LIFE IS CROWDED: Modeling the Cell's Interior

Modelers are using recent gains in computational power to consider the complex interactions of hundreds or thousands of macromolecules at once--a necessary first step toward whole cell simulation

Molecules in cells behave like people in crowded subway cars. Because they can barely budge or stretch out without bumping into a neighbor, they move more slowly, smush themselves into more compact forms, and coalesce into aggregates more often than in a less congested setting, says Allen Minton, PhD, a physical chemist at National Institute of Diabetes and Digestive and Kidney Diseases, who coined the term “macromolecular crowding” in 1981. In addition, short distances separate crowded molecules, so they may also exert forces on one another, sometimes altering the effects of limited space.


The Crowded Cell: This picture shows an atomically detailed model of the crowded E. coli  cytoplasm, including the 50 most abundant macromolecules. RNA is shown as green and yellow. Reprinted from: McGuffee SR, Elcock AH (2010) Diffusion, Crowding & Protein Stability in a Dynamic Molecular Model of the Bacterial Cytoplasm. PLoS Comput Biol 6(3): e1000694.In the past, intracellular crowding was routinely ignored in both experiments (which are typically run in uncrowded solutions) and computer models. As a result, scientists’ understanding of intracellular biology might be inaccurate. But in studies during the past five or six years experimentalists have added crowding agents—complex polysaccharides that take up space—to their test tubes to get a better picture of crowding effects. And modelers are using recent gains in computational power to consider the complex interactions of hundreds or thousands of macromolecules at once. 2010 saw these computer models begin to yield surprising insights about molecular diffusion as well as protein folding and function.


Slow going: Modeling diffusion

Fluorescent-tagged proteins move 10 to 15 times more slowly inside an E. coli bacterium than in a test tube, says Jeffrey Skolnick, PhD, professor of systems biology and director of the Center for the Study of Systems Biology at Georgia Tech. To try to work out the exact causes of this slow down, his team ran Brownian dynamics simulations of a virtual E. coli packed with more than 1000 macromolecules (including 15 unique types). They reported their results in October 2010 in the Proceedings of the National Academy of Sciences.


Crowding alone—just molecules taking up space, or “excluding volume”—explained only about one third of the reduction in diffusion speed. But the combination of excluded volume plus hydrodynamic interactions—molecules creating wakes like sailboats in a lake—achieved the 10 to 15 percent reduction.


“If you have a whole bunch of sailboats, your behavior is going to be modified by the presence of the wakes created by all the other sailboats,” Skolnick says. “In the same way, when one molecule starts to move it creates an eddy in the solvent which perturbs the flow around other molecules.”


Hydrodynamic interactions had largely been ignored in previous cell simulations, because they act over a long range and time frame and thus are computationally expensive to implement. “I’d rather throw it away if I could,” Skolnick says. His team had to reduce the total number of molecules in the simulation to about 400 to keep it computationally tractable.


Skolnick’s team also considered weak attractive interactions, such as van der Waals forces. If you make proteins sufficiently “sticky,” you can slow diffusion to any speed—even zero, Skolnick says. But his team showed that these forces are much more dependent on particle size, when stickiness dominates, as compared to hydrodynamic interactions. “So it seems that crowding and hydrodynamic interactions are the dominant effects,” Skolnick says.


Squished together: Modeling protein folding and function

When space is at a premium, proteins are driven to fold and compact. But accounting for crowding in simulations of protein folding takes enormous computing power.


Protein Compactor: The crowded conditions in a cell cause the enzyme PGK to compact. The protein folds into three states depending on the level of crowding—from a more open conformation (top) to the most closed conformation (bottom). Courtesy of: Margaret Shun Cheung, University of Texas, Houston.“It’s a very intimidating task to think about not only just one protein, but many, many proteins,” says Margaret Shun Cheung, PhD, assistant professor of physics at the University of Texas, Houston. In 2005, she and her mentor—Devarajan Thirumalai, PhD, professor of chemistry and biochemistry at the University of Maryland—published some of the first simulations of protein folding in crowded conditions.


In an October 2010 paper in PNAS, Cheung and her team reported the effects of crowding on PGK, an enzyme involved in glycolysis (the breakdown of sugar). In its native state, PGK is shaped like PacMan—it has two subunits where substrates bind, connected by an open hinge. Researchers thought that substrate binding caused PacMan to close his jaws, bringing the substrates together and igniting the reaction.


But using coarse-grained models, Cheung found that the enzyme actually remains in a closed, non-native state in the crowded cell (see video at: Cheung’s experimental collaborators attached fluorescent tags to PGK’s two subunits and confirmed the finding.


The closed conformation keeps the binding sites near each other, allowing the substrates to bind one another quickly. PGK can therefore act 15 times faster in vivo than in dilute solution. “This indicates that protein function inside a cell may be very different than in a test tube,” Cheung says.


Cheung, like many others, models crowding agents as simple spheres, to save computing power. But such models may miss important protein-macromolecule interactions, says Adrian Elcock, PhD, associate professor of biochemistry at the University of Iowa.


In a March 2010 paper in PLoS Computational Biology, his team described an atomically detailed model of E. coli cytoplasm, including about 1000 instances of the 50 most abundant macromolecules. The molecules were modeled as “hollowed out” rigid shells, with atomic details only on the surface. It took a year to run the simulations.


Crowding is expected to stabilize protein folding. But when Elcock’s team considered the thermodynamics of two particular E. coli proteins, they found that folding was actually less stable in vivo than in vitro. The reason: electrostatic and hydrophobic forces actually countered the excluded volume effects.


So just as Skolnick’s work showed the importance of hydrodynamic interactions in a crowded environment, their work showed the importance of electrostatic and hydrophobic interactions.


“I think both studies are first generation models. Second generation models will have to take aspects of both,” Elcock says.

The Future: Modeling the cell and beyond

Understanding the effects of crowding on macromolecules is a necessary first step toward whole cell simulation, Skolnick concludes. “And now given the algorithms and the computational resources, it’s not a preposterous question to begin to look at these things.”

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