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Force Generation by Actin Assembly: Theories and Experiments
In this segment, I'd like to describe to you some recent work from my group
trying to understand the mechanical basis of the movement
by this bacterial pathogen, Listeria monocytogenes.
In this movie, as we see, an epithelial cell infected in tissue culture
with a single individual of this bacterium soon ends up teeming
with a very large number of bacteria all descended by binary fission
from the one who originally infected the cell and all moving very rapidly
through this extremely dense, thick cytoplasmic matrix
that makes up the interior of the cell.
Now in order to understand how this works, not only do we have
to understand the individual molecules that are involved,
but we have to also understand how they all work together
in order to generate this directed force that is able to generate motion
in such a persistent way over such a long period of time.
Looking in detail at the structures associated with this form of movement,
we see a beautiful example of the type of large scale organization
of cytoskeletal structures that I was describing in the first segment about cell motility.
For this particular bacterium, one thing that we have learned
about the organization of actin filaments associated with its movement
is that the only filaments that are actually growing in the system
are the ones that are immediately adjacent to the bacterial surface.
And it's thought to be the growth of those filaments
that actually pushes the bacteria through the cytoplasm.
So, we want to understand how that works.
We want to understand the mechanics and physics of how that works
as well as just understanding the biochemistry.
In terms of the biochemistry and thermodynamic framework
for thinking about force generation by this mechanism,
there's a very great framework that's already in place,
and we understand simply by thinking of the polymerization reaction
as being a binding reaction
that we can calculate how much energy ought to be available in order
to generate force to push an object.
In particular, when you do this kind of calculation,
the estimate that you come up with is that a single actin filament
should be able to generate on the order of a few picoNewtons
of force under normal biological conditions.
Another question which is not nearly so well resolved
is what is the maximum speed at which this type of movement should be able to occur.
Now the kind of modeling and theory that I'm describing here
is a very good place to start, but in reality, if we want to understand this,
we have to do an experiment.
We have to actually get ahold of an actin filament, make it grow against something,
and find out a way to feel and to measure the amount of force
that it generates during the real process of force generation.
In order to do that, my group has started a collaboration
with the group of Marileen Dogterom
at Amsterdam, trying to answer these two particular questions.
First, how much force can actually be generated by growth of actin filaments
against a rigid barrier in an experimental situation?
Second, how fast can this growth occur?
And also, what are the kinds of parameters that determine how fast that growth can occur
that may regulate how fast a cell is able to move under different sorts of circumstances?
In order to answer these questions experimentally,
Marileen Dogterom and I designed the experiment that's diagrammed here.
Essentially, we envisioned trying to accomplish in reality
the same sort of geometry of organization that I've diagrammed in
theoretical treatments that I've shown you on previous slides.
Now, for technical reasons, it's very difficult to get ahold of
a single actin filament and hold it in place.
Actin filaments are very small and also they're very floppy.
So, any sort of small-scale manipulations that you do to get hold of a single actin filament
tend to cause them to buckle or to bend or to break.
So, in practical terms, we had to start off not with a single actin filament,
but instead with a small bundle of actin filaments, as shown here.
Now, the next thing we wanted to do was be able to bring this bundle of actin filaments
in contact with a rigid barrier (a wall) that we would also have to fabricate.
The question of how to manipulate, how to hold on to this bundle,
of course opens up a series of questions about what's the best way
to actually handle physical objects that are actually microns in scale.
Over the past several decades, a very useful technique that's been developed
for grabbing hold of and physically manipulating objects of this approximate size
is the technique of optical trapping, or using laser tweezers.
In this technique, a beam of laser light is focused through a microscope objective
to a very fine focal point, and because of the way that light interacts
with refractile objects (for example with polystyrene beads)
that focused light actually tends to hold small objects right at its point of focus.
This works actually much better for plastic beads than it does for biological elements,
such as actin filaments, and so to get hold of our rigid bundle of actin filaments,
and manipulate them so they could come up next to a wall,
we had to be able to stick a polystyrene bead (a plastic bead)
onto this bundle of actin filaments that we could then use as a handle
to move it around using these optical tweezers.
After getting the whole thing aligned, bringing it up next to this nanofabricated wall,
the next step here in our ideal experiment would be to
add actin monomers to the solution.
The actin monomers are able to diffuse very rapidly through the solution,
and any actin monomer that finds itself right at the interface here,
between the end of the bundle and the wall,
might have the opportunity to slip in at the end of that bundle,
because of some sort of thermal motion in the system
and thereby exert a pushing force on the wall.
Now, in our imaginary experiment here, the wall is actually completely rigid and can't move,
so when that force is generated at the interface, instead of pushing the wall away,
what we expect to happen is that the growth of the actin filaments at the interface
should in fact push the bead backwards.
In an optical trap, you can measure the amount of force that it takes
by measuring the location of the bead in the trap.
The bead is positioned essentially in what you can imagine
as a well of a harmonic oscillator,
and any displacement to either side of the focus point of laser light
actually takes energy being put into the system in order to displace the bead.
So, in principle, then, if we're able to do this, and we're able to actually
put our wall in the right place, put our bundle in the right place,
see our bead, and then watch the bead deflect in the optical trap,
we should be able to perform a direct force measurement
to understand how accurate the predictions of those theoretical models are,
and also then change the circumstances.
For example, changing protein concentrations, changing temperature,
and looking to see how that affects the process of force generation.
Now, Marileen and I cooked up the idea for this experiment...
then actually doing the experiment is quite something else.
And for that, the particular credit goes to Matthew Footer and Jacob Kerssemakers,
who actually took these ideas and made them into reality.
In order to make this experiment actually work,
there were several different problems that had to be solved.
One problem, of course, is where to come up with
this crosslinked bundle of actin filaments.
And, ideally, we don't just want a bundle of actin filaments
that are pointing in any old direction,
we want a bundle of actin filaments that are all aligned in the parallel direction,
so they all tend to grow at the same end,
specifically the end that's pushing up against the wall.
Now, nature has conveniently, actually, supplied us with a bundle of actin filaments
that fulfills these necessary criteria.
And that bundle of actin filaments is found in the *** of the horseshoe crab.
When the horseshoe crab *** encounters a horseshoe crab egg,
the *** has to actually physically get across the jelly coat of the egg,
so that the two membranes can fuse and the egg can be fertilized.
The horseshoe crabs have come up with a very creative, and, in the animal kingdom,
quite unusual way of getting that membrane across the jelly coat.
Essentially, the *** comes with a little preload of pre-stressed spring
that's coiled around the base of it that is made up of actin filaments
and when contact is made and there's molecular recognition between the *** and egg,
this pre-coiled spring actually springs out and forms a very long process
that pushes all the way through the jelly coat, pushing the membrane
of the *** up close to the membrane of the egg so that the two can then fuse.
Now you can isolate the *** from horseshoe crabs and then trick those ***
into thinking that they've encountered a horseshoe crab egg.
And when that happens, they spring out this bundle of actin filaments
which you can then isolate and purify.
And some of those purified bundles are shown here.
And in particular, what we're showing here
is that they retain the ability to nucleate further growth of actin filaments
at the tips if you simply add actin monomers to them in solution.
This property of the bundles (their ability to nucleate the growth of new actin filaments)
is shown in two different ways.
First, on top, you see here, in phase contrast,
the bundles as they're isolated from the crabs.
And then in this image next to them, what you can see is
fluorescently labeled actin which has been added in monomeric form to these bundles.
So, the bundles elongate and each of these little tufts
(these little bright tufts that you see)
is sort of a little broom of actin filaments
that's growing right off the end of the acrosomal bundle.
Here in this image, the two things are overlaid
so that you can see the position of each of the bright tufts
actually falls right at the end of one of the acrosomal bundles.
Down here below, we're looking at much higher magnification
here in the electron microscope,
so you can see these filaments growing off the end.
Here, the acrosomal bundle appears as a very dark, phase-dense object,
and you can just barely see little individual threads coming out,
which are the individual actin filaments that are growing off
a few of the filaments within the bundle.
This image is taken after a very short time in actin monomers... just a few seconds.
And so you can see the filaments are very, very short that have grown off the end.
Here, this image was taken after a somewhat longer time
(closer to 30 seconds in the presence of actin monomers).
And here, you can see the individual filaments have gotten quite a bit longer.
So that's problem number one solved. We now have an appropriate bundle
that we can use to nucleate growth of our actin filaments against a wall,
but we have to have some way to hold it in place and hold it
in the correct orientation relative to the wall,
so that we can get it positioned to just generate the force
exactly where we want to be able to do the measurement.
So, to solve that problem, Marileen's group, they invented a special variety
of the optical trap that they call a keyhole trap,
where instead of simply focusing a single beam of laser light
to a single point that can hold a single bead,
they take that same beam of laser light and put it through an acousto-optic modulator,
which is a crystal that can be tuned to position the light
at different places very, very rapidly.
They take the laser light then, and spend most of the time focusing on a single location,
where it's able to trap a bead, but then they (over just a very brief period of time)
then actually refocus the position of the light all up and down the bundle
as shown here by these different little spikes.
The effect of this is that the potential well that is holding the bead in place
is also existing in concert with a line trap that is able to trap something like a bundle.
In this way, they have essentially two bits of the handle
that they can use to manipulate these small objects.
They have the main part of the laser beam that's focused on the bead itself,
which holds the bead rigidly and which is the thing that the force
is going to do work against to displace the bead as the actin filaments grow.
And then they have this line trap which enables them to come in
and steer the position of the actin bundle,
so that they can get it right up against the wall and get it perpendicular to the wall
in the perfect geometry for testing our thought experiment.
So, here's everything put together. This now is a nanofabricated wall
with a bead and an acrosomal bundle that is positioned
in this keyhole trap and brought right up against the wall.
And in this, by using joysticks to manipulate the position of the stage
and the position of the keyhole trap,
they're able to *** the bundle right up against the wall,
so that they're able to get it right exactly positioned right next to where the wall is,
and then flow in monomers in order to start this process.
Then, the growth (and therefore the force generation) is monitored
by looking at the displacement of the bead in the trap, measuring how far it has moved,
and then calculating (because we know how much energy is put into the trap,
we know the stiffness of the trap)
calculating how much force that means must be generated at the interface
between the actin filaments and the wall where growth is occurring.
So, the outcome of that experiment is shown here.
This is a curve showing the displacement of the bead as a function of time
after actin monomers have been added.
Down here, at the beginning of trace, the bead is in a resting position,
which we indicate as being 0 nanometers distance traveled.
And, you can see in the gray trace that there are little fluctuations around this position,
but overall the position is held quite steady.
Now, at the time marked 0 on this graph, actin monomers were added to the solution,
but it takes them a while to actually flow down to the place on the microscope
where the acrosomal bundle is being held against the wall.
And so after a delay of the time it takes the actin monomers to diffuse to that point,
then growth begins, and what you can see is that the bead is pushed...
actually, it's pushed a distance of about 900 nanometers.
And, at first, it's pushed very, very quickly, and then the rate of pushing slows down
and slows down and slows down, until eventually it stops and stalls.
The position at which it stalls (about 900 nanometers)
corresponds in this particular trap to a stiffness or a force
equivalent to about 1.5 picoNewtons.
In other words, thinking of the thought experiment here,
we're able to generate force, and we're able to keep pushing the bead out
until the amount of force required to move one more step, to add one more monomer,
is more than about 1.5 picoNewtons... that's the stall force for elongation of the filament.
So this is a way of measuring how strong the motor actually is.
Now there are a couple of things that are very interesting about this number.
The first is, if you take the equation worked out by Terrell Hill
that predicts how much force you should actually be able to generate
by this mechanism of polymerization,
and you calculate what the stall force should be under these circumstances
the number you come up with is almost exactly the number that we observed.
The thing that's surprising about this, though, is that the force that's generated
calculating that equation is the force you expect for a single actin filament.
And you may have noticed that on the acrosomal bundles,
there are actually several different actin filaments that are coming off the end.
It's typical that we get about six individual actin filaments
coming off the end of one of those bundles.
And yet, nonetheless, it seems as if it's only the longest filament
in the bundle that's contacting the wall that's able to generate force,
and the rest of them essentially have no effect on the system.
So now, having been able to do this measurement of actually experimentally
determining how much force can be generated by polymerization of the actin filament,
how fast it can happen, under what sort of circumstances,
the next temptation, of course, is to try to build up its scale.
As I've described in the first segment, when I was talking about cell motility,
most of the interesting questions about mechanics within the cells
require that you have many of these individual force generating elements
working together.
What we've seen so far is that individual filaments can generate
a few picoNewtons of force,
but if you have a couple of filaments that are operating together in a parallel bundle,
they don't get to add together.
It seems like the small parallel bundle is no more efficient at generating force
than a single filament would be on its own.
And obviously, that is not going to get a cell anywhere.
There has to be some way that different filaments are actually able to cooperate
in order to do things like push the leading edge of a crawling cell forward.
One possibility is that the geometry...
the organization of how the filaments are tied together
actually matters quite a lot.
The example that I've shown you with the acrosomal bundle
is a case where you have a bundle of filaments that are all parallel to each other.
But, in many cases, and for example in the comet tail,
(the actin comet tail) associated with moving Listeria monocytogenes,
the filaments are not in parallel bundles.
Instead, they are in a crosslinked meshwork where they're actually
pointing at many different angles.
Is this branched network formation somehow more efficient than bundles
in generating force?
As I've shown you, the Listeria monocytogenes are able to move
very rapidly through extremely dense cytoplasm,
sort of shoving organelles away as they go.
So, it seems likely that the answer to this is going to be, yes,
there's something about being organized in a branched network
that enables filaments to work together so they can generate much more force
than they could on their own.
Well, in order to actually examine how that works and to make the kinds of measurements
from one of these complex, branched, dendritic networks
that I've just described for measurements for small bundles of filaments
we need again some way that we can manipulate, hold onto the object,
and measure the amount of force that the actin polymerizing against the surface
is using to displace it.
Now, you might imagine that we could simple do the same thing that I described before.
Take a laser trap and try to grab hold of this bacterium
and see how much energy we have to put into the laser trap in order to get it to stop.
That should be a way of measuring the stall force of the filaments
that are growing against its surface.
Well, we and many other labs have tried that, and basically it doesn't work.
The problem is, the maximum amount of force you can get,
out of even the best laser trap, is on the order of only a few tens of picoNewtons
maybe a hundred picoNewtons on a really, really good day.
And the force required to stall these bacteria is apparently much greater than that.
When we turned on the laser trap and tried to grab one of the bacteria,
you could practically hear the bacterium laughing as it sailed through the trap.
That amount of force is insufficient.
So we needed to have some other type of method for measuring
these large amounts of forces under conditions where we could grow dendritic networks
in a very particular geometry and organization that's somehow analogous
to what we're able to do with these small bundles,
manipulated by the optical tweezers up against a wall.
In particular, as we've been working for some years,
trying to come up with some way of making this experimental measurement,
there have been a very large number of physicists and mathematicians
who have put a lot of very careful thought into developing careful quantitative
physical models that should predict the outcome of such an experiment.
And I'm giving you a few examples. This is by no means an exhaustive list,
but this is a representative sampling of some of the theoretical work
that I've found particularly useful, where people have thought about how
having these different filaments branch together in this network may affect
their ability to generate force and push a bacterium forward.
Starting over here, in the corner,
is a model (the Mogilner-Oster model), which they call the tethered Brownian ratchet.
The basic idea here is that individual filaments are able to generate force
against the rigid surface of the bacterium
because they're able to undergo thermal fluctuations by bending,
and then individual monomers can come and sneak in between
the end of the filament and the surface of the bacterium,
and those bent filaments essentially act like little springs pushing on the bacterium.
Now, at the same time as there are hundreds or thousands
of filaments in the actin comet tail,
(as you saw in the electron micrograph)
some of those filaments are actually physically bound to the surface.
That's how the bacterium is able to stay in physical contact
with this comet tail, and it doesn't just go diffusing away.
There's a tension between the drag force generated by those filaments
that are physically bound to the surface
versus the pushing force generated by those filaments
that are actually growing and bending against the surface.
By plugging in sort of reasonable numbers for the amounts of proteins
that are present and the strength of these intramolecular bonds,
Mogilner and Oster have been able to come up with estimates
for how much force should actually be generated against the surface of the bacterium,
how fast the bacterium should go,
and in particular, they've also been able to predict the relationship between
force and velocity (the so-called force-velocity curve),
which is a diagnostic for different kinds of force-generating elements in biological systems.
So that's one approach that people have taken to think carefully about individual filaments:
what individual filaments must be going through,
thinking about all the different filaments there
that are operating in this structure together,
and how those individual forces might add together to play off each other.
The sort of opposite approach (the other extreme) is illustrated here in the other corner.
This is what's called a mesoscopic model (a larger scale model, not microscopic)
that was worked out by Jacques Prost and collaborators a few years ago.
In this model, they decided to ignore what we know about actin filaments,
and say that the comet tail... it's more useful to think of it as being an elastic gel,
rather than a series of individual actin filaments that are crosslinked to each other.
And like any other elastic gel, this gel is going to have stiffness,
it's going to require some amount of force to compress it.
And in particular, this gel grows only at the surface of the bacterium.
So, envisioning the shape of the bacterium, which is a little sort of pill-shaped object,
and imagining this elastic gel that's growing on its surface,
it becomes immediately apparent that the geometry of the system
forces a very interesting sort of limitation on it.
You've got the surface here, the gel is trying to grow all the way around the surface,
and as that gel grows out, it's going to set up strain
where it swells as you get further to the back of the bacterium.
That's indicated here by the gray area becoming thicker as it goes back.
That gel is swelling under strain because it's continuing to grow
all along the surface of the bacterium.
What that means is, as the gel is growing, the elasticity of the gel
is essentially pushing back on the bacterium,
and because this is happening all the way around the surface,
it's essentially as if the gel is squeezing the end of the bacterium,
and that squeezing, you can imagine, can actually shoot
the bacterium forward like a watermelon seed.
So, this kind of model has several very appealing characteristics about it.
One thing is, it pays a lot of attention to the actual geometry of the system
(what the actual bacterium is shaped like)
in a way that these microscopic models can't do very easily.
It also makes a very specific prediction which, in principle, we could test experimentally,
which is that, if you grow one of these comet tails that's not absolutely rigid,
you should be able to see that squeezing and some sort of deformation of the object.
Now, obviously, there are elements of truth and elements of falsehood
in both of these different kinds of models.
The microscopic model focuses on individual protein filaments,
which is a very useful level to think about because we know
a lot about the biochemistry involved there,
but ignores geometrical issues, large-scale issues, and also issues like elasticity of the gel.
The mesoscopic models on the other hand, do take those things into account,
but ignore everything that we know about
the detailed interactions of individual proteins in the filaments.
In order to try to come up with the best of both worlds,
there have been a series of groups that have taken a different approach,
rather than these analytical approaches, these mathematical approaches.
Some of the groups have taken computational approaches,
actually setting up large, complex computer systems
to try to simulate all of these different things,
so that they can look at individual filament dynamics,
but do it in the context of a very large scale system
where they have many filaments actually interacting with each other.
A couple of interesting examples of that approach are cited here.
One, which is a very important early work in this field by Anders Carlsson,
simply imagined a group of dendritic, branched actin filaments
where a new actin filament grows off the side of an old actin filament
(exactly the way that we think it works in the comet tail),
and then had them impinging on an imaginary wall, here (a barrier).
So, as these individual filaments would grow, they would push against this barrier,
and he could then calculate in the simulation how much force the barrier was experiencing.
A related, but slightly more complicated version of that was worked out recently by
Jonathan Alberts and Gary O'Dell, where they tried to use
the real geometry of the bacterium,
and also a lot of individual molecular details of all of the proteins on the bacterial surface
and the proteins in solution to build a comet tail
and then let the system run and watch it evolve.
And they were actually able to get very realistic looking simulations
of growth of the entire actin comet tail
and also realistic looking dynamics of how fast it would grow
and how fast the bacterium would move.
So, this was wonderful work on the part of many very talented people in the field,
predicting what the outcome of force and velocity measurement experiments should be.
So, the challenge to us as experimentalists, then, was to actually do a measurement,
compare that measurement to the predictions that all of these different people had made,
and see which set of assumptions was actually closest to reality
as determined by the experiment.
Now, as I mentioned, we can't do this really with just an optical trap.
But, we do have the advantage in the system that we can manipulate
a lot of other things about it.
As I mentioned previously, the proteins that are required for formation
of the comet tail and this sort of growth have all been identified,
so the movement can be reconstituted in the absence of the cell.
For this kind of approach, even more important than that,
we're able to get rid of the bacterium
and replace the bacterium with plastic beads (polystyrene beads)
coated with a single bacterial protein.
Now, as I indicated before the optical trap experiments,
these polystyrene beads are very useful experimentally.
There are a lot of things you can do to them.
You can stick them to things, you can try to hold on to them,
and in reality it doesn't even have to be a bead.
You can replace it with some other artificial object that has some other physical property
that you want to probe.
So, these beads... the technique for doing this was worked out by Lisa Cameron,
who was one of the first graduate students in my lab.
And I just want to show you here that their movement actually
is very similar to the movement of bacteria,
and it really does seem to be a good reconstitution.
In the middle panel, here, what you see is a phase-contrast image
where you can see these polystyrene beads.
And in this series of images from a time-lapse movie,
there's one bead which is stationary, and it's not going to move.
And you can see in the actin image, where the actin is fluorescently labeled,
it's surrounded symmetrically by a cloud of actin filaments.
The other bead, though, the one up here, you can see actually
progresses from point to point,
as you go through these different frames from the time-lapse image.
And then you can see in the fluorescence image, this actin comet tail streaking behind it.
Now, to make that a little more vivid, here's a movie where what we're seeing here
is the fluorescent image of the actin that's been added to the system,
and the beads actually are invisible in fluorescence, but we've had the computer
track their positions with these little red dots.
What you can see is these things are sailing around.
It's really hard... very hard... to look at this and not believe these things are alive.
But these little artificial bacteria are able to move in extracts very fast
with a lot of the characteristics that we're used to seeing from the
kind of bacterial motion that we've been observing for many years.
So, now that we're able to replace the bacterium, which is a complex object itself,
with these objects of our choosing, how do we design an object that we choose
so that we can measure the force that's generated at the surface?
Well, one approach to that was worked out by Paula Giardini a couple of years ago.
She said, well instead of using these rigid plastic beads, which are just like rigid bacteria,
let's instead use deformable vesicles... vesicles made out of phospholipids.
Over here, in Part A, you can see that green lipids made into these vesicles
end up having a variety of sort of floppy, nearly spherical or sort of ovoid shapes.
But once we put the bacterial protein on the surface of these vesicles,
so that they start to nucleate actin growth
and actually grow comet tails and move around,
what you see here is that the vesicles become misshapen.
Instead of being spheres or little ovals, they now actually sort of have points.
They look more like light bulbs.
That's actually quantitated down here. Here, Paula has worked out a measurement
where she can work out look at the distortion from a sphere
to an elongated object in one axis, here,
and then look at the asymmetry in the other axis.
And, as you can see, the vesicles that have actin on them,
which are indicated by the red dots,
are both longer and skinnier and more deformed
than any of the vesicles that don't have actin associated with them.
Now this is a very interesting finding, because it indicates that
the growth of the actin comet tail on the surface of these vesicles
is actually squeezing the vesicle in a way that's causing the end of it to deform,
and you may recall that one of the physical models
that I've described, the watermelon seed model
of Jacques Prost and his colleagues, actually specifically predicts
that the tails should squeeze back on the object.
So this kind of measurement seems to support at least that
particular prediction of that theoretical work.
But still, this isn't a very good way to get a force measurement.
We can estimate force because we know something about how stiff the vesicles are,
and we can guess about how much energy it should take to deform them,
and we come up with numbers that are on the order of a nanoNewton,
which is a very impressive amount of force. This is 1000 picoNewtons.
So, if each one of those filaments is generating a few picoNewtons of force,
this really seems like they're able to all work together to deform the vesicle.
But it's still a very indirect measurement.
We really want something that will actually deflect in the same way
that we could see the bead deflect in the laser trap to measure the force directly.
In order to do that, this design was worked out by Dan Fletcher,
who started as a post-doc in my lab and then began troubleshooting
this experimental design over a period of several years.
By the time he was finished troubleshooting the design, he was no longer a post-doc,
and is now an assistant professor in the bioengineering department at UC Berkeley.
Dan's idea was very elegant in concept and extremely difficult in execution.
The idea essentially was to take advantage of atomic force microscopy technology
to measure these deflections over a range of force
which is not accessible from the laser trap.
The way atomic force microscopy works is that you have a cantilever
that has a very fine needle on one end that essentially operates like a record player stylus,
and as you drag that over a surface, every time the needle comes in contact
with a bump or feature on the surface,
the lever arm deflects. Now, that deflection may be very, very small...
It may be only a couple of nanometers, a couple of microns,
something too small to easily measure.
But, by putting a diode laser into the system, where you bounce reflection
off the back end of the cantilever,
and then watching how that reflection moves on a diode photodetector,
you can actually translate very small movements (nanometer scale movements
of the cantilever) to micron or larger scale movements
of the laser off at some other distance
that can easily be detected on the photodiode.
So, Dan's idea was to take this kind of setup (an AFM setup),
and instead of having a little needle at the end of the cantilever
to drag across the surface,
to replace that needle with one of these plastic beads
coated with the bacterial protein that will nucleate the growth of an actin network.
And that's diagrammed down here.
So, the idea is, if you have this cantilever,
and you have a plastic bead stuck to the end of it,
that you could then bring down in contact with essentially a floor (a rigid, flat surface)
and then initiate the polymerization of actin right under the surface of that bead
to grow one of these branched dendritic networks.
Then, the growth of that actin will deflect the cantilever upward,
we can measure that deflection by the reflection of the laser
onto the photodiode (the photodetector), and thereby measure movement.
Now, we know how stiff the cantilever is... we can make them
different stiffnesses by making the cantilever different thicknesses.
And so looking at this deflection, then we can directly translate deflection of the cantilever
into a force measurement, much the same way that we did for the optical trap.
In order to finally get this very ambitious experiment to work in reality,
several of Dan's students at Berkeley made very particular contributions
that were critical to getting the experiment to work.
One excellent idea was, instead of simply relying on the cantilever itself,
which has a tendency to drift over time, as thermal forces
change in the system and things expand and contract
was to add a second cantilever that would be able to remain in contact
with the floor the entire time.
And so, if there were expansions or changes in the geometry
of the system, you can correct for that
by ensuring that this longer cantilever (the reference cantilever)
always remains in contact.
Another technical problem is how to actually stick the ActA protein
that nucleates actin filament growth onto the end of the cantilever.
This shows one of the solutions they came up with of
actually just supergluing the bead right onto the tip of the cantilever.
Although this, of course, takes very fine motor skills.
Troubleshooting all of these different things... getting the drift of the system
down from a few microns to a few nanometers
again took a period of several years of very focused effort on the part of several people.
But, at the end of the day, what they were able to come up with
was this lovely measurement...
direct measurement of deflection of one of these cantilevers
by growth of the actin comet tail.
This again, much like the image I showed you for the actin filaments
in the optical trap experiment,
shows time versus deflection, and once again, deflection is directly proportional to force
because the cantilever is acting as a simple spring.
What we see down here is early on, there's a phase
where the comet tail is growing very slowly,
and it seems to sort of pick up over time. In other words, the growth accelerates.
Then, and this is very surprising, there's a long phase where the growth
happens at a very, very constant rate.
But, the whole time, the cantilever is bending upwards and upwards and upwards,
and so the force on the system actually is increasing and increasing and increasing.
And yet, the growth stays at a constant rate, despite the fact that the force is going up.
Finally, some sort of threshold is crossed, and the force as it continues to increase
eventually starts to slow down the growth of the gel
until it slows down and stalls out at some particular stall force.
In this particular case, the stall force was very large... it was several hundred nanoNewtons.
A nanoNewton is a thousand picoNewtons, but this was for a very large gel
that has a cross-sectional area of some tens of thousands of filaments,
so that number is not surprising.
But we can take this measurement now, and we can convert this
from being just a force versus time curve
into a force-velocity curve, where we can actually look
at the relationship between the force put on a gel and how fast it grows.
As I mentioned, this is diagnostic, and this was something that was predicted
by all of those different mathematical models that I described before.
So this shows you what the force-velocity curve looks like.
Velocity is on the vertical axis, and force is on the horizontal axis.
This area here where it looks very flat is that interesting region
that I pointed out to you before
where the force increases and increases and increases,
but the speed of growth actually stays very much the same.
And then finally above some threshold, there's a roll-off
where the speed decreases down until you finally hit a stall.
Now, they're able to manipulate the system...
do it under slightly different kinds of geometries,
and one particularly interesting experiment I've shown over here
is where they've compared different shapes at the end of the cantilever.
As I showed you before, we do have some experimental evidence
that the gel squeezes on the object that it's pushing.
So if that's true, you might imagine that there would be different kinds of force
generated if there's a round ball on the end of the cantilever that the gel can actually
squeeze on versus a flat surface where the gel can only push.
In this graph, the red indicates one sort of surface geometry, the blue indicates the other.
And I'm not actually quite sure which is which, but it doesn't matter because you can see
that they line up right on top of each other.
This demonstrates that, although it is possible for a gel to squeeze,
that's not required for its force generation,
and in fact the relationship between force and velocity is the same,
regardless of the shape of the object that it's pushing.
Now we have our force-velocity curve in hand, now we can go back
to these theoretical models
and ask what did they predict. Were they right, in terms
of the actual force-velocity curve that we're now able to measure experimentally?
So this is the first of the models that I described...
this is the microscopic model of Mogilner and Oster.
And, as I mentioned, the elements of this model are biochemically very realistic.
They went to a lot of effort to incorporate all of the things
we know about the proteins involved in this process and how they interact.
Making some assumptions, they ended up predicting a force-velocity curve of this shape.
where, as the force increases, you expect that the speed of gel growth
should actually plummet very quickly
and then eventually flatten out, but continue to move down.
This is strikingly different from what we actually observe.
Let me say that again... this is strikingly different from what we actually observe.
As you see, there's no flat phase in the predictive force-velocity curve,
and the shape of it is concave upward, which is very different
from the shape we observe, which is concave downward.
So at least this particular version of the model does not fit with the experimental data.
What about these other models?
Well, I've mentioned warmly the Prost model... the watermelon seed model
because we do have this evidence that the gel is capable of squeezing
but looking at what they actually predict in terms of a force-velocity curve,
it turns out to be not that different... it's actually very consistent
with what the other model predicted.
Again, there's no flat phase, and depending on various different parameters,
such as the stiffness of the gel,
you expect slightly different shapes but always a concave upward curve with no flat phase.
So, here again, the experiment does not fit the predictions of this particular model,
given the set of parameters that they used to extract these curves.
There is one model, however, that did manage to predict a flat phase
in the force-velocity curve, and that's the model of Anders Carlsson where,
instead of calculating with pure mathematics what the force-velocity curve ought to be,
instead he simulated it by allowing a lot of actin filaments to sort of grow in the computer
and then watching what would happen over time.
And what he saw when he predicted his force-velocity curve in these simulations,
is actually again a flat phase where, as the force increases, the velocity stays the same.
The reason for this actually is very interesting.
In this model, as we believe happens in real life in the case of the comet tail,
the way a new actin filament grows is by forming a branch
off the side of a pre-existing actin filament
Now, when you have a bunch of filaments that are all in contact with the load,
the load may stop the filaments from elongating at the end,
but that's not going to stop them from branching on the side.
So, if you have a load that's slowing down the growth
(the elongation of this filament's end)
you may grow more filaments... you may grow more dense filaments
because the branching rate is going to proportionally increase.
And, according to the simulation... it's not particularly obvious,
but according to the simulation,
those two effects exactly cancel each other out
so that the net growth rate of the gel as a whole
actually remains very constant and remains constant in particular
because the density of the actin filaments is increasing as the force increases.
Now, he didn't carry the simulation far enough out
that we could begin to see the falloff that we actually see in the real experimental data,
but certainly, through this part of the curve, it seems like the predictions
of this kind of model seem best to fit with reality.
Now, at this point, Dan and his students had a wonderful idea.
They said, well if this is true, if this is the reason that we're having
this flat phase in the force-velocity curve,
then when we do the simple experiment of just letting the cantilever
deflect and deflect and deflect,
then the density of the gel that we have when it first
starts to move in this constant phase
should be much less than the density of the gel when it moves later in this constant phase.
In other words, it's a different gel that we're measuring
with actually different kinds of properties...
different kinds of mechanical properties with respect to its force and its growth rate.
So they wanted to see if they could actually get evidence that that might be the case.
The experiment that they did was very simple and very elegant.
They let the simple experiment happen where they allowed the gel to grow,
allowed the cantilever to deflect
for a long part of this constant velocity regime
where here the force is increasing and increasing.
Then, after that had happened for a while, very quickly,
they pulled up on the back end of the cantilever,
so they released some of this stress, some of this bending
that was pressing the cantilever.
In other words, returning the system to a lower level of force.
And you can see that here, in the force trace,
whereas the force was increasing and increasing and increasing,
here suddenly it's dropped back to about half
of what it was before the did the force reduction.
Now this whole time, the actin gel has been growing,
and so far the whole time the actin gel has been growing
at an absolute constant rate, staying absolutely flat.
But once they did the force reduction, what happened to speed?
It jumped up... it almost tripled. The gel started growing much, much faster
than it had before.
And interestingly, it started growing faster than it had before
even though the force that it's experiencing now
was the same as the force it experienced a while ago,
but because these two things are different gels,
they're actually responding in very different ways.
Now one thing about this result that's a little disturbing
is essentially what it means is that the force-velocity curve is not an absolute measure
of the behavior of the system.
It depends on the history.
If you pre-stress a gel, if you pre-load a gel, if you make the gel do a lot of work
then the gel actually grows strong and is able to push faster
if you then go ahead and release the force.
So one conclusion from this is that working out makes you stronger,
which is a very happy result.
But, the other thing that it means is that if you think about what
cells are actually going through as they're crawling through tissues,
what it tells you is that the way they respond to their environment
depends not only on what they're experiencing immediately around them,
but also to some extent to what happened to them in the recent past
and how their gels were trained, if you will, in order to develop their density
and their properties of pushing against resisting loads.
So, for example, a cell crawling through tissue, like a neutrophil
that's going into an infected area of your body,
chasing after bacteria is going to have different properties,
depending on whether it had to go through something dense and stiff
in order to get in there
or whether it was able to get there very easily.
Now, thinking about this result that we're able to see with gels in vitro,
where all we have is proteins, not any sort of live cells,
makes you really begin to wonder about dynamic effects like this
history dependent effects that might happen with whole cell movement.
And I would like to end here by showing you just a couple of intriguing examples
of things that we know that actin gels can do inside of cells,
which may indicate some type of history dependence
or some type of memory that's present in the system.
In the introduction about cell motility, I introduced you to this cell type.
These are fish skin cells that are involved in wound healing.
And as you can see under normal circumstances,
they move very persistently at a very constant rate and in a straight line.
But you can do things to them to disturb their motion.
It's their responses to those disturbances that I think are particularly intriguing,
in the context of history dependent effects for motility.
One thing we can do is we can take these cells,
and we can put them into a little chamber where we've nanofabricated walls.
And these are walls that are fairly similar in nature to the walls
that we were banging the actin filaments against in the optical trap experiment.
When that happens, as you'll see as this movie starts to play,
the cells can crawl up, run into the wall, and then actually bounce off the wall
(reflect away from the wall).
There's no elasticity in this system... it's not like throwing a rubber ball against the wall.
It's much more like throwing a glob of clay against the wall.
And yet, somehow it's able to reorient itself and move away.
What that must mean is that, as one edge of the cell comes in contact with the wall,
somehow there's information transmitted from that edge that's made contact
across the cell to the other edge, telling the back edge now
to start protruding outwards and become the new front.
We don't understand how this is coordinated.
Another type of coordination which is a little more subtle,
but which is very fascinating to watch,
is the oscillation of these cells.
Here, this track shows a cell where the cell body has been labeled with a volume marker,
so it makes it very easy to precisely track the position of the center of the cell.
And the green trace here shows you how the movement of the cell occurs over time.
What you'll notice is that although the cell moves fairly straight, it's not perfectly straight,
and instead it's got this little sinusoidal oscillation (a little samba that it's doing
as it's moving along).
It sort of takes a step to one side and then overcompensates
by taking a step slightly more to the other side.
There are other kinds of large scale coordinations that we're just beginning to understand,
and one example of that is shown down here.
In this movie, what we're looking at is one of these motile cells
where we tricked it into forgetting its polarity.
Now you may recall the determination of polarity (the identification at the front of the cell
and the back end of the cell) is an absolutely critical first step
in any sort of directed motion.
So this cell has forgotten where its back end is.
Essentially it's trying to crawl everywhere at once.
And therefore it's spread out like a fried egg and can't get anywhere.
But as we watch the cell now, in the movie, as it starts to move,
what you can see is it's sort of reaching out,
trying to move in all sorts of different directions.
The nucleus in the middle here isn't really going anywhere
because it's being constantly pulled in all directions.
But this is an intrinsically unstable state.
And after a while, the cell actually spontaneously undergoes a large-scale reorganization,
where it pulls in its back end and starts to move.
And after that symmetry is broken, it will move that way persistently
essentially for as long as you care to watch it.
There's another similar kind of symmetry breaking which we sometimes observe.
where it actually looks like there are waves that are propagated around the cell,
and that's shown in this last movie here.
As you can see, the circular cell is starting to try to move.
It's trying to determine its back end.
And yet, it gets into some sort of confused state,
where instead of moving persistently in one direction,
it instead seems to sort of go in a circle a couple of times
before it gets its act together and is able to move forward.
All of these kinds of large scale coordination must mean that the cell
is able to organize its cytoskeleton (organize its actin gel)
in all of these various, complex kinds of movements.
Not only over cellular distances, which are very large,
but also over time and remember something that's happened recently
in order to adjust to that and evolve its responses to its environment
in some way that's dependent on its history.
None of these things do we actually understand at the molecular level,
but with the kinds of experiments I've been describing,
we're able to probe these kinds of issues in vitro using force measurements
and then compare them back to behavior of cells from real life.
I hope is something that I hope will begin to lead us down the path
towards real mechanistic understanding of these kinds
of mechanical effects during cell motility.
So, to summarize what I've described to you today,
much of the current work of my lab is focused on the challenge
of trying to develop biological toolkits
for studying mechanical problems in cell dynamics, cell organization, force, and movement.
Actin polymerization-based motility has been a particularly rich source
of examples for these kinds of problems.
It's something that we can manipulate a great deal in vitro,
the biochemistry of it is reasonably well understood,
and many of the proteins that manipulate these processes have been identified,
and their functions are known. And it's something that, as I've shown you,
that we also have a reasonably good handle on actually physically manipulating,
and doing force measurements as well.
Bacterial movement, such as the movement of Listeria monocytogenes
is very useful to study.
It's stereotyped, it's geometrically very simple,
it's very uniform in terms of speed and direction,
and it's well-defined at the molecular level.
I think really whole-cell movement is the next frontier:
trying to understand those sort of complex processes
that I was showing you on the last slide.
Now an interesting thing that I'd like you all to think about is
this problem of how force-generating elements have to work in groups.
Because you can never really get any useful action out of a single molecular motor
or a single actin filament growing. In order to accomplish cellular tasks,
you have to have many filaments working together,
many molecular motors working together,
and you have to have some way to get them all to cooperate.
In part, this is done geometrically. It matters how the filaments are arranged.
Some of the data that I've shown you today has sort of suggested
that somehow actin networks are more efficient at cooperating for force generation
than actin bundles are, where all the filaments are parallel.
A particularly interesting thing which I think really throws a monkey wrench
in the works of trying to understand this
is our clear observation that history matters, in terms of organization of the gel,
and also in terms of its force-generating properties.
So, understanding how all these things coordinate in time and in space,
for whole cell movement will be a challenge for many years to come.
And even at the level of understanding all of these behaviors in a single cell,
then the next step after that will be a much more difficult task
of understanding movements of cells in complex tissues:
how tissues are able to develop, change shape,
and grow in a complex multicellular organism such as ourselves.
Now I'd like to end by acknowledging the wonderfully talented group of scientists
that I've had the privilege to work with on these problems over the years.
Today, in the research part of the presentation, I specifically focused
on work by Matthew Footer, Jacob Kerssemakers, and Marileen Dogterom,
as well as Dan Fletcher and his students,
particularly Jason Choy and Sapun Parekh at Berkeley.
I also briefly mentioned or showed you data from a number of other people, including
Erin Barnhart, Catherine Lacayo, Cyrus Wilson,
Patricia Yam, and Lisa Cameron, as well as Paula Giardini.
And many of the other people I've listed on this slide
have contributed in one way or another to this project
or to other projects that I haven't had time to talk to you about.
Thank you very much for your attention.