THINK of the word 鈥渆ngine鈥� and your mind will probably conjure up an image of
some huge, oil-sweating behemoth of iron, rubber and steel鈥攁 200-tonne
railway locomotive, perhaps, or one of the great diesel-fuelled beasts of the
modern motorway. But not all engines are like that. As you read these words,
microscopic motors are guiding your eyes precisely across the page. Meanwhile,
in every cell of your body, tiny pumps are pushing crucial materials through
cell walls, and minuscule transport engines are ferrying raw materials back and
forth along internal cellular highways. Your body is a fully mechanised chemical
factory.
In the past few years, researchers using lasers and microscopes have managed
to spy on nature鈥檚 motors at the molecular level. They have identified the
shapes and sizes of their components, and measured how much energy they burn
moving along. These tiny engines do many of the same things as their far larger
and cruder cousins鈥攖hey move things and transform chemical energy into
useful action. But if you could magnify one, you wouldn鈥檛 find anything even
remotely resembling the heavy machines of the railways or highways. There are no
pistons. And no obvious timing mechanisms to keep all the parts in synchrony. So
how do they work?
In 1824, the French engineer Sadi Carnot probed the theoretical limits of
thermodynamics and laid out the principles of motors and engines. Now, using a
branch of physics known as nonequilibrium thermodynamics, scientists are
following Carnot鈥檚 example and exploring the theoretical limits of what machines
can do鈥攂ut this time in a microscopic, biological setting. These theories
are helping to complete the picture of how molecular motors work, and are also
laying down the principles of a new science of microworld mechanics.
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What is it that makes a molecular motor so different from, say, a car engine?
At first, they don鈥檛 seem so far apart. Just as a car鈥檚 engine burns petrol to
push the vehicle along the road, molecular motors use energy from chemical
reactions to drive molecular vehicles along fixed tracks. In a muscle cell, for
example, long myosin fibres lie alongside other long fibres called actin
filaments. Side branches on the myosin fibres called 鈥渉eads鈥� can attach
themselves at various sites located regularly along the actin filaments
(see Diagram).FIG-21125201.jpg
When the heads are attached, the myosin fibre is like a car parked on an
actin road, and the muscle tissue is rigid. But living cells contain a ready
supply of high-energy ATP (adenosine triphosphate) molecules鈥攖he body鈥檚
fuel. The myosin heads act as enzymes to catalyse the reaction of ATP with water
to produce ADP (adenosine diphosphate). In the process, a myosin head moves from
one site along the fibre to the next. The migrating heads drive the fibres past
one another, and the muscle contracts.
Something similar happens with the kinesins鈥攎otors that move inside
cells along networks of long filaments known as microtubules. Kinesins are long
stringy molecules with a pair of heads at one end and a tail at the other.
鈥淐argo鈥� molecules latch onto the tail. One of the jobs of kinesins is to
separate chromosomes prior to cell division. The heads of a kinesin lock onto
sites along the microtubules and, by reacting with ATP molecules, march from one
position to another, carrying their cargo. A microtubule is polar鈥攆rom a
particular kinesin鈥檚 point of view it is like a one-way street. One end is
termed the 鈥�+鈥� end and the other the 鈥�-鈥� end, and different members of the
kinesin family, such as Nkin and Ncd, travel along it in different
directions.
Mysterious mechanism
Three years ago, biologist Karel Svoboda and colleagues from Harvard and the
Rowland Institute of Science in Cambridge, Massachusetts, managed to catch
kinesins in the act. They attached single kinesins to silica beads, laid the
beads onto a glass slide coated with microtubules
(see Diagram)
and supplied ATP. The beads鈥攄riven by the kinesins鈥攎oved
along the microtubule in regular 8-nanometre steps. Other groups have
watched microtubules glide over kinesin coated slides
(see Diagram).FIG-21125202.jpg
So the biological function and rough manner of movement of molecular motors
are clear. What is puzzling is how they turn chemical energy into mechanical
energy, and how they direct it toward a purpose. There are no chemical or
electrical gradients along microtubules and muscle fibres that might tell the
motors which way to go. And yet, kinesin and myosin molecules 鈥渒now鈥� to go one
way rather than the other.
Remember that these motors, being molecule-sized, live in a hostile world. In
the fluid of a cell, they are subject to a constant and violent battering by
molecules of all sorts. Once in a while, at random, they bind chemically to an
ATP molecule. The ATP reacts with water to make ADP, which remains stuck to the
motor for a time before being stripped off. Each stage in this chemical sequence
triggers a change in the motor molecule鈥檚 shape, but such events happen
randomly. So it is not clear how the molecule moves on a directed path.
Biologists have long suspected that there must be some timing link between the
chemical reactions and the steps of the motor. But researchers have shown that
even when the energy usually supplied by ATP reactions is replaced by random,
externally applied electrical impulses, the motors still work.
快猫短视频s have been dismantling molecular motors and studying their
structures, hoping to find some clues to their mysterious ability to draw
directed energy out of a noisy, fluctuating environment. The kinesin Nkin, which
moves in the 鈥�+鈥� direction along microtubules, has two identical heads connected
by a thin neck. Each head interacts with the microtubule, but when one is
attached, the other dangles free. Somehow, this other head manages to move to
the next site, always in the + direction. Why?
Some researchers believe that the detached head simply diffuses within the
liquid, and has a slightly higher probability of binding again at a site toward
the + end of the microtubule. Others, such as mathematicians George Oster at the
University of California, Berkeley, and Charles Peskin at the Courant Institute
in New York, argue that the motion is more like the expansion of a compressed
spring, and that directionality results from a precisely orchestrated sequence
of attachments and detachments. If the front head detaches when Nkin is
compressed and the rear head when it is stretched, then the two-headed structure
can march right along.
So which is it? 快猫短视频s thought the debate might be settled when more
detailed molecular structures for the motors became available. Maybe there would
be one basic structure for motors that move in the 鈥� direction, and another for
those that move in a + direction? Last year, however, researchers at the
University of California at San Francisco headed by Ron Vale and Robert
Fletterick finally obtained the precise structures for the + and 鈥� kinesin
motors Nkin and Ncd, and they found them to be extremely similar. There doesn鈥檛
seem to be a simple structure responsible for directed motion.
Perhaps more experiments will help to clear things up. But mathematicians and
physicists, my group at the University of Chicago included, are taking an
alternative, minimalist approach to the problem. How is it that something can
exploit random, fluctuating forces to move itself in one direction rather than
another? By working out mathematically the properties of very simple schematic
motors, we hope to find clues to the general, physical principles by which real
motors might work.
Suppose you wanted to design a machine to do what muscle fibres and
microtubules do. The obvious thing to try is a ratchet鈥攖he mechanism at
work in a torque wrench. A ratchet has a set of asymmetric teeth that grab in
one direction and allow free motion in the other. It鈥檚 appealing to think that
the kinesins or myosin might work in this way with ATP providing the energy and
a ratchet mechanism fixing the direction of travel.
One way only
The American physicist Richard Feynman was interested in such 鈥渙ne-way鈥�
machines, and in his Lectures on Physics considered a simple model for
one鈥攁n elementary ratchet and pawl device (see 鈥淔eynman鈥檚 ratchet鈥�). In
Feynman鈥檚 model, the faces of the ratchet鈥檚 teeth are vertical on one side, so
that it is impossible to drag the pawl back up this face. He wondered if such a
machine could derive one-way motion from the random motions of molecules in a
gas. Could the molecules in a box of air drive a paddlewheel? If the wheel
cannot go backward, then molecules hitting the paddle would drive an irregular
but relentless clockwise motion of the wheel.
Seems reasonable. But Feynman showed that such a device would violate the
second law of thermodynamics. By using the icy winter air, for example, you
could raise buckets of water which could in turn drive a water wheel to generate
electricity and heat your home, all for free. So a ratchet like this won鈥檛
really work.
Feynman鈥檚 model is rather abstract. But it has immediate implications for
molecular motors. Think of a kinesin or myosin molecule as being like Feynman鈥檚
wheel, and its motion along a microtubule or actin filament as being like the
wheel鈥檚 rotation. The laws of physics say that a molecular motor based on a
ratchet mechanism simply cannot derive directed motion from its interactions
with chemicals in thermodynamic equilibrium. So what is going on? Do muscles
violate the laws of physics?
Tipping the balance
Fortunately, Feynman also considered a slightly modified ratchet. In the
simplest version, the temperature of the spring holding the pawl and the
temperature of the gas in the box containing the paddle were equal. But they
needn鈥檛 be. Feynman found that with unequal temperatures, the imbalance in the
vigour of the molecular fluctuations in the gas and in the spring could indeed
cause the wheel to rotate.
There are tiny thermal gradients in cells, but they are far too small to have
much effect. So it is not a temperature gradient that moves molecular motors
about. But the crucial element of Feynman鈥檚 second ratchet is not so much the
temperature difference, but the fact that the system has been taken out of
thermodynamic equilibrium. It is the departure from equilibrium that allows
directed motion.
This insight may provide the key to understanding molecular motors. Because
you are eating and breathing, and breaking down food, there is a constant flux
of energy through your body, which shows itself in chemical disequilibrium in
your cells. The supply of ATP, for instance, is constantly being replenished.
Living organisms are sophisticated devices for maintaining thermodynamic
disequilibrium.
In the past few years, following the realisation that a chemical system out
of equilibrium should be able to drive directed motion, physicists have been
inventing and studying a variety of generalised ratchets of the Feynman kind. It
is straightforward, for instance, to devise a simple schematic model for a
kinesin motor.
Imagine a chain of electric dipoles arranged head to tail. These might
represent the individual units of a microtubule filament. If a charged particle
interacts electrically with this chain, then it will be attracted toward
opposite charges on the chain, and be repelled from similar charges. If the
charge on the particle remains fixed, at say 鈥�1, then not much of interest
happens.
But suppose the particle could change its charge
(see Diagram). Like the
kinesins it might act as an enzyme, catalysing some chemical reaction where a
negatively charged S鈥� and a positively charged H+ can go together to form SH.
Enzymes catalyse reactions by binding to each reactant separately and bringing
them together. If the soup surrounding the particle and the chain contains lots
of S鈥�s, H+s and SHs, the particle will sometimes bind one, sometimes the
other, sometimes both and sometimes neither. So its charge will fluctuate
irregularly between 鈥�1 and 0. Its electrical interactions with the chain will
similarly fluctuate.FIG-21125204.jpg
The effects of these fluctuations can be seen through a plot of the potential
energy of the particle. The particle would like to move to positions where its
energy is low鈥攖oward regions of opposing charge. When charged, it sees a
landscape of hills and valleys and when unchanged flat terrain. So, since the
particle reacts randomly with the S鈥�s and H+s, and goes through a random
sequence of charges, it moves through a wildly fluctuating landscape. The forces
do not, on average, tend to point in one direction rather than another. And yet,
mathematical analysis of the motion of a particle in such a strange field shows
that if the chemical reaction between S鈥� and H+ to produce SH is out of
equilibrium鈥攎ore SHs are breaking apart than are being formed鈥攖hen
the particle on average will flow in one direction rather than the other.
In the real kinesin motors, you might think of S鈥� as ATP and H+ as a
water molecule. Kinesin catalyses the reaction between ATP and water to give
ADP. The reaction is in a constant state of disequilibrium because fresh ATP
(the fuel) is continually supplied to replace 鈥渂urnt-out鈥� ADP. That is not to
say that kinesin works in exactly this way. But the model shows how purely
random changes due to a chemical reaction in disequilibrium can give rise to
motion in one direction.
The model鈥檚 crucial ingredients are the asymmetry in the track (its
polarity), the disequilibrium of the chemical soup, and the particle鈥檚 Brownian
motion resulting from the incessant bombardment of molecules in the solution.
Engineers try to minimise the effect of noise in cars and locomotives. But at
the scale of a protein or a cell, the effects of noise are inescapable. And
microscopic motors use them to advantage.
When the forces of evolution were designing biology鈥檚 motors, these may have
been the working principles. Learning from evolution, physicists are now even
building machines based on these ideas which use purely random forces to drive
tiny particles over grids of electrically charged wires. Strikingly, particles
of different sizes go in different directions鈥攋ust like the kinesins Nkin
and Ncd. We seem at last to be getting closer to solving the mystery of how
nature鈥檚 tiny engines work.
* * *
Feynman鈥檚 ratchet
Richard Feynman proved that you cannot drive a one-way machine by using the
random thermal movement of gas molecules alone
(see diagram).
Why not? Feynman realised that for the device to work the pawl has to move up and
down to let the teeth pass, and so it has to be suspended by an elastic attachment
of some sort, such as a spring.FIG-21125203.jpg
Since the energy of single molecular collisions is far too tiny to turn a
wheel of ordinary size, the wheel, axle and spring all have to be microscopic
for the device to have any chance of working. And there鈥檚 the rub. For the
behaviour of a microscopic spring is also disturbed by collisions with
molecules鈥攊n the support to which it is attached, for example鈥攚hich
cause it to vibrate.
When the pawl is down, the device works as planned. But sometimes, rarely, it
will be up, disengaging the one-way mechanism. When such upward movements occur,
the fluctuating molecular force on the paddle will cause forward or backward
motion with equal probability. And the effects of these rare fluctuations in the
pawl are amplified. For when the pawl is up, it takes only a tiny movement of
the wheel backward to set the device back by one tooth, whereas to send it
forward by one tooth requires a far greater motion.
Working out the mathematics of the situation, Feynman found that if the
paddle and pawl are at the same temperature鈥攕o that the fluctuations in
the pawl are as strong as those driving the paddlewheel鈥攖hen the ratchet,
despite appearances, will not rotate.