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Proc Natl Acad Sci U S A. Apr 7, 2009; 106(14): 5475–5480.
Published online Mar 23, 2009. doi:  10.1073/pnas.0810095106
PMCID: PMC2667057
Applied Physical Sciences

The capillarity of nanometric water menisci confined inside closed-geometry viral cages


We present an investigation of water menisci confined in closed geometries by studying the structural effects of their capillary forces on viruses during the final stage of desiccation. We used individual particles of the bacteriophage ϕ29 and the minute virus of mice. In both cases the genomic DNA was ejected from the capsid. However, although the structural integrity of the minute virus of mice was essentially preserved, the ϕ29 capsid underwent a wall-to-wall collapse. We provide evidence that the capillary forces of water confined inside the viruses are mainly responsible for these effects. Moreover, by performing theoretical simulations with a lattice gas model, we found that some structural differences between these 2 viruses may be crucial to explain the different ways in which they are affected by water menisci forces confined at the nanoscale.

Keywords: atomic force microscopy, capillary forces, water, DNA ejection, virus

The action of capillary forces created by water menisci is very important in wetting–dewetting processes taking place at the liquid–gas interface (1). Moreover, water menisci at the nanoscale play a central role in many phenomena, such us hydration forces in biology and colloid science (2, 3). A lot of effort has been dedicated to the understanding of the shape of, and forces exerted by, water menisci in a variety of geometries. All of the systems studied so far consist of nonclosed geometries where water is confined between 2 surfaces, such us surface–nanosphere systems (46) and micro and nanochannels (7, 8); or systems with openings as big as the cavity itself, such us carbon nanotubes (9, 10). Thus far, no attention has been paid to the influence of the water meniscus on the containing structure or to out-of-equilibrium systems. Herein, we present experiments on a closed-geometry container, such as a virus particle, subjected to the capillary action of water menisci confined up to the final stages of a desiccation process. By investigating the initial and final stages of these biological cavities, we deduce the capillarity of the confined water by using numerical simulations.

We have chosen 2 geometrically different icosahedral viral models, Bacillus subtilis bacteriophage ϕ29 and the minute virus of mice (MVM). The capsid of phage ϕ29 (54 × 42 nm in size, Fig. 1A) is assembled from 6 different structural polypeptides and encapsidates a double-stranded (ds) DNA molecule (11, 12). In one of the end caps, the central pentamer is replaced by the connector complex. In the complete virion, a proteinaceous tail complex is attached to the connector. The MVM encloses a single-stranded (ss) DNA molecule and is one of the smallest and structurally simplest (T = 1) viruses known (25 nm in diameter, Fig. 1B) (13). We have used atomic force microscopy (AFM) (14) to investigate the structural effects of desiccation on DNA-filled virions and empty capsids (devoid of DNA), for both ϕ29 and MVM. Desiccation produced the ejection of DNA from both ϕ29 and MVM virions and led to a full collapse of the ϕ29 capsid, whereas the MVM capsid essentially conserved the size and shape relative to that observed in solution. The results are explained in terms of dehydration effects and the action of capillary forces at the final stages of the desiccation process.

Fig. 1.
Drawing of the viruses. Shown are cartoons of ϕ29 (A) and MVM (B).


Fig. 2A shows a single ϕ29 mature virion in physiological buffer conditions showing the expected dimensions (11), i.e., 60 nm in length and 45 nm in width (blue color profile in Fig. 2D Inset). Fig. 2B shows a typical ϕ29 particle after desiccation. Detailed measurements revealed that ≈55% of the viral DNA molecule had been ejected from the virus particle. The height of this particle is ≈15 nm lower than the hydrated one (light gray color profile in Fig. 2D Inset). We found that after desiccation, most ϕ29 virions presented a conspicuous depression in the equatorial zone (Figs. 2 B and C and light gray profile in Fig. 2D Inset), and the ejected DNA is spread over the surface. A few virus particles yielded heights of ≈5 nm. Because these particles are already empty before desiccation, and their height coincides with twice the ϕ29 wall thickness (≈2 nm) (11), they are not considered in these statistics. Fig. 2D depicts the height histograms for DNA-containing ϕ29 viruses before and after desiccation, showing a discrete distribution where ϕ29 DNA-containing capsids are collapsed to ≈60% of the original height. As a control, viruses were imaged under water after washing out the buffer, without finding DNA ejection or any relevant difference in virus height relative to physiological buffer conditions.

Fig. 2.
Desiccation of ϕ29 virions. (A) A DNA-filled ϕ29 particle imaged in buffer conditions. (B) An isolated ϕ29 particle after desiccation. (C) Several ϕ29 viral particles after desiccation. The arrow-marked viruses are wall-to-wall ...

Remarkably, for MVM virions, the effect of desiccation was quite different. Fig. 3A shows a single MVM virion in buffer conditions where the topographic features of the particle around one of the 5-fold symmetry axes are clearly resolved. The height of ≈24 nm corresponds to the diameter previously reported by X-ray crystallography (13). As for ϕ29, desiccation led to the ejection of DNA from the MVM capsid, as it is seen around the viral capsid in Fig. 3B. However, desiccation had no substantial effect on the structural integrity of the MVM capsid, which essentially preserves its size and shape, i.e., ≈90% of the original height (Fig. 3C), well above the ϕ29 value. As a control, viruses were imaged under water after washing the buffer, without finding DNA ejection or any other relevant difference in virus height between buffer and water conditions.

Fig. 3.
Desiccation of MVM virions. (A) A single, DNA-filled MVM particle imaged in buffer conditions. The topographic features around a capsid 5-fold symmetry axis can be observed. (B) MVM particle after desiccation, with its DNA ejected from the capsid. (C ...

We have also performed similar experiments with empty capsids that were already devoid of DNA. In our experiments, both MVM and ϕ29 empty capsids showed the nominal height when imaged in liquid (blue histograms of Fig. 4). All of the ϕ29 capsids were collapsed to heights of ≈6 nm when imaged in air, i.e., close to 10% of the original height in liquid (gray histogram in Fig. 4A). Although the response to desiccation of DNA-filled and empty capsids of MVM was similar (Fig. 4B), the population of wall-to-wall-collapsed ϕ29 particles increased from 10% for the full capsids to 100% for empty capsids. This indicates that the DNA inside the ϕ29 capsid contributes to prevent a full collapse of the protein shell upon desiccation.

Fig. 4.
Desiccation and liophylization of empty capsids. (A) The height histograms of empty ϕ29 capsids: Blue, black, and gray colors indicate liquid, frozen and dried, and air desiccated capsids, respectively. The Inset shows a ϕ29 empty capsid ...

Capillary forces play an important role in the observed effects. During the desiccation process, water may form both an internal meniscus inside each virus particle and an external meniscus surrounding each particle. This would lead to the generation of forces that are in the range of tens of nanonewtons (15), which could be sufficient to deform or break the virus particles (16). To test the role of these forces, viruses were alternatively dehydrated by freeze-drying (see Materials and Methods). The sublimation of water from solid to gas prevented the formation of any liquid meniscus, thus avoiding the generation of capillary forces on the virus. However, the DNA was still ejected from both viruses. Fig. 4 summarizes the effects of freeze-drying on the capsids height profile. In Fig. 4A, we compare the height of ϕ29 empty capsids in liquid (blue), in air after desiccation (gray), and in air after freeze-drying (black). Interestingly, freeze-driying prevented the wall-to-wall collapse of ϕ29 capsids, although the height decreased 20 nm relative to the original height in water, perhaps because of the partial dehydration of the proteins composing the capsid (see Discussion). From the latter, it can be concluded that we have isolated the effect of capillary forces to be responsible for the last 20 nm of height decrease just before wall-to-wall collapse. The same experiment was performed on empty MVM capsids and showed that particles subjected to freeze-drying had a slightly increased height relative to capsids subjected to desiccation in air (Fig. 4B). It means that although capillary forces are responsible of ≈2 nm of height decrease, partial dehydration could reduce the height ≈5 nm in MVM. These results are summarized in Table 1 and could be summed up by saying that capillary forces are much more important in ϕ29 than in MVM capsids.

Table 1.
Desiccation and liophylization data for both viruses


To understand these results, there are a number of important considerations to be discussed. First, ϕ29 phage DNA packaging process takes place through the connector (12, 17) (Fig. 1A). Second, during the first stages of DNA translocation, elastic energy is stored inside the virus, generating an internal pressure of ≈60 atmospheres (18), which is presumably used to inject the viral DNA into the host (19). The analysis of the connector structure before and after DNA packaging shows a conformational difference mainly because of the closure of the longitudinal axis of the particle. This closure is probably involved in the secure maintenance of the DNA inside the viral capsid, and the release of the DNA may require a conformational change of this region to open the channel again. Desiccation of the virus might also provoke such a change, perhaps through a conformational rearrangement of some of the connector and/or tail components (12). Thus, once the connector and tail channel are open, the internal pressure inside the virus would help to eject the DNA from the phage particle. Interestingly, the DNA length that is outside the virus, as measured from AFM images (Fig. 2B) is ≈55% of the total length, very close to the 65% that is ejected in the push stage of the translocation process (19). This suggests that the desiccation-induced ejection of DNA might be similar to the first energy-independent step of physiological ϕ29 DNA injection into bacteria, both being caused by the opening of the connector and the elastic energy of the stored DNA (16, 20). Moreover, the fact that all of the empty ϕ29 capsids are wall-to-wall collapsed in air indicates that DNA ejection is independent of the collapsing process, because the collapsing height depends on the DNA remaining inside the capsid.

Although desiccation of the MVM virion also results in the ejection of the viral DNA, the empty capsid is not collapsed. Some evidence suggests that, in the nucleus of the infected cell, the DNA could exit the MVM capsid through one of the pores located at the 5-fold symmetry axes of the capsid (21). Interestingly, the crystal structure of the MVM virion shows the presence of water-mediated hydrogen bonds between the 5 protein subunits that surround each capsid pore (22). If these water molecules were removed during the desiccation process, the probable weakening of the intersubunit association could lead to the opening of the capsid pores and the release of the DNA, either through diffusion or by depressurization as in ϕ29.

It is important to remark that our experiments effectively isolate capillarity forces during the desiccation process. For example, empty ϕ29 capsids show a height decrease of ≈36 nm from being in water (blue histogram in Fig. 4A) to air desiccated (gray histogram in Fig. 4A). Because the freeze-dried ϕ29 empty capsid height is ≈23 nm (black histogram in Fig. 4A), we can conclude that the capillary forces are responsible of ≈17 nm of height decrease just before the wall-to-wall collapse. The decrease of height between the capsid in water (blue histogram Fig. 4A) and after freeze-drying (black histogram in Fig. 4A) can be attributed to dehydration effects. Even incomplete desiccation will reduce both the hydrophobic effect and the number of water molecules bound to the capsid proteins. This, in turn, should destabilize the native folding and association of the capsid subunits, contributing to the partial collapse of the virus particles. The different contribution of dehydration when the 2 viruses are compared would depend on the many differences in the interactions that hold the capsid subunits natively folded and bound to each other. From Fig. 4B, it is clear that capillary effects are much less important for MVM empty capsid. The wall-to-wall collapse of the empty ϕ29 capsid as opposed to the preservation of the height of the empty MVM capsid could be related to the differences of structure and geometry between both viruses. Our results suggest that the collapse of the ϕ29 virus is partly due to the capillary forces exerted by a water meniscus that are formed on or in the viral particles during the very last stages of the desiccation process (Fig. 5). Our working hypothesis contemplates 2 kinds of menisci acting on the virus: a water bridge joining the external wall of the capsid to the surface and a second one inside the virus cavity. The forces originated by either meniscus at the nanoscale are not negligible. It can be easily estimated (23) that 7 nN is the typical adhesion force created by the water bridge between the AFM tip and the surface, which is very close to the force needed to break a virus (24). Interestingly, it is known that 2 hydrophobic nanoscale plates are attracted between them when the water disappears in their interface (25). Although the geometry of the virus cavity is more complex than in the systems we have just mentioned, the internal liquid meniscus confined inside could contribute to the collapse of the viral particle. Moreover, although the external water meniscus may be similar for both viruses, the structure of the internal water bridge may be determined by the geometry of the internal virus cavity. The MVM capsid has a pore at every 5-fold symmetry axis (12 pores). Inspection of the three-dimensional structure of MVM indicates that water molecules would escape exclusively through the capsid pores during the last stages of desiccation. It results in a water meniscus made of a radial distribution of 12 bridges inside the particle where the capillary forces tend to compensate each other. However, in ϕ29, the only known channel is within the connector at the end of one cap. Following the line of reasoning used with MVM, water would escape faster through the connector, creating a single neck water meniscus not compensated by any other one, that would lead to the collapse the virus.

Fig. 5.
Numerical simulation (see Materials and Methods) of the water menisci evolution during a desiccation process for single (Upper) and multiple (Lower) channel virus cavities. The images represent the average of 100 different water menisci evolutions taken ...

Comparison of the water bridge-formation stages in viral cages can be tackled by using numerical simulations on theoretical models. To do so, we have considered a lattice gas model that mimics the gas–liquid phase transition in water (26). This model has been previously used to study the geometry of the water meniscus formed between an AFM tip and a substrate (27). The fluid is represented by a square lattice with a lattice spacing of 3 Å. We perform a (V, T, μ) Monte Carlo numerical simulation, where each site of our system is either occupied with a water molecule (liquid phase) or empty (gas phase). Each occupied site of our system interacts with its occupied nearest neighbor with an attractive energy ε = 9 kJ/mol. The temperature T of the system is equal to 303 K, and the chemical potential μ is fixed to a relative humidity (RH) of 0.5 [μ = −2ε + kBTln(RH)] corresponding to drying conditions. We consider 2 types of virus cavities: an asymmetric one with a single channel and a symmetric one with pores at every 4-fold symmetry axis. A fluid particle binds to the surface of the virus cavity with energy of value 50 kJ/mol. The parameter calculated by the Monte Carlo simulations is the averaged occupation at each lattice site given by n(i, j) = Σtn(i, j, t)/MCS, being n(i, j, t) = 1 if the lattice site (i, j) is occupied at the Monte Carlo step t and zero otherwise. MCS is the total number of Monte Carlo steps considered.

Every cell is occupied by a water molecule in the starting configuration of each simulation. We consider the different stages of the out-of-equilibrium desiccation process by considering different values of MCS. The final result is averaged over 100 different simulations. On the one hand, a single-neck water meniscus is formed for the virus with a single hole (ϕ29). This evolving water meniscus provokes collapse forces (Fig. 5 Upper) that cannot be compensated by structural forces of the relatively soft regions (low curvature radius) of ϕ29 virus. On the other hand, for the smaller virus with a symmetric location of the pores, the water meniscus is made of as many water necks as pores the virus has and capillary forces would cancel one another (Fig. 5 Lower). Although we have isolated the capillary forces effect on viruses, the many differences in intersubunit interactions and stiffness between the ϕ29 and MVM capsids (24, 28, 29), and possible differences in the structural role of hydration as explained above, also play an important role in the observed effects of desiccation.

To summarize, in this article we have shown that desiccation provokes the ejection of DNA from both a parvovirus (MVM) and a bacteriophage (ϕ29), but the 2 capsids behave differently: Desiccated MVM virions or empty capsids do not suffer a significant collapse. In contrast, desiccated ϕ29 particles suffer a drastic collapse. The comparison between air-desiccation and freeze-drying experiments, as well as the Monte Carlo simulations on viral capsids models, clearly demonstrate the presence of evolving water menisci during desiccation. The capillary forces exerted by water bridges that may be formed inside the capsids during the last stages of desiccation may favor the collapse of a virus capsid, as observed in ϕ29 but not in MVM.

Materials and Methods

MVM and ϕ29 viruses where produced as described in refs. 29 and 24, respectively. Virus particles were imaged under physiological conditions and in air after desiccation by AFM using “Jumping Mode” (30, 31) and dynamic force microscopy (32), respectively. We used 2 different rectangular cantilevers RC800PSA (Olympus) with spring constants of 0.05 ± 0.01 N/m for liquid and 0.73 ± 0.01 N/m for air. For MVM, stocks of purified empty capsids (1 μM) and virions (0.3 μM) in PBS buffer at pH 7.2 were diluted 20 times for AFM experiments. For ϕ29, stocks of purified empty capsids (2 mg/mL) and virions (4.5 mg/mL) in TMS buffer at pH 7.8 were diluted 100 times for AFM experiments. In all of the cases, a single drop (20 μL) of diluted stock was deposited on a sylanized glass surface (24) for liquid and on an APTES mica surface for air. The samples prepared in this way were positively charged. The drop was left on the surface for 30 min and then rinsed twice with 20 μL of buffer for liquid and with clean water and dried out by using nitrogen gas for air.

The freeze-drying process is accomplished by freezing the virus solution on the surface by using LN2. Afterward, the sample at −80 °C was quickly inserted in a high-vacuum chamber. Once the vacuum reaches 2 × 10−4 mbar, the sample is allowed to warm up slowly for ≈60 min. The ice of the sample on the mica disappears completely at a temperature of approximately −15 °C. The chamber is opened to ambient air once the sample temperature is ≈20 °C.

The theoretical model is as follows: The Hamiltonian of interaction between nearest neighbor lattice sites is given by

equation image

Ci being equal to 1 if the site “i” is occupied with a water molecule and zero otherwise (Ci = n(i, j, t) in Discussion). For simplicity, the model takes into account a 2-dimensional lattice, with a lattice parameter equal to the typical distance between 2 water molecules. Two molecules occupying 2 nearest-neighbor sites interact with an attractive energy of value −ε. The model equilibrates with respect to a bulk reservoir specified by a temperature T and a chemical potential μ given by RH = e(μ − μc)/kBT, μc being the critical chemical potential. Because of the existence of a chemical potential, we have an extra term in the Hamiltonian given by

equation image

and the total hamiltonian reads H = Hhum + Hint being equivalent to the well-known Ising model. By using the variable change Ci = (1 − si)/2, we get

equation image

Because of the celebrated Onsager solution, we know that this model has a phase diagram with a horizontal line of first-order phase transitions between the (si = +1 or Ci = 0) and the (si = −1 or Ci = 1) ferro states at zero magnetic field (μc = −2ε), starting at RT = 0 and ending at the critical point RTc = ε/2ln(1 + 2) (R being the gas constant). The critical temperature of real water is located at Tc = 647 K, so we set ε = 2R647 Kln(1 + 2) ≈ 9 kJ/mol and a value for critical chemical potential μc = −18 kJ/mol.

To mimic the conditions found in the laboratory, we set T = 303 K and RH = 0.5 (drying conditions and gas phase at equilibrium). The evolution from the completely liquid initial condition to the gas phase equilibrium condition is done by standard Metropolis Monte Carlo simulations.

We have also modified the Hamiltonian, including the interaction of water with the virus capsid. Several points on the lattice are defined to belong to the surface of the virus. A fluid particle neighbor to a lattice point belonging to the capsid surface binds with energy −b different from −ε. When −b < −ε, the surface is hydrophilic.

Lattice points belonging to the virus are defined through 3 parameters: x-semi axis (ax), y- semi axis (ay), and the capsid thickness (a). A lattice site (xi, yi) in the surface formed between the following 2 ellipses

equation image


equation image

belongs to the virus (x0 and y0 being the center of the simulation box). However, lattice points at the nanochannels (connectors) are discarded to belong to the virus. To define a channel, we use a starting and a finishing angle (θini, θend). Every lattice point (xi, yi) belonging to the surface between both ellipses with (θini < θ < θend) [θ being the polar angle of (xi, yi) from (x0, y0)] belongs to the nanochannel, i.e., does not belongs to the virus and may be occupied by a water molecule.

In this article, we have simulated an asymmetric virus with a single hole and a symmetric virus with 4 holes to understand the water meniscus evolution for different viral capsids The parameters used are a = 6 Å, ax = 150 Å, ay = 100 Å, θini = −0.2, and θend = 0.2 for the virus model with a single channel, whereas for the symmetric virus with 4 holes, we have chosen a = 6 Å, ax = 100 Å, ay = 100 Å, and the 4 pairs of angles (θini, θend) defining the channels are: (−0.2,0.2), (1.3708,1.7708), (2.9416,3.3416), and (5.2248,5.6248).


We acknowledge fruitful discussions with Julio Gómez and Pedro Tarazona. M.C. was a predoctoral fellow from Comunidad de Madrid (CAM). This work was supported by CAM Grants GR-MAT-0254 and 0505/MAT/0303 and Ministerio de Educación y Ciencia (MEC) Grant MAT2008-02533 (to P.J.P.); CAM Grant S-0505/MAT/0303 and MEC Grant BIO2006-00793 (to M.G.M); CAM Grant S-0505/MAT/0303 and MEC Grant FIDI2006-11170-C2–01 (to P.A.S. and MD.); and CAM Grant S0505/MAT-0283 and EU-NEST-029085 and MEC-BFU2005-06487 (to J.L.C.). M.G.M. is an associate member of the Instituto de Biocomputación y Física de los Sistemas Complejos, Zaragoza, Spain.


The authors declare no conflict of interest.

This article is a PNAS Direct Submission.


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