Approximating distance travelled

WEBVTT
Kind: captions
Language: en

00:00:00.923 --> 00:00:02.507
Voiceover: A cyclist starts pedaling

00:00:02.507 --> 00:00:04.858
and accelerates for 12 seconds.

00:00:04.858 --> 00:00:07.338
The velocity v of t of the cyclist at

00:00:07.481 --> 00:00:09.794
two second intervals in feet per

00:00:09.794 --> 00:00:12.345
second is given by the table.

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So they tell us at different times.

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After four seconds the velocity

00:00:16.114 --> 00:00:18.032
is 7.5 feet per second.

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After eight seconds the velocity

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is nine feet per second.

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Consider the graph of
velocity versus time.

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Velocity versus time.

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Let capital r of six be
the sum of the areas of

00:00:31.233 --> 00:00:36.784
six right hand rectangles
with equal sub-divisions.

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It follows that capital r of six is

00:00:39.089 --> 00:00:41.153
an approximation for the total distance

00:00:41.153 --> 00:00:43.778
traveled in feet during the 12 seconds.

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What is the value of capital r of six?

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I encourage you to pause this video

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and try to think about it on your own

00:00:50.009 --> 00:00:51.448
and then I'll work through it and at any

00:00:51.448 --> 00:00:52.824
time while I'm working through it, if you

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get inspired, feel free to pause again

00:00:54.072 --> 00:00:56.905
and try to take it all the way.

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Let's think about what they're saying.

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They say "consider the graph

00:00:59.865 --> 00:01:01.161
of velocity versus time."

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We might as well try to plot that.

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I've got some graph paper here and we can

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focus on the first quadrant because all of

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our time values and all of our

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velocity values are positive.

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Let's see this is time, this is velocity

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as a function of time axis, time goes

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between zero and 12 and they're giving

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it to us in every two seconds.

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So, this is zero, two, four, six, eight,

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ten and 12 seconds, and then our velocity

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goes between zero and ten feet per second.

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So, this is one, two, three, four, five,

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I'll just mark off some of them.

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Six, seven, eight, nine, ten.

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Now, this is in feet per second

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and this over here is in seconds.

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Let's plot these points at time zero,

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velocity is zero.

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Time two velocity is six feet per second.

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Time four at 7.5 gets us right there.

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Time six it's 8.5, that 8, 8.5.

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Time eight at eight seconds

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it's nine feet per second.

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At ten seconds it's 9.5 feet per second,

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and at 12 seconds it's ten feet,

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it's ten feet per second.

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What I've done here is I've just plotted

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the data that they've
given us, considering

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the graph of velocity
versus time, at least

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the data they've given us.

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We can imagine fitting a curve

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that looks something like this.

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If we were to, these
points are just sampled

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from a curve, they might
look something like,

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something like this, over there.

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We are now considering the graph

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of velocity versus time.

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Now let's think about the sum of the areas

00:02:52.976 --> 00:02:55.369
of six right handed rectangles

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with equal sub-divisions.

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When they're talking
about equal sub-divisions,

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they're talking about equal sub-divisions

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along the independent
axis or the time axis

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in this case and we're
talking about the first

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12 seconds, so if we
were to divide the first

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12 seconds into six equal
sections, they would

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each be 2 seconds wide.

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This would be one of them.

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Let me do this in a new color.

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They would each be 2 seconds.

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That's not a new color, oh it is, blue.

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They're each going to be two seconds.

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Let me do one that
contrasts with green better.

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Each of our rectangles are going to be two

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seconds wide and I'm just kind of starting

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them off at the bottom because we have

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to think about how tall to make them.

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Then they say to do
right handed rectangles.

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What's a right handed rectangle?

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That means we define the height of

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the rectangle by the value of

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the function on the right hand side.

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So, for example this first rectangle,

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to make it a right handed
rectangle, we look at

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the right side, we're
at two seconds, velocity

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at two seconds is six feet per second

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and so that's going to be

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the height of our rectangle.

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This next one is going to look like this.

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Now you might say "Well, what's a left

00:04:01.238 --> 00:04:02.230
handed rectangle then?"

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Well, a left handed
rectangle would be doing

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something like, would be
doing something like...

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Okay, for this first rectangle on the left

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hand side of it, my function is zero.

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So, it's just zero.

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Now the next rectangle,
the left hand side,

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my function at two seconds,

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the function is six seconds.

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So, the left hand rectangles would look

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like this, would look something like that.

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But anyway they're telling us to do right

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handed rectangles so let's do

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right handed rectangles.

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Let me clear this a little bit.

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This is our first right handed rectangle.

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This is our second one.

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Let me just draw the tops.

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Third, fourth, fifth and sixth that was

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the tops of them.

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It's just going to look
something like this.

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It's going to look like this.

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This is my third one.

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That's my fourth one.

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That's my fifth one.

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Then, that's my sixth one.

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They're tell us let capital r of six

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be the sum of the areas of these things

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and they tell us that it follows that

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capital r of six is an approximation for

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the total distance traveled

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in feet during the 12 seconds.

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Now why is that?

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Why is the sum of these
areas an approximation

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for the total distance traveled?

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Well before calculus, you learned,

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that if you have a constant rate,

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that distance is equal to rate times time.

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Once again, this is assuming,

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that assumes a constant rate.

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Our rate in this example
is clearly changing.

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We are clearly accelerating
right over here

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but maybe we can approximate the distance

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traveled if we assume a constant rate over

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an interval, say over
two second intervals.

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Then we just, we try to roughly, when

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we assume some velocity
over that interval.

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When we take these
right handed rectangles,

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let's just focus on this first rectangle.

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If I'm taking the area of this

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first rectangle, what am I doing?

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I'm multiplying it's
height times it's width.

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It's height is going to be the velocity

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at the end of two seconds and
it's width is the two seconds.

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If I were to multiply six feet

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per second times two seconds.

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That will get me 12 feet,
let me make that very clear.

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The area for that one area is equal to six

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feet per second, my
velocity, it's actually

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the speed but we're not going to get

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particular about whether we're

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getting the direction as well.

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Six feet per second times two seconds.

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That's going to get me 12 feet.

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That we can say is an
approximation because

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we're saying "Okay, you
trialed at two seconds

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"at some velocity" but is that going

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to be an overestimate or an underestimate?

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It's going to be an overestimate because

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you're taking the fastest velocity

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over the interval.

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The interval started with the cyclist

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going zero feet per second.

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It's clearly overestimating
and if you think

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about it and I encourage you to pause

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the video and think about it on your own.

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If we did a left handed rectangle it would

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be underestimating it because we would

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be taking the slowest
velocity over the interval

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and multiplying it by the interval.

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This is an approximation.

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Let's just calculate what r of six is.

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R of six is going to be the area of

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this rectangle which, as we just said,

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it's six feet per second times two seconds

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so it's going to be 12
feet and then we have

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this rectangle which
is going to be 7.5 feet

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per second times two
seconds which is going

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to be 15 feet, 15 feet
and you can even see

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it in the area right over here.

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It's going to be three feet more.

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One, two and then half of two of these to

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it's going to be three feet more and then

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the area of this one which is going to be

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8.5, so our velocity at the end of

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the interval is going to be 8.5 feet per

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seconds times two seconds which is 17 feet

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and then plus this area
which is our velocity

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at the end of the interval which is nine

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feet per second times two seconds so plus

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18 and then we get the
velocity of this area

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which is going to be this height.

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The velocity at the end of the interval

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which is 9.5 feet per second

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times two seconds so, plus 19.

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Then finally this area
which is the velocity

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at the end of the
interval which is ten feet

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per second times two seconds so, plus 20.

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What does this give us?

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This is the point of which I'm most likely

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going to make an error.

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12 plus 15 is 27 and then 27 plus 10 is 37

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plus another seven is
44, so that gives us 44.

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44 plus 18 is going to give me, let's see,

00:09:12.298 --> 00:09:16.955
I can get to 52 and then
62, so this is going

00:09:16.955 --> 00:09:25.338
to be 62 plus 19 is 81, plus 20 is 101,

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that's going to be in feet.

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Capital r of six, 101 feet, it is an

00:09:31.530 --> 00:09:33.018
approximation for the total distance

00:09:33.018 --> 00:09:35.411
traveled during the 12 seconds but

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it's really an over approximation because

00:09:38.466 --> 00:09:40.322
for every interval, we're taking

00:09:40.322 --> 00:09:42.310
the fastest velocity of the interval.

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If we took the slowest
velocity of the interval

00:09:43.873 --> 00:09:44.929
in would be an underestimate.

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If we did left handed
rectangles and we might

00:09:47.201 --> 00:09:48.865
have gotten something in between if we say

00:09:48.865 --> 00:09:50.738
maybe took the average of these too.

00:09:50.738 --> 00:09:52.498
If we made the height of the rectangle

00:09:52.498 --> 00:09:55.394
three for this first one
or something like that.

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We'll do that in the
future, in future videos.


Cytotoxic T cells and MHC I complexes

WEBVTT
Kind: captions
Language: en

00:00:00.190 --> 00:00:01.811
Voiceover: Everything
we've discussed so far

00:00:01.811 --> 00:00:04.564
involved recognizing and tagging

00:00:04.564 --> 00:00:07.532
or engulfing shady things that were found

00:00:07.532 --> 00:00:13.284
outside of cells.

00:00:13.284 --> 00:00:17.490
We've seen things like a B cell.

00:00:17.490 --> 00:00:28.285
A B cell has its membrane
bound antibodies.

00:00:28.285 --> 00:00:33.059
Maybe one of these might
recognize something shady

00:00:33.059 --> 00:00:36.085
out in the outside of the cell

00:00:36.085 --> 00:00:37.975
and of course this part over here

00:00:37.975 --> 00:00:40.986
as we know they all
have a variable portion

00:00:40.986 --> 00:00:41.580
right over here.

00:00:41.580 --> 00:00:43.466
This is specific to this shady thing

00:00:43.466 --> 00:00:49.658
then this will be engulfed
and then parts of it

00:00:49.658 --> 00:00:53.500
will be attached to an MHC two complex.

00:00:53.500 --> 00:00:55.741
Let me do that in a different color.

00:00:57.479 --> 00:01:01.577
An MHC two complex and then
that will go to the surface,

00:01:01.577 --> 00:01:05.105
that will go to the membrane of the cell

00:01:05.105 --> 00:01:06.797
to present itself.

00:01:06.797 --> 00:01:11.781
That's an MHC two complex.

00:01:11.781 --> 00:01:15.454
It has little bit of the little piece

00:01:15.454 --> 00:01:18.512
of this shady thing out here

00:01:18.512 --> 00:01:20.156
we call this little shady piece,

00:01:20.156 --> 00:01:23.784
this is an antigen presenting cell here.

00:01:23.784 --> 00:01:26.466
We've seen as especially
if this is a B cell

00:01:26.466 --> 00:01:30.701
then a helper T cell that it
also has a variable portion

00:01:30.701 --> 00:01:34.579
that corresponds to this specific antigen.

00:01:36.778 --> 00:01:39.345
This would be helper T
cell right over here.

00:01:40.729 --> 00:01:44.557
This is a helper, T helper cell.

00:01:44.557 --> 00:01:47.246
When it recognizes then
it will start dividing

00:01:47.246 --> 00:01:49.008
into memory helper T cells

00:01:49.008 --> 00:01:50.440
and effector helper T cells.

00:01:50.440 --> 00:01:51.842
The effector helper T cells

00:01:51.842 --> 00:01:53.786
essentially ring the alarm bells

00:01:53.786 --> 00:01:57.807
and start kind of accelerating
the B cell replication

00:01:57.807 --> 00:01:59.958
or I guess you could say
that the B cell activation.

00:01:59.958 --> 00:02:01.651
The theory is that this is kind of a

00:02:01.651 --> 00:02:03.145
double handshake process.

00:02:03.145 --> 00:02:06.098
Once again this is what's
occurring outside of cells.

00:02:06.098 --> 00:02:07.918
When we found stuff outside of cells,

00:02:07.918 --> 00:02:09.660
we engulf them and then we presented them

00:02:09.660 --> 00:02:17.114
on MHC two complexes.

00:02:17.114 --> 00:02:18.778
Now you're probably thinking well,

00:02:18.778 --> 00:02:20.676
I mean that's the outside of cells

00:02:20.676 --> 00:02:24.033
but there's MHC two,
there's this helper T cells

00:02:24.033 --> 00:02:27.759
but we've also referred
to cytotoxic T cells.

00:02:27.759 --> 00:02:28.793
What do those do?

00:02:28.793 --> 00:02:30.529
We've also, if there's MHC two,

00:02:30.529 --> 00:02:32.740
there's probably an MHC one complex.

00:02:32.740 --> 00:02:34.867
What does the MHC one complex do?

00:02:36.467 --> 00:02:37.768
We can recognize shady things

00:02:37.768 --> 00:02:38.882
that are happening outside of cells

00:02:38.882 --> 00:02:41.324
but don't shady things
sometimes happen inside cells

00:02:41.324 --> 00:02:44.899
and how does our immune
system respond to that?

00:02:44.899 --> 00:02:48.175
Actually as you can
imagine all of those things

00:02:48.175 --> 00:02:50.128
will be answered in
the rest of this video.

00:02:50.128 --> 00:02:54.984
Let's think about what
happens when shady things

00:02:54.984 --> 00:02:57.001
start to happen inside the cell.

00:02:57.001 --> 00:03:01.925
For example it might not
even be due to a virus

00:03:01.925 --> 00:03:05.310
or due to some type of bacteria

00:03:05.310 --> 00:03:07.579
could be the cell itself is gone awry.

00:03:07.579 --> 00:03:12.398
Let's say that this right
over here is a cancer cell.

00:03:12.398 --> 00:03:14.431
It's had some mutations.

00:03:14.431 --> 00:03:18.355
It's starting to multiply like crazy.

00:03:18.355 --> 00:03:20.317
This is a cancer cell and a cancer cell

00:03:20.317 --> 00:03:22.182
because it had mutations
are going to produce,

00:03:22.182 --> 00:03:27.185
it's going to produce some weird proteins.

00:03:27.185 --> 00:03:28.750
These cancer cells are going to produce

00:03:28.750 --> 00:03:29.901
some weird proteins.

00:03:29.901 --> 00:03:35.087
Every cell with a nucleus in your body

00:03:35.087 --> 00:03:36.310
and that's pretty much every cell

00:03:36.310 --> 00:03:42.626
except for red blood cells
has MHC one complexes.

00:03:42.626 --> 00:03:46.629
The whole point of the MHC one complex

00:03:46.629 --> 00:03:50.778
is to bind two shady
things that are produced

00:03:50.778 --> 00:03:56.084
inside of the cell,

00:03:56.084 --> 00:03:58.055
and then present them to the membrane.

00:03:58.055 --> 00:04:00.370
Even a malfunctioning cancer cell

00:04:00.370 --> 00:04:02.324
should be doing this.

00:04:02.324 --> 00:04:09.598
This MHC one complex is bound
to this strange proteins

00:04:09.598 --> 00:04:12.541
that are produced by the
mutations inside of the nucleus

00:04:12.541 --> 00:04:17.814
and then it can present them.

00:04:19.229 --> 00:04:21.133
You could imagine what the appropriate

00:04:21.133 --> 00:04:22.654
immune response should be.

00:04:22.654 --> 00:04:29.574
These cancer cells should be killed

00:04:29.574 --> 00:04:31.149
and actually let me label this properly.

00:04:31.149 --> 00:04:32.534
That was MHC two,

00:04:32.534 --> 00:04:34.775
you're presenting an
antigen that was found,

00:04:34.775 --> 00:04:36.856
those initially found outside of the cells

00:04:36.856 --> 00:04:38.051
engulfing and taken out.

00:04:38.051 --> 00:04:43.362
MHC one, it's binding to shady things

00:04:43.362 --> 00:04:46.124
inside the cell and
then presenting it out.

00:04:46.124 --> 00:04:48.600
This thing should be killed.

00:04:48.600 --> 00:04:51.091
Now as you can imagine,
what's going to kill it?

00:04:51.091 --> 00:04:53.846
Well that's where the cytotoxic T cell

00:04:53.846 --> 00:04:55.025
comes into the picture.

00:04:55.025 --> 00:04:58.687
The cytotoxic T cell is going to have,

00:04:58.687 --> 00:05:01.216
that's a receptor right there.

00:05:01.216 --> 00:05:03.769
It will have a variable
portion that's specific

00:05:03.769 --> 00:05:07.963
to this type of an antigen
and so it will bind there.

00:05:07.963 --> 00:05:10.286
Once it does that, it says, oh boy,

00:05:10.286 --> 00:05:12.105
there's all this shady stuff here,

00:05:12.105 --> 00:05:13.956
this shady proteins
that are being produce.

00:05:13.956 --> 00:05:16.444
This cell and all the other ones like it

00:05:16.444 --> 00:05:17.758
need to be killed.

00:05:17.758 --> 00:05:21.681
The cytotoxic T cell
will begin to replicate

00:05:21.681 --> 00:05:24.957
once again like other
types of immune cells

00:05:24.957 --> 00:05:28.385
is going to replicate
into the memory cells

00:05:28.385 --> 00:05:30.747
just in case this type of thing shows up

00:05:30.747 --> 00:05:32.038
10 years in the future

00:05:32.038 --> 00:05:33.855
and also the effector themselves.

00:05:33.855 --> 00:05:41.595
This is memory and also effector cells,

00:05:41.595 --> 00:05:44.725
effector cytotoxic T cells.

00:05:45.817 --> 00:05:48.696
As we always know the
effector version is the thing

00:05:48.696 --> 00:05:49.928
that actual does something,

00:05:49.928 --> 00:05:51.671
it starts to actually affect things.

00:05:51.671 --> 00:05:53.114
What it is going to affect,

00:05:53.114 --> 00:05:56.029
it is going to start binding two things

00:05:56.029 --> 00:05:58.426
that are presenting the same antigen

00:05:58.426 --> 00:06:01.963
as part of their MR on top
of their MHC one complex.

00:06:01.963 --> 00:06:04.294
This character right over here,

00:06:04.294 --> 00:06:09.394
so it's presenting that same antigen

00:06:09.394 --> 00:06:11.151
on this MHC one complex.

00:06:11.151 --> 00:06:13.941
Remember, the variable
portions need to match up.

00:06:13.941 --> 00:06:21.710
Let's say that this is an
effector cytotoxic T cell

00:06:21.710 --> 00:06:24.790
and actually let me draw
in a little bit different.

00:06:24.790 --> 00:06:26.182
Let me draw it like this.

00:06:26.182 --> 00:06:29.916
This is effector cytotoxic T cell.

00:06:29.916 --> 00:06:32.192
Its receptor, its variable portion

00:06:32.192 --> 00:06:35.422
is the one that's
compatible with this antigen

00:06:35.422 --> 00:06:37.022
that's being presented right over here.

00:06:37.022 --> 00:06:38.373
Let me just label this again.

00:06:38.373 --> 00:06:41.793
This is the MHC one complex.

00:06:41.793 --> 00:06:47.192
This is an effector cytotoxic T cell.

00:06:47.192 --> 00:06:49.854
We'll put the C there for cytotoxic

00:06:49.854 --> 00:06:52.374
and what it does is
essentially kind of latches on

00:06:52.374 --> 00:06:55.308
to the cell that needs to die

00:06:55.308 --> 00:06:58.056
and it does it, not
only have this receptor

00:06:58.056 --> 00:07:00.144
interfacing with the MHC one complex

00:07:00.144 --> 00:07:02.686
but actually has a
whole series of proteins

00:07:02.686 --> 00:07:04.879
and I'm not drawing this to scale really.

00:07:04.879 --> 00:07:07.167
This would be much smaller or
relative to the scale cell.

00:07:07.167 --> 00:07:09.272
It essentially latches on between the two

00:07:09.272 --> 00:07:10.705
and I'm not going to go in detail

00:07:10.705 --> 00:07:13.518
but essentially forms what
you can call an immuno synapse

00:07:13.518 --> 00:07:15.239
which is kind of where the two things

00:07:15.239 --> 00:07:16.569
are interacting with each other.

00:07:16.569 --> 00:07:18.827
When it identifies this, it says,

00:07:18.827 --> 00:07:20.189
okay, I need to kill this thing

00:07:20.189 --> 00:07:22.306
or essentially I need to
make this thing kill itself.

00:07:22.306 --> 00:07:24.974
It starts releasing
all of these molecules.

00:07:24.974 --> 00:07:27.615
It can release molecules like perforins

00:07:27.615 --> 00:07:29.853
so to release this preference

00:07:29.853 --> 00:07:32.903
which will essentially cause gaps or holes

00:07:32.903 --> 00:07:38.448
to form in the membrane of
the cell that needs to die

00:07:38.448 --> 00:07:40.808
and it could release other
things like granzymes

00:07:40.808 --> 00:07:45.368
that can go in and
essentially cause this thing

00:07:45.368 --> 00:07:47.151
to kill itself.

00:07:47.151 --> 00:07:50.245
The whole point of this
video is to appreciate

00:07:50.245 --> 00:07:51.848
I guess what we haven't talked about yet.

00:07:51.848 --> 00:07:53.665
We had already talked about what happens

00:07:53.665 --> 00:07:55.896
when you identify shady
things outside of the cells

00:07:55.896 --> 00:07:58.138
and then how you can kind of bring them in

00:07:58.138 --> 00:08:01.422
and then present them and then
use that to further activate

00:08:01.422 --> 00:08:03.086
the immune response.

00:08:03.086 --> 00:08:05.407
Now we're talking about
identifying shady things

00:08:05.407 --> 00:08:06.588
inside the cells.

00:08:06.588 --> 00:08:09.574
Those get presented by MHC one complexes

00:08:09.574 --> 00:08:12.478
and then the cytotoxic
T cells recognize them

00:08:12.478 --> 00:08:14.704
and then force the cell
to kill themselves.

00:08:14.704 --> 00:08:16.152
This wouldn't just be cancer cells,

00:08:16.152 --> 00:08:18.761
this could also apply to a cell

00:08:18.761 --> 00:08:20.885
that has already been affected by a virus.

00:08:20.885 --> 00:08:24.196
For example a cell like this all ready,

00:08:24.196 --> 00:08:25.512
so that's its nucleus.

00:08:25.512 --> 00:08:31.169
It's already been infected by some virus

00:08:31.169 --> 00:08:36.066
so the virus has hijacked the
cell's replication machinery

00:08:36.066 --> 00:08:37.519
in order to replicate itself.

00:08:37.519 --> 00:08:39.516
The proper immune response is hey look,

00:08:39.516 --> 00:08:42.359
I'm a virus making machine.

00:08:42.359 --> 00:08:44.834
I should kill myself.

00:08:44.834 --> 00:08:48.165
It will wreck some of the antigens

00:08:48.165 --> 00:08:52.580
that are being produced
inside by the viruses.

00:08:52.580 --> 00:08:58.530
They're going to bind
to MHC one complexes.

00:08:58.530 --> 00:09:01.379
Pieces of the virus are going
to bind to MHC one complexes

00:09:01.379 --> 00:09:03.097
and then they're going to be presented

00:09:03.097 --> 00:09:05.059
on the surface.

00:09:06.805 --> 00:09:11.102
Let me do it this way,
presented on the surface.

00:09:11.102 --> 00:09:14.150
This exact process can happen again.


Hardy-Weinberg equation

WEBVTT
Kind: captions
Language: en

00:00:00.716 --> 00:00:03.215
Voiceover: Now that we're
familiar with the idea

00:00:03.215 --> 00:00:06.048
of allele frequency, let's build on that

00:00:06.048 --> 00:00:11.064
to develop the Hardy,
do this in a new color,

00:00:11.064 --> 00:00:13.715
and actually, let me
do it right over here,

00:00:13.715 --> 00:00:20.880
the Hardy Weinberg
principle, which is a really

00:00:20.880 --> 00:00:25.430
useful principle for thinking through what

00:00:25.430 --> 00:00:28.347
allele frequencies might
be, or what probability

00:00:28.347 --> 00:00:32.130
you would have if you found someone,

00:00:32.130 --> 00:00:33.710
what percentage of the population might be

00:00:33.710 --> 00:00:36.433
homozygous recessive,
or homozygous dominant,

00:00:36.433 --> 00:00:38.451
or might be a heterozygote.

00:00:38.451 --> 00:00:39.750
And it really builds on the work

00:00:39.750 --> 00:00:41.967
we've already seen with
allele frequencies.

00:00:41.967 --> 00:00:43.451
Now before we go into
that, we're gonna make

00:00:43.451 --> 00:00:45.884
some assumptions, and these
are all just assumptions

00:00:45.884 --> 00:00:49.368
that get us a stable allele
frequency in the population

00:00:49.368 --> 00:00:51.417
from generation to generation.

00:00:51.417 --> 00:00:55.618
We're going to assume
that there's no selection,

00:00:55.618 --> 00:00:59.818
no natural selection is, or
even unnatural selection,

00:00:59.818 --> 00:01:02.351
is going on that would change
the allele frequencies.

00:01:02.351 --> 00:01:05.735
So it's not like people with
one of the alleles or another

00:01:05.735 --> 00:01:07.151
are going to be more or less likely

00:01:07.151 --> 00:01:10.216
to reproduce and have viable offspring.

00:01:10.216 --> 00:01:14.151
We're also going to assume no mutation,

00:01:14.151 --> 00:01:16.966
so we're going to assume that
one of these alleles can't,

00:01:16.966 --> 00:01:18.984
isn't from generation to
generation turning into

00:01:18.984 --> 00:01:22.567
another one, or turning
into maybe a different,

00:01:22.567 --> 00:01:25.734
a new type of trait,
whether it's green eyes,

00:01:25.734 --> 00:01:27.734
or whatever else it might be.

00:01:27.734 --> 00:01:32.168
And we're also going to
assume large populations.

00:01:32.168 --> 00:01:34.535
So that would definitely
throw out the example

00:01:34.535 --> 00:01:36.850
that we looked at in the last
video, which I did just to

00:01:36.850 --> 00:01:39.818
understand the notion of allele
frequencies, where we said,

00:01:39.818 --> 00:01:44.984
hey, look, one out of
the four of the genes

00:01:44.984 --> 00:01:47.067
in this population, or
one-fourth of the alleles

00:01:47.067 --> 00:01:50.402
in this population,
are the dominant brown,

00:01:50.402 --> 00:01:54.683
while three-fourths, or 75
percent, were the recessive blue.

00:01:54.683 --> 00:01:57.318
We're gonna assume large
populations, so many, many, many,

00:01:57.318 --> 00:02:00.451
and so that's so that if you
have very small populations,

00:02:00.451 --> 00:02:02.801
you can imagine that, depending
on how these reproduce,

00:02:02.801 --> 00:02:06.701
it's very easy to get to
changes in frequencies,

00:02:06.701 --> 00:02:09.485
but at larger populations, that
helps us make the assumption

00:02:09.485 --> 00:02:12.153
that we have stable allele frequencies.

00:02:12.153 --> 00:02:13.985
So once again, this is also that we have

00:02:13.985 --> 00:02:21.520
stable allele frequencies.

00:02:21.520 --> 00:02:23.001
Now based on that,
we've already seen if we

00:02:23.001 --> 00:02:27.452
take the frequency of the dominant trait,

00:02:27.452 --> 00:02:30.701
which we can denote with
p, and to that we add

00:02:30.701 --> 00:02:32.600
the frequency of the recessive trait,

00:02:32.600 --> 00:02:34.619
of the recessive, I
should say, allele, let me

00:02:34.619 --> 00:02:37.117
be very careful here, the frequency of the

00:02:37.117 --> 00:02:40.166
dominant allele, and to
that we add the frequency of

00:02:40.166 --> 00:02:43.617
the recessive allele,
what's that going to be?

00:02:43.617 --> 00:02:46.151
Well, you see in this case,
it adds up to 100 percent, or

00:02:46.151 --> 00:02:49.451
one, and it's always going to
add up to 100 percent, or one.

00:02:49.451 --> 00:02:50.986
Because we're assuming that there's only

00:02:50.986 --> 00:02:53.683
one of two alleles in the population,

00:02:53.683 --> 00:02:57.500
so you have 100 percent chance
of getting one of these two,

00:02:57.500 --> 00:03:01.136
that whatever percentage is going to be,

00:03:01.136 --> 00:03:02.867
whatever the frequency here is,

00:03:02.867 --> 00:03:06.200
100 percent minus that is
going to be whatever q is.

00:03:06.200 --> 00:03:07.432
So these two things are going to be

00:03:07.432 --> 00:03:10.133
equal to 100 percent, or equal to one.

00:03:10.133 --> 00:03:11.368
And now we can start to do a little bit

00:03:11.368 --> 00:03:12.583
of interesting mathematics.

00:03:12.583 --> 00:03:14.117
It'll allow us to start thinking about

00:03:14.117 --> 00:03:17.383
things like homozygotes and heterozygotes,

00:03:17.383 --> 00:03:20.283
and so to do that,
let's square both sides.

00:03:20.283 --> 00:03:22.299
So let's square both sides of this,

00:03:22.299 --> 00:03:24.868
a little bit of algebra in biology class.

00:03:24.868 --> 00:03:26.451
And so when you square the left-hand side,

00:03:26.451 --> 00:03:29.334
this is just squaring a
binomial, you might want to

00:03:29.334 --> 00:03:33.333
review it if this looks like
Latin to you, there's many

00:03:33.333 --> 00:03:35.850
algebra videos on Khan
academy that go into this,

00:03:35.850 --> 00:03:49.883
this is going to be p
squared, plus two times pq,

00:03:49.883 --> 00:03:52.084
plus q squared, and of course one squared

00:03:52.084 --> 00:03:54.783
is still going to be equal to one.

00:03:54.783 --> 00:03:56.783
Now what are each of these terms here?

00:03:56.783 --> 00:03:58.617
What are each of these terms?

00:03:58.617 --> 00:04:00.850
Well, let's just think about something.

00:04:00.850 --> 00:04:05.535
p squared is the same thing as p times p.

00:04:05.535 --> 00:04:09.149
Well, p is the frequency
of your dominant allele.

00:04:09.149 --> 00:04:10.867
So this is the frequency
of your dominant allele,

00:04:10.867 --> 00:04:13.467
the percentage of the
allele population, I guess

00:04:13.467 --> 00:04:16.466
you could say, the allele
frequency, that is dominant,

00:04:16.466 --> 00:04:17.752
and you're multiplying
that times it again.

00:04:17.752 --> 00:04:19.283
Well, another way to
think about p, is this is

00:04:19.283 --> 00:04:22.867
the probability, if you
were randomly to pick

00:04:22.867 --> 00:04:28.583
one of these four genes,
and here I'm using my

00:04:28.583 --> 00:04:30.217
over-simplified population, of course,

00:04:30.217 --> 00:04:33.267
the truths that we're about
to surface to be true,

00:04:33.267 --> 00:04:35.467
you're going to have to
assume a large population,

00:04:35.467 --> 00:04:37.867
but in this one right over
here, one way to view p is

00:04:37.867 --> 00:04:41.750
what's the probability if I
were to pick a gene at random,

00:04:41.750 --> 00:04:44.316
what's the probability
that it is the variant,

00:04:44.316 --> 00:04:47.966
or it is the dominant allele,
what is the probability

00:04:47.966 --> 00:04:50.451
that it represents the brown variant?

00:04:50.451 --> 00:04:58.150
So that's one way to view
p, so, the probability

00:04:58.150 --> 00:05:03.883
of getting a, let's
just write it that way,

00:05:03.883 --> 00:05:07.216
a capital B, a dominant brown allele.

00:05:07.216 --> 00:05:08.751
So what's p times p?

00:05:08.751 --> 00:05:12.583
That's the probability of
getting two dominant alleles.

00:05:12.583 --> 00:05:15.932
Or another way of thinking about
it, this is the probability

00:05:15.932 --> 00:05:22.451
for someone in the population
to be homozygous dominant,

00:05:22.451 --> 00:05:25.466
so it's the probability of someone

00:05:25.466 --> 00:05:33.833
being capital B and capital B.

00:05:33.833 --> 00:05:37.868
And so by the same
logic, what is q squared?

00:05:37.868 --> 00:05:39.932
Well, q squared, that's just q times q,

00:05:39.932 --> 00:05:43.133
q is the probability of
getting one recessive allele,

00:05:43.133 --> 00:05:45.951
so this is the probability of
getting two recessive alleles.

00:05:45.951 --> 00:05:48.417
One from your mother,
and one from your father,

00:05:48.417 --> 00:05:54.983
so this is the probability of,

00:05:54.983 --> 00:05:57.882
if you were kind of randomly
born into this population,

00:05:57.882 --> 00:06:01.266
of getting two recessive alleles.

00:06:01.266 --> 00:06:05.617
Now what is this middle
term, right over here?

00:06:05.617 --> 00:06:11.535
Well, p times q, so pq, so
one way to think about it,

00:06:11.535 --> 00:06:14.084
if you said, what's the
probability that from your mother,

00:06:14.084 --> 00:06:17.001
you get, randomly, you
know nothing about them,

00:06:17.001 --> 00:06:20.118
or if you pick a random
mother and a random father,

00:06:20.118 --> 00:06:23.083
what's the probability, I
have to be careful here,

00:06:23.083 --> 00:06:26.600
so if you're just
randomly getting alleles,

00:06:26.600 --> 00:06:28.550
what's the probability
that from on one side

00:06:28.550 --> 00:06:30.417
you're gonna get the dominant, and

00:06:30.417 --> 00:06:32.700
from the second side you're
gonna get the recessive?

00:06:32.700 --> 00:06:41.700
So that would be pq,
that would be p times q,

00:06:41.700 --> 00:06:44.549
so that's getting it from,
say, from one parent,

00:06:44.549 --> 00:06:45.751
and then that's from the second parent,

00:06:45.751 --> 00:06:47.200
but what about the other way around?

00:06:47.200 --> 00:06:49.951
From the first parent,
you have a q probability

00:06:49.951 --> 00:06:53.750
of getting the recessive one,
and from the second parent,

00:06:53.750 --> 00:06:57.000
you have a p probability of
getting the dominant one.

00:06:57.000 --> 00:07:00.334
So there's two ways of
becoming a heterozygote.

00:07:00.334 --> 00:07:03.367
And so if you add these two
probabilities, what do you get?

00:07:03.367 --> 00:07:04.882
These are both pq, I'm just changing

00:07:04.882 --> 00:07:06.464
the order of multiplication.

00:07:06.464 --> 00:07:12.017
You sum these two, you get two pq.

00:07:12.017 --> 00:07:22.933
So this is the probability
of being a heterozygote.

00:07:22.933 --> 00:07:25.382
So this is a pretty neat result.

00:07:25.382 --> 00:07:27.083
Just by making a few assumptions,

00:07:27.083 --> 00:07:29.800
and reasoning through this
notion of allele frequency,

00:07:29.800 --> 00:07:33.983
we're able to come up with this expression

00:07:33.983 --> 00:07:37.417
that actually is fairly
powerful in thinking

00:07:37.417 --> 00:07:40.849
about allele frequency in
a population, and actually,

00:07:40.849 --> 00:07:44.417
the different genotype
frequencies in a population.

00:07:44.417 --> 00:07:46.899
You see it all makes sense,
these all add up to one.

00:07:46.899 --> 00:07:50.300
The probability of someone
being homozygous dominant,

00:07:50.300 --> 00:07:52.700
plus the probability of
someone being a heterozygote,

00:07:52.700 --> 00:07:53.951
plus the probability of someone being

00:07:53.951 --> 00:07:57.952
a homozygous recessive, they're
gonna add up to 100 percent,

00:07:57.952 --> 00:07:59.400
because someone's going to have to be

00:07:59.400 --> 00:08:01.682
one of these three things.

00:08:01.682 --> 00:08:03.049
Now I'm gonna leave you
there in this video,

00:08:03.049 --> 00:08:04.816
and the next video,
we're actually gonna use

00:08:04.816 --> 00:08:09.583
this Hardy Weinberg equation
to actually come up with

00:08:09.583 --> 00:08:13.540
some very interesting
results about a population.


Applying the Hardy-Weinberg equation

WEBVTT
Kind: captions
Language: en

00:00:00.233 --> 00:00:02.566
Voiceover: Let's stick with
this idea, the simplification,

00:00:02.566 --> 00:00:04.966
that there's a gene for eye color,

00:00:04.966 --> 00:00:06.967
and it only comes with two variants.

00:00:06.967 --> 00:00:09.166
It has the dominant variant,

00:00:09.166 --> 00:00:11.367
which codes for brown eye color,

00:00:11.367 --> 00:00:15.500
and it has the recessive variant,

00:00:15.500 --> 00:00:17.833
which codes for blue eye color.

00:00:17.833 --> 00:00:21.233
So if either one of your
alleles is this capital B,

00:00:21.233 --> 00:00:22.433
you're going to have brown eyes,

00:00:22.433 --> 00:00:24.367
the only way to have blue
eyes is to have a lower case,

00:00:24.367 --> 00:00:29.100
is to be homozygous for
the recessive allele.

00:00:29.100 --> 00:00:30.833
Now let's say that in a population,

00:00:30.833 --> 00:00:32.500
it's a large population, one that meets

00:00:32.500 --> 00:00:37.500
all the Hardy-Weinberg
Equilibrium assumptions,

00:00:37.500 --> 00:00:39.900
let's say that you were to
observe that nine percent

00:00:39.900 --> 00:00:43.833
of this population has blue eyes.

00:00:43.833 --> 00:00:45.300
So now we're talking about the phenotype.

00:00:45.300 --> 00:00:47.633
You can actually observe
that they have blue eyes.

00:00:47.633 --> 00:00:52.700
Based on this, can we figure out p,

00:00:52.700 --> 00:00:56.300
which is the frequency
of the dominant allele.

00:00:56.300 --> 00:00:57.833
Can we figure this out?

00:00:57.833 --> 00:01:01.433
And can we figure out q,
which is the frequency

00:01:01.433 --> 00:01:04.833
of the recessive allele, can
we figure that out as well?

00:01:04.833 --> 00:01:06.300
I would encourage you to pause this video

00:01:06.300 --> 00:01:09.433
and based on what we saw of
the Hardy-Weinberg Equation,

00:01:09.433 --> 00:01:14.330
can we figure these things
out, given this information?

00:01:14.330 --> 00:01:16.366
Well let's revisit the
Hardy-Weinberg equation.

00:01:16.366 --> 00:01:18.100
We've worked it out in a previous video,

00:01:18.100 --> 00:01:20.366
but I'll rewrite it right now.

00:01:20.366 --> 00:01:23.633
It says, the allele frequency for

00:01:23.633 --> 00:01:27.233
the dominant allele frequency squared,

00:01:27.233 --> 00:01:30.166
plus two times the
dominant allele frequency

00:01:30.166 --> 00:01:32.767
times the recessive allele frequency,

00:01:32.767 --> 00:01:35.566
plus the recessive
allele frequency squared,

00:01:35.566 --> 00:01:36.967
is equal to one.

00:01:36.967 --> 00:01:38.766
And we saw that this
just comes from the idea

00:01:38.766 --> 00:01:41.366
that p plus q is going to be equal to one.

00:01:41.366 --> 00:01:42.766
There is a 100 percent chance,
if you were to randomly

00:01:42.766 --> 00:01:47.300
pick a gene, that it's
one of these two variants.

00:01:47.300 --> 00:01:49.833
Now when we say nine
percent has blue eyes,

00:01:49.833 --> 00:01:51.166
what does that mean?

00:01:51.166 --> 00:01:52.966
Well the only way to have blue eyes

00:01:52.966 --> 00:01:57.700
is if your genotype is
homozygous recessive.

00:01:57.700 --> 00:01:59.330
Because if you have a capital B in here

00:01:59.330 --> 00:02:00.567
then you're going to have brown eyes.

00:02:00.567 --> 00:02:04.167
So we can say that nine
percent also has this genotype.

00:02:04.167 --> 00:02:06.166
Or you can say that the
frequency in the population

00:02:06.166 --> 00:02:09.330
of this genotype is nine percent.

00:02:09.330 --> 00:02:11.863
But we've already seen, that's exactly

00:02:11.863 --> 00:02:13.833
what this term right over here is.

00:02:13.833 --> 00:02:15.700
That's this q squared term.

00:02:15.700 --> 00:02:17.966
This is the probability,
one way to think about it,

00:02:17.966 --> 00:02:21.500
of getting, q of course is the frequency

00:02:21.500 --> 00:02:25.100
of the recessive allele,
now you could view this

00:02:25.100 --> 00:02:29.449
as the probability of getting
two of the recessive alleles.

00:02:29.449 --> 00:02:32.566
In your population, it's
going to be nine percent.

00:02:32.566 --> 00:02:37.700
So we could say q squared
is equal to nine percent.

00:02:37.700 --> 00:02:38.766
Or another way to think about it,

00:02:38.766 --> 00:02:46.909
this term over here is
nine percent, or 0.09.

00:02:46.909 --> 00:02:48.766
Nine percent has this genotype,

00:02:48.766 --> 00:02:50.966
that's what this tells us right over here.

00:02:50.966 --> 00:02:52.633
So then we can solve for q.

00:02:52.633 --> 00:02:56.100
If q squared, I'll write
it as a decimal, 0.09,

00:02:56.100 --> 00:02:57.634
that means that q is going to be

00:02:57.634 --> 00:03:04.300
the square root of 0.09,
which is equal to 0.3.

00:03:04.300 --> 00:03:06.566
Just like that, we were able to figure out

00:03:06.566 --> 00:03:09.166
the allele frequency of
the recessive allele.

00:03:09.166 --> 00:03:13.165
And I could write that as a
percentage, 0.3 or 30 percent,

00:03:13.165 --> 00:03:15.834
if you were looking at the
genes in the population,

00:03:15.834 --> 00:03:20.233
30 percent express our code for

00:03:20.233 --> 00:03:25.033
the recessive allele, or
the recessive variant.

00:03:25.033 --> 00:03:26.433
Based on that, we can figure out

00:03:26.433 --> 00:03:28.833
what percentage code for
the dominant variant.

00:03:28.833 --> 00:03:30.966
The rest of the genes must code

00:03:30.966 --> 00:03:32.033
for the dominant one, because we're

00:03:32.033 --> 00:03:33.366
assuming there's only two of them.

00:03:33.366 --> 00:03:35.166
P plus q equals 100 percent,

00:03:35.166 --> 00:03:37.766
or p plus q is equal to one.

00:03:37.766 --> 00:03:41.500
So this must be 70 percent.

00:03:41.500 --> 00:03:43.869
So just based on that, we can kind of

00:03:43.869 --> 00:03:44.966
dig a little bit deeper here.

00:03:44.966 --> 00:03:46.500
So what is p squared?

00:03:46.500 --> 00:03:51.633
P squared is going to be 70
percent squared, or 0.7 squared.

00:03:51.633 --> 00:03:57.900
So this right over here is
0.7 squared, which is 0.49.

00:03:57.900 --> 00:04:00.966
So one way to think about
it is, based on this,

00:04:00.966 --> 00:04:02.566
and once again, it's a simple equation,

00:04:02.566 --> 00:04:04.100
but these really neat ideas are starting

00:04:04.100 --> 00:04:06.700
to pop out of it based
on just this information.

00:04:06.700 --> 00:04:09.300
We're now able to say that 49 percent

00:04:09.300 --> 00:04:12.756
of the population is
going to have a genotype

00:04:12.756 --> 00:04:17.033
of capital B, they're going
to be homozygous dominant.

00:04:17.033 --> 00:04:19.500
And then we can figure
out this right over here.

00:04:19.500 --> 00:04:22.807
Two times p times q, that's going to be

00:04:22.807 --> 00:04:32.489
two times 0.7, times 0.3.

00:04:32.489 --> 00:04:36.833
So let's see, that's going
to be two times 0.21,

00:04:36.833 --> 00:04:42.166
so this right over here
is going to be 0.42.

00:04:42.166 --> 00:04:44.700
Or another way to think
about it is, 42 percent

00:04:44.700 --> 00:04:46.233
of this population is going to have

00:04:46.233 --> 00:04:49.300
the genotype upper case
B and lower case b.

00:04:49.300 --> 00:04:50.833
And you see they all add up.

00:04:50.833 --> 00:04:54.366
49 percent plus 42 percent is 91 percent,

00:04:54.366 --> 00:04:58.976
plus nine percent all
adds up to 100 percent.

00:04:58.976 --> 00:05:00.566
So you get a little bit
of information here,

00:05:00.566 --> 00:05:02.766
and based on what we know
about allele frequencies,

00:05:02.766 --> 00:05:04.567
making a few assumptions,
we're able to get

00:05:04.567 --> 00:05:07.633
a lot more knowledge
about this population.

00:05:07.633 --> 00:05:10.463
And this is actually
very useful in real life,

00:05:10.463 --> 00:05:13.966
when people think about,
say, a recessive allele

00:05:13.966 --> 00:05:16.499
that might cause some type of a disease,

00:05:16.499 --> 00:05:20.166
based on the incidents of that disease,

00:05:20.166 --> 00:05:21.366
people can start to think about,

00:05:21.366 --> 00:05:23.900
"What percentage of the
population is a carrier?"

00:05:23.900 --> 00:05:26.233
Say they're heterzygotes for that disease.

00:05:26.233 --> 00:05:29.482
So this is actually very
useful in real life.


Allele frequency

WEBVTT
Kind: captions
Language: en

00:00:00.371 --> 00:00:01.812
Voiceover: What I want
to do with this video

00:00:01.812 --> 00:00:06.278
is explore the idea of allele frequency.

00:00:07.111 --> 00:00:08.578
Allele frequency.

00:00:08.578 --> 00:00:12.444
Just as a reminder, an allele
is a variant of a gene.

00:00:12.737 --> 00:00:15.794
You get a variant of a
gene from your mother,

00:00:15.794 --> 00:00:17.267
and you get another variant of the gene

00:00:17.267 --> 00:00:18.480
from the father.

00:00:18.480 --> 00:00:20.241
So, when we're talking about
the allele, we're talking

00:00:20.241 --> 00:00:21.960
about that specific
variant that you got from

00:00:21.960 --> 00:00:24.449
your mother or your father.

00:00:24.449 --> 00:00:25.993
We've seen this before, but now let's dig

00:00:25.993 --> 00:00:27.537
a little bit deeper.

00:00:27.537 --> 00:00:30.858
To help us get our heads
around this, we'll start

00:00:30.858 --> 00:00:35.848
with a fairly common model for this.

00:00:35.848 --> 00:00:37.312
We're going to think about eye color.

00:00:37.312 --> 00:00:39.453
Obviously, this is a very
large simplification, but

00:00:39.453 --> 00:00:42.424
let's just assume that we
have a population where

00:00:42.424 --> 00:00:44.936
there's only two variants
of an eye color gene.

00:00:44.936 --> 00:00:46.800
Let's first assume there
is an eye color gene.

00:00:46.800 --> 00:00:48.569
Let's assume there's two variants.

00:00:48.569 --> 00:00:52.393
One variant, one allele for
eye color, we'll use the

00:00:52.393 --> 00:00:54.072
shorthand, capital B.

00:00:54.072 --> 00:00:56.601
Let's say that's the allele for brown.

00:00:57.248 --> 00:00:58.909
Brown eye color.

00:00:59.217 --> 00:01:01.829
We're going to assume
that this one is dominant.

00:01:02.153 --> 00:01:04.609
It's dominant over the other allele.

00:01:04.609 --> 00:01:07.081
Now the other allele, we're
going to assume is for

00:01:07.081 --> 00:01:08.969
blue eye color, and we'll
represent that with a

00:01:08.969 --> 00:01:10.205
lower case B.

00:01:10.529 --> 00:01:14.144
So that is blue eye color,
and we're going to assume

00:01:14.144 --> 00:01:16.305
that this is recessive.

00:01:16.305 --> 00:01:17.849
Once again, this is review.

00:01:17.849 --> 00:01:21.840
Someone who has one of
the big B alleles, the

00:01:21.840 --> 00:01:23.936
brown alleles, it doesn't
matter what their other

00:01:23.936 --> 00:01:25.987
allele is going to be, because
it's either going to be

00:01:25.987 --> 00:01:28.862
another brown or it's
going to be a blue, they're

00:01:28.862 --> 00:01:30.833
going to show brown eyes.

00:01:30.833 --> 00:01:34.216
This is going to be brown
eyes, and this is going

00:01:34.216 --> 00:01:36.073
to be brown eyes, because the capital B is

00:01:36.073 --> 00:01:37.180
dominant.

00:01:37.180 --> 00:01:42.752
The only way to get blue
eyes is to be a homozygote

00:01:42.752 --> 00:01:45.528
for the recessive allele.

00:01:45.928 --> 00:01:48.153
All of that, of course, is review.

00:01:48.153 --> 00:01:49.608
We've seen that before.

00:01:49.608 --> 00:01:52.200
Now let's think about allele frequency.

00:01:52.200 --> 00:01:55.329
To think about that, I'll
set up a very artificially

00:01:55.329 --> 00:01:56.930
small population.

00:01:56.930 --> 00:02:01.137
Let's say our population has
exactly two people in it.

00:02:01.737 --> 00:02:04.408
Population has exactly
two people in it, Person 1

00:02:04.408 --> 00:02:08.409
and Person 2, and let's
say we're able to look

00:02:08.409 --> 00:02:12.753
into their DNA and figure
out their genotypes.

00:02:12.753 --> 00:02:18.352
Person 1, say, has a capital
B allele, has a brown

00:02:18.352 --> 00:02:22.424
allele and a blue allele,
while Person 2 has two

00:02:22.424 --> 00:02:25.540
blue, two blue alleles.

00:02:25.817 --> 00:02:28.333
Given that we know the
genotypes in this artificially

00:02:28.333 --> 00:02:31.060
small population, we
could start thinking about

00:02:31.060 --> 00:02:32.240
the allele frequencies.

00:02:32.240 --> 00:02:34.688
Or the frequencies of
the different alleles.

00:02:34.688 --> 00:02:38.281
What do you think is
going to be the frequency

00:02:38.281 --> 00:02:43.196
the frequency of the brown
allele in this population?

00:02:44.117 --> 00:02:45.740
I encourage you to pause
this video and think

00:02:45.740 --> 00:02:47.624
about this on your own.

00:02:47.624 --> 00:02:50.968
I'm assuming you've had a
go at it, so you might be

00:02:50.968 --> 00:02:52.655
tempted to say, "Looks
like one out of two people

00:02:52.671 --> 00:02:54.660
"have it, maybe it's 50%."

00:02:54.660 --> 00:02:56.177
But that wouldn't be the
right way to think about

00:02:56.177 --> 00:02:57.416
allele frequencies.

00:02:57.416 --> 00:02:59.135
In allele frequencies, you
want to dig a little bit

00:02:59.135 --> 00:03:01.976
deeper and look at the individual alleles.

00:03:01.976 --> 00:03:03.345
When you look at that,
you say, "Okay, there's

00:03:03.345 --> 00:03:08.337
"four individual alleles in
this population, or there's

00:03:08.337 --> 00:03:12.041
"four variants, or there's
literally four chromosomes

00:03:12.041 --> 00:03:15.662
"that are carrying that
gene in this population."

00:03:15.662 --> 00:03:20.065
Out of them, one of them
carry, one of them is the

00:03:20.065 --> 00:03:26.392
capital B allele, so we could
say that that is going to

00:03:26.392 --> 00:03:30.873
be zero point two five, or 25%.

00:03:30.873 --> 00:03:38.488
Once again, 25% of the
genes for eye color have the

00:03:38.488 --> 00:03:42.904
capital B allele, have the brown allele.

00:03:42.904 --> 00:03:46.248
Now we can do the same,
ask ourselves the same

00:03:46.248 --> 00:03:49.960
question for the lower case B allele.

00:03:49.960 --> 00:03:54.536
What fraction of the genes
in this population are

00:03:54.536 --> 00:03:59.872
code for or represent
the lower case B, the

00:03:59.872 --> 00:04:01.104
blue allele?

00:04:01.104 --> 00:04:02.654
Once again, I encourage
you to pause the video

00:04:02.654 --> 00:04:03.857
and think about it.

00:04:03.857 --> 00:04:05.489
Well, very similar idea.

00:04:05.489 --> 00:04:09.962
There's four genes in
the population that are

00:04:09.962 --> 00:04:11.112
coding for eye color.

00:04:11.112 --> 00:04:18.585
Of them, one, two, three
code for or are the lower

00:04:18.585 --> 00:04:22.129
case blue allele.

00:04:22.129 --> 00:04:27.513
So that's zero point seven five or 75%.

00:04:27.513 --> 00:04:33.494
75% of the genes code for
the lower case blue allele,

00:04:33.494 --> 00:04:39.134
while 25 are the brown allele.

00:04:39.134 --> 00:04:41.150
I really want to hit this
point home, how this is

00:04:41.150 --> 00:04:44.126
different than, say,
the phenotype frequency.

00:04:44.126 --> 00:04:49.407
If I asked you, in the
population, if I asked you the

00:04:49.407 --> 00:04:58.758
percent of brown-eyed
people, so now I'm talking

00:04:58.758 --> 00:05:01.238
about phenotype, what would that be?

00:05:01.238 --> 00:05:03.031
Well, there's two people
in the population.

00:05:03.031 --> 00:05:05.609
One of them is exhibiting
brown eyes, so that's

00:05:05.609 --> 00:05:06.950
going to be one-half.

00:05:06.950 --> 00:05:11.160
Similarly, if I were to ask
you what is the percentage

00:05:11.160 --> 00:05:13.366
of people who are
blue-eyed that, too, would

00:05:13.366 --> 00:05:14.713
be one-half.

00:05:14.713 --> 00:05:16.282
This person is one of
the two people, they're

00:05:16.282 --> 00:05:17.539
exhibiting blue eyes.

00:05:17.539 --> 00:05:19.184
But allele frequency,
we're digging deeper, we're

00:05:19.184 --> 00:05:21.066
looking at the genotypes.

00:05:21.066 --> 00:05:26.952
We're saying out of the
four genes here, one of

00:05:26.952 --> 00:05:34.896
them is the big B allele,
so that's 25% of the gene

00:05:34.896 --> 00:05:38.798
population codes for the brown allele and

00:05:38.798 --> 00:05:41.416
75% is the blue allele.

00:05:41.416 --> 00:05:43.000
This is really important to internalize.

00:05:43.000 --> 00:05:45.608
Because once we internalize
this, then as we'll see,

00:05:45.608 --> 00:05:48.690
that the ideas in the
Hardy-Weinberg principle

00:05:48.690 --> 00:05:50.390
start to make a lot of sense.

00:05:50.390 --> 00:05:51.736
I'll do a little bit of foreshadowing.

00:05:51.736 --> 00:05:56.136
We can denote this, this
is just a convention that's

00:05:56.136 --> 00:05:59.904
often used, by the lower
case letter P, and we can

00:05:59.904 --> 00:06:04.760
use lower case Q to denote the frequency.

00:06:04.760 --> 00:06:07.096
So lower case P is the
frequency of the dominant

00:06:07.096 --> 00:06:09.530
allele, lower case Q the frequency of the

00:06:09.530 --> 00:06:10.976
recessive allele.

00:06:10.976 --> 00:06:12.496
What's true here?

00:06:12.496 --> 00:06:16.744
What's true of P, what's
going to be true of

00:06:16.744 --> 00:06:22.349
P plus Q, what's P plus
Q going to be equal to?

00:06:22.349 --> 00:06:24.187
I encourage you to pause the video again

00:06:24.187 --> 00:06:25.544
and think about that.

00:06:25.544 --> 00:06:27.816
What is this going to be equal to?

00:06:27.816 --> 00:06:30.872
Well, when we started
off, we said that there's

00:06:30.872 --> 00:06:33.424
only two potential, that's
one of the assumptions

00:06:33.424 --> 00:06:35.432
we assumed, we assumed
there's only two alleles

00:06:35.432 --> 00:06:37.864
in this population, in kind of the allele

00:06:37.864 --> 00:06:41.608
population for this gene
population for this trait.

00:06:41.608 --> 00:06:45.388
The frequency of the
dominant ones plus the

00:06:45.388 --> 00:06:47.808
frequency of recessive
ones, well everyone's going

00:06:47.808 --> 00:06:50.080
to have one of those two,
so if you add those two

00:06:50.080 --> 00:06:55.442
frequencies, it's going
to have to add to 100%.

00:06:55.442 --> 00:06:56.433
We see that there.

00:06:56.433 --> 00:07:00.090
One-fourth plus three-fourths
is one, or 100%.

00:07:00.090 --> 00:07:04.672
And 25% plus 75% is also 100%.

00:07:04.672 --> 00:07:06.920
So we could say P plus Q
is equal to 100%, or we

00:07:06.920 --> 00:07:13.104
could say that P plus Q is equal to one.

00:07:13.104 --> 00:07:15.150
Is equal to one.

00:07:15.150 --> 00:07:17.090
So, in the next video, we're
going to start from the

00:07:17.090 --> 00:07:21.020
seemingly fairly simple
idea, to get to a more richer

00:07:21.020 --> 00:07:23.228
and fairly neat idea
that's expressed in the

00:07:23.228 --> 00:07:26.073
Hardy-Weinberg equation.


Zygote differentiating into somatic and germ cells

WEBVTT
Kind: captions
Language: en

00:00:00.365 --> 00:00:02.603
Voiceover: In the last
video, we saw an egg

00:00:02.603 --> 00:00:06.121
from our mothers fuse with
a sperm from our fathers

00:00:06.121 --> 00:00:09.412
to form a zygote that
would keep replicating

00:00:09.412 --> 00:00:12.278
and turn into us, if this...

00:00:12.278 --> 00:00:15.870
Let's say this was the
sperm from my father

00:00:15.870 --> 00:00:18.168
that fuses with the egg from my mother,

00:00:18.168 --> 00:00:20.498
and then this zygote will keep replicating

00:00:20.498 --> 00:00:23.243
and eventually turn into Sal,

00:00:23.243 --> 00:00:26.807
and make a video about fertilization.

00:00:26.807 --> 00:00:29.306
So how does that actually happen?

00:00:29.306 --> 00:00:31.775
So now that this zygote has the diploid

00:00:31.775 --> 00:00:34.484
number of chromosomes, and once again

00:00:34.484 --> 00:00:36.384
they're referring to that as 2N,

00:00:36.384 --> 00:00:38.066
where N would be the haploid number,

00:00:38.066 --> 00:00:39.965
2N would be the diploid number,

00:00:39.965 --> 00:00:41.541
and in the case of human beings,

00:00:41.541 --> 00:00:45.288
N is 23, so in the case of human beings,

00:00:45.288 --> 00:00:47.275
N is 23 and two times N of course

00:00:47.275 --> 00:00:49.656
would be 46 chromosomes.

00:00:49.656 --> 00:00:51.984
I have my full contingency
of chromosomes here.

00:00:51.984 --> 00:00:54.984
I got a Y sex chromosome from my father,

00:00:54.984 --> 00:00:56.414
X of course from my mother,

00:00:56.414 --> 00:00:59.588
so I'm going to be a male.

00:00:59.588 --> 00:01:02.532
And so what then happens?

00:01:02.532 --> 00:01:05.259
Well now, through mitosis, this zygote

00:01:05.259 --> 00:01:07.618
is going to keep replicating.

00:01:07.618 --> 00:01:11.129
So it will, you know, after one,

00:01:11.129 --> 00:01:14.072
so after one, and we're
going to go into the details

00:01:14.072 --> 00:01:16.454
of the mechanics of mitosis,

00:01:16.454 --> 00:01:20.734
but after one round of
mitosis, it is now two cells.

00:01:20.734 --> 00:01:21.658
It is now two cells.

00:01:21.658 --> 00:01:22.727
And I'm going to draw it, once again,

00:01:22.727 --> 00:01:24.669
I'm not going to draw it at scale.

00:01:24.669 --> 00:01:26.138
It's now two cells.

00:01:26.138 --> 00:01:27.132
I want to make sure I have enough space

00:01:27.132 --> 00:01:28.990
on my little chalkboard here.

00:01:28.990 --> 00:01:29.770
It has two cells.

00:01:29.770 --> 00:01:31.337
Instead of drawing all of the chromosomes,

00:01:31.337 --> 00:01:32.821
let me just say that each of these,

00:01:32.821 --> 00:01:36.843
in my nucleus, I still have 2N.

00:01:36.843 --> 00:01:38.428
I have the diploid number.

00:01:38.428 --> 00:01:41.360
So each of these two cells

00:01:41.360 --> 00:01:42.575
that it has differentiated to

00:01:42.575 --> 00:01:44.423
still have the full contingency.

00:01:44.423 --> 00:01:45.700
That's what mitosis does.

00:01:45.700 --> 00:01:48.357
It essentially replicates
the entire cells.

00:01:48.357 --> 00:01:50.814
You have the same number of chromosomes.

00:01:50.814 --> 00:01:51.843
And then this process is

00:01:51.843 --> 00:01:53.012
just going to keep happening.

00:01:53.012 --> 00:01:57.134
These two characters
are going to replicate,

00:01:57.134 --> 00:02:00.325
are going to replicate, and so then

00:02:00.325 --> 00:02:03.030
you're going to have, through mitosis,

00:02:03.030 --> 00:02:03.853
and now you're going...

00:02:03.853 --> 00:02:06.920
So this is another round
of mitosis right over here.

00:02:06.920 --> 00:02:07.853
Mitsosis.

00:02:07.853 --> 00:02:09.516
So they just keep duplicating themselves.

00:02:09.516 --> 00:02:13.568
And each of these cells
have the full contingency.

00:02:13.568 --> 00:02:16.660
2N, the diploid number of chromosomes

00:02:16.660 --> 00:02:19.025
for, well, in this case
it's going to be 46

00:02:19.025 --> 00:02:19.896
for a human being.

00:02:19.896 --> 00:02:20.610
And then this process

00:02:20.610 --> 00:02:22.488
is just going to keep happening.

00:02:22.488 --> 00:02:24.993
So this process is
going to keep happening.

00:02:24.993 --> 00:02:27.053
I'll do dot dot dot to
show that, you know,

00:02:27.053 --> 00:02:28.926
a lot of this has been going on.

00:02:28.926 --> 00:02:32.251
So mitosis is just
going to keep happening.

00:02:32.251 --> 00:02:33.818
And so eventually you're going to have

00:02:33.818 --> 00:02:35.881
thousands of these cells,

00:02:35.881 --> 00:02:37.211
and eventually as we'll
see, you're going to have

00:02:37.211 --> 00:02:39.297
millions and ten millions of them.

00:02:39.297 --> 00:02:41.852
So let me draw them really
really really small.

00:02:41.852 --> 00:02:43.964
There's a bunch of them there.

00:02:43.964 --> 00:02:50.340
And each of them, each
of them are going to have

00:02:50.340 --> 00:02:53.456
the diploid number of chromosomes.

00:02:53.456 --> 00:02:55.889
They're going to have 46 chromosomes.

00:02:55.889 --> 00:03:00.399
23 pair of homologous chromosomes.

00:03:00.399 --> 00:03:03.638
So we now have a big ball of these here.

00:03:03.638 --> 00:03:06.677
And these cells, some
of them are going to,

00:03:06.677 --> 00:03:09.050
they're going to differentiate into me.

00:03:09.050 --> 00:03:10.059
They're going to differentiate into

00:03:10.059 --> 00:03:11.833
the different parts of my body.

00:03:11.833 --> 00:03:14.549
So for example, these
cells right over here

00:03:14.549 --> 00:03:17.448
might eventually,
they'll keep replicating,

00:03:17.448 --> 00:03:19.470
but then it's them and their offspring

00:03:19.470 --> 00:03:23.403
might eventually differentiate
into my brain cells.

00:03:23.403 --> 00:03:26.211
These cells here will keep replicating,

00:03:26.211 --> 00:03:29.383
and them and their offspring,
I guess you could say,

00:03:29.383 --> 00:03:31.391
or the things that they replicate into,

00:03:31.391 --> 00:03:33.693
might differentiate into my heart.

00:03:33.693 --> 00:03:37.056
These right over here might differentiate

00:03:37.056 --> 00:03:40.353
into my lungs, and of course

00:03:40.353 --> 00:03:41.976
all of these eventually will differentiate

00:03:41.976 --> 00:03:45.958
into all the different, and
they and their offspring

00:03:45.958 --> 00:03:47.267
will differentiate into all of the things

00:03:47.267 --> 00:03:48.760
that make me me.

00:03:48.760 --> 00:03:52.681
And so you have a lot
more of this mitosis.

00:03:52.681 --> 00:03:57.424
You're eventually going
to have a human being.

00:03:57.424 --> 00:04:00.708
So let me just say this
is more mitosis going on.

00:04:00.708 --> 00:04:02.653
Mitosis.

00:04:02.653 --> 00:04:04.283
And now let me make an attempt

00:04:04.283 --> 00:04:07.090
to draw a human being.

00:04:08.935 --> 00:04:11.168
That doesn't really look like me, but...

00:04:11.168 --> 00:04:13.804
Well, I have a lot of
hair, so that's my...

00:04:13.804 --> 00:04:15.434
I have big eyebrows as well.

00:04:15.434 --> 00:04:17.258
Still doesn't look like me, but anyway.

00:04:17.258 --> 00:04:18.612
You get the point.

00:04:18.612 --> 00:04:25.049
And so, and I'll try
to draw fairly quickly.

00:04:25.784 --> 00:04:29.768
But this is obviously not my best

00:04:29.768 --> 00:04:31.097
rendering of a human being.

00:04:31.097 --> 00:04:34.396
But you get the general idea.

00:04:35.080 --> 00:04:37.444
Nice broad shoulders, that's nice.

00:04:37.444 --> 00:04:42.834
All right, so let me, let me...

00:04:43.312 --> 00:04:46.635
I'm focusing too much on
drawing this human being.

00:04:48.003 --> 00:04:51.719
Anyway, you get the general idea.

00:04:51.719 --> 00:04:54.171
My stomach isn't quite that flat,

00:04:54.171 --> 00:04:56.397
but anyway, you get the general idea.

00:04:56.397 --> 00:04:58.221
So this, it'll eventually differentiate

00:04:58.221 --> 00:04:59.695
into a human being.

00:04:59.695 --> 00:05:02.767
These cells here in pink
eventually differentiate

00:05:02.767 --> 00:05:05.980
into the cells in the brain.

00:05:05.980 --> 00:05:07.772
These cells here eventually differentiate

00:05:07.772 --> 00:05:09.270
into the cells into the lungs,

00:05:09.270 --> 00:05:10.669
and obviously at this scale,

00:05:10.669 --> 00:05:13.223
the cells are way too small to even see.

00:05:13.223 --> 00:05:16.502
These cells differentiate into the cells

00:05:16.502 --> 00:05:18.443
of the heart.

00:05:18.443 --> 00:05:21.188
Now, I want to draw an
important distinction here.

00:05:21.188 --> 00:05:23.397
Because most of the cells that I've just

00:05:23.397 --> 00:05:26.529
depicted here that are
just a product of mitosis,

00:05:26.529 --> 00:05:28.339
these are your, I guess you could say

00:05:28.339 --> 00:05:29.609
these are your body cells,

00:05:29.609 --> 00:05:31.586
or these are your somatic cells.

00:05:31.586 --> 00:05:34.849
So these, all of these
cells that I'm pointing out

00:05:34.849 --> 00:05:37.273
in your heart, your lung, your brain,

00:05:37.273 --> 00:05:40.633
these are somatic cells, or body cells.

00:05:40.633 --> 00:05:41.946
Somatic cells.

00:05:42.427 --> 00:05:43.428
And so you're probably wondering,

00:05:43.428 --> 00:05:45.689
well how do I eventually get these

00:05:45.689 --> 00:05:47.090
haploid number cells?

00:05:47.090 --> 00:05:48.632
How do I eventually get,

00:05:48.632 --> 00:05:50.037
if I'm talking about a male,

00:05:50.037 --> 00:05:52.626
how do I eventually get
these haploid sex cells,

00:05:52.626 --> 00:05:54.407
these gametes, these sperm cells?

00:05:54.407 --> 00:05:56.375
I'm talking about a
female, how do I eventually

00:05:56.375 --> 00:05:58.436
get these ova, these egg cells

00:05:58.436 --> 00:06:00.273
that have a haploid number?

00:06:00.273 --> 00:06:03.069
And the way that happens
is some of these cells

00:06:03.069 --> 00:06:07.642
up here are going to
differentiate into germ cells.

00:06:07.642 --> 00:06:10.185
So they're going to
differentiate into germ cells.

00:06:10.185 --> 00:06:14.974
In the case of, and they're
going to differentiate

00:06:14.974 --> 00:06:16.516
when I say into germ cells,

00:06:16.516 --> 00:06:18.464
they're going to differentiate
into your gonads.

00:06:18.464 --> 00:06:24.270
In the case of a female,
the gonads are the ovaries.

00:06:28.044 --> 00:06:32.253
And in the case of a male,
the gonads are the testes.

00:06:32.307 --> 00:06:34.430
The gonads are the testes.

00:06:35.481 --> 00:06:38.371
And the germ cells in the gonads

00:06:38.371 --> 00:06:42.518
or the cells that have differentiated into

00:06:42.518 --> 00:06:44.768
being part of the testes and ovaries,

00:06:44.768 --> 00:06:46.404
those germ cells.

00:06:46.404 --> 00:06:51.197
So we differentiate
them from somatic cells.

00:06:51.197 --> 00:06:52.918
So there are germ cells there.

00:06:52.977 --> 00:06:56.421
Germ cells in your ovaries and testes.

00:06:56.628 --> 00:07:00.315
They, through the process of meiosis,

00:07:00.315 --> 00:07:02.656
they through the process of meiosis,

00:07:02.656 --> 00:07:05.069
can produce the gametes.

00:07:05.069 --> 00:07:07.775
So if you're female you're
going to produce eggs.

00:07:07.775 --> 00:07:11.599
If you're male you're
going to produce sperm.

00:07:11.861 --> 00:07:14.807
But this is through
the process of meiosis.

00:07:15.323 --> 00:07:18.517
Meiosis you're going to produce sperm

00:07:18.517 --> 00:07:19.911
in the case of a man,

00:07:19.911 --> 00:07:23.046
and you're going to produce ova

00:07:23.046 --> 00:07:25.735
in the case of a female.

00:07:25.906 --> 00:07:27.571
And this brings up a
really interesting thing,

00:07:27.571 --> 00:07:30.075
because throughout biology
we talk about mutations

00:07:30.075 --> 00:07:33.728
and natural selection and whatever else.

00:07:33.728 --> 00:07:37.674
And it's important to
realize how mutations

00:07:37.674 --> 00:07:41.013
may affect you and your offspring.

00:07:41.286 --> 00:07:42.575
So if you have a mutation

00:07:42.575 --> 00:07:44.485
in one of the somatic cells here,

00:07:44.485 --> 00:07:47.634
let's say in a skin cell, or in you brain,

00:07:47.634 --> 00:07:49.418
or in the heart,

00:07:49.418 --> 00:07:53.891
that may affect your ability to, you know,

00:07:53.891 --> 00:07:55.450
especially if God forbid it's a really

00:07:55.450 --> 00:07:57.026
dangerous thing like cancer,

00:07:57.026 --> 00:07:58.606
and it happens when you're young,

00:07:58.606 --> 00:08:00.193
before you've had a chance to reproduce

00:08:00.193 --> 00:08:02.363
and you're not able to survive,

00:08:02.363 --> 00:08:05.653
that might affect your
ability to reproduce.

00:08:05.653 --> 00:08:07.738
But if this is happening
in a somatic cell,

00:08:07.738 --> 00:08:10.436
it's not going to affect the DNA make-up

00:08:10.436 --> 00:08:12.519
of what you pass on.

00:08:12.519 --> 00:08:14.948
The DNA make-up of what you pass on,

00:08:14.948 --> 00:08:17.130
that's determined by what's going on

00:08:17.130 --> 00:08:18.966
in the gametes.

00:08:18.966 --> 00:08:23.018
So a mutation, if on the
way to differentiating

00:08:23.018 --> 00:08:25.470
into gametes a mutation happens,

00:08:25.470 --> 00:08:28.118
so if one of these mutate

00:08:28.118 --> 00:08:30.448
and then keep replicating,

00:08:30.448 --> 00:08:32.562
so let's say there's a mutation here,

00:08:32.562 --> 00:08:33.819
and they keep replicating and

00:08:33.819 --> 00:08:36.605
they differentiate into the germ cells

00:08:36.605 --> 00:08:37.964
the mutation is right over there,

00:08:37.964 --> 00:08:40.154
then through meiosis that produces

00:08:40.154 --> 00:08:42.090
some mutated sperm.

00:08:42.090 --> 00:08:46.001
Then that would pass on to your, well,

00:08:46.001 --> 00:08:48.535
that has a chance of
passing on to your children.

00:08:48.535 --> 00:08:50.178
Because once again, it might not be

00:08:50.178 --> 00:08:52.269
all of the sperm cells
that have that mutation.

00:08:52.269 --> 00:08:54.501
It could be only a handful of the

00:08:54.501 --> 00:08:58.411
two to three hundred
million of the sperm cells,

00:08:58.411 --> 00:09:01.542
and so if that mutation
somehow makes it harder

00:09:01.542 --> 00:09:03.343
for some of the sperm cells

00:09:03.343 --> 00:09:06.299
to kind of function,
either fuse with an egg

00:09:06.299 --> 00:09:09.391
or even potentailly
develop and kind of swim

00:09:09.391 --> 00:09:12.918
through fluid, then it still might not be

00:09:12.918 --> 00:09:14.914
the thing that makes it.

00:09:14.914 --> 00:09:19.727
So mutations only affect your offspring

00:09:19.727 --> 00:09:24.202
in the situation where those, the cells

00:09:24.202 --> 00:09:26.496
in which they happen are
eventually differentiated

00:09:26.496 --> 00:09:29.747
into things, into gametes that you will

00:09:29.747 --> 00:09:33.245
pass on to your children.


Fertilization terminology: gametes, zygotes, haploid, diploid

WEBVTT
Kind: captions
Language: en

00:00:00.500 --> 00:00:02.310
Voiceover: So let's
talk a little bit about

00:00:02.310 --> 00:00:04.901
how we all came into being.

00:00:04.901 --> 00:00:08.568
What we see right over
here, this is a picture

00:00:08.568 --> 00:00:14.575
of a sperm cell fusing with an egg cell.

00:00:14.575 --> 00:00:17.502
So that's a sperm cell
and this is an egg cell

00:00:17.502 --> 00:00:21.244
or we could call this an ovum.

00:00:21.244 --> 00:00:23.907
And even this scene
depicted right over here,

00:00:23.907 --> 00:00:28.169
this is the end of an
epic competition because

00:00:28.169 --> 00:00:30.910
this sperm cell is one
of one of two to three

00:00:30.910 --> 00:00:36.179
hundred million that
is vying for this ovum.

00:00:36.179 --> 00:00:38.509
So there's two to three hundred
million of these characters

00:00:38.509 --> 00:00:43.369
and they're all vying
for this ovum and the one

00:00:43.369 --> 00:00:45.045
that you see that's about to fuse for it,

00:00:45.045 --> 00:00:47.575
this is the winner of this incredibly -

00:00:47.575 --> 00:00:49.701
remember two to three hundred,

00:00:49.701 --> 00:00:54.571
200 million to 300 million
sperm are trying to get here

00:00:54.571 --> 00:00:57.640
so this is a major
victory and to some degree

00:00:57.640 --> 00:01:00.703
we should all feel pretty
good about ourselves

00:01:00.703 --> 00:01:03.112
because we are all the by-product of that

00:01:03.112 --> 00:01:07.174
one in 200 to 300 million sperm cells

00:01:07.174 --> 00:01:11.700
that won this race getting
to our mother's ovum.

00:01:11.700 --> 00:01:15.876
So the sperm cell came from
our father and the egg cell,

00:01:15.876 --> 00:01:18.716
this is all happening
inside of our mothers,

00:01:18.716 --> 00:01:21.181
the egg cell is from our mother.

00:01:21.181 --> 00:01:22.972
Now, once this happens,

00:01:22.972 --> 00:01:24.911
let's talk a little bit
about the terminology.

00:01:24.911 --> 00:01:29.450
So once these two fuse, or
the process of them fusing,

00:01:29.450 --> 00:01:32.197
we call that fertilization.

00:01:33.167 --> 00:01:37.303
Fertilization.

00:01:39.238 --> 00:01:42.233
And it produces a cell
that then differentiates

00:01:42.233 --> 00:01:45.443
into all of the cells of our body,

00:01:45.443 --> 00:01:47.575
so you can imagine that this
is an important process.

00:01:47.575 --> 00:01:49.767
So let's make sure that we
understand the different

00:01:49.767 --> 00:01:53.042
terminology, the different
words for the different things

00:01:53.042 --> 00:01:56.837
that are acting in this process.

00:01:56.837 --> 00:02:01.844
So each of these sex cells,
I guess we could say,

00:02:01.844 --> 00:02:05.776
the sperm cell and the ovum,
these are each called gametes.

00:02:05.776 --> 00:02:11.305
So this right over here is a gamete

00:02:11.305 --> 00:02:13.312
and the ovum is a gamete,

00:02:13.312 --> 00:02:17.101
the egg cell is also a gamete.

00:02:17.101 --> 00:02:21.350
And as we'll see, each
gamete has half the number

00:02:21.350 --> 00:02:26.903
of chromosomes as your
body cells or most of

00:02:26.903 --> 00:02:30.445
the somatic cells of your body
so outside of your sex cells

00:02:30.445 --> 00:02:35.708
that might be in your
ovaries or your testes,

00:02:35.708 --> 00:02:38.498
depending on whether
you're male or female,

00:02:38.498 --> 00:02:40.644
these have half the number

00:02:40.644 --> 00:02:43.777
so let's dig a little bit
deeper into what I mean there.

00:02:43.777 --> 00:02:46.708
So let's just do a blow up

00:02:46.708 --> 00:02:51.438
of this sperm cell right over here,

00:02:51.438 --> 00:02:54.301
so a blow up of a sperm cell and I'm not

00:02:54.301 --> 00:02:56.301
going to draw it to scale,
you see the sperm cell

00:02:56.301 --> 00:02:58.242
is much smaller than the egg cell but just

00:02:58.242 --> 00:03:01.845
to get a sense, so let me draw the nucleus

00:03:01.845 --> 00:03:05.842
of this sperm cell, so just like that.

00:03:05.842 --> 00:03:08.378
If we're talking about a
human being, and I'm assuming

00:03:08.378 --> 00:03:10.433
you are a human being, so that might be

00:03:10.433 --> 00:03:13.567
of interest to you, this will have 23

00:03:13.567 --> 00:03:16.452
chromosomes from your
father so let's do them.

00:03:16.502 --> 00:03:18.969
One, two, three, four, five,
six, seven, eight, nine,

00:03:18.969 --> 00:03:22.325
10, 11, 12, 13, 14, 15,

00:03:22.325 --> 00:03:25.681
16, 17, 18, 19, 20, 21, 22

00:03:25.681 --> 00:03:29.370
and for the 23rd one, that's going to be

00:03:29.370 --> 00:03:31.504
your sex-determining chromosome

00:03:31.504 --> 00:03:34.378
so if your father contributes an x,

00:03:34.378 --> 00:03:36.641
you are going to be female,

00:03:36.641 --> 00:03:39.580
if your father contributes a y,

00:03:39.580 --> 00:03:42.300
you are going to be male.

00:03:42.300 --> 00:03:44.638
So these are the chromosomes in

00:03:44.638 --> 00:03:47.365
the male gamete or I guess
I should say the gamete

00:03:47.365 --> 00:03:50.175
that your father's
contributing, the sperm.

00:03:50.175 --> 00:03:53.902
So this is a gamete right
over here and that's going to

00:03:53.902 --> 00:03:57.908
fuse with the egg, the ovum
that your mother is contributing

00:03:57.908 --> 00:04:00.577
and once again, I'm not
drawing that to scale.

00:04:00.577 --> 00:04:06.247
So this is the egg, and
let me draw it's nucleus.

00:04:06.247 --> 00:04:07.510
So that's it's nucleus, once again

00:04:07.510 --> 00:04:09.648
none of this is drawn to scale.

00:04:09.648 --> 00:04:12.441
And your mother is also going
to contribute 23 chromosomes.

00:04:12.441 --> 00:04:15.646
So one, two, three, four,
five, six, seven, eight, nine,

00:04:15.646 --> 00:04:17.635
10, 11, 12, 13, 14, 15,

00:04:17.635 --> 00:04:21.443
16, 17, 18, 19, 20, 21, 22

00:04:21.443 --> 00:04:25.174
and then she will
contribute an x chromosome

00:04:25.174 --> 00:04:28.177
for the sex determining
so your sex determining

00:04:28.177 --> 00:04:30.978
chromosomes are going to be
xy, you're going to be male,

00:04:30.978 --> 00:04:33.970
if this was xx, you're going to be female

00:04:33.970 --> 00:04:36.514
so this is also a gamete here.

00:04:36.514 --> 00:04:41.441
So a gamete is the general term
for either a sperm or an egg.

00:04:41.441 --> 00:04:49.647
Now once these two things
are fused, what do we have?

00:04:49.647 --> 00:04:53.247
Once they're fused,
then we're going to have

00:04:53.247 --> 00:04:55.379
you could say a fertilized egg

00:04:55.379 --> 00:04:57.109
but we are going to call that a zygote

00:04:57.109 --> 00:04:58.766
so let me draw that.

00:04:58.766 --> 00:05:00.513
I'm going to do this in a new color,

00:05:00.513 --> 00:05:02.108
and I'm running out of space
and I want this all to fit

00:05:02.108 --> 00:05:09.301
on the same screen so I'll
draw it not quite at scale

00:05:09.301 --> 00:05:11.244
and so let me draw the
nucleus of the zygote,

00:05:11.244 --> 00:05:13.839
I'm going to make the nucleus
fairly large so that we can

00:05:13.839 --> 00:05:15.377
focus on the chromosomes in it,

00:05:15.377 --> 00:05:17.512
once again none of this is drawn to scale.

00:05:17.512 --> 00:05:19.376
So you're going to have the 23 chromosomes

00:05:19.376 --> 00:05:22.310
from your father, so let me do that.

00:05:22.310 --> 00:05:28.241
One, two, three, four, five,
six, seven, eight, nine,

00:05:28.241 --> 00:05:31.372
10, 11, 12, 13, 14, 15,

00:05:31.372 --> 00:05:38.633
16, 17, 18, 19, 20, 21, 22 and 23,

00:05:38.633 --> 00:05:40.771
and then the 23 chromosomes
from your mother.

00:05:40.771 --> 00:05:48.589
One, two, three, four, five,
six, seven, eight, nine,

00:05:48.589 --> 00:05:53.578
10, 11, 12, 13, 14, 15,

00:05:53.578 --> 00:06:02.969
16, 17, 18, 19, 20, 21, 22 and 23

00:06:02.969 --> 00:06:05.773
so you got that x
chromosome from your mother.

00:06:05.773 --> 00:06:08.771
And as you might have notice,
I've drawn them in pairs

00:06:08.771 --> 00:06:10.841
so you now have a total,
let me make it clear,

00:06:10.841 --> 00:06:13.643
you have 23 chromosomes here,

00:06:13.643 --> 00:06:18.975
23 chromosomes in the sperm,

00:06:18.975 --> 00:06:25.512
you have 23 chromosomes in the egg

00:06:25.512 --> 00:06:30.444
and now you have 46 chromosomes
in the fertilized egg,

00:06:30.444 --> 00:06:33.846
46 chromosomes, and now that we have

00:06:33.846 --> 00:06:36.902
a full contingent of chromosomes

00:06:36.902 --> 00:06:39.707
and then this cell can
now keep replicating,

00:06:39.707 --> 00:06:41.707
keep splitting and
differentiating into all of what

00:06:41.707 --> 00:06:44.971
makes you, you, we call
this right over here,

00:06:44.971 --> 00:06:49.300
we call this a zygote.

00:06:49.300 --> 00:06:53.171
So one way to think about it,
the gametes are the sex cells

00:06:53.171 --> 00:06:55.371
that have half the number of chromosomes

00:06:55.371 --> 00:06:58.370
and the zygote is the cell
that's now ready to differentiate

00:06:58.370 --> 00:07:01.909
into an actual organism
that has double the number

00:07:01.909 --> 00:07:04.367
or that has a full
contingency of chromosomes,

00:07:04.367 --> 00:07:07.500
that has 46 chromosomes, and you see that

00:07:07.500 --> 00:07:09.433
I've made them in pairs and these pairs,

00:07:09.433 --> 00:07:11.166
we call these homologous pairs

00:07:11.166 --> 00:07:12.779
and in each of these pairs,

00:07:12.779 --> 00:07:25.179
this is a pair of homologous chromosomes.

00:07:25.179 --> 00:07:26.835
So what does that mean?

00:07:26.835 --> 00:07:29.448
Well that means that in
general, these two chromosomes,

00:07:29.448 --> 00:07:32.109
you got one from your
father, one from your mother,

00:07:32.109 --> 00:07:36.578
they code for the same
things, they code for the same

00:07:36.578 --> 00:07:39.774
proteins but there are different
variants of how they code

00:07:39.774 --> 00:07:43.579
for those proteins, those
traits that you have

00:07:43.579 --> 00:07:46.236
so gross oversimplification is,

00:07:46.236 --> 00:07:52.901
let's say that there is a gene on,

00:07:52.901 --> 00:07:56.367
that one from your father
that helps code for hair color

00:07:56.367 --> 00:07:57.970
well there would be a similar,

00:07:57.970 --> 00:08:00.372
there would be another
variant of that gene

00:08:00.372 --> 00:08:02.512
on the chromosome from your mother

00:08:02.512 --> 00:08:05.038
that helps code for hair color as well.

00:08:05.038 --> 00:08:06.713
So these are homologous chromosomes,

00:08:06.713 --> 00:08:10.178
these two chromosomes code, in general,

00:08:10.178 --> 00:08:13.843
for the same things and
so the zygote now has,

00:08:13.843 --> 00:08:16.437
you could say it has 46
chromosomes or you could say

00:08:16.437 --> 00:08:20.444
it has 23 pairs of homologous chromosomes.

00:08:20.444 --> 00:08:23.312
And this is, once again, this
is the case for human beings.

00:08:23.312 --> 00:08:25.501
If we're talking about some
other species, instead of

00:08:25.501 --> 00:08:29.238
23 pairs of homologous
chromosomes or 46 chromosomes

00:08:29.238 --> 00:08:31.840
in total, you might be
talking about 10 pairs of

00:08:31.840 --> 00:08:36.509
homologous chromosomes with
20 chromosomes in general.

00:08:36.509 --> 00:08:41.707
Now to help biologists, to
help clarify when they're

00:08:41.707 --> 00:08:43.173
talking about the number
of chromosomes for

00:08:43.173 --> 00:08:46.236
a given species, they introduce two words,

00:08:46.236 --> 00:08:49.433
haploid and diploid.

00:08:49.433 --> 00:08:52.506
And haploid is referring
to when you have half

00:08:52.506 --> 00:08:56.174
the full contingency of chromosomes.

00:08:56.174 --> 00:09:01.307
So for human beings, the
haploid number is 23.

00:09:01.307 --> 00:09:11.771
So, this is the haploid number, it is 23.

00:09:11.771 --> 00:09:14.233
For another species it
would be something else

00:09:14.233 --> 00:09:18.770
and haploid is based on the prefix "hapl",

00:09:18.770 --> 00:09:24.041
that's the prefix for single,
so you have a single member

00:09:24.041 --> 00:09:25.645
I guess you could think of it,

00:09:25.645 --> 00:09:29.240
of each of the pairs and now you have both

00:09:29.240 --> 00:09:32.845
of each pair, you have
both chromosomes in each

00:09:32.845 --> 00:09:37.512
pair or you have the full
contingency and this 46 chromosomes,

00:09:37.512 --> 00:09:45.033
this is called the
diploid number for humans.

00:09:45.033 --> 00:09:47.448
The diploid number right over here.

00:09:47.448 --> 00:09:49.776
And when people talk in general,
and we will speak in general

00:09:49.776 --> 00:09:52.633
when we start talking
about mitosis and meiosis

00:09:52.633 --> 00:09:55.911
for a given species they will
refer to the haploid number,

00:09:55.911 --> 00:09:59.042
they will refer to the haploid
number as n chromosomes

00:09:59.042 --> 00:10:01.839
and they will refer to the
diploid number as just twice that,

00:10:01.839 --> 00:10:04.979
as two n chromosomes.

00:10:04.979 --> 00:10:08.380
So hopefully this gets you familiar
with some of the vocabulary

00:10:08.380 --> 00:10:11.705
around fertilization
and haploid and diploid

00:10:11.705 --> 00:10:14.577
and zygotes and gametes
and also makes you feel

00:10:14.577 --> 00:10:17.777
a little bit better about
yourself that, just to exist,

00:10:17.777 --> 00:10:20.903
at least half of your
chromosomes had to win

00:10:20.903 --> 00:10:24.903
an incredibly competitive race.