The real e-coli

CSGnet Archive CSG2000
1

[Martin Taylor 20000112 17:09]

We talk a lot about the e-coli method of approaching an optimum value
in a multidimensional space. The January 2000 issue of "Physics Today"
has an interesting article about how the real e-coli does it ["Motile
Behavior of Bacteria", Howard C. Berg, Physics Today, January 2000,
24-29]. There's too much to quote in detail, but here's a few tid-bits.

A single e-coli cell has six separate motors, each of which rotates
a helical "flagellum" that acts like a propellor on a small aircraft to
drive the cell in one direction or other. The motors can run clockwise
(CW) or counterclockwise (CCW). When the motors are running CW, they run
independently, and the cell moves erratically ("tumbles"). When the
motors run CCW, the filaments work as a bundle that drives the cell
in a steady forward motion ("runs"). If the cell is in a region of uniform
concentration of nutrients, these two types of motion alternate with
an exponential distribution of the time in each phase. (There's a 3-D
picture of such a track in the article). It doesn't matter what the
concentration is, the time distributions remain the same.

The real e-coli has limitations that the "e-coli method" does not have.
For one, the real e-coli has a limited memory for where it is heading,
and is subject to "Brownian" changes of direction even when it is "running".
So it tumbles even when heading up the gradient, and it runs when
heading down the gradient. The "method" does neither.

The exponential distribution of times has a slightly longer time
constant when the cell is moving up the gradient than when it is in
a uniform concentration, but the time constants are the same when it is
moving down the gradient as they are in a uniform concentration. It's
a one-sided control system, in that sense.

The operation is said to be like this: Aspartate is the nutrient in the
example described, but there are other chemoreceptors, which presumably
operate similarly. There's a chemical that tends to stabilize the CW
state (tumble), but it's an unstable chemical, being continuously built
and destroyed. Aspartate reception reduces the rate at which it is built,
thereby reducing the stability of the CW phase, and enhancing the
stability of the CCW (running) phase. So one would think that the more
aspartate the cell detects, the more it would run in the same direction
and the less it would tumble. But there is also another effect, which the
author calls adaptation, but we might call control.

The catalyst for the building of the CW-stabilizer has been reduced by
the aspartate, but it is involved in a negative feedback loop whereby it
inhibits its own production. Hence when it is disturbed by the aspartate,
it reduces the inhibition on its own production, and comes back to the
original level. This restores the CW-CCW balance, but it takes time
to do so.

In a uniform concentration, the adaptation balances the CW and CCW phases
at the same stability ratio no matter what level the concentration is at.
When the concentration is increasing, the rate of adaptation is slower
than the rate of destabilising the CW phase, so there is more "running"
and less "tumbling" until the concentration is no longer rising. In effect,
the cell compares the concentration "now" with the concentration "a moment
ago" and tumbles less if the concentration "now" is greater.

According to the article, there is no excess stabilisation of the CW
(tumble) phase when the concentration of aspartate is decreasing, though
one would think there should be.

There's lots more in the article, such as the mechanical construction of
the motors, and the torque-speed relations when e-coli is warm or cold,
and so forth. But I think the above is most of what might be marginally
relevant to CGSnet--just as a matter of interest. I think the "e-coli
method" probably works better than the e-coli bacterium!

There's no reference in the article to a Web site, though one would think
it a perfect subject for a very pretty one!

Martin

2

[From Rick Marken (2000.01.12.1550)]

Martin Taylor (20000112 17:09) --

The real e-coli has limitations that the "e-coli method" does not have.
For one, the real e-coli has a limited memory for where it is heading,
and is subject to "Brownian" changes of direction even when it is "running".
So it tumbles even when heading up the gradient, and it runs when
heading down the gradient. The "method" does neither.

Not true. See Marken & Powers, "Random-Walk Chemotaxis" in _Mind
Readings". The "method" (model) has no memory (or knowledge) of where
it is heading and it works when subject to "Brownian" disturbances
to its direction (see p. 101).

The other stuff in the article about the possible mechanisms of the
"tumbling" process are pretty interesting, though.

Best

Rick

ยทยทยท

---
Richard S. Marken Phone or Fax: 310 474-0313
Life Learning Associates mailto: rmarken@earthlink.net
http://home.earthlink.net/~rmarken

3

[Martin Taylor 20000112 23:01]

[From Rick Marken (2000.01.12.1550)]

Martin Taylor (20000112 17:09) --

> The real e-coli has limitations that the "e-coli method" does not have.
> For one, the real e-coli has a limited memory for where it is heading,
> and is subject to "Brownian" changes of direction even when it is
"running".
> So it tumbles even when heading up the gradient, and it runs when
> heading down the gradient. The "method" does neither.

Not true. See Marken & Powers, "Random-Walk Chemotaxis" in _Mind
Readings". The "method" (model) has no memory (or knowledge) of where
it is heading and it works when subject to "Brownian" disturbances
to its direction (see p. 101).

Are we talking about the same thing, here? My understanding of the "method"
was that the model e-coli moved in a straight line until it tumbles. Is
that wrong? The real e-coli may deviate by as much as 90 degrees from
its initial course along a single run before it happens to tumble.
That's
the sense in which it has a limited memory. The model remembers its
heading perfectly until it tumbles.

On re-reading the paper in Mind Readings, I can't see its relevance to
the question of direction change while "running". You point to p101,
but there's nothing about it there, or in the program on p92.

And unless I totally misread the paper, the model e-coli doesn't tumble
when it is going up the gradient, and it doesn't run when going down the
gradient. You say it does both. Maybe the paper needs rewriting to
make that clearer, and to show how the program on p92 is not the one
used in the model, because the program generates a tumble immediately
the e-coli starts going downgradient, and never tumbles when it is going
upgradient.

The other stuff in the article about the possible mechanisms of the
"tumbling" process are pretty interesting, though.

I think the author thinks it a bit more definite than a "possible"
mechanism. There's a nice mechanical drawing of the structure of the
motor, for example, as well as an electron micrograph of the base of the
rotor, and a description of the eight stator elements...and so on. The
chemical and genetic aspects are also described in enough detail and
with no hedging, so as to make one assume that they represent accepted
"facts." Whether they are true is another matter.

Martin

4

[From Bill Powers (2000.01.13.0836 MDT)]

[Martin Taylor 20000112 17:09]

I'm glad to see some independent confirmation concerning the E. coli
method, but your information is a bit inaccurate. Mine, by the way, came
from a book by Daniel Koshland (a former editor of Science and a
biochemist), _Bacterial Chemotaxis as a Model Behavioral System_ (New York:
Raven Press, 1980). Koshland did a good deal of the research himself.
Berg's report does not agree with Koshland's findings in several regards.

A single e-coli cell has six separate motors, each of which rotates
a helical "flagellum" that acts like a propellor on a small aircraft to
drive the cell in one direction or other. The motors can run clockwise
(CW) or counterclockwise (CCW). When the motors are running CW, they run
independently, and the cell moves erratically ("tumbles"). When the
motors run CCW, the filaments work as a bundle that drives the cell
in a steady forward motion ("runs").

According to Koshland: The flagellae work together for both forward and
reverse motion, although reverse motion is somewhat slower than forward.
The tumbles appear to take place near the switching point between forward
and reverse; I inferred that the exact switching point differed slightly
among flagellae, so when some were pushing while others were pulling,
tumbling took place. See Koshland, p. 52-53. Tumbling is definitely not
caused by reversing all the flagellae; that results in smooth backward
swimming.

If the cell is in a region of uniform
concentration of nutrients, these two types of motion alternate with
an exponential distribution of the time in each phase. (There's a 3-D
picture of such a track in the article). It doesn't matter what the
concentration is, the time distributions remain the same.

That's for uniform concentrations. In a gradient, the time between tumbles
varies about the mean time with the cross product of gradient and swimming
velocity.

The real e-coli has limitations that the "e-coli method" does not have.
For one, the real e-coli has a limited memory for where it is heading,
and is subject to "Brownian" changes of direction even when it is "running".
So it tumbles even when heading up the gradient, and it runs when
heading down the gradient. The "method" does neither.

As far as I can tell, the real E. coli has no memory at all for where it is
heading, and for that matter no perception of where it is heading to have a
memory of. Its only perceptual signal involved in steering, according to
Koshland, corresponds to the time rate of change of concentration at its
chemical receptors, or at the next stage inward. Certainly the model has no
such memory.

Actually, the original model did work just like the real E. coli: there was
a mean interval between tumbles which existed in a uniform concentration.
The interval was increased by swimming up the gradient and decreased by
swimming down it. A gain factor determined how much increase or decrease of
interval is produced by a given positive or negative time rate of change.
This gain factor was the only parameter that needed to be adjusted to match
the model to the observations.

A more efficient mode (in the model) turned out to make tumbling occur
whenever the time rate of concentration was decreasing, and never to occur
when it was increasing. This amounts simply to setting the gain of the real
system very high. It's also very easy to compute.

The exponential distribution of times has a slightly longer time
constant when the cell is moving up the gradient than when it is in
a uniform concentration, but the time constants are the same when it is
moving down the gradient as they are in a uniform concentration. It's
a one-sided control system, in that sense.

I don't know what that means. According to Koshland, when the rate of
change of concentration is varied, the percent of smooth swimming (measured
over times of 20 seconds to 2 minutes) can vary between 100% and 0%. See
plots on p. 87. So the exponential distribution of timesm, whatever that
means, has little relationship to the time spend swimming or tumbling,
evidently.

Koshland did many experiments with bacteria "tethered" in a gel, so he
could perfuse the medium with variable concentrations of attractants and
repellents, measuring the motion of the flagellae under a microscope. What
he saw was completely consistent with the free-swimming behavior.

The operation is said to be like this: Aspartate is the nutrient in the
example described, but there are other chemoreceptors, which presumably
operate similarly. There's a chemical that tends to stabilize the CW
state (tumble), but it's an unstable chemical, being continuously built
and destroyed. Aspartate reception reduces the rate at which it is built,
thereby reducing the stability of the CW phase, and enhancing the
stability of the CCW (running) phase. So one would think that the more
aspartate the cell detects, the more it would run in the same direction
and the less it would tumble. But there is also another effect, which the
author calls adaptation, but we might call control.

If you combine sensing a concentration and adaptation due to breakdown of
the chemical, you get time rate of change sensing. See Koshland's chapter 6
on "Adaptation" (p.107-125, esp. p. 122).

The catalyst for the building of the CW-stabilizer has been reduced by
the aspartate, but it is involved in a negative feedback loop whereby it
inhibits its own production. Hence when it is disturbed by the aspartate,
it reduces the inhibition on its own production, and comes back to the
original level. This restores the CW-CCW balance, but it takes time
to do so.

Frankly, that sounds like hogwash to me. What does "stablizing" the CW
rotation mean? I don't think Berg even has the facts right, but of course
that would be between him and Koshland (and the other workers Koshland
cites). Also, if CW and CCW were in balance, the bacterium would be
continuosly tumbling, wouldn't it?

In a uniform concentration, the adaptation balances the CW and CCW phases
at the same stability ratio no matter what level the concentration is at.
When the concentration is increasing, the rate of adaptation is slower
than the rate of destabilising the CW phase, so there is more "running"
and less "tumbling" until the concentration is no longer rising. In effect,
the cell compares the concentration "now" with the concentration "a moment
ago" and tumbles less if the concentration "now" is greater.

This might be fine if tumbling went with CW and running went with CCW
rotation of the flagellae. But I don't think there's even a chance that
this is correct. If you read Koshland, I think you'll agree: he would have
had to invent most of his data if what Berg says is true. I think Berg's
model is vague to the point of nonexistence, not to mention that it
represents a nonexistent phenomenon. do you have any reason to suppose that
Berg knows what he's talking about?

According to the article, there is no excess stabilisation of the CW
(tumble) phase when the concentration of aspartate is decreasing, though
one would think there should be.

Especially since it is observed that a negative time rate of change of
concentration of attractant (swimming down the gradient) decreases the
interval to the next tumble, while a positive rate of change increases it,
both relative to the rate in a uniform concentration. What would "excess
stabilization of the CW phase" mean?

There's lots more in the article, such as the mechanical construction of
the motors, and the torque-speed relations when e-coli is warm or cold,
and so forth. But I think the above is most of what might be marginally
relevant to CGSnet--just as a matter of interest. I think the "e-coli
method" probably works better than the e-coli bacterium!

I'm sure there is much interesting information in the article, but one has
to question the author's understanding of the material -- either that, or
Koshland's integrity.

You're quite right about the model working better than the bacterium -- the
gain in the model is far higher than in the bacterium. For reorganizing in
the manner I have proposed, it is more efficient. However, I wouldn't claim
that it is "better" in terms of E. coli's ecology. E. coli can approach and
avoid as many as 27 substances at the same time (according to Koshland),
and it may be quite necessary for the various control systems to operate
with less than maximum gain in order to make this possible.

There's no reference in the article to a Web site, though one would think
it a perfect subject for a very pretty one!

More to the point, is there any reference to Koshland's 1980 work?

Best,

Bill P.

5

[From Bill Powers (2000.01.13.0953 MDT)]

Martin Taylor 20000112 23:01--

Are we talking about the same thing, here? My understanding of the "method"
was that the model e-coli moved in a straight line until it tumbles. Is
that wrong? The real e-coli may deviate by as much as 90 degrees from
its initial course along a single run before it happens to tumble.
That's
the sense in which it has a limited memory. The model remembers its
heading perfectly until it tumbles.

The model remembers nothing. It operates according to Newton's laws, in the
sense that it continues in a straight line until some lateral force acts on
it. We could easily make it curve. Most bacteria swim in reasonably
straight lines. Some curve gradually. It makes essentially no difference in
the final behavior; the relationship of tumbling to time rate of change of
concentration is no different. The only detail that would be changed by a
curving bacterium is that the mean tumble rate would be _slightly_ higher,
since the path would not automatically continue up the gradient, once
started that way, in the absence of tumbling.

By the way, E. coli cannot coast. According to Koshland, after the
flagellae abruptly stop spinning, E. coli would coast no more than one
millionth of its body length, due to "the viscosity of the medium and the
low Reynolds number." Any curvature in the path must be due to a slight
cocking of the flagellae, or some asymmetry in their construction. The
motors necessarily turn at the same rate, because the flagellae coalesce
into a single spiral (whether going CW or CCW). If they turned at different
rates, they could not coalesce. Any departure from coalescence probably
produces countertorques that tend to synchronize the spinning.

Perhaps Berg, or someone he used as a reference, misconstrued the caption
of Fig. 9 on p. 5. This caption says "Tumbling causes by dispersion of
flagella bundle. On left, bacterium swims smoothly with flagella filaments
forming stable bundle. REVERSAL OF ROTATION DISPERSES BUNDLE, CAUSING
TUMBLING. [caps added]. As bacterium swims in new direction, bundle reforms
and bacterium swims smoothly again."

This could easily be miscontrued, by someone who only skimmed the rest of
the book, as saying that if the flagellae spin in the direction opposite to
normal, the flagellae disperse, causing tumbling. But that is not what it
means. It means that _during the process of reversal_ there is a stage when
the flagellae disperse and cause tumbling. If the reversal is complete, the
flagellae once again coalesce into a spiral, although with a somewhat
different configuration, and again produce smooth swimming, now backward
(the flagellae pull instead of pushing). My interpretation of this is that
near the reversal point, some flagellae reverse before others, and when
some are going CW while others are going CCW, they disperse and tumbling
occurs. The diagram on the next page (Fig. 10, p. 52) shows flagellar
rotation and structure arranged this way:

Smooth Swimming

Random (normal)

Tumbling

Random (inverse)

Inverse Smooth Swimming

from this I infer that tumbling occurs at the point just where the
"Relative level of response regulator" (in the left column that I didn't
copy) crosses the boundary between driving forward and reverse swimming.
Koshland doesn't quite commit himself, but he does say "The dynamics of
bundle stability suggest that only a few flagella (perhaps only one)
reversing should be enough to cause a tumble" (p. 53).

I think the author thinks it a bit more definite than a "possible"
mechanism. There's a nice mechanical drawing of the structure of the
motor, for example, as well as an electron micrograph of the base of the
rotor, and a description of the eight stator elements...and so on. The
chemical and genetic aspects are also described in enough detail and
with no hedging, so as to make one assume that they represent accepted
"facts." Whether they are true is another matter.

There's a nice discussion of the structure and energy source of the motors
in Koshland's chapter 4, "The Motor Apparatus." This chapter begins "The
flagellar structure has been largely elucidated through studies with the
electron microscope and genetic tools (5 references). It is encoded in
approximately 25 genes" (p. 47). On page 48 is an electron micrograph of
the motor, with a nice line drawing beneath it.

_SURELY_ Berg must have referred to Koshland! If not, we have some reason
to question his thoroughness in crib\\\\ researching the literature.

Best,

Bill P.

6

[From Bill Powers (2000.01.13.1141)]

Martin Taylor 20000112 23:01--

In my reply, I said

_SURELY_ Berg must have referred to Koshland! If not, we have some reason

to >>question his thoroughness in crib\\\\ researching the literature.

I see that the backslash key is just beneath the backspace key, which would
have deleted the "crib" if I had hit it four times.

Best,

Bill P.

7

[Martin Taylor 20000113 14:29]

[From Bill Powers (2000.01.13.0953 MDT)]

Martin Taylor 20000112 23:01--

>Are we talking about the same thing, here? My understanding of the "method"
>was that the model e-coli moved in a straight line until it tumbles. Is
>that wrong? The real e-coli may deviate by as much as 90 degrees from
>its initial course along a single run before it happens to tumble.
>That's
>the sense in which it has a limited memory. The model remembers its
>heading perfectly until it tumbles.

The model remembers nothing.

I gather we are playing word games again. To keep going in the direction
it was going, it _has to_ remember what direction it was going. But that
doesn't imply the e-coli has a brain with an internal representation of
its direction.

The model, however, does have an internal representation of its
direction,and it remembers its direction explicitly until a tumble
happens (in
the Mind Readings paper, in the algorithm on p92, the direction is
remembered in the variable "a"). The real e-coli doesn't remember as
well as that. In a simulation of the real e-coli, the variable "a" would
be given a small random increment or decrement at each iteration, so
that after about 10 seconds, the direction would be randomly oriented
with respect to the initial direction.

It operates according to Newton's laws, in the
sense that it continues in a straight line until some lateral force acts on
it.

That's what I said. But it doesn't operate according to Newton's laws
at all in managing to continue in a straight line, as you yourself
emphasise when you say:

By the way, E. coli cannot coast. According to Koshland, after the
flagellae abruptly stop spinning, E. coli would coast no more than one
millionth of its body length, due to "the viscosity of the medium and the
low Reynolds number."

We could easily make it curve. Most bacteria swim in reasonably
straight lines. ...

Not e-coli, apparently. Sometimes it does, and sometimes it will curve
over as much as 90 degrees before tumbling. According to Berg, on average
it curves by about 30 degrees in a second, and after 10 seconds it is
likely to have gone off course by more than 90 degrees.

Any curvature in the path must be due to a slight
cocking of the flagellae, or some asymmetry in their construction.

The curvature is not consistent during a single run, which this
explanation would suggest. Berg calls it Brownian, and the 3-D
picture of a single track certainly looks like that, with straight(ish)
parts and parts where it curves fairly sharply. Part of the point is that
this doesn't matter (much) for its efficiency in climbing the gradient.

It makes essentially no difference in
the final behavior; the relationship of tumbling to time rate of change of
concentration is no different.

That's what Berg says, yes. To add to what I said before, "a cell
compares the concentration observed over the past 1 s with the
concentration observed over the previous 3 s and responds to the
difference." (Berg, p27).

Berg and Koshland clearly disagree over some aspects of the way the real
e-coli moves. One of them has to be wrong, and I'm not betting on which
it is. However, here are some clear disagreements, using your quotes to
stand in for Koshland's opinions.

This could easily be miscontrued, by someone who only skimmed the rest of
the book, as saying that if the flagellae spin in the direction opposite to
normal, the flagellae disperse, causing tumbling. But that is not what it
means. It means that _during the process of reversal_ there is a stage when
the flagellae disperse and cause tumbling. If the reversal is complete, the
flagellae once again coalesce into a spiral, although with a somewhat
different configuration, and again produce smooth swimming, now backward
(the flagellae pull instead of pushing). ...
The
motors necessarily turn at the same rate, because the flagellae coalesce
into a single spiral (whether going CW or CCW).

Not according to Berg. CCW is coordinated, CW is not. And each direction
of rotation can last for a substantial length of time, during which th
e-coli is tumbling if the rotation is CW and is running more or less
straight if the rotation is CCW. Here's the direct quote (Berg p26):

   "When the motors turn CW, the flagellar filaments work independently,
   and the cell body moves erratically with little net displacement; the
   cell is said to "tumble." When the motors turn CCW, the filaments rotate
   in parallel in a bundle that pushes the cell body steadily forward, and
   the cell is said to "run." The two modes alternate."

From this I infer that tumbling occurs at the point just where the
"Relative level of response regulator" (in the left column that I didn't
copy) crosses the boundary between driving forward and reverse swimming.
Koshland doesn't quite commit himself, but he does say "The dynamics of
bundle stability suggest that only a few flagella (perhaps only one)
reversing should be enough to cause a tumble" (p. 53).

According to Berg, there is no such singular event as "a tumble." There
is a period during which the e-coli is tumbling. The length of the
tumbling period is exponentially distributed, just as is the length
of the "running" period. Sometimes the e-coli tumbles (motors running
clockwise) for a long time, sometimes for a short time. Clearly Berg
and Koshland disagree. Berg quotes a lot of his own research (among
others), but he doesn't quote Koshland. Does Koshland quote Berg?

There's a nice discussion of the structure and energy source of the motors
in Koshland's chapter 4, "The Motor Apparatus." This chapter begins "The
flagellar structure has been largely elucidated through studies with the
electron microscope and genetic tools (5 references). It is encoded in
approximately 25 genes" (p. 47). On page 48 is an electron micrograph of
the motor, with a nice line drawing beneath it.

Berg's equivalent picture and drawing are credited to David DeRosier
of Brandeis. He says about 50 different proteins are involved in the
chemotaxis, which I presume to imply 50 genes (out of the 4288 he says
there are in the whole e-coli).

What does Koshland say about the structure of the motor? According to Berg,
it's a stepping motor with 8 stator elements, and during a rotation there
are at least 50 discrete stepping motions per stator, or over 400 per
revolution.

_SURELY_ Berg must have referred to Koshland! If not, we have some reason
to question his thoroughness in crib\\\\ researching the literature.

I guess he preferred to cite original research rather than the secondary
literature, though he does cite a couple of books. What's the date of
Koshland's book? Berg does include 1999 citations (to other people's
research, not his own).

Whoever is right about the details, Berg or Koshland, it is interesting
to contemplate whether differences between the model and the real
e-coli gain the model efficiency over the real e-coli at the cost of
robustness to non-monotonic gradients (as must be common in flow regimes),
or whether they make no difference either way. Maybe Rick could add the
various differences to his Java simulation demo.

Martin

8

[Martin Taylor 2000.01.13.18:02]

[From Bill Powers (2000.01.13.0836 MDT)]

>[Martin Taylor 20000112 17:09]

I'm glad to see some independent confirmation concerning the E. coli
method, but your information is a bit inaccurate.

Any innacuracy of mine is in th paraphrasing of what Berg says.

Mine, by the way, came
from a book by Daniel Koshland (a former editor of Science and a
biochemist), _Bacterial Chemotaxis as a Model Behavioral System_ (New York:
Raven Press, 1980). Koshland did a good deal of the research himself.
Berg's report does not agree with Koshland's findings in several regards.

We know that. But is a 1980 reference to be regarded as more reliable
than a 1999 reference that cites quite a bit of work from the 1990's?

>If the cell is in a region of uniform
>concentration of nutrients, these two types of motion alternate with
>an exponential distribution of the time in each phase. (There's a 3-D
>picture of such a track in the article). It doesn't matter what the
>concentration is, the time distributions remain the same.

That's for uniform concentrations. In a gradient, the time between tumbles
varies about the mean time with the cross product of gradient and swimming
velocity.

It seems a waste of bandwidth to repeat all of what I said initially
that Berg said. Why bother? There is some point in highlighting the
differences between the two sources, but to repeat the points in
common seems unnecessary.

>The exponential distribution of times has a slightly longer time
>constant when the cell is moving up the gradient than when it is in
>a uniform concentration, but the time constants are the same when it is
>moving down the gradient as they are in a uniform concentration. It's
>a one-sided control system, in that sense.

I don't know what that means.

What's difficult about it? If the rate constants of the exponential
differ, so does the ratio betwene the times spent running or tumbling.

If you combine sensing a concentration and adaptation due to breakdown of
the chemical, you get time rate of change sensing. See Koshland's chapter 6
on "Adaptation" (p.107-125, esp. p. 122).

I tried to explain exactly that, from Berg. Again, why highlight the
common elements as if there were a point of contention?

>The catalyst for the building of the CW-stabilizer has been reduced by
>the aspartate, but it is involved in a negative feedback loop whereby it
>inhibits its own production. Hence when it is disturbed by the aspartate,
>it reduces the inhibition on its own production, and comes back to the
>original level. This restores the CW-CCW balance, but it takes time
>to do so.

Frankly, that sounds like hogwash to me.

I can only say that my attempt to summarize a careful and exact description
by Berg in the much smaller space of an e-mail message was clearly
unsuccessful.

What does "stablizing" the CW
rotation mean?

It means that the likelihood of a switch to CCW rotation in any
particular millisecond is reduced. Or, in other words, the time constant
of the exponential time distribution is increased.

I don't think Berg even has the facts right, but of course
that would be between him and Koshland (and the other workers Koshland
cites). Also, if CW and CCW were in balance, the bacterium would be
continuosly tumbling, wouldn't it?

CW and CCW are in balance in the sense that the time constants for switching
from one mode to the other are the same as they are in a uniform
concentration of nutrient.

>In a uniform concentration, the adaptation balances the CW and CCW phases
>at the same stability ratio no matter what level the concentration is at.
>When the concentration is increasing, the rate of adaptation is slower
>than the rate of destabilising the CW phase, so there is more "running"
>and less "tumbling" until the concentration is no longer rising. In effect,
>the cell compares the concentration "now" with the concentration "a moment
>ago" and tumbles less if the concentration "now" is greater.

This might be fine if tumbling went with CW and running went with CCW
rotation of the flagellae. But I don't think there's even a chance that
this is correct. If you read Koshland, I think you'll agree: he would have
had to invent most of his data if what Berg says is true. I think Berg's
model is vague to the point of nonexistence, not to mention that it
represents a nonexistent phenomenon.

My description of it may be vague. His describes exactly how each of the
receptors is constructed and how each of the chemicals act on each other.

do you have any reason to suppose that
Berg knows what he's talking about?

He certainly sounds detailed and convincing, and cites modern references.
I know you don't go for appeals to authority, but he is a dual professor
of physics and of molecular and cellular biology at Harvard, which I
suppose counts for something.

Especially since it is observed that a negative time rate of change of
concentration of attractant (swimming down the gradient) decreases the
interval to the next tumble, while a positive rate of change increases it,
both relative to the rate in a uniform concentration.

Berg says that isn't true. Down-gradient is the same as uniform, according
to him.

>There's no reference in the article to a Web site, though one would think
>it a perfect subject for a very pretty one!

More to the point, is there any reference to Koshland's 1980 work?

No. Does Koshland reference Berg's work in the 1970s?

I don't think either of us has any basis on which to say whether Berg
or Koshland is right. The possibility exists that they both are, since
Berg points out early in the article that there are many strains of e-coli,
some of which don't swim at all. Maybe some of them both push and pull,
whereas others only pull; maybe some of them tumble more going down
gradient whereas others tumble the same down-gradient as on the flat.

Who knows? The interest is really in what nature might say about methods,
and vice-versa.

Martin

9

[From Bill Powers (2000.01.13.1838 MDT)]

Martin Taylor 2000.01.13.18:02 --

More to the point, is there any reference to Koshland's 1980 work?

No. Does Koshland reference Berg's work in the 1970s?

Yes (if this is H. C. Berg), there are 8 references, the earliest being in
1971. Koshland's earliest reference to himself was in 1977.

Without reading everything both people wrote, I don't have any way to
choose between them. Koshland does show data indicating a lengthening of
tumbling interval for negative rates of change of concentration, which you
say Berg denies. That certainly raises some doubts.

I suppose I should read Berg's article. Later.

Best,

Bill P.