Even the simplest living system is extraordinarily complicated. A bacterium, for example, is a single-celled organism that hunts for food, evades predators, grows, and reproduces itself. It’s not surprising, then, that its genome includes thousands of genes, and that spectacular advances in understanding bacteria and other “simple” organisms have been made without resorting to a reductionist approach to biology—the notion that living systems can be understood from interactions at the scale of atoms and molecules.
Nevertheless, much of the thinking and language of generations of scientists has been inspired and bolstered by the basic belief that such systems obey the laws of chemistry and physics. There isn’t any contradiction between the laws of physics—mechanics and thermodynamics—and the principles of biology. The controversy centers instead on how simple a biological system must be before attempts to understand it from a purely physical point of view are fruitful.
Viruses have played a special role in both philosophical and practical treatments of that question. They may be considered living insofar as they replicate and their genomes evolve in the same way as those of bacteria, plants, and animals. But they are not strictly alive because they depend on hosts for that replication and because they do not grow—or do anything at all, for that matter—in between being replicated. It is precisely because of their obligate dependence on living hosts that viruses can be so many orders of magnitude simpler than any truly living system. For example, viruses can have as few as two genes and as few as two constituent components. Indeed, some infectious viruses can be reconstituted in buffer solution by combining purified copies of a single nucleic-acid molecule and a single protein molecule. Between replication cycles, viral particles, each about a tenth of a micron, behave no differently from any colloidal particle of that size; they diffuse and respond to electric fields no differently from, say, charged polystyrene spheres.
Their monodispersity in size and shape—specifically, the fact that all copies of a given type of virus are essentially identical—allows many viral particles to form crystals. Their structures can thus be determined to angstrom resolution. Indeed, Wendell Stanley’s crystallization of tobacco mosaic virus 1 in 1935 dramatically put to rest any notion that viruses might simply be smaller versions of the usual microbes. A key follow-up demonstration by Heinz Fraenkel-Conrat and Robley Williams in 1955 showed that infectious particles of TMV could be synthesized from scratch—reconstituted from purified viral components, in this case a particular RNA molecule and a particular protein molecule. 2
From the 1930s through the 1950s, another kind of virus played a quite different but no less fundamental role in revolutionizing biology. 3 In particular, the physicist-turned-biologist Max Delbrück initiated the pursuit of quantitative biology by demonstrating—with the inspired help of the quickly growing “phage group” of scientists—that the replication of viruses could be harnessed to elucidate the basic molecular aspects of genetics and the synthesis of proteins by DNA. Bacterial viruses were chosen for that demonstration largely because their hosts were so much better understood and easier to manipulate than the hosts of plant and animal viruses. Today, more than 50 years after that period, it turns out that the bacterial viruses—commonly called bacteriophages, or more simply phages—are again occupying center stage, but this time in a very different context. Using 21st-century ideas and methods, researchers have been able to measure the physical properties of phages as the inanimate, mechanical objects that they are.
Fitting genes in a virus
By the mid-1950s it was already clear from electron microscopy and x-ray crystallography that most viruses were spherical and that their diameters were typically tens of nanometers. But it was not known whether the protective protein shell, or capsid, of a virus consisted of a single, ultrahigh-molecular-weight protein or a large number of small protein subunits bound together. In 1956, before the genetic code had been worked out and at a time when no genome of any kind had been sequenced, Francis Crick and James Watson argued in a two-page paper that only the second possibility made sense because the viral genome wasn’t big enough to encode for a super megadalton protein (1 dalton = 1 atomic mass unit). They further concluded that the symmetry of spherical viral capsids should be icosahedral. 4 How could they make such clear and bold predictions? The answer lies in simple physical considerations.
First let’s estimate the surface area of a capsid. With a typical radius of 20 nm, the area is about 5000 nm2. Assuming 10 nm2 as the typical area occupied by a low-molecular-weight (say, 30 kDa) protein, it appears that either a single 15 MDa protein or about 500 copies of the much smaller protein is required to make up the single-protein-thick capsid. With those facts, and the emerging idea that gene size was proportional to protein size, Crick and Watson realized that the shell must consist of hundreds of copies of a single low-molecular-weight gene product. A single gene—and a small one at that—was therefore required for the capsid.
How many other genes might be needed? That’s a biological question, requiring knowledge of the role of enzymes and structural proteins in the life cycle of the particular virus. But what if the question were simply, How many genes can fit into a viral capsid? First, how big is a gene? From the structure of the genetic code, which is written in the sequence of the nucleotide bases that constitute the genome, we know that three nucleotides—one codon—are required for each amino acid in a protein. This suggests that about 1000 nucleotides are necessary to code for a 30-kDa protein, for example, because the average molecular weight of an amino acid is about 100 Da. In molecular-weight terms, a nucleotide is about 330 Da, so a 1000-nucleotide gene (in single-stranded form) must weigh about 330 kDa. How much nucleic acid can fit inside the capsid? Assuming a maximum density of 1 g/cm3 and a capsid volume (from a 20-nm radius) of 3 × 104 nm3, there’s room inside the capsid for a 20-MDa molecule and hence for about 50 genes. So, from a simple consideration of the area and volume of a protein shell, we conclude that viral capsids must involve aggregates of hundreds of protein subunits and that their genomes contain on the order of tens of genes.
The much more exciting and brilliant inference of Crick and Watson was their prediction of icosahedral symmetry. Here, again, they were guided by the overwhelming economy gained by having a viral shell assembled from many copies of a single gene product. They needed to account for how a large number of identical molecules could occupy energetically equivalent, optimum positions in the capsid. Essentially, they were asking, What are the relevant symmetry operations that relate each of the protein subunits to the others in the shell? After eliminating translations (because capsids are finite, not extended, structures) and mirror planes (because the proteins are chiral), one is left with the cubic point groups. And the largest of those groups is icosahedral, with 15 twofold, 10 threefold, and 6 fivefold rotation axes. Indeed, within just a few years, many x-ray crystallography studies confirmed the icosahedral symmetry of spherical viruses (see Physics Today, Physics Today 0031-9228 57 12 2004 27 https://doi.org/10.1063/1.1878326 December 2004, page 27 ).
How and why is a phage pressurized?
Figure 1 shows bacteriophage Λ, arguably the phage most broadly studied from genetic, biochemical, and structural points of view. The head, a shell of protein having icosahedral symmetry and containing the genome, has a radius of about 30 nm. The tail is about 150 nm long and has an outer diameter of about 10 nm; its inner diameter is just large enough to accommodate the double-stranded (“duplex”) DNA genome, whose diameter is 2–3 nm. The head in the figure appears dark because the DNA inside it is packed to crystalline density. Early x-ray diffraction studies 5 and more recent cryo-electron microscope imaging 6 have established that DNA helices are packed hexagonally side-by-side on average, with interaxial spacings as small as 2.5 nm. At that spacing the repulsions between interacting parts of the double-stranded DNA molecule are very strong.
Figure 1. A Λ phage, as shown in an electron micrograph. Its double-stranded DNA genome is confined at crystalline density in an icosahedral protein head, or capsid. When the tip of the phage’s tubular tail binds to the surface of a bacterium, conformational changes in the tail proteins cause the DNA to be ejected through the tail into the host. Energy stored in the highly confined and stressed DNA drives the ejection, much like it does a compressed spring once it is allowed to expand.
Figure 1. A Λ phage, as shown in an electron micrograph. Its double-stranded DNA genome is confined at crystalline density in an icosahedral protein head, or capsid. When the tip of the phage’s tubular tail binds to the surface of a bacterium, conformational changes in the tail proteins cause the DNA to be ejected through the tail into the host. Energy stored in the highly confined and stressed DNA drives the ejection, much like it does a compressed spring once it is allowed to expand.
Knowledge of what “very strong” means comes from measurements of DNA–DNA interactions in bulk solutions at comparable interaxial spacings. One can then calculate the energy difference between the unconstrained DNA genome free in solution and its packaged state in the head of the virus. In addition to self-repulsion, DNA is also difficult to bend. The length scale over which DNA can bend spontaneously due to thermal fluctuations—its persistence length—is about 50 nm. But the capsid radius is nearly half that size, so the packaged DNA remains strongly bent along all of its length.
Simple descriptions of strong self-repulsion and bending persistence allow us to estimate the work of packaging the DNA. The repulsions between neighboring DNA duplex portions arise primarily from electrostatic interactions and can be determined from studies of DNA solutions subjected to an osmotic pressure due, say, to high-molecular-weight polyethylene glycol. The dependence of interaxial spacing d on osmotic pressure Π has been measured in x-ray diffraction studies of DNA in equilibrium with PEG solutions of different concentrations. 7 Under a wide range of ionic conditions, the pressure falls off exponentially with increasing values of d. The magnitude of the pressure drop depends on the valence and concentration of cations such as Na + and Mg 2+ that moderate the repulsions between DNA strands. Integration of the measured Π(d) over the hexagonal unit cell from large distances down to d gives the interaction energy per unit length. Multiplying by the total length of the genome and evaluating the result for the average interaxial spacing provides an estimate of the total work done to overcome the DNA–DNA repulsion: 5 × 104 kT, where k is Boltzmann’s constant and T is the cell temperature.
The work done to bend the DNA turns out to be smaller. DNA behaves much like a uniform elastic string, even though its local bendability depends on sequence. The DNA’s total length, generally 10–30 µm for bacteriophage genomes, is two to three orders of magnitude larger than its persistence length. Accordingly, its one-dimensional bending modulus κ can be written in terms of the persistence length ξ as κ= ξkT and the energy per unit length as κ(1/R)2, where R is the local radius of curvature. Taking an average value of R = 10 nm and multiplying by the overall genome length gives an estimate of about 103 kT to bend the DNA; more careful estimates give a somewhat larger value but still confirm that the work of packaging is dominated by the short-range repulsions due to neighboring portions of the genome crowded upon each other.
With that much energy required to confine the genome, there is a correspondingly large pressure in the capsid, on the order of 40 atmospheres. With pressures that high, the capsid must be very strong, even though it is a noncovalently bound, single-molecule-thick shell; its protein subunits are connected not by chemical bonds but by electrostatic, hydrogen-bonding, and hydrophobic interactions. If the capsid were to break, the DNA would burst out, as pictured in figure 2, relieving the pressure by assuming an unconfined, free state. 8 Note that the freed DNA is rarely bent into a radius smaller than its persistence length because only thermal energy is available to it.
Figure 2. A T2 phage burst open as a result of osmotic shock. The electronmicroscope image was made when an intact phage was deposited on an air–water interface. The capsid acts like a rigid semipermeable membrane: It confines the DNA, but water and salt ions can pass through its pores. An osmotic pressure develops when water flows into the capsid in response to a high concentration of confined DNA. Eventually, the capsid ruptures and frees the DNA.
Figure 2. A T2 phage burst open as a result of osmotic shock. The electronmicroscope image was made when an intact phage was deposited on an air–water interface. The capsid acts like a rigid semipermeable membrane: It confines the DNA, but water and salt ions can pass through its pores. An osmotic pressure develops when water flows into the capsid in response to a high concentration of confined DNA. Eventually, the capsid ruptures and frees the DNA.
What are the biological consequences of a highly pressurized capsid? To appreciate this question, consider the typical life cycle of a bacterial virus. Figure 3 shows a salmonella cell about 30 minutes after being infected. Two P22 phages have bound to receptors in the outer membrane of the bacterium. That triggers the opening of the capsid and releases the genome. Unlike the situation pictured in figure 2, in which the capsid is ruptured and the DNA spills out in all directions, here the head and tail remain intact and the DNA is ejected along its length through the tail into the bacterial cell. That kind of controlled and directed release is essential to the survival of the virus because its genome can only be replicated, and its genes translated into protein products, if its DNA gets inside the host cell. The genome replication and expression of viral protein result in the production of a large number of new viral particles. They accumulate to high densities, as witnessed by their formation of an ordered array in the cell’s interior before they are released when the cell ruptures.
Figure 3. Infection of a salmonella cell by bacteriophage P22. Two phages have bound to the outer membrane and ejected their DNA into the cell, leaving behind their empty capsids (identified by arrows here; a more detailed view of P22 is shown on the cover). The DNA is replicated and its genes are expressed, leading to the synthesis of a large number of new copies of the virus. On completion of that process, the cell wall will rupture, allowing the close-packed array of new phages to escape and infect other bacteria.
Figure 3. Infection of a salmonella cell by bacteriophage P22. Two phages have bound to the outer membrane and ejected their DNA into the cell, leaving behind their empty capsids (identified by arrows here; a more detailed view of P22 is shown on the cover). The DNA is replicated and its genes are expressed, leading to the synthesis of a large number of new copies of the virus. On completion of that process, the cell wall will rupture, allowing the close-packed array of new phages to escape and infect other bacteria.
The above scenario was established after many years of work by the phage group, 3 culminating in Alfred Hershey and Martha Chase’s famous 1952 experiment 9 in which the protein shell was definitively shown to remain outside the host cell, with only the viral genome entering. The demonstration confirmed DNA as the “transforming principle” of life because it, not protein, carries the genetic information. Less conspicuously, the experiment raised the physical question of what drives the injection of the phage genome into the cell, an issue that lay dormant for decades because of the ensuing rush to confront the more fundamental questions of molecular biology, such as how DNA replication and protein syntheses occur.
Packaging and ejecting viral DNA
Tens of atmospheres of pressure build up in the capsid as a single molecule, the viral genome, is stuffed inside its rigid frame. A powerful molecular motor does the job. The motor is a protein that forms a complex with other viral proteins at a hole in one of the fivefold vertices on the capsid and essentially spools in lengthwise a copy of the replicated DNA. Afterward, the hole in the capsid is closed by joining to the tail, which self-assembles separately from other viral proteins.
The motor is powered by energy from the hydrolysis of ATP (adenosine triphosphate), the basic fuel of all cells. The applied force integrated over the length of the genome adds up to the energy stored in the capsid by the packaged genome. And it is precisely the pressure associated with that stored energy that ejects the DNA when the tail binds to its receptor in the bacterial membrane and opens the capsid. Theoretical estimates of the associated pressure have been made along these lines. 10 And in the past few years, researchers have experimentally determined the packaging and ejection forces as a function of the fraction of the genome within the capsid.
In an elegant single-molecule study, researchers from the University of California, Berkeley, and the University of Minnesota directly measured the force exerted by phage φ29’s packaging motor. 11 Its capsid was anchored to a polystyrene microsphere held stationary on the tip of a pipette. The viral DNA molecule was then linked to another microsphere held in the grip of optical tweezers. Adding ATP to the solution activated the phage motor, and packaging began, signaled by the motion of the microsphere held by the tweezers. The process of packaging the DNA into the capsid was followed by tracking one microsphere’s motion while it was pulled toward the other, while the DNA was held taut using a low (5 pN) constant force.
The initial packaging rate of 100 base pairs (bp) per second decreased to zero by the time the entire genome length—about 19.3 kbp, or 6800 nm—had been packaged. Other experiments, in which the distance between the optical trap and the pipette was kept fixed, allowed the researchers to determine the packaging rate as a function of the force acting on the microspheres. Combining those data, they could infer how the internal force varied as the DNA is packaged. The force rises steeply when the capsid is half full and reaches more than 50 pN when the process is complete, as shown in figure 4.
Figure 4. Single-molecule measurements determine the force exerted by bacteriophage φ29’s molecular motor as a function of the fraction of the genome packaged. Little force is required to insert DNA into an empty capsid, but that force rises nonlinearly as the DNA molecule starts crowding in on itself, and it exceeds 50 pN as the entire genome is stuffed in. The initial packaging rate is as high as 100 base pairs per second but gradually falls to zero as the capsid is filled.
Figure 4. Single-molecule measurements determine the force exerted by bacteriophage φ29’s molecular motor as a function of the fraction of the genome packaged. Little force is required to insert DNA into an empty capsid, but that force rises nonlinearly as the DNA molecule starts crowding in on itself, and it exceeds 50 pN as the entire genome is stuffed in. The initial packaging rate is as high as 100 base pairs per second but gradually falls to zero as the capsid is filled.
Another route to determining the stress in the capsid is to start with fully packaged, infectious viruses and study the course of ejection when a receptor is added. Our group followed that approach, 12 choosing to use a Λ phage since a strain of its receptor is known to work in vitro to trigger ejection. When the receptor is added to a solution of purified Λ, the entire genome is ejected from the capsid. During that process, the capsid’s pressure drops as the DNA remaining inside becomes progressively less crowded and less bent. Moreover, we can control the amount of DNA ejected simply by adding high-molecular-weight PEG to the solution. The PEG produces an osmotic pressure that offsets the capsid pressure.
Figure 5 shows the fraction of the molecule ejected as a function of the osmotic pressure for each of three different genome lengths: 48.5 kbp (blue), 41.5 kbp (black), and 37.7 kbp (red). 13 (Mutants of infectious Λ viruses have genomes ranging in length by as much as 25%.) In each case the fraction of DNA ejected falls rapidly with increasing counterpressure until the driving and opposing forces just balance each other, at which point none of the phage DNA is ejected. If multivalent ions are added to the phage solution, they diffuse into the capsid and reduce the electrostatic repulsions between strands. That effect is most dramatic for the tetravalent cation spermine, for which a 1-millimolar concentration is sufficient to reduce the pressure by a factor of 10 (see the green line in figure 5). Physiological concentrations, on the order of 10 millimolar of divalent cations, also significantly reduce the capsid pressure.
Figure 5. The force required to pack DNA in a Λ phage depends on how strongly parts of the molecule repel each other and how severely it bends. But osmotic pressure inhibits the DNA’s ejection once the capsid opens. The curves plot, for different genome lengths, the fraction of DNA ejected as a function of osmotic pressure. A 48.5-kbp-long “wild-type” phage (blue) requires 30 atm to completely inhibit the release of its DNA. Mutant phages that have 14% and 22% shorter genomes, respectively (black and red), require progressively less. A low (1 millimolar) concentration of the cationic polyamine spermine reduces significantly the DNA’s self-repulsion and thus the osmotic pressure required to offset it (green).
Figure 5. The force required to pack DNA in a Λ phage depends on how strongly parts of the molecule repel each other and how severely it bends. But osmotic pressure inhibits the DNA’s ejection once the capsid opens. The curves plot, for different genome lengths, the fraction of DNA ejected as a function of osmotic pressure. A 48.5-kbp-long “wild-type” phage (blue) requires 30 atm to completely inhibit the release of its DNA. Mutant phages that have 14% and 22% shorter genomes, respectively (black and red), require progressively less. A low (1 millimolar) concentration of the cationic polyamine spermine reduces significantly the DNA’s self-repulsion and thus the osmotic pressure required to offset it (green).
Ejection of DNA from single phage particles can be observed directly in a microfluidic flow cell mounted on the stage of a fluorescence microscope. In one experiment, T5 phage capsids are first adsorbed on the lower glass surface of the cell, and a solution containing the receptor and a fluorescent dye flows through it. 14 The dye binds to and lights up the ejected DNA, which is stretched in the flow. The kinetics of the ejection can be determined by measuring the length of the stretched DNA as a function of time.
The ejection of DNA has also been studied by elastic light scattering, again with T5. 15 Researchers took advantage of the fact that the intensity of light scattered by ejected DNA is orders of magnitude smaller than that scattered from the DNA confined in the capsid. Consequently, as ejection proceeds, the scattered-light intensity drops. The process occurs on time scales of tens of seconds, consistent with the results obtained in the microfluidic experiments. Measurements made using high concentrations of polyvalent cations indicate that ejection was highly incomplete. As much as half of the genome remained inside the capsid, sufficiently condensed by the presence of cations that the genome was no longer stressed by its confinement. 10
The different choices of experimental techniques and virus samples confirm that capsid pressure provides the initial force that ejects DNA from phages. Generally, if the capsid is to remain outside the host cell, that force must overcome a bacterium’s natural osmotic pressure, on the order of 3 atm from the high concentration of macromolecules in its cytoplasm. But as figure 5 shows, as much as half of the viral DNA remains in the capsid when the ejection pressure matches that of the bacterial cytoplasm. In vivo studies of the phages T7 and φ29 have demonstrated that the remaining part of the genome is pulled into the host cell by the molecular motor activity of the enzyme RNA polymerase that transcribes the viral genes. 16
In 2006 a group from UCLA, together with researchers at the Free University of Amsterdam, measured the elastic properties of the cowpea chlorotic mottle plant virus by repeatedly pressing the tip of an atomic force microscope against it. More specifically, the tip was pressed against empty viral capsids adsorbed on a glass surface in a buffer solution. The force curves shown below reveal the extent to which the capsid elastically deforms as the tip indents its surface by a few nanometers. The steep black line reflects the comparatively incompressible nature of glass. The colored lines indicate the capsid’s response to force as the tip moves toward and away from it. At each force, the difference between the black and colored lines gives the measurement of the tip’s indentation into the virus. For indentations smaller than 25% of the capsid’s diameter, the curves are linear and reversible, which is evidence of elasticity.
By comparing the AFM measurements with a finite-element analysis of the elasticity, the team determined the plant virus’s Young’s modulus, an indicator of its strength. Points of highest stress (red) in the icosahedral 30-nm-diameter capsid contrast against its unstressed regions (blue), as pictured above. On the right is a rendering of the capsid indented by 25%, showing the enhanced stress that eventually leads to failure. Measurements of phage capsids show that they are an order of magnitude stronger than those of the plant virus. That’s consistent with the fact that the RNA genome of the plant virus is never highly compressed.
The evolution of pressure
Clearly, pressure is essential to a phage’s ability to infect a host, and DNA viruses have evolved to depend on that pressure; indeed, their survival requires that a lot of work go into packaging their genomes. In addition, scientists know from basic mechanics that a spherical pressurized shell necessarily involves a lateral stress σ = Rp, where R is the radius of the shell and p the internal pressure. Because the capsid shell consists of a curved, 2D crystal of noncovalently bound proteins, a maximum stress can be tolerated before rupture—the maximum attractive force per unit length exerted by neighboring proteins. To deliver a sufficient length of genome, the internal pressure is expected to be essentially the same in phages of all sizes. The equation suggests that larger capsids must be stronger than smaller ones, to handle larger stresses.
Although experiments have confirmed that the internal pressures in different phages are similar, the extent to which it is the case in phages of different sizes and shapes under similar buffer conditions remains unclear. X-ray diffraction and electron microscopy have measured average interaxial spacings, or densities, for a wide variety of phages, especially the many plant and animal viruses that depend on pressure to deliver their genomes. They include herpes simplex, a virus that ejects its genome into the nucleus of mammalian cells, and the giant 200-nm-diameter chlorovirus, which ejects its DNA into unicellular algae. Most dramatically, the molecular spacings in a range of T4 mutant phages, whose capsid sizes vary by a factor of 10, are known to be essentially the same, 17 independent of whether 1 or 10 copies of the genome are packaged. The amount of DNA put into the capsid is proportional to its volume and is consistent with constant genome density and, hence, pressure.
It is no accident that most bacterial viruses have double-stranded DNA genomes, while most plant and animal viruses have single-stranded RNA genomes. That apparent quirk of evolution occurred because most bacterial viruses remain outside their host cell and inject only their genome, whereas most plant and animal viruses fully enter their hosts, capsid and all. In the latter cases, no need developed for a motor to package the genome or for the capsid to withstand high pressures. Instead, single-stranded RNA viruses need only disassemble, or uncoat, to make their genomes available for replication and gene expression. Whereas double-stranded DNA, a stiff and hard-to-compress molecule, provides the most efficient way to build up pressure, single-stranded RNA is relatively flexible and compressible. Force-microscopy studies on viruses bear out the comparison. The Λ and φ29 bacteriophage capsids, for example, are an order of magnitude stronger than those of the cowpea chlorotic mottle virus (see the box on page 46). 18
Continuing to probe
The physical properties of nucleic acids and proteins have attracted intense and fundamental studies for more than half a century. And during that time modern microscopy and crystallography have determined the structure of whole viral particles. But only recently have the life cycles of virus particles—how they enter host cells, how new copies form in those cells, and how those copies get back out—become the object of quantitative study. Researchers can now image and track single viruses in single cells, design a host of single-molecule spectroscopy and force-measurement experiments to probe viral mechanics, and perform cryo-electron microscopy analysis of single viruses (see the article by Bob Glaeser on page 48).
On the theoretical side, both atomistic and coarse-grained simulations of viral self-assembly are already beginning to address many detailed questions about the interactions between nucleic acid, proteins, and cell membranes during the viral life cycle. The work of this next decade will surely help close the gap between our understanding of viruses as disease agents and as physical objects.
REFERENCES
Bill Gelbart and Chuck Knobler are professors of chemistry at the University of California, Los Angeles.