those theories or it you're clueless well I think that the spatial aspect is a very important thing and and it's also something something we should look at I mean to me and random fluctuations are very important in forensic fluctuations because you can't separate them from the dynamics of the system and they're always there at least some of the of the fluctuations and also the spatially effects are very important because you have these you not only have these different compartments where the reactions happen but your auto concentration gradients across the cell especially with calcium people have looked into calcium puffs and calcium waves because when you have a channel that allows calcium to enter of course directly at that channel you get a much higher calcium concentration and then in some cases you get waves that are travelling across the the cell and to me it sounds plausible that this also has a major impact on the information processing yeah thank you thank you in this case you can thank you for your talk and please give a very warm applause to him [Applause]