Temperature-induced DNA density transition in phage λ capsid revealed with contrast-matching SANS

Fig. 2 A and B show the central cross sections of the 3D cryo-EM icosahedral reconstruction of phage λ-capsid filled with wt λ-DNA [length 48,500 base pairs (bp)] as well as empty λ-capsid at 20 °C in 10 mmol/L (mM) Mg-Tris buffer. The cryo-EM structure reveals that the entire capsid volume is filled with DNA (red color), extending all the way to the center of the capsid. To better visualize the distribution of DNA within a capsid, we calculated the radial average density profile from the cryo-EM 3D electron density maps using Chimera software, displayed in Fig. 2C. The density profiles on the y axis are shown in arbitrary units relative to averaged background density, but the relevant structural information is in the location of the maximums reflecting the DNA density distribution within the capsid. The density profile for the empty capsid (black line) shows a flat line in the void volume, displaying only the location of the capsid wall. EM cross-sections show identical capsid radii for DNA-filled and empty capsids, as observed from overlapping capsid wall density peak positions at ~300 Å (Fig. 2C). The increase in the DNA density profile from the capsid wall toward the capsid center is attributed to an artifact resulting from icosahedral averaging for single-particle reconstruction, as we verified with SANS data analysis below. [The effect of DNA density increase toward the capsid center is due to the Fourier-based reconstruction strategies typically used for EM data analysis. The interpolation strategy used during Fourier reconstruction can produce a radial falloff in the real-space image due to the entire particle volume being filled with DNA matter, scattering the electron beam. For comparison, an empty capsid is missing DNA matter in the capsid interior (besides buffer background) and the reconstruction process of image averaging does not contribute to the radial density from the inner capsid wall to its center. Other authors have observed the same trend in radial DNA distribution using similar reconstruction algorithms, e.g., see ref. 29 showing DNA distribution in phage P22. Also, it can be noted that there is a negative density in the radial distribution from the cryo-EM map on both sides of the intensity maxima corresponding to the protein capsid wall. This is attributed to imperfections in estimating and correcting the objective aberrations introduced during data collection along with intensity normalization procedure. Thus, it is the relative and not the absolute intensity values that are meaningful.] The density profile for the DNA-filled capsid shows, however, how DNA is structurally arranged from the inner capsid wall toward the center. Along the capsid wall, there are well-ordered, multiple concentric DNA layers (∼7 to 8 layers). The layers are evenly spaced, suggesting that DNA has adopted an ordered liquid crystalline state (shown as dashed grey vertical lines). The spacings between the DNA layers were determined by fitting a Lorentzian function to each of the local maxima on the DNA density curve versus the distance from the capsid center (Fig. 2C). Those maxima provide the location of ordered DNA layers in the capsid. The interlayer distance displays periodicity for DNA in the periphery of the capsid (9). However, the DNA density profile in Fig. 2C shows that DNA layer periodicity is lost toward the capsid center, suggesting that intracapsid DNA structure coexists in two phases—ordered in the capsid periphery and less ordered (or disordered) in the center. The cutoff radius for the less-ordered core-DNA phase from the capsid center, r_core, can be determined from the density profile plot (r_core ∼ 95 Å), shown as a red dashed vertical line (Fig. 2C). [We locate the position for each DNA density maximum in Fig. 2C using a Lorentzian function. We previously determined the average interlayer distance of a_H = 22.7 Å from cryo-EM map for phage λ (9). Then, we calculated the interlayer distance towards the capsid center between the density peaks within a deviation value of 10% from its average value. Based on this criterion, we defined the cutoff radius for the disordered DNA phase. The oscillations beyond the cutoff radius are outside of our criterion].

Complementary to the cryo-EM data, we performed SAXS analysis of DNA-filled and empty phage λ particles in the temperature range 10 °C to 40 °C in TM-buffer (10 mM Tris+10 mM MgCl₂); see Fig. 3. Small-angle scattering methods (SAXS and SANS) are powerful experimental techniques for the structural analysis of biological matter due to their range of resolution, from some tens of Ångstroms to a few hundreds of nanometers. Ordered structures, such as icosahedral capsids or packaged DNA ordered in the periphery of the capsid, produce Bragg scattering peaks. Fig. 3A shows SAXS scattering intensity versus magnitude of the scattering vector q (called wave number) for empty λ-capsid (green curve) and wt DNA-filled phage λ (red curve). The interpretation of the structure reflected by the scattering intensity pattern depends on the value of the wave number q, which is inversely proportional to the length scale L of the analyzed structure, i.e., $q\sim L^{-1}$   . Thus, the scattering signal from DNA-filled phage λ in the low q-region ~0.006 to 0.06 Å⁻¹ provides scattering information at the large-length scales (tens to hundreds of nm), corresponding to the whole viral particle and reflecting structures of both capsid and global packaged DNA arrangement inside (called the “form factor” in the scattering analysis). On the contrary, at high q-region ≥ 0.1 Å⁻¹, Bragg peak reflects the coherent scattering at short-length scales (tens of Angstroms) from the averaged local ordering of dsDNA helices packaged in a capsid (DNA “structure factor” in the scattering analysis), providing average distance between ordered DNA centers, d_s (10, 30). This is illustrated in Fig. 3A. For comparison, the scattering profile from an empty λ-capsid is missing the DNA Bragg peak in the high q-region, while the capsid structural features are visible as ripples in the low q-region (Fig. 3A). SAXS data for DNA-filled λ-capsid can be interpreted by fitting the scattering intensity versus q. Our fit combines two models that separately describe the data at low and high q-regions (black line), since they reflect different structural features of the packaged DNA, as explained above. At low q, a simple spherical model (approximating the icosahedral capsid with a solid sphere, not differentiating between the protein shell and the packaged DNA) describes the scattering profile, providing information on the capsid size. At high q, the broad peak (BP) model is used to fit the observed Bragg peak, which can then be used to accurately locate the position of peak maximum, which reflects the interaxial distance between ordered DNA strands in the capsid (31, 32). The BP model consists of a power law term (usually referred to as linear background) and a Lorentzian term (33, 34). As mentioned above, previous X-ray scattering analysis of bulk DNA phases condensed by an osmolyte at packing density corresponding to that in phage λ (10) has demonstrated hexagonal DNA ordering (10, 30). The interaxial distance of <∼30 Å corresponds to a hexagonal order (35–37) consistent with the packaged DNA structure found in phage λ capsid. The disordered DNA in the core of the capsid should not contribute to the SAXS scattering signal at high q (due to the incoherent scattering, the disordered structures do not produce a Bragg peak). The characteristic Bragg peak for the hexagonally ordered DNA structure in the capsid periphery (10, 30) in Fig. 3A displays a maximum at q_Bragg ~0.26 Å⁻¹. Using the relationship for a hexagonal lattice $d_s=4\pi /\sqrt{3}{q}_{\mathit{Bragg}}$   , we obtained d_s-value of 27.6 Å, which remained constant in the entire temperature range of 10 to 40 °C, see Fig. 3B. This SAXS-obtained interaxial distance value corresponds to the interlayer distance, a_H, between radially ordered DNA layers in the cryo-EM map cross-section above, through a relationship $a_H=\sqrt{3}/2d_s$   for a hexagonally ordered DNA lattice, connecting SAXS and cryo-EM data together (6, 9).

If we assume that full-length λ-DNA is hexagonally ordered through the capsid volume with interaxial DNA–DNA distance d_s = 27.6 Å, then a volume unoccupied by DNA would exist toward the center of the capsid (12, 38). However, as observed by cryo-EM reconstruction in Fig. 2, DNA is in fact dispersed throughout the entire λ-capsid volume without a void in the center. As described above, the apparent interlayer ordering in the cryo-EM cross section disappears toward the center of the capsid, suggesting that DNA is in a disordered state in the capsid core. Similar dsDNA distributions within the capsids were also observed for other viruses (39–43). As shown in Fig. 3B, the interaxial distance d_s for ordered DNA in the capsid periphery is constant in the entire temperature range (10 to 40 °C), suggesting that its structure is unaffected (SAXS raw data and model fits at all temperatures are shown in SI Appendix, Fig. S1). At the same time, we earlier observed with ITC and AFM an abrupt transition in intracapsid DNA properties at ~32 °C, see Fig. 1 (16). We hypothesize that a temperature-induced mechanical and density DNA transition occurs in the core of the capsid, rather than in the capsid periphery, affecting the boundary between coexisting high-density (in the capsid periphery) and low-density (in the capsid center) DNA phases. We use a spherical core–shell model based on cryo-EM and SAXS data (Figs. 2 and 3) to fit the SANS data for DNA structure packaged in phage λ capsid as a function of temperature, where contribution from the capsid protein is contrast matched by a deuterated solvent. This provides a stringent test of our hypothesis. Here, structural analysis data are used to describe packaged DNA structure in a viral capsid as a coexisting two-phase system of different DNA densities. Alternatively, one-phase, hexagonally ordered DNA in the capsid [as was proposed in the earlier works (10, 44)] cannot explain the observed DNA transition behavior and is not supported by the cryo-EM density data (9).

As mentioned above, SAXS provides structural information from the scattering mainly attributed to both protein capsid and DNA, as well as contributions from the cross-correlated scattering terms from all viral components (including phage tail proteins). We are interested in the unique scattering contribution from the global DNA structure confined in the capsid, reflected in the low-q region. However, the scattering intensity contributions from the capsid and the cross-correlation terms do not allow us to fit the SAXS scattering data with a model suggested by cryo-EM data, which separates the scattering signal contribution from the apparent two-phase packaged DNA structural densities from the capsid scattering signal. To resolve this issue, we performed SANS contrast matching experiments, where the scattering contributions from all virus protein components are removed, allowing us to resolve the large-scale structural features of the genome packaged in phage λ capsid [in contrast to the small-scale DNA–DNA spacings determined in the past from SAXS Bragg peak at high q (10)].

SAXS provides a scattering signal from the interaction of X-ray radiation with the electron cloud of atoms, while SANS provides scattering from the short-range interaction of a neutron beam with the nuclei of atoms. Hence, one of the principal advantages of a neutron beam is its selectivity to specific nuclear isotopes, which are not differentiated by X-rays. Of particular interest are the dissimilar values of both coherent and incoherent neutron scattering from hydrogen (H) and deuterium (D). As described above, since biological matter is “bathed” in an aqueous buffer solution containing hydrogen atoms, we can change the SLD of the buffer by replacing the fraction of water with heavy water (deuterium oxide), resulting in different ratios of H/D atoms, allowing us to achieve a large range of SLDs for the buffer solution. Thus, the SLD for both viral capsid (proteins) and DNA can be contrast matched to an aqueous buffer containing different fractions of deuterium, making either of these components “invisible” to the neutron beam (i.e., indistinguishable from buffer SLD and resulting in zero scattering contribution upon buffer signal subtraction), see Fig. 4A. For X-rays, the parallel method of contrast matching is challenging to achieve since contrast depends primarily on the differences in the electron densities of molecules; it can be difficult to obtain sufficient contrast match between biomacromolecules and the surrounding buffer without significantly affecting buffer properties [e.g., by addition of high sucrose fraction (45)].

Fig. 4A shows the variation in SLD for the TM-buffer used in this study (Materials and Methods), phage λ proteins (capsid and tail) and λ-DNA versus D₂O/H₂ O fraction in the buffer solution. SLDs are computed specifically for phage λ, taking into account all amino acids of virus protein components, and for λ-DNA, taking into account the sequence of the 48,500 bp λ-genome. Buffer SLD increases linearly with increasing fraction of D₂O (46). As shown in Fig. 4A, the contrast match point for phage λ proteins (termed “capsid” in the figure legend and throughout the text) occurs at 43% volume fraction of D₂O/H₂O in TM-buffer, where the capsid SLD line intercepts the buffer SLD line. Fig. 4B shows SANS measurement of scattering intensity for empty λ-capsid at contrast match point in 43% D₂O/H₂O TM-buffer mixture and at full contrast in 100% D₂O TM-buffer. Due to the neutron scattering properties of deuterium (47, 48), the SANS scattering signal at 100% D₂O full contrast accentuates the structural features of the icosahedral-shaped empty capsid, showing characteristic ripples. On the contrary, at 43% D₂O/H₂O contrast match, the SANS scattering signal lacks any structural features in the entire q-range, showing essentially a flat line at the level of buffer contribution to the scattering signal (buffer signal contribution has not been subtracted here since it would result in predominantly noise). The observed slight increase in SANS intensities at 100% and 43% D₂O/H₂O toward the low q-limit suggests small particle aggregation (stable monodisperse capsid suspension should display a plateau in the low q -limit). This is due to the protocol used to empty λ-capsids from DNA, where DNA-filled phage solution is first heated to 78 °C and subsequently cooled to room temperature (49). This procedure destabilizes the portal cap proteins, leading to DNA ejection, while the rest of the capsid structure remains intact (as we demonstrated in ref. 50). The ejected DNA is then digested with DNase I prior to SANS measurement. Heating, however, can lead to partial aggregation of a fraction of broken capsid (50). Regardless of the partial capsid aggregation, this SANS measurement shows a stark difference in the scattering signals between contrast-matched and full-contrast empty phage capsids, illustrating the effectiveness of using the contrast-matching method to visualize packaged DNA structure in DNA-filled phage without scattering contribution from the capsid structure.

Next, we conducted SANS measurements on DNA-filled phage λ with contrast matching of the protein capsid in 43% D₂O/H₂O TM-buffer solution. This allows us to isolate and explore the structural changes of the encapsidated DNA as temperature is increased from 20 °C to 40 °C [our AFM data showed that the solid-to-fluid-like DNA transition in phage λ occurs at ~32 °C (51, 52)]. We separately confirmed with SAXS that the scattering profile from empty λ-capsids remains unchanged between 20 °C and 40 °C, showing that capsid structure is unaffected (17). Fig. 4C shows a representative scattering intensity profile, I versus wave number q for DNA in phage λ capsids at 20 °C, where scattering contribution from the solvent has been subtracted to further highlight the scattering features (I versus q SANS raw data for DNA in phage λ capsids in 43% D₂O/H₂O TM-buffer solution at 20 °C, 25 °C, 30 °C, 35 °C, and 40 °C are shown in SI Appendix, Fig. S2). The scattering profile shows a plateau in the low q-limit, confirming that no particle aggregation occurs. SANS data are typically analyzed by fitting the scattering data with a model of the investigated structure (53). Since we are interested in the effect of temperature on the behavior of two coexisting phases of encapsidated DNA (hexagonally ordered shell-DNA and less-ordered core-DNA), we have chosen a spherical core–shell model approximation (33, 34) (Materials and Methods), shown schematically in the inset of Fig. 4C. Core-DNA radius, r_core, is measured from the capsid center, and thickness of shell-DNA is provided by t = r_shell – r_core, where r_shell is the outer DNA radius confined by the capsid wall, measured from the capsid center, see details in Materials and Methods section. We assume that the outer shell-DNA radius is equal to that of the inner capsid radius. The inner capsid radius was determined by subtracting the λ-capsid wall thickness of 2 nm [obtained by cryo-EM (54)] from the outer capsid radius value obtained by fitting the SAXS data with a sphere model in the low q-region (Fig. 3A). The spherically averaged inner λ-capsid radius is ~29.9 nm and is constant at all temperatures (15, 17). [It can be noted that our SANS data for DNA-filled phage with contrast-matched capsid suggests that the radius of the outer DNA layer is ~1.6 nm smaller than the inner capsid wall radius, likely due to the repulsion between DNA and the negatively charged capsid wall (9, 54)]. This “empty” space between the outer DNA layer and the inner capsid wall was indeed observed with cryo-EM (Fig. 2A). However, the DNA-capsid wall separation distance does not change with temperature, as verified by our SANS data, and for simplicity is omitted in the core–shell model.

Our core–shell SANS model has two fitting variables (or degrees of freedom)—core-DNA radius (r_core) and core-DNA SLD (ρ_core). The remaining model parameters in the core–shell fitting model have been derived from the SAXS and cryo-EM data above, see Materials and Methods. Shell-DNA thickness, t, can be calculated for any given value of r_core since the outer shell radius is constant (r_shell = 28.3 nm). The initial fitting value for r_core at 20 °C was determined from the cryo-EM DNA density plot versus distance from the capsid center, shown with the red dashed vertical line in Fig. 2D, where DNA layer periodicity is lost (the phage sample was incubated at 20 °C prior to cryo-freezing to collect the EM density map). Note that the initial r_core and _ρcore values were determined (see Materials and Methods section) only to start the computational iteration. A representative core–shell model fit to the SANS data for DNA-filled phage λ with contrast matched capsid at 20 °C shows a good agreement between the SANS data and the fitting model (Fig. 4C). (Core–shell model fits to SANS data at all temperatures in the range 20 °C to 40 °C are shown in SI Appendix, Fig. S2). In the low q -region, the DNA structure displays ripples (subsidiary maxima) that reflect the overall shape and structural features of the entire λ-genome packaged in the capsid (with characteristic distance correlation from tens to a few hundreds of nm). At higher q-values, the intensity declines to low levels comparable to the buffer scattering intensity, which results in predominantly noise when the buffer scattering background is subtracted from the sample scattering signal. In SI Appendix, Fig. S3, we plot all spherical core–shell model fits (I versus q) at different temperatures in one plot in a narrow q-range of 0.015 to 0.038 Å⁻¹, focusing on DNA form factor. Since total DNA size is constrained by the capsid wall and is constant with temperature, the change is observed only in the absolute intensity of the form factor peak. SI Appendix, Table S1 summarizes all model fitting parameters and shows goodness of each fit (χ²).

Fig. 5A shows the variation in the core-DNA radius, r_core, with increasing temperature obtained from the core–shell model fit to our SANS data between 20 °C and 40 °C for the DNA-filled phage λ sample with capsid contrast matched at 43% D₂O/H₂O (as mentioned above, both SLDs, ρ_core and r_core, are model fitting parameters varying with temperature). This allows us in turn to calculate the temperature-induced change in the shell-DNA thickness, Fig. 5A. Using values for the core-DNA radius and shell-DNA thickness obtained from the core–shell SANS data model, we computed the variation in volume for the core- and shell-DNA phases with temperature, Fig. 5B. Since DNA is organized in a hexagonal lattice in the shell-DNA phase, the DNA density (bp/nm³) in the shell phase was calculated from $densit{y}_{\mathit{shell}}=2/\sqrt{3}{d}_s^{2}0.34$   , where 0.34 nm is the average distance between each bp and d_s = 2.76 nm (17). This yields DNA density in the shell phase of ~0.446 bp/nm³, which remains unchanged in the entire temperature range since the DNA–DNA interaxial distance is constant with temperature, as shown with SAXS in Fig. 3B. This implies that the SLD for shell-DNA (ρ_shell) also remains constant with temperature, ρ_shell = 3.68 × 10¹⁰ cm⁻² at 43% D₂O/H₂ O (it includes contributions from both DNA and water hydrating the DNA, ρ_shell = ϕ_DNA x SLD_DNA + ϕD₂O/H₂O x SLD_D2O/H2O, where ϕ_DNA = V_DNA/V_shell and the volume fraction of water in the shell is ϕ_D2O/H2O = V_D2O/H2O/V_shell); see the details in Materials and Methods. Knowing the volume of the shell-DNA phase as well as the constant density of DNA ordered in a hexagonal lattice, we determined the number of bp of DNA that fits into the shell phase, shown as % DNA bp relative to wt λ-DNA length (48,500 bp), versus temperature; see Fig. 5C. Once the DNA fraction that fits in the shell phase is known, the remaining DNA must fit into the core phase region; see Fig. 5C. Hence, the DNA density in the core can be computed using the core-DNA volume values. Core-DNA density variation with temperature is shown in bp/nm³ in Fig. 5D. In summary, our core–shell model SANS data analysis provides a comprehensive description of the changes in DNA packing density and volume distribution between two coexisting DNA phases in a phage capsid, occurring as temperature is increased from 20 °C to 40 °C. [It is important to reiterate that ρ_shell and ρ_core are treated as SLDs of two components (shell-DNA and core-DNA component, respectively) in a finite volume of the capsid, where each component contains both DNA and D₂O/H₂O at different ratios and not pure DNA alone with an infinite volume. DNA density in the shell-DNA phase component is homogeneous and is constant with temperature due to unchanged d_s-value of the ordered DNA phase, which leads to a constant ρ_shell value with temperature, based on our definition of ρ_shell above. However, the extent of core-DNA density ordering is unknown, and ρ_core values obtained from the model fit do not follow the trend of the core-DNA density variation with temperature [see SI Appendix, Table S1 showing ρ_core (T)]. This further confirms that DNA density in the core phase is not homogeneous.

Fig. 5A shows that the core-DNA radius increases linearly between 20 °C and 30 °C but then declines as temperature is further increased to 40 °C. The change in shell-DNA thickness shows the opposite behavior since capsid volume is constant and is coupled to changes in core-DNA radius. Shell-DNA thickness shows a decrease between 20 °C and 30 °C followed by an increase between 35 °C and 40 °C. In Fig. 5B, we also calculate volume variation with temperature of core- and shell-DNA phases. It is interesting to note that the volume of the less-ordered core-DNA phase is approximately doubled as the temperature is raised from 20 °C to 30 °C, suggesting that temperature has a significant effect on the extent of DNA disordering in the capsid. This expansion of the less-ordered DNA phase in the capsid core occurs at the expense of the highly ordered DNA phase in the shell (where DNA always remains hexagonally ordered). This is illustrated in Fig. 5C; when temperature is increased from 20 °C to 30 °C, the number of bp in the ordered shell phase is reduced as DNA layers are moved from the shell into the less-ordered core phase. When temperature is further increased from 35 °C to 40 °C, this behavior is reversed. Fig. 5D shows that the DNA density in the core is increasing fivefold as the temperature increases from 20 °C to 30 °C. However, the core density change reverses and begins to show a decline between 35 °C and 40 °C, suggesting a DNA density transition occurring between 30 °C and 35 °C. This temperature interval for the apparent density transition in core-DNA phase correlates directly with the DNA enthalpy transition temperature interval measured with ITC (15) (shown as solid grey area in all graphs in Fig. 5) and with our earlier AFM observation of solid-to-fluid like mechanical DNA transition in the capsid occurring at ~32 °C (15). To illustrate this, we plotted both the AFM data for the spring constant (N/m) of DNA-filled phage λ capsids (red triangles) and the intracapsid DNA density change obtained from the SANS data analysis (Fig. 5D). The spring constant shows an initial increase in DNA stiffness between 20 °C and 30 °C, which is in agreement with increasing core-DNA density, as higher DNA packaging density is expected to yield higher DNA stiffness. Following the DNA transition at ~32 °C, there is an abrupt drop in DNA stiffness followed by a continued decrease in stiffness between 33 °C and 37 °C. The decrease in stiffness correlates with the observed decrease in the core-DNA density in the same temperature range. It should be noted that the SANS data analysis shows that core-DNA density is significantly lower than shell-DNA density in the whole temperature range (e.g., ~2 times lower at the transition temperature of ~32 °C). The opposite trend was observed in the cryo-EM density map (Fig. 2C), where DNA packing density gradually increased toward the capsid center. This discrepancy can be attributed to an artifact in cryo-EM analysis, resulting from icosahedral averaging of EM data. It is worth mentioning that a two-phase coexistence of DNA structure in a capsid with lower DNA density in the center has been theoretically predicted with a continuum approach to the equation of state for encapsidated DNA (55). This model predicts a coexistence between line hexatic (high density) and cholesteric (low density) phases, which translates to a nonhomogeneous DNA distribution inside the capsid, consistent with our SANS and cryo-EM observations. However, in this model (55), the temperature is kept constant and temperature effect on the coexisting DNA phases was not investigated.

The observed changes in the volume and density of the core-DNA can be explained by a temperature effect on DNA–DNA interactions, bending stress, and packing defects (30, 56, 57)—all of which determine tertiary DNA structure in the capsid. The interplay between these parameters with increasing temperature can explain the initial increase in the density and volume of the core-DNA phase (between 20 and 30 °C, with corresponding decrease in the volume of the shell-DNA phase, which retains constant density), the density transition (at 30 to 35 °C), and the decrease in the core-DNA volume and density (between 35 and 40 °C, with shell-DNA volume increasing again). First, we consider temperature effect on DNA–DNA interaction energy. We previously analyzed the effect of temperature on DNA–DNA interaction energy alone, without contribution from DNA bending and packing defects induced by viral capsid confinement (15, 17). We used SAXS to determine the DNA interaxial spacing for bulk DNA arrays condensed in solution by an osmotic stress polymer (polyethylene glycol, PEG), under ionic conditions identical to the SANS measurements in this work (17, 58). We found that DNA–DNA interaxial distance remained constant in the temperature range 5 °C to 50 °C. This indicates that repulsive interactions for linearly packaged DNA are not affected by temperature at a DNA packing density corresponding to that in phage λ capsid. Next, we review the scenario when DNA is confined in phage λ capsid. The intracapsid confinement requires DNA to bend along radii that are energetically unfavorable given the internal λ-capsid radius of ∼30 nm (54) and the dsDNA persistence length of 50 nm (11, 59), which creates bending stress on the packaged genome. (Persistence length defines the stiffness of a polymer, describing the minimum radius of curvature it can adopt by the available thermal energy. Bending it to a smaller radius requires additional work). To relieve the bending stress, helices are packed closer to the capsid wall, decreasing the bending radius and also decreasing the spacing, therefore increasing the interaction energy. At the same time, the repulsive DNA–DNA interactions will push DNA strands as far from each other as possible, filling the entire capsid volume and maximizing the interstrand separations (9). Thus, there is a trade-off between bending and interaction energies. Furthermore, when DNA is bending inside the capsid, the initial correlation between two helices that have slightly different radii of curvature is lost, and the mutual orientation between helices must be reestablished. This leads to packing defects, which are absent for linear packaging of DNA in solution but are necessary here to reestablish a favorable phosphate–phosphate “phasing” of helices to reduce the repulsive interactions due to bending (9, 57, 60). The higher temperature likely hinders optimum correlation between the helices. The spacing remains the same in the hexagonally ordered shell-DNA phase since DNA is simply filling a volume (Fig. 3B), but the interhelical repulsion will increase. This is confirmed by an initial increase in the stiffness of DNA in the capsid measured by AFM, when temperature is increased from 25 to 32 °C (preceding the DNA transition, Figs. 1B and 5D). In parallel with the increasing interstrand repulsions, the increase in temperature will decrease the DNA persistence length (61), leading to less bending stress. If the bending stress decreases and if there is room to expand in the capsid, then spacings would increase and interaction energy decrease. While volume of the capsid is fixed and DNA cannot expand in total volume, it can expand into the core volume of the capsid, where DNA density is significantly lower than in the hexagonally ordered DNA phase in the periphery of the capsid (shell-DNA). SANS data in Fig. 5B (volume of DNA phases) and Fig. 5 C and D (% bp and density of DNA phases) show that this partial DNA expansion occurs; a portion of DNA in the high-density ordered shell phase is forced into the core phase in the capsid with significantly lower packing density. As a result, the volume of the core-DNA is increased while the volume of the shell-DNA is decreased (shell-DNA density always remains constant). It is striking to observe that DNA density in the core phase is increasing by a factor of ~5 (from ~0.05 bp/nm³ to ~0.25 bp/nm³) when temperature is increased from 20 °C to 30 °C, prior to the DNA phase transition.

The number of DNA packing defects, however, also increases with increasing DNA density and volume in the core [packing defects occur more frequently closer to the capsid center due to higher DNA bending curvature resulting in poor alignment between neighboring DNA helices (57)], leading to increasing energy in the core-DNA phase. (As described above, our SANS data does not provide information on the ordering of DNA but only on the size and shape of core- and shell-DNA phases. Hence, partial ordering can occur in the core-DNA phase, which leads to packing defects in both core- and shell-DNA phases). There appears to be a maximum threshold core-DNA density value at ~30 °C before density transition occurs and the core-DNA adopts a new interhelical conformation with packing density decreasing between 35 and 40 °C (Fig. 5B). This reduces the number of packing defects at temperatures >30 °C due to decreased density and volume. The DNA is moved from core phase back to shell-DNA phase, so the volume of the core is decreasing again with a corresponding increase in the shell-DNA volume (Fig. 5B). Thus, as shown in Fig. 5, our core–shell model of contrast matched SANS data for phage λ as a function of temperature (describing the effect of temperature on the two-phase coexistence in intracapsid DNA) confirms a structural DNA transition in the capsid core between 30 °C and 35 °C, which supports the AFM- and ITC-measured solid-to-fluid like transition in the same temperature range. The transition yields a lower energy state of DNA in the capsid core (with lower density and reduced packing defects), increasing its mobility, which is required to initiate rapid DNA ejection from the core of the virus capsid into a host cell (7). As mentioned above, core-DNA is packaged last into the capsid volume during virus assembly (due to high DNA bending stress) and is therefore ejected first during infection. Furthermore, it should be mentioned that the 10 mM Mg²⁺ buffer concentration used in this study corresponds to the most favorable physiological Mg-ion conditions for phage λ adsorption to Escherichia coli cells and subsequent infection (17). Indeed, we have previously observed that phage λ replication dynamics is significantly increased above the DNA transition temperature of ~32 °C (17).

wt bacteriophage λ, strain cI857, with 100% wt (48.5kb) was purified according to the protocols described in ref. 7. Briefly, phage λ production was achieved by thermally inducing the lysogenic E. coli strain AE1 derived from S2773. The purified virus particles were dialyzed and stored in TM buffer (10 mM MgCl₂, 50 mM Tris HCl, pH = 7.4). To produce empty phage λ particles, DNA-filled capsids were heated to 78 °C to trigger genome ejection through the phage tail while capsid remains intact (50). The ejected viral DNA was digested with DNase to avoid its contribution to the scattering signal.

Cryo-EM samples were stored at 20 °C in TM-buffer (50 mM TrisHCl + 10 mM MgCl₂) prior to plunge freezing. Cryo-EM data were collected on Tecnai F20 Twin transmission electron microscope operating at 200 keV equipped with Gatan 4kx4k CCD using the Leginon automated electron microscopy package, see ref. 70 for more details. Cryo-EM cross sections from icosahedral reconstructions and average radial density were obtained using Chimera software (71).

SAXS measurements were carried out at the 12-ID B station at Advanced Photon Source at Argonne National Laboratory. A 12keV X-ray beam was used to illuminate the sample. Forty scans with 1s X-ray exposure time were collected and averaged. A buffer solution of the dialysis buffer (TM-buffer) was measured using the same SAXS setup and buffer scattering signal subtracted as the background (17).

SANS measurements were performed at Center for High Resolution Neutron Scattering (CHRNS) NG3 vSANS beamline at NIST Center for Neutron Research (NCNR), Gaithersburg MD, USA and at ILL D11 beamline, Grenoble, France. Because the neutron flux is lower than X-rays, the sample was exposed several minutes at each configuration of the experiment, without damage or degradation of the sample in 1-mm pathlength quartz cells. The solvent exchange from 100% H₂O to 43% D₂O/H₂ O ratio was done by dialysis. The scattering signal from TM-buffer was measured separately and subtracted from the sample (DNA-filled phage λ in TM-buffer) scattering signal as background. The data reduction and model analysis were done with the NCNR SANS macros in Igor Pro (34). SANS scattering intensity I(q), on an absolute scale, versus wave number q (magnitude of scattering vector $q=4\pi sin\left(\theta \right)/\lambda$ , where $\lambda$ is the neutron wavelength and $2\theta$ is the scattering angle) was modeled with a spherical core-shell model with DNA in both the core and shell. We used NCNR macros to compute the SD values between the experimental data points and the fitting model parameters.

The core-DNA is the less-ordered/disordered DNA in the center in Fig. 2A and the shell-DNA is the ordered DNA near the periphery in Fig. 2A with water in between the strands. The initial value for the core SLD, ρ_core = 3.21 × 10¹⁰ cm⁻² at 43% D₂O/H₂O, was obtained by fitting the SANS data at 20 °C and the initial value for r_core = 9.51 nm was calculated from the cryo-EM density map at 20 °C shown in Fig. 2C. We kept ρ_shell fixed at 3.68 × 10¹⁰ cm⁻² at 43% D₂O/H₂O (corresponding to the constant DNA packing density in the entire temperature interval, which includes the SLD for both DNA and the water-filled fraction between the DNA strands at 43% D₂O/H₂O). The ρ_shell value was obtained from the cryo-EM DNA density map in Fig. 2C, where the initial values of core-DNA radius and shell-DNA thickness at 20 °C were converted to volumes, V_core and V_shell (note that V_shell refers to the volume of the shell thickness where V_capsid = V_core + V_shell). Based on the hexagonal lattice model for DNA packaged in the shell thickness (12), we calculated the length of DNA that can fit into V_shell. Thus, we were able to calculate the volume occupied by DNA, V_DNA (by considering the cross-sectional area of a dsDNA helix). The difference between V_shell and V_DNA is occupied by water molecules at 43% D₂O/H₂O ratio. SLD_DNA and SLD_43%D2O/H2O are known values (72–74). Hence, based on the volume fraction of DNA and water in V_shell, we estimated ρ_shell value. If we define the volume fraction of DNA in the shell thickness as ϕ_DNA = V_DNA/V_shell and the volume fraction of water in the shell as ϕ_D2O/H2O = V_D2O/H2O/V_shell, then ρ_shell = ϕ_DNA x SLD_DNA + ϕD₂O/H₂O x SLD_D2O/H2O.

The spherical core–shell model used to fit SANS data is given by equation below:

where $r_{\mathit{core}}$ is the core-DNA radius; $r_{\mathit{shell}}=r_{\mathit{core}}+t$ is the shell-DNA radius = 28.3 nm (equal to the inner capsid radius), t is the shell-DNA thickness; $V_i=\left(4\pi /3\right)r_i^3$ is the core (i = core) or capsid (i = capsid) volume; ${\rho }_i$ is the SLD for core-DNA (i = core), shell-DNA (i = shell) and solvent (i = solv), φ is a scaling factor that was kept constant at all temperatures, and q is wave number. SI Appendix, Fig. S3 shows a panel of the resultant core–shell profiles at all temperatures with all curves combined within a selected low q-range, reflecting DNA form factor. SI Appendix, Table S1 summarizes the SANS fitting parameters obtained with the smeared core-shell model.

Certain commercial equipment, materials, software, or suppliers are identified in this paper to foster understanding. Such identification does not imply recommendation or endorsement by the National Institute of Standards and Technology nor does it imply that the materials or equipment identified are necessarily the best available for the purpose.

A.E. designed research; J.R.V.V., E.T., and A.E. performed research; J.R.V.V., E.T., S.K., and A.E. contributed new reagents/analytic tools; J.R.V.V., S.K., and A.E. analyzed data; and J.R.V.V. and A.E. wrote the paper.

The authors declare no competing interest.