kinetics? Something must be wrong with
your experiment,’ ” recalls Attila Szabo
of the National Institute of Diabetes
and Digestive and Kidney Diseases in
Bethesda, Md.
In 2005, Xie resolved the paradox. He
and his colleagues found a partner molecule that let off a burst of fluorescence
after reacting with an enzyme. The
researchers watched the molecular fireworks show for roughly 20,000 reaction
cycles, about 40 times more reactions
than were captured in the 1998 studies.
The enzyme was still wiggling and
shifting its efficiency every few reactions,
the researchers found. But given enough
reaction cycles, the differences averaged
out. “Enzymes seem to have a changing
personality,” Xie says. “But in spite of
that, the Michaelis-Menten equation
still holds.”
The biochemistry community seemed
to breathe a sigh of relief. The 2006 issue
of Nature Chemical Biology where Xie’s
paper appeared also included a com-
mentary titled, “Michaelis-Menten is
dead; long live Michaelis-Menten!”
Back-alley trysts
Yet, as Xie and others predicted, still
another challenge to the classic equation
has been brewing. Recent studies of individual cells suggest that while some of
the basic assumptions behind Michaelis-Menten may work in the lab, they don’t
always work for real cells.
“In test tubes, you have a very
artificial environment,” says Grima, who
has explored the basic question of how
reactions actually happen in cells.
t. dubÉ
Cells have a few obvious differences
from test tubes. For one thing, cells are
crowded. Just the largest molecules
inside take up between 5 and 40 percent
of the physical volume of a cell. What
free space remains is found in tiny
compartments that range from about
50 nanometers to just a few micrometers
on a side. Enzymes themselves may be
between a few and a hundred nanometers
long. Some enzyme-assisted reactions
can take place only inside the nucleus
or other cellular organelles. Inside real
cells, liaisons between enzymes and
their partners may be relegated to the
back alleys, where only a few individual
molecules can fit at a time.
This means that it’s not always easy
for enzymes and their partners to find
each other. Biologists have shown that
cells have what are called active transport networks, filaments that molecules
can slide along to travel between meeting places. If enzymes can’t meet locally,
they have to take public transport.
If reactions inside cells are like back-alley trysts, reactions inside test tubes
are like square dances in a big hall. With
such a large space to move around and
researchers constantly mixing the solution, every enzyme is almost guaranteed
to dance with every potential partner.
These differences ought to influence
how quickly enzyme-aided reactions go,
Grima reasoned. There should be some
big departures from the Michaelis-Menten equation inside real cells.
In 2009, Grima used mathematical models and computer simulations
to show that two basic assumptions
behind the Michaelis-Menten equation throw its predictions off in real
cells. First, he considered the number of molecules interacting. In a test
tube, billions of molecules could come
together. But in a cell, only 10 to 100
may meet at any given time.
Accounting for this and other “noise”
in a cell, Grima’s model suggests that
enzyme reactions in real cells proceed
as much as 20 percent slower than
Michaelis-Menten predicts. Next, he
considered active transport. If partners must ride intracellular subway
lines to meet up with their enzymes,
Grima found, Michaelis-Menten may
overshoot the real reaction rate in a cell
by as much as several hundred percent.
A faster reaction rate translates into
more reaction products from the same
amount of enzyme. For drug designers,
miscalculating the amount of product
throws off the prediction of how much
enzyme should be added to begin with.
To explore such implications, Grima
ran his simulations for a made-up drug
that works by binding to an enzyme
before the enzyme’s proper partner can
Flip-flopping forms As an enzyme (blue)
shifts its shape, its fit with a substrate molecule (green) shifts too, changing the enzyme’s
ability to drive a reaction. Frequent changes in
form translate into more variability in reaction
rate than the michaelis-menten equation takes
into account. but the average reaction rate, it
turns out, is in line with the equation.
reach it, a phenomenon called enzyme
inhibition. In the case Grima studied,
the amount of the drug needed to effectively combat the theoretical disease
was seven times higher than the amount
predicted by Michaelis-Menten.
“When I computed those estimates
for drug dosages, that’s when I had the
‘aha!’ moment,” Grima says. “That’s
when I thought, oh wow, these things
may be actually important.”
Population effects
Price and Pan-Jun Kim of the University
of Illinois at Urbana-Champaign think
their results, like Grima’s, could have
important implications for drug development. Even if Michaelis-Menten does
work for one particular cell, variations
between cells can pose another threat
to the equation — and to the efficacy of
drugs designed using it.
“Any enzyme in a chemical soup
has a potential chance to catalyze substrates anywhere else in the chemical
