so we put a Monday of here theology from these this whole set of sums and integrals some general system so I was going in take clothes going out and then we have two reactions K going on inside so we get these giant equations this is the mass balance for a component the left here the accumulation of final minus T initial or some time grid for the time 0 to time final and then each of these streams we can we can integrate our mass flow rate from initial upon time we can sum over all the streams in the streams now we can integrate from the beginning to the end of time and then sum of all the streams out and then for each reaction K because this extent of reactions iodized all these to be functions of time rate that’s a function of time that’s of time and then preach reaction coefficients those are the moles react but claims to make it’s a good starting place to organize them with eachother these are transmembrane proteins called G couple g-protein coupled receptors so this is the cell membrane and so these are proteins that sit in the milk membrane and they’re essentially sensors that sense things going on in the environment they have the structure of them you can see these out with these Gila C’s in the protein there’s 70 back important this tends to be a really gentle form for membrane proteins memories hydrophobic you need to keep protein going to see it for the parts at the top of the bottle because of g-protein coupled receptors the receptors that bind small molecules and then these small molecules will change the confirmation of this protein molecule if you look on the inside of the cells is the cells you point you see one thing that you see something else is it opens up so it makes its big conformational change and then what happens is G proteins are coupled to these and come in and find it in one conformation the G proteins don’t line don’t be actin another protein side they do and this conformational change allows gtp exchange factor to exchange yeah gtp GED exchange that there’s James GDP for gtp so this is quantity of diphosphate lunding triphosphates of eternity it’s the base of DNA with different numbers of phosphate groups but this is often used for signaling inside the cell to change the number of phosphates it makes it more negative and it changes what these things can bind to so all the sides started signaling Cascades a good outlet change transcription these things are used to detect ones smell so so I wrote Dobson and you’re in your eyeballs is the seven transmitted protein and the small molecule is actually a photo sensitive – it absorbs a photon and then changes conformation does this suit lady tooth one of these proteins smells your nose and your tongue abilities hormones are often sets with these and neurotransmitters so don’t demean home instead of trains so these are pretty important protein so this is why this got the Nobel Prize Robert Lefkowitz and variety will then determine these structures which is no small feat we usually it starts as a proteins by making the crystal of proteins and then you see x-rays – oh you get scattering patterns and you’re back out the regular structure of the protein but you have to have a three-dimensional crystal so you

have to have proteins that can line up next to each other so that’s already a tricky with solution proteins we’ve done a lot of remembering proteins to do these crystallize it’s kind of crazy with it is they use detergents and things to get how the membrane what a limit is so go around the outside they’re supposed to be oily and they got these to personalize hey they said that’s that sorting of why I invited my this morning can be both it’s actually really important my lab right now we’ve been doing a lot of attention to and brain proteins because they’re not really known how to calculate the structures of these find how they interact with the Merriman remember ages oh it’s changing its fluctuates dynamic attack Foley there’s not a lot of laughs determine the grade point instructions and interaction design then more broadly 20% of drugs target these these are censorship of the cell so it’s a great place to tell the cell to do something and that’s how this connects to the so what minute drugs one of these sensors so so you want to get drugs into these sensors are you want to block one of these transmembrane channels and send this signal or stop the signal for visa so we do that with small molecules one of the issues is you want to give the dosage right you want to have enough but not too much for side-effects you don’t want it too low that you’re not gonna affect I’m so if you just inject a drug you’re gonna get all of the drug at once and then your body is going to get rid of it so that’s gonna be pretty high doses it away take a pill it’s a continual time to come up to speed and then you’ve also got a picture of the gastrointestinal tract there’s going to be justice so I’m sure you guys have all heard of patches they’re typically made of polymer so that they’re infused with the drug and then you rely on diffusion of the polymer that drug out of that however to get through and then diffusion through the skin and the blood streams this is a great angle into a problem transport class you talk all about diffusion than what controls that fast it goes so you’ll probably see this example again and then for this class I want to talk about the balance this is a great example of some integral or differential to got some things changing in funded by xoxo line is a path there’s a whole bunch of things right that you can make a team birth control really nothing is left patch now this is the agency it fits into what acetylcholine receptor signal choline is your one of the neurotransmitters in your brain cells so XY is a medication that inhibits cholinesterase is so your your Co choline as the translator between the neurons and acetylcholine breaks that down if you blocked the acetyl that side it’s the only esterase breaks down the acetylcholine you can block the acetylcholine esterase then i can keep the acetylcholine around the water so you’re not actually messing with so here’s my transmembrane proteins and I’ve got siegel choline co choline it’s being released from one cell lattice maybe these sensors on another cell well the cecile choline esterase is getting degraded by cycle acetylcholine is degraded by a seal choline esterase to go away but if we bring in this drug and the drug blocks acetylcholine esterase you stop that and keep these super cool back a few steps mileage something like that effective one thing affecting another affecting all these feedback loops so that’s this problem that this exelon which I guess is treating Alzheimer’s and Parkinson’s now dementia so excellent is a passion for the Alzheimer’s medication hibbons acetylcholinesterase is in the brain to make higher levels of the neurotransmitters like acetylcholine let’s say we load 60 milligrams and the drugging will patch the drug is released at a rate of 25 times e to the minus 0.5 milligram per day so the rate changes because we’re depleting this drug and the polymer and so that rates gonna go down it’s time it’s T here is in hours

these an hour’s evocation patched what fraction the drug is released after one week is question number one so how much drug gets released in one week and then question we’re going to ask is how when do I need to replace the patch the second question that kidneys filter the drug out of the bloodstream a mass of throughout the bloodstream vary as a function of time after application of a patch so there’s the drug dose question how much is in the blood that’s what you want to know see what’s gonna do this job what time is the consecration highest would know what how long is that going to take and how high is it gonna be that’s a new pre important because you logically this is the can be probable question is the problem well determined they have enough information yeah which means what was that mean we do next and one else what’s the human weird what’s the one with the story of the stream with this they’re coming from coming from the patch like to in what’s your system we’re gonna use the system so the body so the system is the body then we could be using for these terms as we have mass component compounds compounds just this broad right so X minus 2 these are comments so this is any massive drug final in the body when it’s massive drug addition in the body these the audience our system yeah any of you have anything else for boxes and diagrams city to catch what’s what’s key lighting to the patch of the system is we can ask now we could have mass of drug to the patch massive drug pulling into the patch match of truck out of Dodge so we can use it patches the system because use the bodies the system I want this outlook that’s the kidney so the kidneys filter the drug out so could do something like that and then taking part of the body so what we typically do is talk about the bloodstream so often we do the Department of kinetic problems is it started by we also that this problems pretty simple we don’t talk about other tissues but sometimes we can also talk about disappointment of what rain there’s companies to do this for this person they have not angry system so assistant we can choose different things and so forth it’s actually much better system for number two when we’re talking about the mass in the bloodstream for two then we definitely don’t want what is their system okay so far uh so for number one I we’ve got this equation so we’re gonna do this component to the drugs or I it’s gonna be the drug here and the system is the patch alright so now we need pieces for each of this way where do these numbers go in it we have a few numbers 60 milligrams we’ve got 25 into the minus 25 t we’ve got a week we’ve got five milligrams a day okay everybody hear that so why on the

initial mass in the patch finalists actually kind of what we’re looking for exactly what fraction is release so we don’t want to say they’re finally launched at least are actually released is this disappointed the masks the change of mass and the batch is how much is released or the accumulation of the patches to be the opposite of what’s released so the final exits initial the initial is other 60 milligrams okay so mass drug initial is 60 milligrams what’s the way know that 60 milligrams is the accumulation and looks like and rightly says we’re doing is there 60 milligrams of the drug is loaded into the patch so the key thing to think about is the time when does the 60 milligrams be put into the patch before and then when does the nice thing happen during some time we know and then there’s – you almost want to do put back from the empties we have this cartoon forms so the poor take the patch and blow this and dirty we take the patch we’ve got stuff coming out and after you peel patch off anyway load get some additional massive drug and we’ve got some mass and in the middle we got this whole material balance so this is this material that goes from three different times here is and this we do this interval we’ve got one particular time yeah that’s a zero how about 25 divided by T which term is that Amy Anna the other is the system of the patch and this is going out because when 25 into the minus T over 2 this is how they actually get the bucket of blood to the out of the back so and that’s drug in this 25 neither – to end up out of the pouch ok into the passionate no reactions in the patch nothing there so simulations in – Alex we said there’s no reaction so massive trauma final – massive drug initial equals there’s no me neither – out 25 leaves the minus T over 2 integral T 0 this is integral T 0 T map M drugged-out that’s it integral of mask initial this exponential minus 25 52 yes it’s the change in Mass the change in Mass same as how much is released great from time zero at a time ten days if I call that days so I could be either

minus 10 over to the minus 5 – 5207 okay so 50 and either – seven cats is 0.03 just one means 0.6 times 50 is the change of mass 5 milligrams released that’s the accumulation the change in masses – renewed goodbye so that’s how much mass is removed in the that someone a change in the past so – that is 48 that will be released yes questions but backed up a little bit here 15 mean the minus T over 2 minus 1 and I’ve actually bought this changing that opposite change in mass as a time it’s number two kidneys filter the drug of flood street there’s rating a five milligrams a day where does that go to my picture out of the blood five milligrams per day how does the massive drug in the bloodstream vary as a function of time after application of action okay so we said that this one we’re going to choose a different system blood straining that is often the case in chemical engineering any differences just answer different questions and then we’ll look at the blood now this is going to be massive drug in dots and this is going to be where is this in the cartoon these are piece of food during the process which writing that amateur bouts and to no GenCon we do have in with you about we do have accumulation of the body yeah looks good this being MDOT in this being and that d out and we’re assuming we’ve done burpees step four we convert all the units all gotta be milligrams per day and it’s gotta be milligrams and tees got a good day that’s all gonna match all the questions about material balance okay what’s we know anything after to be no avi initial or funnel drunk we couldn’t let this one equal zero and just saying let’s say it’s a fresh patch but it’s the second they took one off yesterday put one on let’s say it’s zero and final massive drug and it’s going to be a great this from zero to seven days twenty five PT over two seven five i’ma get 50-50 e minus T or two from 0 to 7 minus 5 TV from 0 to 7 the next thing to do is to wait until

the end to put your numbers in so we put T final here it says e to the minus T final over 2 minus 2 0 minus 5 TF minus there was one minus sign I can distribute in I get 50 times 1 minus each – – then we can plug in that seven days okay so we get equation this for final massive drug and then we can plot a final massive drug versus time if we use this one with the ty minutes and we should get is something that shoots up and then eventually comes back down and eventually goes negative Louis euro much across doesn’t make any sense this can’t remove any work activity that is in the body I was the best various function time so that’s it give this expression and that what time is the pro concentration highest how do we find that point take the derivative it’s gotten equal to zero so I take this equation we would say deed and final T equals and we set that to 0 and we solve for T we should get we should get T equals there 22 times T equals 3.2 to anybody else plugging that in its life and plugging that into the end where we should get a maximum concentration of 23.9 milligrams this is about three this is about seven last thing is this will determine its do degrees of freedom on this last one variables how many Street variables one two icy stream where to screen variables in now how many system variables system variables are number of reactions plus number of things that accumulate so in this case we do everything Malaysia so we have one it’s basically this final quantity assuming you’re given some initial condition equations Louis get 225 a 2-2 at 5 so I got too close you