How do proteins move around amidst the jumble of molecules inside a living cell?

I've been reading Philip Ball's book on "How Life Works" and I find it increasingly frustrating because he consistently describes things that he's "discovered" that biochemists like me must have missed. Here's an example from pages 231-232.

He presents a cartoon image of a cell showing that it's full of all kinds of molecules packed closely together, then he says,

A factory? The cell looks more like a packed nightclub. How does any molecule even cross the floor, let alone find its intended partner? In many gorgeous computer animations of cell components in action, molecules zoom into the frame to dock on their targets like GPS-guided drones. This is a telling simplification, for it betrays how hard it is to make sense of what goes on in cells without imputing some teleology, some intentional agency, to the components. No molecule can pinpoint its destination remotely and navigate its way purposefully there, just as no molecule can summon ("recruit") others into its presence. While it's true that systems like the microtubule/motor protein assembly can create a degree of directional motion, molecules floating in the cytoplasm merely drift at random, buffeted by neighbors thronging in on all sides. Even the water molecules that pervade this space don't act in quite the same way as those in a tumbler of water, for in such cramped confines they "feel" and respond to all the biomolecules around them. Biochemistry textbooks often treat the cell as though it was a dilute bag of chemicals, yet it is anything but.

You can see then, why I stressed earlier how noisy the cell is. It's astonishing that this frenzied molecular party maintains enough order to keep life viable at all. That around 37 trillion of these noisy microsystems collaborate in an entity billions of times bigger—you and me, beings with a sense of self, with purpose and memory and feelings—could seem miraculous. Even today, plenty of people question whether a purely materialistic position—the idea that molecules and and atoms is all we are—is adequate to explain life, and you can understand why.

Life obeys the laws of chemistry and physics. That's a purely materialistic position that I support.

There's no mysterious purpose or agency governing the movement of molecules inside the cell. It's true that we often simplify processes in order to explain the basic interactions but teachers and textbook writers know that what happens in a crowed cell environment is a bit more complicated. Molecules bump and jostle each other many times before there's a productive interaction.

Like most other biochemistry textbooks authors, I was excited to see the drawings of David Goodsell when they first appeared in the literature in the early 1990s. Goodsell was a structural biologist at the Scripps Research Institute in San Diego, California (USA) and he was keen to depict the actual crowded interior of a cell with all the molecules to scale. Our publishers scrambled to get permission to publish these drawings and Goodsell was very obliging. The first figure below is one of Goodsell's drawings and it first appeared in my 1994 textbook (Moran, Scrimgeour et al. 1994).

Although biochemistry textbooks had previously addressed the problems of molecular crowding, Goodsell's drawings gave us a hook to explain things in more detail. The key parameter is diffusion and that's governed by Fick's laws of diffusion. The diffusion properties of each type of molecule are described by a diffusion coefficient (D) and for diffusion in liquids that's determined using some version of the Stokes-Einstein equation.¹

The diffusion coefficient depends on the size, shape, and mass of the diffusing molecule. As you might imagine, big globular proteins diffuse more slowly than small molecules like glucose. Ribosome are even slower and odd-shaped molecules such as mRNAs have complicated properties. The properties of the medium are also important. Diffusion is slower in viscous media than in pure water. The rate of diffusion is also affected by the presence of other molecules, especially if we're dealing with large molecules. This is a concentration effect but we can think if it as a crowd effect—the crowded nightclub analogy described by Philip Ball is appropriate.

Biochemists have studied all these problems and worked out the parameters. A lot of it involves scary mathematics, including (gasp!) calculus, so most textbook authors, including me and my colleagues, avoided the details in our textbooks for fear of scaring off professors.²

But we still tried to explain the issue in the first few chapters of our books in order to justify downplaying these diffusion effects in the rest of the book.³ I'll reproduce the 2012 version of the explanation that I first wrote in 1994 in order to show that we can answer Philip Ball's questions. We don't treat the cell as a dilute bag of chemicals as Ball suggests, but we still treat it as a bag of chemicals and we can justify that treatment.

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1.9 A Picture of the Living Cell

We have now introduced the major structures found within cells and described their roles. These structures are immense compared to the molecules and polymers that will be our focus for the rest of this book. Cells contain thousands of different metabolites and many millions of molecules. In the cytosol of every cell there are hundreds of different enzymes, each acting specifically on only one or possibly a few related metabolites. There may be 100,000 copies of some enzymes per cell but only a few copies of other enzymes. Each enzyme is bombarded with potential substrates.

Molecular biologist and artist David S. Goodsell has produced captivating images showing the molecular contents of an E. coli cell magnified 1 million times (Figure 1.20 on page 26). Approximately 600 cubes of this size represent the volume of the E. coli cell. At this scale individual atoms are smaller than the dot in the letter i and small metabolites are barely visible. Proteins are the size of a grain of rice.

A drawing of the molecules in a cell shows how densely packed the cytoplasm can be, but it cannot give a sense of activity at the atomic scale. All the molecules in a cell are moving and colliding with each other. The collisions between molecules are fully elastic—the energy of a collision is conserved in the energy of the rebound. As molecules bounce off each other they travel a wildly crooked path in space, called the random walk of diffusion. For a small molecule such as water, the mean distance traveled between collisions is less than the dimensions of the molecule and the path includes many reversals of direction. Despite its convoluted path, a water molecule can diffuse the length of an E. coli cell in 1/10 second.

An enzyme and a small molecule will collide 1 million times per second. Under these conditions, a rate of catalysis typical of many enzymes could be achieved even if only 1 in about 1000 collisions results in a reaction. Nevertheless, some enzymes catalyze reactions with an efficiency far greater than 1 reaction per 1000 collisions. In fact, a few enzymes catalyze reactions with almost every molecule of substrate their active sites encounter—an example of the astounding potency of enzyme-directed chemistry. The study of the reaction rates of enzymes, or enzyme kinetics, is one of the most fundamental aspects of biochemistry. It will be covered in Chapter 6.

Lipids in membranes also diffuse vigorously, though only within the two-dimensional plane of the lipid bilayer. Lipid molecules exchange places with neighboring molecules in membranes about 6 million times per second. Some membrane proteins can also diffuse rapidly within the membrane.

Large molecules diffuse more slowly than small ones. In eukaryotic cells the diffusion of large molecules such as enzymes is retarded even further by the complex network of the cytoskeleton. Large molecules diffuse across a given distance as much as 10 times more slowly in the cytosol than in pure water.

The full extent of cytosolic organization is not yet known. A number of proteins and enzymes form large complexes that carry out a series of reactions. We will encounter several such complexes in our study of metabolism. They are often referred to as protein machines. This arrangement has the advantage that metabolites pass directly from one enzyme to the next without diffusing away into the cytosol.Many researchers are sympathetic to the idea that the cytosol is not merely a random mixture of soluble molecules but is highly organized in contrast to the long-held impression that simple solution chemistry governs cytosolic activity. The concept of a highly organized cytosol is a relatively new idea in biochemistry. It may lead to important new insights about how cells work at the molecular level.

2.3B. Cellular Concentrations and Diffusion

The inside of a cell can be very crowded as suggested by David Goodsell’s drawings (Figure 1.20). Consequently, the behavior of solutes in the cytoplasm will be different from their behavior in a simple solution of water. One of the most important differences is reduction of the diffusion rate inside cells.

There are three reasons why solutes diffuse more slowly in cytoplasm.

1. The viscosity of cytoplasm is higher than that of water due to the presence of many solutes such as sugars. This is not an important factor because recent measurements suggest that the viscosity of cytoplasm is only slightly greater than water even in densely packed organelles.
2. Charged molecules bind transiently to each other inside cells and this restricts their mobility. These binding effects have a small but significant effect on diffusion rates.
3. Collisions with other molecules inhibit diffusion due to an effect called molecular crowding. This is the main reason why diffusion is slowed in the cytoplasm.

For small molecules, the diffusion rate inside cells is never more than one-quarter the rate in pure water. For large molecules, such as proteins, the diffusion rate in the cytoplasm may be slowed to about 5% to 10% of the rate in water. This slowdown is due largely to molecular crowding.

For an individual molecule, the rate of diffusion in water at 20°C is described by the diffusion coefficient (D_20,w). For the protein myoglobin, D_20,w = 11.3 x 10^–7 cm² s^–1. From this value we can calculate that the average time to diffuse from one end of a cell to the other (~10 μm) is about 0.44 seconds.

But this diffusion time represents the diffusion time in pure water. In the crowed environment of a typical cell it could take about 10 times longer (4 s). The slower rate is due to the fact that a protein like myoglobin will be constantly bumping into other large molecules. Nevertheless, 4 seconds is still a short time. It means that most molecules, including smaller metabolites and ions, will encounter each other frequently inside a typical cell (Figure 2.8). Recent direct measurements of diffusion inside cells reveal that the effects of molecular crowding are less significant than we used to believe.

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The figures are from the 2012 edition of my textbook (Moran et al. 2012: © Pearson/Prentice Hall). The photo of David Goodsell is from Wikipedia.

1. George Gabriel Stokes and Albert Einstein were biochemists who studied diffusion and Brownian motion. Albert made some contributions to other fields.

2. I first learned about this stuff in a 1968 graduate course taught by Bruce Alberts. He wasn't scared of the math (I was). We had to know the normal rates of diffusion in order to understand the behavior of molecules in a centrifuge and sedimentation coefficients (see Svedberg). I still have the occasional anxious moments whenever I hear about Stokes radius and frictional coefficients. Does anybody teach this anymore?

3. We don't ignore them completely. They come up again when we discuss facilitated diffusion across a membrane and the diffusion of lipids within a membrane. It's also important when we discuss how DNA binding proteins find a binding site on DNA since that rate is often 100 times greater that the theoretical maximum for a diffusion-limited second order reaction [Slip Slidin' Along - How DNA Binding Proteins Find Their Target]. Diffusion effects are also important when we discuss enzyme-catalyzed reaction rates. Some of those rates are limited by the diffusion of substrates and product. Some enzymes can catalyze reactions at a rate that's faster than the diffusion-limited rate! [Superoxide Dismutase Is a Really Fast Enzyme]

Moran, L.A., Horton, H.R., Scrimgeour, K.G., and Perry, M.D. (2012) Principles of Biochemistry 5th ed., Pearson Education Inc.

Moran, L.A., Scrimgeour, K.G., Horton, H.R., Ochs, R.S., and Rawn, J.D. (1994) Biochemistry Neil Patterson Publishers/Prentice Hall