Enzyme Screencasts

Here is a link to a screencast from last year, I think, about enzymes and energy. It's 55 minutes long. But, you might find sections of it helpful. Kate: you might especially benefit from this.

Enzyme Kinetics

Enzyme Kintetics


Most of the images for this article were taken from the Wikipedia entry on Enzyme kinetics. You can read that here. It gets a little intense for our purposes.
Some Words:
Enzyme: a biocatalyst that acts to speed up the rate of a reaction, often by many orders of magnitude (that is, many factors of ten). Most enzymes are protein, though some important ones are RNA.
Substrate:
the starting material acted upon by the enzyme to make the product.
Active site: the site in the enzyme in which the substrate binds. It is the site at which the catalysis takes place.
Saturation Kinetics
We’ll call the above graph, “fig 1.”
Notice firstly that the graph is determined from a series of points and that Y axis is a rate (usually in mol/L*s that is change in concentration over change in time). The X axis is
initial concentration of substrate. So, each point is from an experiment in which you had an initial concentration of substrate and then measured the change in that concentration versus change in time (the initial rate). The points on this Fig.1 are each the initial slope of one experiment from Fig. 2, below.
The image below was taken from Campbell’s website.
EnzymeRatesFig 2
It represents three experiments tracking a reaction where A B and following the rate of disappearance of A. The three experiments have different initial concentrations and different initial rates. The slope of each of those lines becomes a point on Fig 1. The sign of the slope is changed so that it is positive (remember from chemistry that Δ[B]/Δt = -Δ[A]/Δt).
Experiment 1 above might be one of the high points on Fig 1. Experiment 3 would be at lower concentration.
Saturation Kinetics:
The pattern seen in Fig. 1 is called saturation kinetics for reasons that should be obvious.
Please Note: the flat part of Fig 1 is not when the rate of the reaction is zero.
It shows that above a certain concentration of "A," the initial rate no longer increases. Saturation kinetics are also called “Michaelis-Menten” kinetics after the people who first explained it. You should know that almost no enzymes follow this model exactly. It also deals with a single substrate...but can be adapted to deal with more. Nevertheless, it is an important model that helps explain a lot. The idea is that there are at least two steps to the overall reaction: Binding of substrate to enzyme; and catalysis.
You can think of the process of catalysis as proceeding in at least two steps (there are usually more): a binding step and a catalytic step.
EnzymeStepsFig.3
“E” is enzyme, “S” is substrate, “ES” is enzyme bound to substrate and “P” is product.
There is an “on” rate and an “off” rate (k
1 and k-1) indicating that a substrate molecule can bind and then come off again. The second step is determined by something internal to the enzyme: its catalytic constant. Note that if I blocked the second step, the binding step would come to equilibrium, with substrate binding and releasing at equal rates. The third step is the release of product. Each individual step is reversible and the entire process is reversible.

Important Points on Figure 1.


There are two important points on Fig. 1. We have already talked about the first, V
max. That is, the maximum velocity, or rate, of the reaction once all of the enzyme molecules are busy.
The other point is a substrate concentration known as “K
M,” which is the concentration at which the rate is ½ of the Vmax.

High or Low Substrate concentrations.


Imagine two situations, one in which substrate concentration is low and one in which it is high.

EnzymeCartoonFig 4.

In the first case, the slow step (rate-determining step) is the binding (first) step. The catalysis step may seem instantaneous, by comparison. This gives us the steep initial portion of Fig. 1. The rate is determined by the rate of binding.
In the latter case, essentially all the enzyme molecules are occupied. No enzymes are sitting around idle. Thus, the reaction is going at its maximum velocity (V
max), the (nearly) horizontal portion of the graph at the top. At that point, the overall rate is governed by the catalytic step, give by k2.

The Starbuck’s Model


Think of the reaction being catalyzed as production of cappuccino at Starbucks. The enzyme is the “Barista” and the customers are the substrate. If you count cappuccino per hour, you get a rate. If there is a low concentration of coffee drinkers wandering down Torrey Pines Road, you get a slow rate. If you increase their numbers, the rate of cappuccino production increase. The rate is ‘diffusion limited,’ that is, set by the number of coffee drinkers that wander into the store…until a line forms. At that point, the Barista is working at maximum rate (saturation kinetics) and the rate of cappuccino production is limited by the catalytic rate, how fast the Barista can work. The only way to increase the rate is to add more enzyme…in this case, just open another Starbuck’s 100 meters away.
Inhibitors
Let’s consider two types of inhibitors: one that purely inhibits the first step (binding) and one that alters the enzyme so that it is not as good at catalysis (the second step), but otherwise has no effect on binding.
Competitive: Enzyme-Inhibitor (E-I) complex or Enzyme Substrate (E-S)
Inhibitor1Fig 5.
The substrate does not bind the E-I complex and the inhibitor does not bind the E-S complex. Shown here the two are actually binding to the same site. Inhibitor physically blocks access of the substrate to the enzyme. This could be the idiot who gets to the front of the line at Starbuck’s and cannot think of what he wants to order, but just stands there and won’t let others order.

The substrate will have its binding constant (approximately K
M) and the inhibitor with have its binding constant (lets call that Ki). Note that the second step governed by k2 in Fig. 3 is NOT affected by the presence of the inhibitor (The Barista works at the same rate…he’s just not able to get working). If the substrate binds, it will be catalyzed at the same rate as it would if the inhibitor were not in solution. It’s just that fewer substrate molecules get to bind.
Since both the inhibitor and the substrate have an “off rate,” I can assume that even in the presence of the inhibitor, substrate will have some opportunity to get access to the enzyme when the inhibitor comes off.
Let’s assume a simple case in which the inhibitor and the substrate have similar binding constants for the enzyme. Then, if I had equal amounts of each, I would expect at any given time that half the enzyme will have substrate bound and half will have inhibitor bound. If I increase the concentration of substrate, I would be able to get more of it to bind (out-compete the inhibitor for the site) and the enzyme would be able to do its job as normal. At a great enough excess substrate concentration, the probability of substrate binding is much higher than that of inhibitor binding; so most enzymes would have substrate bound. I could eventually get the rate up to the V
max. But, the KM becomes much higher...you need much more substrate to get the enzyme to work at half the max rate.
So, a competitive inhibitor raises the Km, but does not affect the Vmax.

Note:
while the mechanism of competition strictly results in inhibition, the other types of interactions described below could just as easily activate the enzyme, or increase, the rate.

Non-competitive: Lower the rate “k2.”
Another type of inhibitor does not affect binding of substrate. Instead, it alters the rate of the catalytic step. How can it do that? Remember that these are proteins. A small shift tertiary structure caused by the binding of inhibitor could change the ability of the enzyme to catalyze the reaction.
This effect where binding of a regulator (inhibitor or activator) changes the shape of the enzyme and alters its rate are call
“Allosteric effects.”
In that case, I’d get binding at the same rate. So, K
M would not change. However, since k2 is lower, I have a lower Vmax.
Easy. This would be the girl behind the counter who is really “into” the Barista and is chatting to him non-stop. That slows down his catalytic rate, but doesn’t affect the rate at which customers wander in.
Regulation
The very astute among you may have noticed that I left something off in Figure 3. You can see what I’m talking about in Fig. 5. The substrate has a binding constant, what about the product? Wouldn’t I expect the product to have some binding affinity for the enzyme? And, the product has to leave the binding pocket in order for new substrate to fill it. In effect, the product can act as a competitive inhibitor of the enzyme that produced it. This is the very simplest form of “feedback inhibition,” an important concept we will talk more about. We refer to this property of an enzyme in terms of its “turnover rate.” That is, how fast it let’s go of product and is therefore available to do its job again.

Most of the time, I don’t want an enzyme to work at full speed all the time. One very important way of regulating an enzyme is feedback inhibition, as in the simple product competitive inhibition mentioned above. Suppose I have a pathway requiring 3 enzyme steps.
Pathway
Once I have enough D, I don’t want the pathway to be running at full speed. Maybe “A” is also needed for another pathway (not at all unlikely) and once I have enough D, I want to divert A down that other pathway.
One real world example would be if "A" were glucose. Sometimes I want to use my glucose to get energy right now. Sometimes I want to store glucose in glycogen for later use. Which path I choose would depend on changing conditions. A well-evolved system should adjust to needs.
One way to regulate this is if D is an inhibitor of enzyme 1. It may be competitive or non-competitive.
Oh, Allosteric
activation is common as well.

This sounds magical, until you remember that we are talking about proteins, composed of helices and sheets arranged in specific tertiary structure. Couldn't the binding of some activator on one face of the protein cause to helices to shift relative to each other? Of course. Couldn't the shift slide a helix out of the way of the active site, allowing better access? Sure.
The possibilities for regulation seem endless, really. And every possibility I've ever thought of and about 100x more that I never thought of can be found operating in nature.

Study guide

Here is the link to the study guide for the next test. Read More…

Using Spreadsheets

Here is a link to a short screencast going over the way you can use google sheets to do calculations and make graphs.
I got the sizing all wrong. Sorry, it's huge. You can size it down in your browser.
Read More…

Membrane Transport

As usual, images taken from Wikicommons.

Passive Diffusion


A very small number of things can just diffuse across the membrane. These include gases like O
2 and CO2, small amounts of water, alcohols and other small, polar molecules. Also, steroid hormones can diffuse across the membrane. More on this later. These things will move toward equilibrium, from an area of higher concentration to one of lower concentration.

Facilitated Diffusion through Channel Proteins: Water Transport


Another way larger molecules can diffuse through the membrane is through specific pore, or channel proteins. In general, these channels are fairly specific, letting through only the molecules or ions they have evolved to allow through.
I will use the water channel, made by a protein called “aquaporin,” as an example.
For a long time, scientists thought that water just diffused across the lipid bilayer (a small amount does). However, it turns out that the rapid movement of water across the membrane is through a specific channel and is regulated. Here is a “ribbon diagram” of the channel:
Aquaporin-Sideview

Here is a little protein-structure review: Remember that the spirals are alpha helices? The complete complex is made of four separate polypeptides (two in the foreground are shown in red and blue), each of which is a channel. So, there are four water channels in that one structure.
What is the level of structure that describes the interaction among different polypeptide chains to form the full protein?
These four subunits each form an “hourglass” channel. The loops shown connecting the helices are on the outside (top) or inside (bottom) of the membrane. Here is a cartoon showing something like how it works:
800px-AQP-channel
Yes, I know, the labels are in German. The labels at the constriction in the center show you specific amino-acid residues in the proteins. They are labeled “N76” for asparagine found at position 76, or H180 for a histadine found at position 180. These amino acids have charged “R” side chains as indicated. To fit through, these side chains force the water molecule to line up in a specific orientation, then actually “flip” to get out of the center of the hourglass. Only water has the size and polarity necessary to fit through.
I won’t go into the other examples in as much detail. I wanted you to see how a protein could make a channel.
Other things with their own channel proteins include metal ions such as Ca
2+, Na+ and K+.

Here’s a little health point: The calcium channel has to be rather big to allow calcium ions through. It only allows divalent cations through (remember what that means?). Well, Lead also makes a divalent cation, and it is just big enough to fit into the opening but cannot get through…it clogs the channel. One major reason for the effects of lead poisoning is that the lead ion blocks calcium release in nerve and muscle cells, preventing them from working correctly.
There are other forms of facilitated diffusion with other structures to allow things in or out, such as the “flipping door” I modeled with my hands. But they operate on the same principle.

Active Transport or “Pumps”


All of the above examples only allow transport “down gradient,” that is, in the direction favored by diffusion. They cannot lead to an increase of concentration beyond equilibrium.
But, the cell needs to concentrate many molecules and ions on one side or the other. For this, they need “active transport,” which expends energy to move molecules or ions “up gradient.”
I will use the analogy of the “revolving door” for this. It is an analogy, not a realistic portrayal of what happens.
Imagine a revolving door in the membrane that can only spin in one direction. Suppose you want to move molecule
Revolving Door“A” from outside to inside, but there is already more A inside. Diffusion won’t help you. If A can enter the door on either side of the membrane, you would only get to equilibrium. But, suppose the door stops every time A is in a quadrant open to the inside. Then, a device uses energy from ATP to kick A out into the cell and the door starts to spin before any more can get back in. Over time, you would increase the concentration of A inside the cell.
This is conceptually how a pump might work.

Cotransport


The other type of active transport is called cotransport. This uses a gradient of one molecule or ion (perhaps established by a pump), to drive the transport of some other molecule or ion.
Imagine our revolving door this time requiring that ion “B” can only enter the door if it is with ion “C.” Suppose ion B is already in a steep gradient favoring going into the cell. But, it cannot diffuse through the door unless it is also with C. As a result, C can be transported into the cell well past equilibrium, driven by the gradient in C. This cotransport of two things in the same direction is called “symsport.” The channel carrying it out is a symporter.
But, you can set it up so that the gradient is lots of C in the cell and the revolving door only turns if both outside an inside quadrants are filled. Now, C wants to go out of the cell, but can only do so if B gets into the outside of the door. This transports B into the cell. This is called an antiporter.
In the diagram below, I would be a pump, II would be cotransport in the same direction (symport) and III would be an antiporter.
TransportProtein

Bulk Transport.



The last type of active transport is “bulk transport” by phagocytosis. This is where the membrane “gobbles up” relatively large things and brings them into the cells in a vesicle. This is important for uptake of food globules.
Smaller gobbles are called “pinocytosis,” and are regulated a little differently. Finally, we have “receptor-mediated endocytosis,” where a specific thing, bound to a receptor

What follows is from the AH bio blog. It recaps a lot of what is above but adds some more detail. It also provides some more detail on how the pumps actually work. You can read over it.

Gradients


As we said, the membrane is impermeable to most dissolved solutes. Gases can pass freely through the membrane, so oxygen and CO2 can be traded as necessary. But things dissolved in the water that surrounds the cell and is inside the cell generally are hydrophilic. As such, they cannot pass through the membrane directly.
For this reason, there are transport proteins that are responsible for moving all of the small molecules, ions and even fairly large molecules across the membrane. We will talk a little bit later about the protein that allows water to move across the membrane. For right now we will talk about transport in terms of several overlapping concepts shown in the diagram.


transportImage from www.physiologyweb.com

Passive diffusion


all forms of passive diffusion are "down gradient." That is to say, one side of the membrane has more of the solute while the other side has less. Given any pathway through which the solute can move it will tend to distribute more evenly. I can divide this further into simple diffusion for molecules that can diffuse again across the membrane directly, passive diffusion for molecules that pass through a channel protein (which is just what it sounds like, a protein that forms a channel through the membrane), and facilitated diffusion, where the solute is carried by a protein from one side of the membrane to the other, sort of like a shuttle. The important thing to remember is that all three of these are diffusion down gradient and require no input energy. No work needs to be done for molecules to diffuse. In fact as we will see later, a gradient can be used to do work.

Active transport.


All forms of active transport require the expenditure of energy at some point in the overall pathway and result in even greater disparities in concentration between the two sides of the membrane. That is, something moves from an area where there is a low concentration to an area where there is already a high concentration of that solute.
Active transport can be separated further into "pumps," which directly expend energy in a cycle to move solutes from one side of the membrane to the other, and "co-transport." Co-transport uses a gradient that was established by a pump or exists for some other reason to drive transport of some other molecule up its own gradient. This is one of those things that is hard to explain in writing. However the diagram below does a pretty good job of showing it.
Symport is when the molecule that is moving down gradient is moving in the same direction as the molecule you want to move up gradient.
SucroseTransportimage from your textbook, Campbell Biology ninth edition

In the diagram, we see that ATP is expended to pump protons to the external side of the cell membrane.Those protons, given a pathway, would diffuse down their gradient back into the cell. The trick here is to use a pathway (that is to say, a protein in the membrane) that will only allow protons to diffuse down gradient if a sucrose molecule accompanies it.
You can think of it sort of as a revolving door that will allow protons to enter but will only revolve if sucrose is there also.
The other related concept is the "antiporter." you can think of this as a revolving door where the two players have to enter opposite sides in order for the door to turn. In either case one molecule or ion diffuses down its gradient (passive diffusion) while the other molecule moves up its gradient (active transport).

Ion pumps and the electrochemical gradient


In order to carry out co-transport, one needs to have a gradient established of one or more ions. This is generally achieved by proteins that we call "pumps." While there are many that are crucial to cell function, one has an outsized role in establishing what we call the "electrochemical gradient."That protein is the sodium-potassium pump. Sometimes you will hear it called the sodium-potassium antiporter ( which makes sense because sodium and potassium ions are moving in opposite directions – but is misleading since both will move up gradient against the direction favored by diffusion.) Another name you may hear is the sodium/potassium ATPase.
Here is a moderately
amusing GIF based on Drake's music video for "hotline bling" appof a couple years ago.
Here is the gist of it: the pump can bind two potassium ions when it is open to the outside, but cannot find sodium ions at all. When open to the inside it will no longer bind potassium ions, but can bind three sodium ions. ATP is hydrolyzed to force the switch between the two states (open to the inside versus open to the outside). The net result of this is that as it goes through a cycle two potassium ions are pumped into the cell and three sodium ions are pumped out. This results in a gradient of potassium (high on the inside, low on the outside) and sodium ions (high on the outside, low on the inside). This is the "chemical" part of the gradient. Because two positive ions are pumped in for every three that are pumped out, there is also an electrical component to the gradient. The inside of the cell ends up being negatively charged overall to a level of about -70 mV.

I would like you to read David G’s really nice blog on the pump. I think you will find some of the numbers, frankly, shocking. Also, understanding the way this works will help you with other proteins we consider.
For example, some may be interested in proton pumps in the cells of the stomach that make the stomach acidic...it works like this protein, as David explains.

Proceeding from specific to general:

The Pump


  • This protein has binding sites for ions. Below is an image of two ions bound. In this case, the protein crystallographers have used a trick and bound Rubidium+ to the sites. But, it works similarly. What would bind a positive ion? Well, you should hold it between negative ions, like deprotonated acid side chains. What are the acid side chains in amino acids?: Aspartic Acid (D) and Glutamic Acid (E). Look at the image below:

  • IonBindinginPump
  • D804, E327 and E779 (the numbers correspond to the residue number in the amino acid sequence, or primary structure) all come together to make a really nice pocket that binds the ions (greenish). That makes sense. There are others I didn’t label. All three residues that bind the cation are on different helices. If you slide those helices relative to each other, the components of the binding site move closer or farther away from each other. Now, check out the ionic radii of Na+ and K+ at the wikipedia page. K+ is 30% bigger than Na+ (Rb+ is only slightly larger than K+). So, by sliding the helices, I can change the sized of the pocket and whether K+ or Na+ is favored.
  • ATP hydrolysis transfers a phosphate to a serene on the pump (Serine 33 on our pump), causing the helices to shift. This opens the pump to the outside and changes the shape of the binding pocket so that Na+ cannot really be held tightly anymore and K+ fits in well.
  • The Binding of K+ changes the shape a little more. This favors hydrolysis of the phosphate from the serine, shifts the helices back to be open inside the cell and makes the pocket too small for K+, but allows Na+ back in. Of course, I didn’t explain exactly, but the three Na+ sites only reconstruct 2 K+ sites once the helices move.

This type of pump could be modified to pump other cations.


  • As Goodsell points out, this same mechanism can be used to pump protons. You just have to change the size of the binding pocket. That probably just involves some shifting of the positions of the acidic residues.

Gradients are useful


  • Once you establish a gradient, you can use it to do stuff. The pump establishes an electrochemical gradient. Every cell at “resting potential” has more K+ on the inside and more Na+ on the outside. The inside is also more negative. Maybe I could use that gradient to do something.
  • For example, suppose I had a protein that would allow Na+ to come back in...but it would only do that if there was also a glucose molecule bound. I could use the gradient to transport glucose into the cell.
  • Suppose I had a channel that I opened in response to some signal...maybe something binding to the channel, and that channel would allow sodium to pass through it. All the sodium ions would start racing into the cell, down their chemical gradient. But that would also make the inside positively charged...that would be a dramatic effect. It get’s even more complicated, but that’s the start of an action potential in nerve cells.
  • Or...what if I stacked a whole bunch of cells on top of one another and made a little battery of cells, each with a small voltage across the membrane...then released all of them at once. That would be really interesting.
  • Phosphorylation and interactions with other molecules change the shape of proteins

  • A more general mechanism exists by which any protein could have a set of possible shapes, each favored under different conditions. Imagine a protein that binds to microtubules, for example. Maybe you could come up with a series of shapes that change depending on whether ATP is bound, or ADP is bound, or the protein is bound to tubulin or not... Could you imagine a series of steps like: Bind ATP and Release from tubulin; hydrolyze ATP and move forward; bind again, release ADP....what would that look like?