1
00:00:11,000 --> 00:00:13,280
PROFESSOR: So let's think
of a specific virus,

2
00:00:13,280 --> 00:00:17,670
the coronavirus, including
the case of interest today,

3
00:00:17,670 --> 00:00:21,920
which is the SARS-CoV-2
novel coronavirus.

4
00:00:21,920 --> 00:00:26,210
So this virus comes
in the form of virion,

5
00:00:26,210 --> 00:00:29,390
which is the capsid
containing RNA, which

6
00:00:29,390 --> 00:00:31,940
is then going to infect a cell.

7
00:00:31,940 --> 00:00:37,700
And the size of that virion is
around 120 nanometer diameter,

8
00:00:37,700 --> 00:00:40,980
and it's nearly
a perfect sphere.

9
00:00:40,980 --> 00:00:46,320
Now, the size here of 120
nanometers compared to bacteria

10
00:00:46,320 --> 00:00:55,550
is about 1,000 times
smaller than [some] bacteria.

11
00:00:55,550 --> 00:00:58,720
So this actually has
a very big implication

12
00:00:58,720 --> 00:01:03,790
in terms of how a virion can
be spread from one organism

13
00:01:03,790 --> 00:01:04,370
to another.

14
00:01:04,370 --> 00:01:05,890
So the bacteria,
if you recall, are

15
00:01:05,890 --> 00:01:07,480
the size of several microns.

16
00:01:07,480 --> 00:01:10,690
That's the scale of large
droplets, which sediment --

17
00:01:10,690 --> 00:01:12,250
or larger than that,
they would begin

18
00:01:12,250 --> 00:01:13,700
to sediment out of the air.

19
00:01:13,700 --> 00:01:16,600
And we can think about
transmission through coughing.

20
00:01:16,600 --> 00:01:19,510
Also, besides the fact that
the virus is much smaller,

21
00:01:19,510 --> 00:01:20,380
it cannot swim.

22
00:01:24,970 --> 00:01:28,060
So bacteria have various
means of locomotion -- cilia,

23
00:01:28,060 --> 00:01:32,380
flagella, et cetera, whereas
the virion essentially

24
00:01:32,380 --> 00:01:34,060
is a little hard sphere.

25
00:01:34,060 --> 00:01:37,430
So how can a virion
actually transmit itself?

26
00:01:37,430 --> 00:01:41,789
Well, if we draw
a droplet, which

27
00:01:41,789 --> 00:01:47,250
is released by
respiration, then the virus

28
00:01:47,250 --> 00:01:51,780
is actually extremely small, at
the scale of typical droplets

29
00:01:51,780 --> 00:01:55,509
that come from respiration,
which, as we've discussed,

30
00:01:55,509 --> 00:01:58,770
have a typical, most
probable size around half

31
00:01:58,770 --> 00:02:01,740
a micron, and then
have mostly droplets

32
00:02:01,740 --> 00:02:03,610
that are larger than that.

33
00:02:03,610 --> 00:02:07,440
So at that scale, if we think of
this as a micron scale droplet,

34
00:02:07,440 --> 00:02:10,470
this little virus
is extremely small.

35
00:02:10,470 --> 00:02:13,270
It's like a little
point, essentially.

36
00:02:13,270 --> 00:02:17,230
And so a single droplet may
contain a couple viruses,

37
00:02:17,230 --> 00:02:19,860
a couple virions.

38
00:02:19,860 --> 00:02:24,060
And so in order for the
virion to escape the droplet

39
00:02:24,060 --> 00:02:27,930
and make connection
with a cell in a host,

40
00:02:27,930 --> 00:02:30,670
let's say it's been breathed
in, and in the lungs,

41
00:02:30,670 --> 00:02:32,340
it's going to try to
meet with some cell

42
00:02:32,340 --> 00:02:33,900
and begin to infect it.

43
00:02:33,900 --> 00:02:38,040
Or conversely, if the virion
is being shed and released

44
00:02:38,040 --> 00:02:40,440
from an infected
cell and then needs

45
00:02:40,440 --> 00:02:43,200
to go into a droplet to
then be exhaled and spread

46
00:02:43,200 --> 00:02:46,170
to somebody else,
either way, the virion

47
00:02:46,170 --> 00:02:48,220
has to get in and
out of this droplet.

48
00:02:48,220 --> 00:02:51,240
And since it cannot swim,
the only way can do it is

49
00:02:51,240 --> 00:02:54,780
by essentially a random
walk or a diffusion process,

50
00:02:54,780 --> 00:02:57,360
where it's just bouncing around
due to thermal fluctuations.

51
00:02:57,360 --> 00:03:02,040
And eventually, at some
point, it gets out.

52
00:03:02,040 --> 00:03:09,640
So the diffusion process -- we
can estimate the typical time

53
00:03:09,640 --> 00:03:10,140
to escape.

54
00:03:13,500 --> 00:03:16,650
I'll write it this way --

55
00:03:16,650 --> 00:03:20,730
[it] can be shown if the
radius of the droplet

56
00:03:20,730 --> 00:03:25,710
is R, the average
time for a randomly

57
00:03:25,710 --> 00:03:28,680
distributed and selected virion
anywhere in this droplet,

58
00:03:28,680 --> 00:03:32,280
the time for it to escape is
of order R squared over D,

59
00:03:32,280 --> 00:03:34,260
where D if the diffusivity.

60
00:03:34,260 --> 00:03:37,350
And if you do a precise
calculation for a sphere,

61
00:03:37,350 --> 00:03:41,030
then there's a
factor of 15 here.

62
00:03:41,030 --> 00:03:52,470
And so that is basically average
escape time by diffusion.

63
00:03:57,320 --> 00:03:59,680
So that gives you a sense
of how quickly the virion is

64
00:03:59,680 --> 00:04:01,390
able to get out of the cell --

65
00:04:04,660 --> 00:04:07,060
or out of the
droplet, excuse me.

66
00:04:07,060 --> 00:04:10,000
Now, how big is the diffusivity?

67
00:04:10,000 --> 00:04:14,680
Well, the diffusivity
of the virus,

68
00:04:14,680 --> 00:04:16,810
if you think of it just
as a fluctuating sphere

69
00:04:16,810 --> 00:04:21,899
in a viscous medium, then we can
use the Stokes-Einstein formula

70
00:04:21,899 --> 00:04:25,940
for the diffusivity,
which is k_B*T,

71
00:04:25,940 --> 00:04:28,950
where k is Boltzmann constant
and T is the temperature.

72
00:04:28,950 --> 00:04:32,100
So k*T is the thermal
energy of the fluctuations.

73
00:04:32,100 --> 00:04:38,940
And that's divided by 6*pi
times the radius of the virus,

74
00:04:38,940 --> 00:04:43,950
and then the viscosity
of the liquid or fluid

75
00:04:43,950 --> 00:04:45,480
containing the droplet.

76
00:04:45,480 --> 00:04:47,340
So essentially, this
denominator here

77
00:04:47,340 --> 00:04:50,580
is the Stokes drag coefficient
for a sphere fluctuating

78
00:04:50,580 --> 00:04:52,650
in a viscous medium.

79
00:04:52,650 --> 00:04:54,030
So that's the diffusivity.

80
00:04:54,030 --> 00:04:58,470
And if you figure out for the
size of 120 nanometers, if we

81
00:04:58,470 --> 00:05:02,040
use the viscosity of water, if
we assume the droplets are just

82
00:05:02,040 --> 00:05:08,280
water, then this is
3.6e-8 centimeters

83
00:05:08,280 --> 00:05:12,270
squared per second
in water, where

84
00:05:12,270 --> 00:05:15,920
we use the viscosity of water.

85
00:05:15,920 --> 00:05:18,500
But the droplets
are not just water.

86
00:05:18,500 --> 00:05:19,610
In fact, they cannot be.

87
00:05:19,610 --> 00:05:22,460
As we've already discussed,
water droplets at this size

88
00:05:22,460 --> 00:05:26,120
range would very quickly
evaporate and disappear,

89
00:05:26,120 --> 00:05:28,400
or they would leave
the virus essentially,

90
00:05:28,400 --> 00:05:32,990
a virion no longer
contained in such a droplet.

91
00:05:32,990 --> 00:05:38,150
So what's more typical is
that the droplet in fact

92
00:05:38,150 --> 00:05:40,670
contains many
macromolecules and is

93
00:05:40,670 --> 00:05:46,280
coming from mucus in the
pharynx, in the vocal cords,

94
00:05:46,280 --> 00:05:48,680
coming from the lungs directly.

95
00:05:48,680 --> 00:05:51,590
And mucus has a much
higher viscosity.

96
00:05:51,590 --> 00:05:54,260
So notice, here, we
have the viscosity

97
00:05:54,260 --> 00:05:55,790
of the liquid coming in.

98
00:05:55,790 --> 00:05:57,710
And if we take into
account the fact

99
00:05:57,710 --> 00:06:03,260
that the viscosity of mucus
relative to the viscosity

100
00:06:03,260 --> 00:06:07,220
of water is roughly --

101
00:06:07,220 --> 00:06:09,890
it depends where the
samples are taken

102
00:06:09,890 --> 00:06:11,180
and also what's the shear rate.

103
00:06:11,180 --> 00:06:12,770
So we're talking
about low shear rate.

104
00:06:12,770 --> 00:06:14,120
These are sort of moving slowly.

105
00:06:14,120 --> 00:06:16,100
The viscosity of
mucus is dependent

106
00:06:16,100 --> 00:06:18,060
how quickly you're shearing it.

107
00:06:18,060 --> 00:06:23,240
But if it's a low shear rate,
then this is on the order of

108
00:06:23,240 --> 00:06:28,340
1e3 to 1e5 at low shear rates.

109
00:06:34,900 --> 00:06:40,330
And because the viscosity
has that factor,

110
00:06:40,330 --> 00:06:43,730
the diffusivity is then
divided by that factor.

111
00:06:43,730 --> 00:06:46,030
So what that's telling us is
instead of being around

112
00:06:46,030 --> 00:06:48,730
1e-8 centimeters
squared per second,

113
00:06:48,730 --> 00:06:51,670
we're really looking at
more like 1e-11

114
00:06:51,670 --> 00:06:54,430
1e-13 centimeters

115
00:06:54,430 --> 00:06:58,190
squared per second in mucus.

116
00:06:58,190 --> 00:07:00,400
So we assume these are
actually mucus droplets, which

117
00:07:00,400 --> 00:07:05,500
are not fully evaporating and
are contained in aerosol form,

118
00:07:05,500 --> 00:07:07,390
then this is the
kind of diffusivity.

119
00:07:07,390 --> 00:07:09,310
And if we plug into
this formula here,

120
00:07:09,310 --> 00:07:12,990
we can get a sense of what is
the average time for the virion

121
00:07:12,990 --> 00:07:14,740
to actually escape.

122
00:07:14,740 --> 00:07:32,680
So why don't we make a
little table of that result.

123
00:07:32,680 --> 00:07:37,050
So let's look at the radius.

124
00:07:37,050 --> 00:07:41,880
First, let's consider here 0.5
microns, or 500 nanometers.

125
00:07:41,880 --> 00:07:45,180
So that would be a
1-micron diameter droplet.

126
00:07:45,180 --> 00:07:48,090
So that would be kind of a
typical aerosol droplet coming

127
00:07:48,090 --> 00:07:49,320
from breathing.

128
00:07:49,320 --> 00:07:51,500
Let's also consider
larger droplets.

129
00:07:51,500 --> 00:07:52,980
So let's look at
5 microns, which

130
00:07:52,980 --> 00:07:55,740
is kind of on the upper
end of the aerosol range.

131
00:07:55,740 --> 00:07:59,159
And then we could
look at 50 microns.

132
00:07:59,159 --> 00:08:01,740
And I should say this
is R of the drop.

133
00:08:01,740 --> 00:08:04,530
So the R here, just to be
careful, is they R of the drop,

134
00:08:04,530 --> 00:08:09,330
as opposed to the R of
the virus, which is R_v

135
00:08:09,330 --> 00:08:17,270
is half d, so that's
60 nanometers.

136
00:08:17,270 --> 00:08:19,670
OK, so that's the diameter.

137
00:08:19,670 --> 00:08:21,800
So this is the different
size of the drops.

138
00:08:21,800 --> 00:08:26,870
And just for comparison, let's
look at water versus mucus.

139
00:08:26,870 --> 00:08:28,680
And from mucus,
why don't we take

140
00:08:28,680 --> 00:08:35,520
that the viscosity of the
mucus is 1e4 times

141
00:08:35,520 --> 00:08:37,169
the viscosity of water?

142
00:08:37,169 --> 00:08:40,480
So we just pick something kind
of in the middle of this range.

143
00:08:40,480 --> 00:08:43,000
OK, well, if we plug
in then the numbers

144
00:08:43,000 --> 00:08:47,530
and we try to plot the average
escape time that I've just

145
00:08:47,530 --> 00:08:51,250
written here, R^2/(15*D),
then in water,

146
00:08:51,250 --> 00:08:54,820
this turns out to be
about 5 milliseconds

147
00:08:54,820 --> 00:08:56,290
for an aerosol droplet.

148
00:08:56,290 --> 00:08:58,960
So we know the aerosol droplets
are evaporating quickly

149
00:08:58,960 --> 00:09:00,850
and also that a
virus can diffuse out

150
00:09:00,850 --> 00:09:03,280
of it relatively quickly,
because the water is not

151
00:09:03,280 --> 00:09:04,510
really that this.

152
00:09:04,510 --> 00:09:06,820
Now, if we move
in this direction,

153
00:09:06,820 --> 00:09:09,400
we're multiplying R by 10.

154
00:09:09,400 --> 00:09:12,230
And notice, the time scale
goes like R^2.

155
00:09:12,230 --> 00:09:14,350
So there is a pretty
strong size dependence.

156
00:09:14,350 --> 00:09:17,380
So as we think of a 10
times larger droplet,

157
00:09:17,380 --> 00:09:19,610
it's 100 times longer time.

158
00:09:19,610 --> 00:09:25,750
So that would be 500
milliseconds, or 0.5 seconds.

159
00:09:25,750 --> 00:09:27,610
And if we go another
factor of 10,

160
00:09:27,610 --> 00:09:29,410
that's another factor
of 100 in time.

161
00:09:29,410 --> 00:09:32,410
And if we convert
seconds to minutes,

162
00:09:32,410 --> 00:09:34,960
it turns out to be
around 8 minutes

163
00:09:34,960 --> 00:09:37,150
for a fairly large drop.

164
00:09:37,150 --> 00:09:39,010
Now, what if we're in a mucus?

165
00:09:39,010 --> 00:09:41,500
So now, we go in this direction.

166
00:09:41,500 --> 00:09:46,940
The timescale goes like 1/D, and
D goes like 1 over viscosity.

167
00:09:46,940 --> 00:09:49,590
So the timescale is
proportional to viscosity.

168
00:09:49,590 --> 00:09:52,390
So we're getting this
factor of 1e4.

169
00:09:52,390 --> 00:09:55,800
That's a pretty big factor.

170
00:09:55,800 --> 00:09:59,290
And so, for example, this
5 milliseconds for mucus

171
00:09:59,290 --> 00:10:01,390
can turn into 1 minute.

172
00:10:01,390 --> 00:10:03,550
So from an aerosol
droplet, which

173
00:10:03,550 --> 00:10:08,200
is sort of at the most probable
size from respiration, which

174
00:10:08,200 --> 00:10:11,300
is on the order of a
little bit below 1 micron,

175
00:10:11,300 --> 00:10:14,170
a typical virion would
take about a minute

176
00:10:14,170 --> 00:10:18,910
to diffuse out of that droplet
and infect a nearby cell

177
00:10:18,910 --> 00:10:20,900
or tissue.

178
00:10:20,900 --> 00:10:24,010
Now, if we look at a little bit
bigger droplets, this 1 minute,

179
00:10:24,010 --> 00:10:26,170
we multiply by 100,
it's 100 minutes, which

180
00:10:26,170 --> 00:10:30,150
is on the order of 1.5 hours.

181
00:10:30,150 --> 00:10:33,180
And what if we keep going
another factor of 100?

182
00:10:33,180 --> 00:10:37,110
That turns into around 7 days.

183
00:10:37,110 --> 00:10:40,220
So if the virion is contained
in one of the larger droplets

184
00:10:40,220 --> 00:10:42,350
that comes from
coughing or sneezing,

185
00:10:42,350 --> 00:10:46,850
it could take it hours to days
to escape from that droplet

186
00:10:46,850 --> 00:10:50,760
and have any chance of
infecting a host cell.

187
00:10:50,760 --> 00:10:53,150
So you can immediately see
the problem for a virus

188
00:10:53,150 --> 00:10:55,880
in terms of transmitting
is it can't swim.

189
00:10:55,880 --> 00:10:57,560
It's extremely small.

190
00:10:57,560 --> 00:11:00,320
And so it's not a good
way to transmit itself

191
00:11:00,320 --> 00:11:03,740
to be sitting in a large
droplet or a pool of liquid,

192
00:11:03,740 --> 00:11:06,770
imagine a pool of
saliva or some phlegm

193
00:11:06,770 --> 00:11:08,600
that you've just
coughed up, which

194
00:11:08,600 --> 00:11:10,970
is very common for
bacterial transmission.

195
00:11:10,970 --> 00:11:12,790
For a virus, it's
much more difficult

196
00:11:12,790 --> 00:11:16,520
for a significant amount of
virus to actually get out.

197
00:11:16,520 --> 00:11:19,070
So if the virus is going
to transmit itself,

198
00:11:19,070 --> 00:11:22,440
it makes a lot more sense
to be in aerosol droplets.

199
00:11:22,440 --> 00:11:28,480
And so it's really here,
the aerosol droplets

200
00:11:28,480 --> 00:11:35,970
are the most infectious,
because basically,

201
00:11:35,970 --> 00:11:37,060
the virus able to get out.

202
00:11:37,060 --> 00:11:40,190
And based on this
calculation, roughly speaking,

203
00:11:40,190 --> 00:11:45,790
if R of the droplet, which
we're just calling R,

204
00:11:45,790 --> 00:11:48,850
if R is less than
around 5 microns,

205
00:11:48,850 --> 00:11:50,590
those are the ones
we would expect

206
00:11:50,590 --> 00:11:52,900
to be the most infectious.

207
00:11:52,900 --> 00:11:54,760
And interestingly
for SARS-CoV-2,

208
00:11:54,760 --> 00:11:58,540
recent experiments have sampled
droplets from sick patients

209
00:11:58,540 --> 00:12:01,570
with COVID-19 at
different sizes.

210
00:12:01,570 --> 00:12:04,390
And it was found that
the droplets that

211
00:12:04,390 --> 00:12:09,160
had a diameter less
than about 4 microns

212
00:12:09,160 --> 00:12:11,260
were the most infectious
and clearly you

213
00:12:11,260 --> 00:12:15,880
could see replication
of the viral RNA

214
00:12:15,880 --> 00:12:18,430
in samples of those
droplets, whereas larger

215
00:12:18,430 --> 00:12:20,740
droplets in this
range here, kind

216
00:12:20,740 --> 00:12:25,660
of larger than a few microns,
were less infectious.

217
00:12:25,660 --> 00:12:28,420
And in fact, the virus was
less able to replicate.

218
00:12:28,420 --> 00:12:32,570
So it's kind of consistent
with this physical argument.

219
00:12:32,570 --> 00:12:36,350
So basically what we
would probably say

220
00:12:36,350 --> 00:12:44,150
is that in this range, the
virions are mostly trapped.

221
00:12:44,150 --> 00:12:47,570
They have a hard time
getting out of those droplets

222
00:12:47,570 --> 00:12:53,180
and can deactivate over time,
because that's also happening.

223
00:12:53,180 --> 00:12:56,730
They are believed to have
a certain finite lifetime.

224
00:12:56,730 --> 00:12:59,570
And so this is the
case that the virions

225
00:12:59,570 --> 00:13:06,670
are trapped and deactivate in
large drops or the fomites,

226
00:13:06,670 --> 00:13:10,030
which are infectious residues
on surfaces that are left over

227
00:13:10,030 --> 00:13:11,860
from those droplets.

228
00:13:11,860 --> 00:13:13,840
So this really shows
us that our focus

229
00:13:13,840 --> 00:13:16,480
should be on looking
at aerosol droplets

230
00:13:16,480 --> 00:13:19,200
for viral transmission.