Biochemistry Disaccharides

Hello and welcome back to Educator.com, and welcome back to Biochemistry.0000

Today, we are going to start talking about disaccharides, putting 2 monosaccharides together in something that is called a glycosidic bond.0004

Let's go ahead and get started.0013

Alright, let's see how can we do this.0016

A disacch is exactly what it sounds like.0020

CCH, I always forget how to write that.0028

Disacch is made of 2 monosacchs joined covalently- actually, you know what, let me just - joined by a covalent bond called an O-glycosidic bond- very, very, very important bond in biochemistry.0033

The hydroxy group of 1 sugar has reacted with the anomeric carbon of the other sugar.0083

Now, when we say the hydroxyl group of 1 sugar, the truth is, it can actually be any of the hydroxyl groups; but in general, it is going to be specific hydroxy groups that are going to react with the anomeric carbon of the other sugar.0127

Again, you will see from the bond, which particular hydroxy is going to react; but it actually can be any one of them.0143

OK, let's just go ahead and do examples of these.0151

We will just go through several examples to get a sense of how to put the structure together, how the bonds are drawn, the perspective drawings that we are going to be using, and how we are going to name them systematically.0155

That is what's important.0168

Let's do examples of disacchs and how to name them systematically.0172

OK, let's go ahead and start with a particular disaccharide.0189

Let's start with alpha-D-glucose, and connect it to beta-D-glucose in something called a 1→4 connection.0193

OK, let's go ahead and draw out our alpha-D-glucose.0200

Again, always proceed systematically.0206

Start with your basic unit.0209

Alpha-D-glucose, we are looking at this thing right here.0212

God, I really love the blue; I think it is my favorite.0215

OK.0218

CH₂OH, this is alpha-D-glucose.0222

And now, we are going to be joining it with - I'll go ahead and put a little plus sign here - beta-D-glucose.0231

Let me draw out the beta-D-glucose first, here.0238

Beta is going to be up here, but everything else is the same because we are talking about glucose, so CH₂O₄.0244

OK, now, when we put this and this together - let me go ahead and do a red - I'm going to number my carbons.0255

This is no. 1, no. 2, no. 3, no. 4, no. 5.0263

And again, 1, 2, 3, 4, 5, I'll go ahead and put 6 too; it is not a problem0270

And again, standard position, oxygen is in the back right; the anomeric carbon is on the right.0276

That is the reducing end of the sugar; this, over here on the left, is the non-reducing end of the sugar.0281

In this particular case, let me go ahead and write, so this is beta-D-glucose.0287

Again, there is a bunch of hydroxys here that can actually react with this anomeric carbon.0296

In this particular case, we are going to form a 1→4 connection.0301

The anomeric carbon, the no.1 carbon, is going to be connected to the no. 4 carbon; and here is the reaction that is going to take place.0306

This is a condensation reaction.0316

In other words, the elements of water are going to be taken away from this, the elements of water that we are going to be taking away right there.0318

This hydroxy on the anomeric carbon is going to go away, and this hydrogen connected to the oxygen on the no.4 is going to go away.0329

So, the oxygen that is going to go between this unit and this unit, actually belongs to this carbon, the no.4 carbon.0338

What you end up with is the following.0347

Let me go ahead and draw a couple of arrows, one this way and this way; and if we go this way, we are actually losing water.0350

If we come this way, we are actually adding water, so this is a hydrolysis.0358

When you hydrolyze a disaccharide, you get 2 monosaccharides.0363

When you condense 2 monosaccharides, you are getting the disaccharide.0366

OK, this is how it is going to look.0370

I'll do this one in red, boom, boom, boom, boom, boom.0374

OK, I'll go like this, and up like that; and then I've got that, that, that, that, that, that.0380

OK, this is the beta, and now, I'll go ahead and fill in my rest.0389

This is up; this is down.0395

This is CH₂OH; this is down.0400

This is up; this is involved in the bond.0404

This is CH₂OH.0407

OK, this particular sugar is called maltose.0410

Maltose- this is the common name.0416

In the sugar, maltose, what has happened is that an alpha-D-glucose has reacted with the beta-D-glucose.0422

The anomeric carbon has reacted with the no. 4, with the hydroxy on the no. 4 carbon, to create this right here.0430

This right here, this is your O-glycoside bond.0440

OK, that is your O-glycoside.0446

O, because the O is involved; and notice, down, down.0447

That is why it is drawn this way.0453

This is how we actually represent the arrangement in space, but we keep this particular perspective, so that we see how the molecules, how the individual units are arranged.0456

This is how we do a disaccharide.0466

OK, the name for this is alpha-D - because it is a polymer - glucosyl, the first (1→4)-D-glucose.0469

Alpha-D-glucosyl, that is the first monomer arranged in a 1→4 pattern.0495

One on the left connected to the no. 4 carbon on the right- that is where this 1→4 in parentheses means, and a little arrow going from the 1 to the 4.0502

We go from left to right- D-glucose.0509

OK.0512

I should actually write this as...because we have actually specified the stereo chemistry on this particular monomer, it is the B.0517

This is beta-D-glucose.0525

Now, there is a slightly longer name, but we are actually going to be dealing with a shorter name.0529

I'm going to write the longer name, but then we are going to exclusively start dealing with the shorter name.0533

This is also called - and I'm not going to draw out the structure again, you can just flip back - alpha-D-glucopyranosyl.0539

Remember, pyranose, 6, gluco, pyro, glucose pyranosyl- it is a little redundant, but you will see it, pyranosyl(1→4)-beta-D-glucopyranose.0553

Now, obviously, you can't use something like this, so here is the shortened version.0574

All of the sugars just like the amino acids, they have 3-letter shortcuts for them, like Ala is alanine.0580

Well, in this particular case, glucose is Glc; and there is list in your book of the 3-letter shorthand notation for all of the individual sugars, galactose, glucose, ribose, deoxyribose, whatever it happens to be.0588

In this particular case, the name is going to be written this way: Glc for glucose.0605

We write the configuration at the carbons that are attached by the O-glycoside bond.0614

The 2 carbons that are involved in the bond, we give their configurations: alpha 1 to 4.0620

The fourth carbon, we don't do alpha-beta because the alpha-beta designation is only for the anomeric carbon.0635

Alpha(1→4)-beta-Glc, also written as Glc-alpha(1→4)Glc.0641

Often, the monomer on the right, the fact of the matter is, well, I'll tell you in just a second why it is I wrote beta here and not there.0654

Let me go ahead and tell you what is going on.0667

This does not mention the beta explicitly on the second monosacch because something called mutarotation, it often switches the configuration.0670

Even though, we know that we use the beta version of the second monosaccharide, the fact of the matter is, the alpha and beta forms, they actually often switch.0712

So, the stereo chemistry on the reducing end of the sugar, the one that has the free anomeric carbon, it is often unspecified.0722

Sometimes, you don't necessarily have to put the beta there; it is not a problem, unless, specifically, they want you to.0730

In this particular case, we put together an alpha-glucose with a beta-glucose, and what we ended up with is Glc, glucose, alpha-1 configuration at the anomeric carbon connected to the no. 4 carbon, the hydroxy on the no. 4 carbon, and the other disaccharide was a glucose.0736

That is all that happens- switches the alpha-beta-configurations.0755

Again, either one of these is fine.0764

If you want to specifically write the beta, that is fine; if not, you are not going to have any points taken away.0765

OK, now, again, as I said, if the anomeric carbon on the second monosacch, in other words, the one on the right, on the monosacch is free like it was with maltose, then this is called the reducing end of the sugar because now, you have a disaccharide, which happens to be a reducing sugar.0770

Fe³⁺ of Cu²⁺ will still oxidize that end.0815

It is available to be oxidized; it isn't always the case.0820

In a minute, you will see an example of something that is not a reducing sugar, a disaccharide; but this one, because the anomeric carbon, that hydroxy was not involved in the O-glycoside bond, it is still free, it is a reducing sugar.0823

It is called the reducing end.0839

And again, we have a reducing sugar.0845

Let me read that again.0855

If the anomeric carbon on the second monosaccharide is free, then this is called the reducing end; and again, we have a reducing sugar.0857

And, of course, the other end, the one on the left, the one that cannot be oxidized, that is the non-reducing end.0864

OK, maltose, what we just did, is a reducing sugar.0870

Maltose is a reducing sugar.0880

OK, now, as we said, any of the OH groups on the second monosacch can react with the anomeric carbon of the first monosacch - OK, excuse me - even the hydroxy on the anomeric monosacch, even the OH on the anomeric C.0885

Let's look at an example.0943

OK, now, let's go ahead and look at the sugar trehalose.0946

Let's look at the disacch trehalose.0958

OK, let's see what we have here.0964

Now, trehalose, we are going to have an alpha-D-glucose and an alpha-D-glucose that are going to be connected by their anomeric carbons.0966

Let's go ahead and draw the alpha-D-glucose.0974

We have, this alpha is right there; that is there.0978

That is there; that is there.0988

This is CH₂OH.0990

This is alpha-D, and I will just put Glc for glucose.0993

Now, we are going to connect it to another alpha-D-glucose- down, up, down.0998

OK, this time, they are connected; the no. 1 carbon is connected to the no. 1 carbon.1018

How are we going to show that?1028

OK, but now, the OH on the...no...the OH on the no. 1 carbon of the second sugar, no. 1 carbon, the anomeric carbon of the second sugar, is going to react with the anomeric carbon of the first.1030

Sugar reacts with the no. 1 carbon of the first sugar.1070

OK, how are we going to deal with this, and how are we going to represent it?1083

We are going to do this in 3 different ways.1087

Well, let's see.1092

How do we deal with that?1095

How do we represent this schematically?1099

How do we actually show the bond?1103

How do we represent this?1105

OK, here is how we do it.1107

We either flip or spin the second sugar so that the Ns that are going to be reacting are close to each other.1111

When we do that, we are going to have to change the arrangement of the second sugar.1120

In other words, now, it is no longer going to have the conventional representation of the oxygen being on the back right.1124

Let's go ahead and how do we deal with this?1135

Well, we flip or spin the second monosacch for a new arrangement on the page.1136

OK, let's go ahead and do the first one; I'm going to do both.1163

I'm going to do a flip first; I'm going to do a spin first because you are going to probably see them both.1168

My guess is, more often than not, in most biochemistry books, you are actually going to see it flipped; but you will see the spin version, too.1173

This is really, really, really important.1180

There is lots of carbons and oxygens and hydrogens floating around here.1183

Do not go through these structures quickly.1189

Make sure you understand, make sure you pay very close attention to where each individual atom is, particularly that oxygen because that is what's going to give away the structure, and what it is that is going on.1192

OK, because all of these things look alike, the only thing that actually tells you what is different is the arrangement of this particular oxygen in the second monosaccharide.1205

If it happens to be back, if it happens to be forward, that tells you which carbons have reacted.1216

OK, let's go ahead and deal with the flips.1220

We are going to actually end up flipping this one; and the reason we are flipping it, in other words, I'm saying "flip it this way", because you want this carbon to be over on this side, because you want it to be close to the carbon that it is going to be reacting.1223

We have already told you that trehalose has connected the anomeric carbon; carbon no. 1 and carbon no.1 are the ones that are connected via the glycosidic bond.1236

So, we need a way to represent this on paper, so we want to flip this, so that this bond over here, we don't just want to draw the line connecting them.1245

OK, let's draw this one.1254

Again, let's do it in blue.1256

We have got this, this, this, that, that, that; and this is alpha.1260

This is going to be here.1269

OK, we've got CH₂OH.1276

Now, what I'm going to do is I'm going to...wait, where am I?1279

OK, yes, now, I'm going to flip this.1286

OK, when I flip this, I'm just flipping it like this.1290

Everything that is on the right goes to lo the left; everything that is on the top goes to the bottom.1300

Thing move around.1304

I'm going to redraw it like this.1306

OK, I've taken it and I've flipped it.1313

Now, what used to be...let me number these.1315

Oops, I want to do this in red.1321

1, 2, 3, 4, 5, 6, now, what you have is, I've flipped it, so now, it is 1, 2, 3, 4, 5; and let me actually finish off the structure.1324

Let me do the structures here.1341

When I flip this, this is on the bottom; it goes over to the right, and now, it is up here.1344

This O has moved over here; this C has moved over here, this 5 carbon, but now, this is up.1352

Now, this is down- CH₂OH.1359

OK, the no. 2 carbon, it is down; so this is going to be up.1363

No. 3 carbon, this is up; so it is going to be down.1369

No. 4 carbon is down, so now, it is going to be up.1373

This is the flipped arrangement.1376

Now, OK, does that make sense?1380

Notice where each group is; 1, 2, 3, 4, 5, I have flipped it.1382

It is not a mirror image.1387

OK, it is not a mirror image.1389

I have actually flipped it; everything is reversed, not mirror-wise, but this way.1392

That is what's going on.1401

What I need it to do was I need it to bring my no. 1 carbon to put it in close proximity with the no. 1 carbon of my first monosaccharide.1403

Now, this thing is going to react with this thing.1414

OK, 1, 1.1425

The elements of water that are going to disappear is the hydroxy there, the H here.1428

This oxygen is going to be attached to that carbon.1435

When I put those together, this is the arrangement that is going to take place.1438

What I end up with is the following.1442

This is the same; we haven't done anything to the first monosaccharide.1467

That is CH₂OH, but this one, things are a little different.1475

We have flipped this other one.1478

So, this does not look the same.1481

You might think it does, but it does not.1485

Then it is very, very important that you realize where the oxygen is.1489

OK, here the oxygen is on the top right, back.1495

Let me draw the perspective.1498

OK, here the oxygen is on the back left.1508

Here, the CH₂OH is on the upper left above the ring; here it is on the back left, but the CH₂OH is below the ring.1511

OK, this 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, I have flipped it, so that I could put these 2 carbons, the ones that are reacting in close proximity, so that I can represent this glycosidic bond in this fashion.1520

OK, when this is an alpha, the hydroxy is below the ring.1557

This is also an alpha; in conventional position, the hydroxy is below the ring, but because I flipped it, I now, have the hydroxy above the ring at that carbon.1562

That is why I draw it this way.1574

This is alpha-D-glucosil-1↔1 - a double arrow, when you are connecting anomeric carbons - alpha-D-glucose.1577

A shorthand notation, Glc for the first monosaccharide; alpha-1 configuration, that carbon, the no. 1 carbon, it is an alpha-configuration that is involved in the glycosidic bond.1598

The other one is also the no.1 carbon of the second monosaccharide in alpha-configuration, that is the other carbon involved in the glycosidic bond; and just go ahead and put that.1615

This is what you want to write: Glc-alpha-1↔alpha-1-Glc.1627

This is trehalose.1634

OK, now, you notice, the anomeric carbon, the reducing end of 1 carbon reacted with the reducing end of the other.1637

This end over here, it is not available for oxidation.1645

OK, it is not available for oxidation, so this particular sugar does not have a reducing end.1649

Therefore, this is a non-reducing sugar.1656

Trehalose is a non-reducing sugar.1659

This changes the chemistry entirely.1661

They behave in completely different ways.1664

Notice, if you were to just look at this really, really quickly without even, sort of, thinking about it, it would look almost exactly the same as the sugar that we just did, which was maltose.1668

I mean, yes, you might notice that this particular thing is different, but you might think to yourself "oh, maybe they just drew it differently, that's all".1677

No, there is nothing random here; everything is drawn with a specific purpose.1684

What you would notice on maltose, is that on both monosaccharides, the oxygen is on the back right.1688

Here, the first monosacch is on the back right; the second monosacch, the oxygen is on the back left.1694

We have specifically drawn it like this.1699

This is what is important.1702

So, you really, really have to pay a very close, detailed attention to these particular structures.1703

OK, I'm going to go ahead and do the spin version of this really quickly.1708

Again, this is just something that you may see.1719

I'm going to take my alpha-D-glucose, so let me draw that under standard.1723

Alpha-D-glucose, hydroxide, hydroxide, hydroxide there, hydroxide here, and CH₂OH.1730

Now, instead of flipping that second monosaccharide, I'm going to go ahead and spin it.1739

When I spin it, I end up with the following.1745

Let me see.1749

Yes.1754

OK, when I spin it, it means I'm not flipping it, I'm just spinning it 180°.1756

I'm rotating it this way.1764

Flipping means like that; spinning or rotating means like this.1767

So, here is what it ends up looking like, boom, boom.1772

Now, the oxygen is on the front left.1776

OK, basically, just follow all of these things and just go to the opposite pole.1780

This goes here; this goes here.1785

This goes here; that is all you are doing.1788

It ends up like this; that OH goes there.1792

This ends up coming, CH₂OH.1797

This is down, so it is going to stay down.1805

This is up; it is going to stay up, except now, it is going to be in the back, and I think, I have covered everything.1808

So, what you have got is 1, 2, 3, 4, 5, 6; now, what you have is 1, 2, 3, 4, 5, 6.1815

Now, notice, in this particular case with this spin arrangement, now, my oxygen is down below the ring.1831

So, when I draw my trehalose structure, here is what my structure is going to look like.1837

This stays the same; that, that, that, that, that and that.1842

That is going to go like that; and here, oxygen is there, so, OH, OH, OH, CO₂OH.1854

And now, we have OH, OH, OH; and we have CH₂OH.1871

OK, this is again, glucose, alpha-1, alpha-1, in parentheses, double arrow, because now, double arrow, I'm connecting the anomeric carbon with the anomeric carbon.1884

Each one has an alpha-configuration, and they are both glucose monomers.1898

Notice, this is the exact same thing as this.1904

Notice, here, the glycosidic bond is represented this way, below, above.1908

The oxygen on the second monosaccharide is in the back left, but this was based on the flip.1915

Here, I have decided to spin it; and now, the glycosidic bond is represented this way.1922

This is the same molecule; this is not a different molecular.1927

It is just that the second monosaccharide is arranged in a different way.1930

The first monosaccharide is exactly the same.1933

This is why it is really, really important to be able to distinguish, watch for where this oxygen is, watch for where the no. 1, no, 2, no. 3, and no, 4 carbons are.1937

Here, it is 1, 2, 3, 4, 5, 6; Here it is 1, 2, 3, 4, 5, 6.1947

This is the same molecule, different arrangements in space.1957

OK, so, you have seen the spin; you have seen the flip.1962

I am actually not going to go ahead and show you the third version.1965

I don't think your teacher actually wants you to do that anyway.1968

OK, now, let's see.1975

Trehalose, again, is a non-reducing sugar because there is no anomeric carbon that might open up to release a free aldehyde that can be oxidized, so it completely changes the biochemistry.1979

OK, let's go ahead and do an example.1990

Well, we have done a couple of examples; this is just some sort of a free example.1995

OK, sucrose, which is table sugar, is Glc-alpha-1-beta-2-Fru.2002

OK, sucrose is a disaccharide, and it is made up of a glucose unit and a fructose monomer.2016

So, glucose is a hexose; it is a 6-membered sugar.2025

Fructose, remember, is a 5-membered ring sugar.2027

The connection between the two, the glycoside bond that connects them, connects the anomeric carbon, which is alpha and the no. 2 carbon, which is beta-configuration on the fructose.2030

Let's go ahead and draw out the structure.2046

That is our assignment; this is what we want to do.2048

In this particular case, we haven't given you a structure.2050

What we have done is give you the name, in shortened form; and we want you to draw the structure- very, very typical question on an exam.2053

OK, in this particular case, well, let me just go ahead and draw the...should I go ahead and...well, that is fine.2065

In this particular case, I am joining the anomeric carbon of both.2078

Again, I am going to have to bring the carbons in close proximity.2084

I am going to have to flip or spin the second monosaccharide.2089

I am going to choose the flip version.2091

Let me go ahead and draw out my...I choose to flip the second monosaccharide.2094

OK, and again, when you see an alpha or a beta on this second carbon here, this second sugar, that is what's going to tell you that you are probably going to have to do some spinning or flipping.2108

If there was just a number here like 4 or 5 or 3 or something like that, then you can just leave them alone, and just connect the carbons.2119

OK, let's go ahead and draw out our alpha-glucose.2129

That is going to be like this, alpha which means the hydroxy is down here, and this is there, and this is there, and this is CH₂OH.2133

OK, now, flip the beta.2149

Let me see.2155

I'm actually going to go through the process of putting this particular fructose together.2158

I'm going to start the process this way - I'm going to do this in blue - just so you see again, a little bit of review on how it is that we actually create this particular ring sugar.2163

Fructose, again, is a 6-membered ring, so we have 1, 2, 3, 4, 5, 6.2174

That is up; that is going to be down.2186

Yes, OK.2188

Except this time, C, this is H₂OH.2190

So, this is a ketone; this is a ketose.2196

The no. 2 carbon actually has the carbonyl.2198

Here, OH, I'm drawing out the linear form, the 1, 2, 3, 4, 5...oops, I forgot.2201

This is OH, and this is CH₂OH.2212

So, this is the linear form.2214

I'm going to go ahead and take this linear form, and draw it in such a way, in order to create my ring.2216

Let's see, I have got C, carbonyl.2224

This is CH₂OH here.2232

This is C; this is C.2235

That is C, and then I have my OH, and I have my CH₂OH here.2240

This is in freeform that I've taken and rotated; I have brought the other thing around.2245

Now, 1, 2, 3, 4, 5- that is right.2250

I am going to end up attacking that right there, and what I'm going to end up creating is my beta-fructose.2256

My fructose is going to look like this, and I have that.2266

So, beta, that means, so this is the no.1 carbon, right?2271

No. 1 carbon, no. 2 carbon, so CH₂OH, let me go ahead and number these.2276

This is 1; this is 2,2284

This is 3; this is 4, and this is 5, and I will do no. 6 in just a minute.2286

Let me go ahead and put all of my substituents on here.2294

Oops, as you can see, things get very, very, very involved.2299

Let me go ahead and put my hydroxy there.2306

Let me put my hydroxy there.2309

Let me put my CH₂OH over here, and I have my beta-configuration.2312

This is my - write these out - this is my alpha-glucose; and this is going to be my beta-fructose.2318

I started with my fructose, linear form; I created my regular beta-fructose.2329

This is the standard, conventional arrangement.2335

I am going to be reacting this with this, alpha-1, beta-2.2338

I am actually going to be connecting this carbon with this carbon, which means that I am going to have to flip this, so that I can bring this carbon in close proximity to this carbon.2343

Now, when I flip this, here is what it is going to look like.2353

I am going to do that in red.2358

The flipped fructose, I am going to flip it.2365

Well, the arrangement, that way, actually stays the same; but, of course, the substituents look different, this.2369

Now, what I have is, this is down, so it is going to be up.2376

This is going to be CH₂OH.2384

This is up; it is going to be down.2387

This is CH₂OH; this is down.2390

This is up, so it is going to be down over here; and this is going to be up.2393

This OH is up; over here on the right, it is going to flip around this way.2404

It is going to end up being down here.2408

It almost looks the same, except the carbons are numbered differently now.2410

Now, we have our no. 1 carbon, no.2, no. 3, no. 4, no. 5, and no. 6.2416

Oops, go ahead and do that.2427

Now, I am going to connect.2430

This is our first sugar; this is our flipped fructose.2437

I am going to connect that carbon with this carbon, the no. 2 carbon.2441

So, you notice, this hydroxy is down, and over here, this hydroxy is down, below the ring.2450

My final fructose structure - I'm sorry - my final sucrose structure is going to look like this.2457

I have got this; let me make this kind of big.2464

OK, I have got 1, 2, there, there, there.2471

Let me go ahead and draw my glycosidic bond, 1, 2, 3, 4, 5.2477

This is an oxygen, and now, I can put my substituents in, hydroxy down, hydroxy up, hydroxy down, CH₂OH.2486

Now, I have got a hydroxy down here; I have got a hydroxy up there.2497

I have got a CH₂OH here, and I have got a CH₂OH - actually, let me draw it to the left because there is plenty of room on the left - CH₂OH, and there we go.2504

Now, I have my alpha-1 configuration, alpha-1-carbon on my glucose.2519

This is my beta-2; you can write b2 2-beta.2526

It does not matter, the order, as long as the alpha-1 is on the left of the arrow.2531

OK, we have Glc-alpha-1↔beta-2-Fru- this is sucrose.2537

This is table sugar, and you notice, there is no anomeric carbon that is available.2553

This is a non-reducing sugar; the 2 anomeric carbons are connected by an O-glycosidic bond.2559

It is arranged this way.2566

This is not the standard, conventional arrangement; I had to flip this fructose monomer, in order to bring this carbon in close proximity with this carbon.2568

This is the process that you go through.2579

Again, glucose, glycosidic bond, glucose is connected to fructose; the glycosidic bond is the alpha-1, no. 1 carbon alpha-configuration connected to the no. 2 carbon beta-configuration.2580

That is it.2595

We will do more of these; don't worry about that.2597

We will do plenty of these because it is very, very important that we would be able to go back and forth, that you see a structure, be able to name it, that you'd be given a name, and be able to draw out a structure for it.2599

OK, thank you so much for joining us here at Educator.com.2609

We will see you next time, bye-bye.2611