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0:01
- I'm Jeff Yarger. I'm Professor of Chemistry, Biochemistry and Physics at Arizona State University. Today I'd like to introduce thermodynamics, specifically biological thermodynamics, and its implications in biology and life sciences.
0:20
Thermodynamics is generally the study of energy.
0:24
We write at its most fundamental level, we split energy up and look at its contributions from various forms. Because we're always in a biological system thinking about a part of the universe, that part we'll call the system and everything else being the surroundings, and really most of thermodynamics is about bookkeeping of where various types of energy goes. Now from introductory physics, one of the first bifurcations we think in energy is what we learned in physics,
0:56
that you can split up energy into kinetic and potential energy terms. And this is often very useful for problems. In thermodynamics, the useful way of splitting up different types of energy is in different types of work, whether it be some type of mechanical work, some type of chemical work process, some type of electrical work, et cetera. And then we also have another type of energy, which is typically called heat, for the obvious implications of practicality
1:29
that it comes about most commonly to our senses by a change in temperature or a thermal effect. In fact, this is how thermodynamics got its name in general.
1:41
So by keeping track of a unique type of energy called heat and then the various types of other energy, which we split up into different types of work,
1:51
is how we're gonna be able to look and frame thermodynamics or basically the theory of the macroscopic for biological systems. And one of the nice things about this is that we're gonna find out that the energies that we look at all end up being state functions, which we're gonna define later when we look at the mathematics of thermodynamics. But it has the implication that we really just have to, we usually think about just the change in some energy process, not the absolute energy itself
2:26
but the change during some process. So almost always when we talk about energy, we often even leave out that we're saying the change in energy. But really that's almost always what we're looking at, is the change in energy. And specifically we're gonna call it internal energy and use a capital U to define it. And this is just to remind us that we're talking about the internal energy or the energy of a part of the universe that we're gonna call the system.
2:54
And so that's the biological system that we're interested in this case.
3:01
Again, almost all biological processes when we're looking at macroscopically can be framed in thermodynamics to look at its energy or how it changes. So from things as simple as mechanical type work, for example, some force over some derivative in some length property, to changing the concentration of compounds, some chemical work, some nuances in the chemical work, like looking at just how you change or move electrons,
3:39
the concentration of electrons and how their potential changes, electrical work. We can even interact with light in various forms, whether to change the energy of a system in things like bioluminescence and things in photosynthesis, et cetera. And almost all of these has some process where we're looking at some type of energy that's related to a work type function, chemical and mechanical, et cetera, electrical work, and then also keeping track of the heat associated with it.
4:12
So in thermodynamics, it's usually putting everything in terms of these work functions and also heat. And keeping track of that keeps track of the entire energy
4:25
of the system of interest. So what I think of as the fundamental equation of thermodynamics, the one that summarizes the laws, is one I keep showing over and over throughout these slides, which is that the change in internal energy, because it's usually the change that we're always measuring, has a heat component. And that goes as the temperature turns the change in the entropy. And then however many some of the different works that are involved in the process.
4:53
In biological systems, this is often something, mechanical work, pressure, volume, mechanical work, and then chemical work, the change in the number of moles and chemical potential of a system. And usually this encompasses most of what we need for a lot of biological processes. However, when we need other specific work functions, whether it be, say, something that is undergoing a change in its magnetic properties, magnetic moment into a magnetic field,
5:22
we can always add these extra work terms on. But a lot of biology can be very well looked at by just looking at how biochemistry or chemical work is happening in a system. And that's why I've explicitly shown it here.
5:43
Really the big distinguishing thing, kind of like we said we distinguish potential and kinetic energy when we look at energy in fundamental physics often, in thermodynamics, we split it up into a heat component, which always has the same variables that define it, temperature and entropy, and then we also the addition of different types of work that are involved in a specific problem, whether it be what I've shown here, the two most common mechanical work in pressure, volume, space,
6:16
three-dimensional space we're working in, and the change in the chemistry, the biochemistry, that's happening through a chemical work term. But everything, as the top equation shows, has this general formula that you have a heat and then it adds this conjugate field of all the different works that are important. And the lower equation shows the two that are most commonly used when we are introducing and working problems in biological thermodynamics.
6:43
Below shows what we kind of think of more of almost a molecular level of what is giving these type of effects, what's the difference in work in heat type of parameters?
6:58
So when we look at the internal energy or the energy of a system, we often will want to reframe the energy into variables that are more natural for the case in which we're working. And in this case, this is what leads to different types of energy besides the internal energy that we talk about in biological thermodynamics. One of the most common is enthalpy. And we use a capital H
7:30
to represent the enthalpy of a system. And like it's an energy, just like the internal energy is, but it has different properties where it's dependent on different variables and has a practical sense for being able to be used, therefore, under different conditions. And this is vague. Let's be a little more specific. Specifically, the enthalpy of a system, that type of energy, is basically directly proportional to the heat, so the heat absorbed or transmitted in a system at constant pressure.
8:08
And so this will give us, this type of energy is directly related to the heat of a system when you're under constant pressure conditions. So what do we mean by dependent variables? Well, you can see that the internal energy is dependent on the entropy, its dependent variables are entropy, volume, and number of moles. So in biological systems, often volume is a very hard variable to fix, et cetera.
8:40
Often it's pressure that we can take constant in a system. So when we're not wanting to look at mechanical work type systems and we wanna be able to get an intuition for how the energy is directly to just the heat component, we use enthalpy. Now we define enthalpy, so enthalpy is defined to be U plus P V. But as I said earlier, we always look at the change in energy. So we're gonna look at the change in this type of energy as well. So it'll be the change in enthalpy
9:15
that we're interested in looking at, which goes as the change in internal energy plus the change in the product P V.
9:23
So expanding this out, you can see that it's the change in internal energy plus P d V plus V d P, or expanding this out.
9:39
Now we can tell that, if we're, you know, this right here for a closed system where you don't have any change in the number of moles,
9:54
is U plus P V is T S. So this is, or basically heat. But I'm gonna put it so this is the change in the heat of the system.
10:09
Also we just said that we want this under constant, so if we make this under constant pressure conditions, then this goes to zero. And so the change in enthalpy goes as just how the heat changes in the system. More specifically, as we'll talk about further in this course,
10:33
a lot of thermodynamics is trying to get an intuition and a feel for entropy. And you can see that it's really the enthalpy goes as the entropy changes and it's scaled by the temperature in the system.
10:48
As we've defined enthalpy here, and we're gonna show this later, but when we look at the mathematics of thermodynamics through the property of exact differentiation, we can use what's known as a Legendre transform to kind of show the fundamental equation for enthalpy. In a sense what it has the property of is changing this mechanical work from its dependent variable in internal energy, being volume, to its dependent variable being pressure. So now in a closed system,
11:24
where you don't have any change in the number of moles, under isobaric conditions or constant pressure, then the change in the energy, which we call enthalpy, is just the change in the heat, which we will see through the second law is T d S for a reversible system. So that's how we come about this. And a lot of what we do in biology, most biological reactions end up being under constant pressure condition. So this allows us to see where the heat, or where this type of energy that we call heat,
12:02
is going when you're doing different types of processes. So we even say as the terminology that if delta H is negative, that it's exothermic, that it releases heat into its surrounding. Or if it's delta H or the change in enthalpy is positive, that it's endothermic, that it requires heat into the system for that type of process to happen, et cetera. So this ends up being very useful, one of the very useful types of energy, because of its direct relation to being just the energy of heat
12:40
under constant pressure conditions for biological systems.
12:47
As we've seen, heat is,
12:52
you know, can be broken up into conjugate field of temperature and entropy. And a lot, as thermodynamics, as the name implies, is oftentimes focused on the study of heat. And the study of heat really involves this idea of entropy. And we're gonna spend most of our time in thermodynamics trying to get a better intuition for this variable.
13:18
One of the key insights came when Boltzmann was able to equate this concept of heat or entropy to the change in the number of configurations in the system, a probabilistic, how many probabilistic ways microstates exist in a system. This is one of our key insights to get from the macroscopic of thermodynamics to the microscopic world, a molecular-level world, is through looking at this. And we look at the statistics or probability of different things happening
13:55
for all these millions, Avogadro's number, of microstates, particles, et cetera, in a system. And it gives us a sense and helps us understand how we think of entropy from a microscopic standpoint. One of the first things we often learn when we look at entropy we learned in some of our introductory physics and chemistry classes, it has a lot to do with the amount of order and/or disorder in a system. And this is a very useful kind of practical analogy to how entropy can behave,
14:32
that when you mix something, like you have some molecules, say sucrose, sugar, in a water system and then you have pure water where you put on top of it, we know that those molecules distribute themselves. They increase their number of microstates to occupy as many potential different configurations as possible. And you never see the opposite. Once it forms this, you never see it kind of go back in this direction, to a lower entropy state. So we often think of things thermodynamically
15:06
as one of the axioms of thermodynamics is this idea that entropy tends to maximize, or the amount of disorder tends to. Keep in mind this is also always scaled by temperature. And it's at really high temperatures where this really takes hold the most.
15:25
So we can now start talking about what are low entropy and high entropy states in biological systems by how ordered or disordered they are, how many available microstates there are in a system. There are more ways to take the water molecules and to configure them when you have something like water, even more if you do something like steam or vaporize it. Then if you confine those molecules to lattice positions in a solid crystal, like ice is,
15:58
which will have a much lower entropy state, et cetera. Same when you take something like diamond and you're able to vaporize that carbon. You give it a lot more configurations for those carbon atoms to explore, and hence a higher entropy, et cetera. So it has a lot to do with the number of ways you can configure microstates. So it has a lot to with probability and statistics of looking at degenerate microstates in a system. And it gives us really a peer into microscopic
16:32
for biological thermodynamics.
16:35
We have, you know, it helps us explain, from a fundamental theory standpoint, some things that we're very familiar with and seem very intuitive by nature. If we take, you know, a separate container that has some oxygen gas,
16:52
one that has some hydrogen gas, we put 'em, sorry, hydrogen gas and we put 'em next to each other with a barrier and then we release that barrier, you know, these gases mix, right? And this is increasing the entropy of the system. And you don't see, and this happens spontaneously. You don't see spontaneously the other process happen, taking a mixed gas like this and seeing it spontaneously separate into these two. The opposite you often do work
17:26
or do something to make this type of process happen. So there's an action that its entropy gives a directionality to spontaneity or to the time, or to time's arrow itself, to the flow of processes in a system. You can further think about this system more. You have oxygen and hydrogen in a container. And, right, we know that oxygen and hydrogen can react to form water vapor.
17:55
Now is this increasing its entropy in the system?
18:02
No, this has a higher entropy here than this. This is actually has fewer, right? You've now taken, you've made it in fewer configurations. You've taken two diatomics and made a triatomic molecule into it.
18:18
So for this to happen,
18:22
we say that, how do we explain this as far as entropy increasing? Well, entropy does increase in this process, just not if we just look at the system. The system's entropy actually decreases. But the total entropy, which is the entropy of both the surroundings, the entire universe, and the system itself, that does increase in any process that does happen.
18:52
This is often one of the big confusing points, is focusing what really thermodynamics says is the entropy of the universe or the entropy of both the system and the surroundings, increases in any spontaneous or process that happens.
19:09
We oftentimes, as biochemists, we're looking at just the system. And that can either increase or decrease,
19:20
depending on overall energy, which this can play just one role in.
19:31
Now we've kind of looked more at the heat. We've even seen that we often define new ways of looking at energy so that they're equated to just this heat type of energy, like enthalpy is most commonly used when we want it to basically eliminate all other work terms and just make the energy equal to the amount of heat in a system, by doing things like constant pressure in closed systems, et cetera.
20:02
There's another energy, in fact, there's several. But probably the next most commonly used in biological thermodynamics is the idea of free energy, how much extra energy we have
20:17
to do different processes. And this was first developed by Gibbs, and so we often call it the Gibbs Free Energy.
20:26
And this is, in a sense, an extra, it's an energy term itself and it has the enthalpy component in it, in a sense. So it has the enthalpy component and it also takes into account the heat component. So it's the Gibbs Energy is defined as U plus P V minus T S.
20:52
So you can say that it's also defined as H, because H is U plus P V, the product of P V. So it's, in a sense, H minus T S.
21:04
And what this has the property of doing is, like we said before with the enthalpy of a system, we can do a Legendre transform on this because of its property that it's a state function and exact differential. We're gonna show this again more in a video separate from this. But as we showed before, H has the property of flipping the dependent and independent variables and it flips the sign. And, you know, this one does the same. So while U, the internal energy,
21:38
is dependent on entropy, volume and number of moles,
21:43
enthalpy flips this one and it's entropy, pressure, the number of moles. So now you can see the Gibbs Free Energy is temperature, pressure and number of moles.
21:57
This is very commonly used in chemistry, biochemistry and biological processes because to look at any type of reaction or the chemical work term,
22:09
fundamentally, the easiest thing practically for us to hold constant is the pressure and the temperature. It's not easy to think of ways that you could hold the entropy and volume constant to look at how the chemical work uniquely affects an energy. But it is much easier to do things under isothermal conditions and isobaric conditions. In fact, that's what we often think of doing in most biological systems. They're done at more or less the same temperature
22:42
and at atmospheric pressure, for the most part. And then we can look at how, you know, the energy just depends on a chemical work term, et cetera. The other thing that's probably most critical about this, we use these concepts so much, this idea of free energy, this idea of enthalpy, which we often equate to the heat in the system under certain conditions, and this concept of entropy, temperature entropy and its relation to heat, that probably the most fundamental thermodynamic formula
23:20
you use in biological thermodynamics is a consequence of looking at the change in this function right here, which we've written here, and under constant temperature conditions,
23:35
for this equation. So at isothermal conditions, this is probably one of the most fundamental equations we use. And we often look at the change in the energy by looking at it as an enthalpy term and an entropy term, or looking at its enthalpy as a type of energy
23:56
and its T d S entropy term as another type of energy.
24:02
And looking at those two to help explain how the overall energy changes and whether something will likely happen or not, or whether it's, we call it spontaneous or not spontaneous type of process.
24:18
And so we often think of these as, you know, because we so commonly look at this as enthalpy, you know, trying to find its way into decrease or find its way into a minimum (mumbles) and entropy being the one, as you increase temperature, that helps maximize it or helps it get out of these type of processes, is kind of a way that often in a very simplistic view
24:45
gets used to try to help us come to grips with some of these concepts.
24:52
But it's very clear that when we wanna know whether we think a biological process will happen, for it to be spontaneous it needs that, its change in free energy needs to be negative.
25:05
So it needs to decrease overall during the process. So we often look at that as, how does the enthalpy and its entropy change? And you can see I've given a couple scenarios here. We often will say when things are, for example,
25:26
entropically driven because it's really the entropy term that's driving the Gibbs Free Energy negative more than it is per se an enthalpy term. And it's things like this that we often equate to biology itself. Well, at very high temperature, entropy dominates everything. As you decrease temperature and get to physiological conditions, conditions that our weather supply here on Earth, which is significant, you know, substantially low enough so that you can often have enthalpy help dominate this
26:05
and allow bigger structures to form that aren't entropically favored, they're enthalpically favored.
26:13
So from a microscopic or a molecular standpoint, we often think of these enthalpies as giving us some insight into what's changing about the bonding and interaction of the molecules, the biological molecules of interest. While the entropy telling us more about the arrangement of some of those molecules, their order or disorder in the system, et cetera.
26:40
I like to end with an example or so which we'll be giving a lot of biological examples where we work things explicitly, but where we look at things in just kind of general terms. So when we look at this, for example a common process of a protein where a ligand might bind to it. We wanna thermodynamics to understand does it bind, does it not under certain conditions, et cetera? And again, we often think about this as, how does it change the energy of the system
27:10
when we think of enthalpy of this system as something that is gonna change the bonding, you know, how that ligands bonds or interacts with the protein, while things like the entropy is how much it limits its configurational, probably had a lot more flexibility when it's unbound. And now you're gonna limit it by binding it in a pocket. You might also change the ordering of the solvent around a system that might give it more order around a system,
27:42
or something that causes more disorder in a system. So we often think of biological processes in terms of its enthalpic and entropic effects and how those come together to either make things enthalpy-driven, entropy-driven, or sometimes equally weighted in this case.
28:05
To help us figure out if something like a protein plus its ligand are gonna form a protein-ligand complex,
28:12
and it's its Gibbs Free Energy that helps define its equilibrium of this, how much of these you're going to form. So a lot of things binding in biology is dictated by the Gibbs Free Energy, its equilibrium concentrations in this. And we often thermodynamically bring it back down to the entropic and the enthalpic effects that go into these effects happening or not at various temperatures and pressures of interest.
28:48
Finally, so we've now looked at several different types of energy, the internal energy,
28:57
the enthalpy of a system,
29:01
T d S, basically the heat or the entropy of a system, and the Gibbs Free Energy, all energy terms here, and their dependence on different variables. For example what we said here, that this is dependent on entropy, volume and the number of moles.
29:20
One of the things that's really quite astonishing about equilibrium in thermodynamics is that the energy is dependent on such a few number of variables, basically one for every, one for the heat term and one for every work term that is applicable to a problem. So it's oftentimes something like this, where it's just three microscopic variables that more or less define all of thermodynamics or define all of the thermodynamic quantities and all the macroscopic behavior in a system like this.
29:58
And this is one of the powers of thermodynamics. It also translates, both computationally and experimentally, because oftentimes a single calorimetric or a computational experiment can done that also that provides these macroscopic variables, measurables of them, and therefore by defining such a few variables, now you can calculate all other thermodynamics quantities in a system. So oftentimes a single calorimetric experiment can be used for a specific temperature and pressure
30:31
to define the biological thermodynamics of a system.
30:38
So I hope that gave you a good introduction to biological thermodynamics. We're gonna continue in this lecture series with future videos on the mathematics of thermodynamics, an introduction to calorimetry, to computational thermodynamics, and we're really gonna delve into a lot of specific biological examples, use cases of using energy, entropy, temperature, thermodynamic properties to really give us insight about biological systems and understand biological thermodynamics better.
31:14
All of this can be found at biopchem.education website. Thank you.
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