Pylaiella littoralis, share a nearly identical primary sequence yet the published 3D structures appear quite different. Relatively long restrained MD simulations using the original NMR restraint data identified the presence of a small set of violated distance restraints in one structure and a possibly incorrect trapped bulge nucleotide conformation in the other structure. The removal of problematic distance restraints and the addition of a heating step yielded representative ensembles with very similar 3D structures and much lower pairwise RMSD values. Analysis of ion density during the restrained simulations helped to explain chemical shift perturbation data published previously. These results suggest that restrained MD simulations, with proper caution, can be used to “update” older structures or aid in the refinement of new structures that lack sufficient experimental data to produce a high quality result. Notable cautions include the need for sufficient sampling, awareness of potential force field bias , and a proper balance between the various restraint weights.Restrained molecular dynamics simulations are a robust, though perhaps underused, tool for the end-stage refinement of biomolecular structures. We demonstrate their utility—using modern simulation protocols, optimized force fields, and inclusion of explicit solvent and mobile counterions—by re-investigating the solution structures of two RNA hairpins that had previously been refined using conventional techniques. The structures, both domain 5 group II intron ribozymes from yeast ai5γ and The online version of this article (doi:10.1007/s10858-012-9642-5) contains supplementary material, which is available to authorized users. Molecular dynamics (MD) simulations are often used with restraints derived from crystallography or nuclear magnetic resonance (NMR) experiments for the end-stage atomistic refinement of biological macromolecular structures , while the lower helix, upper helix, and tetraloop features are all very similar. The bulge conformation as reported in the earlier crystal structure of ai5γ-D5 (PDB: 1KXK)   provide an intriguing opportunity to validate the MD simulations, to assess simulation refinement protocols which use explicit solvent and modern force fields, and to ultimately determine whether the significant differences in these structures reported are real or artifacts from the refinement process. We show that re-refinement leads to two very similar structures that appear to better satisfy the NMR data. In addition, beyond the bulge region (which is strongly influenced by packing effects and tertiary interactions), the stem and loop regions around the bulge better match the ai5γ-D5 (PDB: 1KXK) crystal structure than the previously published NMR structures. Yet, the results also suggest that a careful balance between relative weights of the force field compared to the experimental data is required, that the experimental data has to be carefully screened, that there are clear sampling limitations, and that there are still known and emerging force field limitations. Taken together, these observations preclude the use of automation to automatically refine structures. The previous and current success of these methods suggest that some published structures might be improved using explicit solvent MD refinements and that such techniques should be more routinely applied in future structure refinement projects.2 outside this range, unless otherwise noted. The applied dihedral restraint data from the two earlier refinements were consolidated and reconfigured to produce a more consistent and liberal set of dihedral restraints and also to eliminate minor differences in the conventions used by the ai5γ_NMR and PL_NMR authors. Backbone torsions of the helical regions  were restrained to A-form values (±15°) while those in the remaining non-canonical regions were left unrestrained. The χ torsion angle was restrained to syn (70 ± 30°) for G26 and anti (−160 ± 15°) for all others. Sugar puckers were restrained  in a similar manner as described in the original publications: for ai5γ-D5, A16 and C25 were restrained to C2′-endo, whereas G15, A17, and A18 were unrestrained, and the remaining were restrained to C3′-endo; for PL-D5, A16, A24, and A25 were restrained to C2′-endo, and the remaining were restrained to C3′-endo. Torsion restraints were weighted at 500 kcal/mol-rad within 1° of the bounds of the flatwell restraint and at 500 kcal/mol-rad2 outside this range, unless otherwise noted. Relative RDC restraint weighting, set with the “dwt” keyword in AMBER, was chosen to be the highest value that did not cause SHAKE errors during simulation . Base pair planarity restraints were not applied. All restraints were converted to the AMBER formats using in-house scripts and scripts available in AmberTools. The restraint files used during the refinement are supplied in the Supporting Information.The coordinates and restraint data for the ai5γ_NMR and PL_NMR structures were retrieved from the RCSB Protein Data Bank website using the PDB codes 1R2P and 2F88, respectively. Of the ten conformers contained in each PDB file, only the first five were used in simulations. The distance restraint data was thoroughly checked for atom naming mismatches between the restraint file and the PDB files. Mismatched restraints were corrected based on visual inspection of the structures (common mismatches included H62 → H61 or H5′1 → H5′2 transpositions). Distance restraints were weighted at 20 kcal/mol-Å within 0.5 Å of the bounds of the flatwell restraint and at 20 kcal/mol-Å+ ions and addition of ~200 mM NaCl using the Joung and Cheatham ion parameters  files, the positions of all the ions in the coordinate files were randomized using ptraj, ensuring that ions were at least 6 Å from an RNA atom and 4 Å from each other. The particle mesh Ewald method  and equilibrated at constant pressure (for 50 ps each round) using gradually weaker positional restraints . For restrained simulations, distance and torsion restraints as previously described were enforced during each step of the equilibration process. A final equilibration step for the restrained simulations was included following the 0.5 kcal/mol-Å2 position restrained equilibration. This step consisted of a relaxation period of 2 ns at constant pressure without positional restraints and with distance and torsion restraints at 10 % of normal strength.All MD simulations were performed using the AMBER and AmberTools suites of software  restraints imposed . The resulting trajectories were clustered and a representative structure from the most populated cluster for each trajectory was minimized. These minimized structures , served together as representative structures for each type of simulation  as compared to the original ai5γ_NMR structures 4.09 Å). Other than global compaction of the structure, the most significant differences between the ai5γ_NMR and ai5γ_DAR structures occur in the bulge region. In four out of the first five ai5γ_NMR structures, U9 is positioned below residues 24 and 25. For ai5γ_DAR, U9 is directly adjacent to A24 and appears to form Watson–Crick bonding in three of the five structures. The other two structures show U9 disengaged from A24 while still maintaining an adjacent stance. In all five ai5γ_DAR structures, C25 is pressed against the major groove side of the A8-U27 base pair, forming a hydrogen bond between A8 H62 and C25 N3  than for the PL_NMR (1.30 Å). One of the most obvious differences between the PL_DAR and PL_NMR structures is that during equilibration and relaxation, residue A25 of model 4 shifted from a partially extruded position in the minor groove to a stacked position within the helix. Thus the PL_DAR ensemble has three of five structures with A25 stacked, whereas the PL_NMR structures have two of five (ignoring structures 6–10 in the published PDB structure file). All five representative structures for PL_DAR show U9 participating in a hydrogen bond with either A24, A25 or G26. In the two structures with A25 extruded, U9 interacts with A24. Of the three structures with A25 stacked in the helix, two show U9 interacting with A25 and one shows a hydrogen bond between U9 H3 and G26 N7. During simulations of the former case, U9 shifts back and forth between interactions with A24 and A25. In the latter, the U9 H3–G26 N7 hydrogen bond is particularly stable throughout the trajectory, leaving A24 and A25 stacked above U9. In all five simulations, these interactions close the “hole” described by Seetharaman et al. in reference to the PL_NMR structures. Interestingly, for the three structures with A25 in the stacked position, G26 no longer “packs into the major groove against G8” , but points away from the major groove with the base plane parallel with that of U9. For the two structures with A25 extruded into the minor groove, G26 remains oriented towards the major groove.On closer inspection of the refined models, some features of both the ai5γ_DAR and PL_DAR structures seemed problematic. For ai5γ_DAR, there were three distance restraints in the bulge region with consistently large upper bound violations during simulation . Two of these involved the atom G26 H8. On closer inspection it seemed possible that these two restraints were responsible for the severe kink in the backbone noted by the authors of ai5γ_NMR structures as being a very unusual conformation. Given the high upper and lower bounds of these restraints, one of the corresponding authors  suggested to us that these restraints were derived from weak NOEs that may be mediated by spin diffusion. Even though the U7 H1′–A28 H2 restraint violation was probably a side effect of the other two restraints, we decided to investigate the effect of removing all three problematic restraints. Identical simulations to ai5γ_DAR were then run with the three aforementioned restraints removed to generate the simulations that are designated as ai5γ_mDAR.anti conformation (a frequent problem for previous attempts) while the heating period was intended to enhance conformational sampling. These simulations were named PL_mDAR.Additionally, the unrestrained simulations suggested that the positioning of the A25 residue in the PL_DAR structures might also be problematic. Although the unrestrained simulations are imperfect due to force field deficiencies, we never observed A25 extruded into the minor groove during the 100 ns of unrestrained simulations. As mentioned previously, we also found that one fully restrained simulation showed A25 move from the extruded position to the stacked position and we therefore considered whether this conformation might be preferred. To investigate this, we tested several different equilibration and relaxation conditions before choosing a procedure for the modified restrained simulations. Many of the conditions resulted in either one or two of the three extruded structures transitioning to a stacked structure. Critically, in none of these conditions did A25 transition from a stacked conformation to an extruded conformation. In one condition, all three of the extruded structures transitioned to stacked structures. This condition involved three alterations to the PL_DAR simulation procedure: (1) the removal of the Watson–Crick base pair restraints, but not the NOESY restraints, between residues G8 and C27 (which are not present for A8/U27 in ai5γ_DAR), (2) increasing the weight of distance restraints from 20 to 50 kcal/mol as well as increasing the G26 χ dihedral restraint from 500 kcal/rad to 1,000 kcal/rad, and (3) heating to 700 K with restraints at 8 % strength to allow structural relaxation, followed by a smooth increase of restraint weight to 100 % strength prior to the production simulation. The rationale for removing the Watson–Crick base pair restraints was to allow structural transitions in the bulge region that may otherwise be hindered. The changes to the restraint weighting were made to ensure the enforcement of distance restraints and prevent G26 from flipping to the The removal of the three problematic restraints from the ai5γ restraint list makes a significant difference in the bulge region of the ai5γ_mDAR structures. First, the intra-structure pairwise RMSD of the ai5γ_mDAR structures 1.04 Å) is significantly lower than ai5γ_DAR 2.10 Å)  than that of the PL_DAR structures 2.56 Å), although not as low as the original NMR structures (1.30 Å). During the five PL_mDAR simulations, three different bulge motifs dominate, all of which are more packed than the open bulge observed in the original PL_NMR structures. In Model 1, the U9H3-G26N7 hydrogen bond forms . However, some variation in the backbone torsions are observed, such as that of the γ torsion of residue A16, which we attribute to the bsc0 modifications of the AMBER ff99 parameters which disfavor γ in the  Swinger  identifi+ binding features. As both loop conformations are observed, and each is consistent with experimental data, it is not possible to directly ascertain which conformation is preferred and/or if the loops interconvert between the two conformations, although likely the two conformations are close in energy which suggests population of both.The second feature of interest identified by Correll and Swinger in GNRA tetraloops is the hydrogen bonding network of the first and fourth residues in the tetraloop . In the first case (which we name the “outward orientation”), G15 N2 forms a bifurcated hydrogen bond between both A18 N7 and A18 O2P, while G15 N1 also hydrogen bonds with A18 O2P. In the second case (the “inward orientation”), G15 and A18 shift slightly relative to the backbone which allows for the same bifurcated hydrogen bond between G15 N2–A18 N7/A18 O2P as well as a hydrogen bond between G15 N3 and A18 N6. Interestingly, the ai5γ_mDAR structures seem to fit the outward orientation, whereas the PL_mDAR structures fit the inward orientation  from the RCSB website (http://www.rcsb.org). The origin of the deviations results from the use of shared, transferable and rather generic atom types for the nucleobases  rather than specific types for each different atom to more accurately represent nucleoside geometry. Although the deviations (on the order of ~5° or less) are outside the range observed in experimental databases , suggests that the RDCs primarily affect the structural compactness of these RNA structures, but not the local conformations. Both the ai5γ_mDAR and PL_mDAR simulations resulted in an increase of overall structural length (measured by the distance between A16 P and C34 P). The average structure length for ai5γ_mDA and ai5γ_mDAR, taken from representative structures, was 47.0 and 54.5 Å, respectively. The increase was less dramatic for PL, for which the average structure length was 52.8 and 53.4 Å for PL_mDA and PL_mDAR, respectively.These results are consistent with a recent study by Tolbert et al.  of a pur2+. The results for ai5γ_NMR, which only tracked 1D proton shift changes, differ somewhat from those for PL_NMR, which included more detailed 2D 1H–13C and 1H–15N chemical shift data. However, these differences could be attributed to either a real difference in structure, simply a difference in the experimental techniques, or perhaps a combination of these differences. A detailed examination of Na+ position during the simulation provided a plausible explanation for the results observed in the Mg2+ binding experiments. Our simulations were performed with monovalent salt due to the lack of good parameters for divalent cations, the absence of polarization, and conformational sampling limitations. Although the replacement of Mg2+ with monovalent salt can destabilize RNA, for small RNAs high monovalent salt concentrations are generally a good substitute for physiological Mg2+, and typically provide similar structures . Occupancy analysis of Na+ within 2.8 Å of these two atoms show that for both ai5γ_mDAR and PL_mDAR they rank among the highest in Na+ binding out of all N7 atoms .One of the more significant differences between the results for ai5γ_NMR and PL_NMR involved the triad region . For ai5γ_NMR, Sigel et al.  found thres Fig. . This dares Fig.  who sugg2+ titration, whereas only the aromatic carbon and nitrogen atoms in residue 24 of PL_NMR were affected. As was observed for the triad region, we suspect that carbon and nitrogen chemical shifts in residue 24 would have also been perturbed in ai5γ_NMR if they had been monitored. However, the shifts of C1′ in residues 9 and 25 of PL_NMR were not affected by Mg2+ as was seen for the analogous H1′ for ai5γ_NMR. The simulation data clearly accounts for this difference. Visual inspection of the Na + density grid for ai5γ_mDAR reveals a large, high density region straddling the minor groove surface of residues 9, 25 and 27 . Na+ ions in this region are likely stabilized by the O2 atom of U9, C25, and U27. The positioning of this high density region is therefore quite close to the H1′ atoms of these same residues and occupancy analysis using a 5 Å cutoff reveals that these H1′ atoms are among the nearest to Na+ during simulation  the occurrence of adenine at residue 25, rather than cytosine in ai5γ-D5, places a hydrogen atom in the binding region, rather than an oxygen atom, and therefore does not support metal binding and (2) replacement of the A8-U27 base pair in ai5γ-D5 with the G8-C27 base for PL-D5 produces a stronger base pair and does not allow the twisting conformation that permits ai5γ-D5′s U27 O2 to interact with a Na+ atom.Another region of interest is the bulge . Chemical shift perturbation analysis showed that H1′ protons in residues 9 and 25 of ai5γ_NMR were greatly affected by Mg+ binding that is identified using grid analysis . As noted earlier, the ai5γ_mDAR and PL_mDAR loop structures adopt slightly different conformations . A close inspection of the water and Na+ density in the tetraloop region reveals that these subtle differences in loop geometry lead to differences in ion binding and solvation . For PL_mDAR, the Na+ is also located between N7 and O6 of G15, but A17 O2P is more distant and any possible coordination interaction is intervened by a region of water density . In this case, the highly ordered water density that forms around the Na+ density is also very similar to that seen in crystal structures, although the ion presence was not reported  when the ion binding appears to be limited to the major groove according to the simulation Na+ density grid results. Inspection of the medium density solvation shell around the tetraloop region reveals that the base atoms are much more exposed to the bulk solvent than base atoms in the rest of the RNA molecule (data not shown). We propose that this lack of solvent shielding may explain the large Mg2+ induced chemical shift perturbations in the tetraloop.The large simulated Nan et al. ) and thuTo compare the results of our explicit solvent refinement with traditional refinement methods, we performed simulated annealing on the completely extended ai5γ and PL RNA, both in vacuo and with Generalized-Born (GB) implicit solvent, using the mDAR restraint sets. One notable feature of in vacuo results is the presence of sharp kinks near the bulge for both the ai5γ and PL ensembles. Given that these kinks are not observed in the GB ensembles or the explicitly solvated ensembles, these results suggest that in regions with sparse distance restraints, such as the bulge, the lack of a solvation environment can lead to anomalous conformations. Other than the kinked bulge conformation in the in vacuo ensemble, the local conformation of both simulated annealing ensembles are very similar to the explicity solvated ensemble. In contrast, comparison of the average structural length of the GB ensembles reveals that they are somewhat more extended than the explicit ensembles: for ai5γ_mDAR the average structural lengths are 56.9 and 54.5 Å for the GB and explicit, respectively; for PL_mDAR the average lengths are 58.2 and 53.4 Å. In contrast to what was observed for the explicit ensembles, the pairwise RMSD was higher for ai5γ_mDAR GB ensemble (2.54 Å) than that of the PL_mDAR GB ensemble (0.74 Å). The reasons for these differences likely lie with the representative structure selection method. Whereas the explicit solvation representative structures were chosen by their proximity to the centroid of the major cluster during a long simulation, the simulated annealing structures are simply the lowest energy structures which satisfy restraints from a few hundred simulated annealing cycles. It is possible that performing 10,000 or 20,000 simulated annealing cycles (a similar quantity to the frame count in the explicitly solvated simulations) would produce representative structures that are in better agreement with the explicit results. However this has yet to be investigated.The results presented in this study are immediately relevant to research in experimental structure determination and, more specifically, to refinement of RNA structure from NMR data. First, for structure refinement projects, we find that currently available MD tools with modern simulation protocols, force fields, inclusion of water and mobile counterions, and longer molecular dynamics simulations, offer robust environments for probing structural features that may not be adequately modeled by older and more conventional structure refinement techniques. Our restrained simulations of ai5γ-D5 and PL-D5 produced a set of refined structures that differed significantly from the previously published NMR structures and offer new insights into the similarities and differences of these RNA molecules. For instance, the simulation refined ai5γ_mDAR structures are much more compact than the original NMR structures and more closely resemble both the NMR and simulation structures of PL-D5. Moreover, for regions outside the bulge region  the re-refined structures better match the ai5γ-D5 crystal structure (PDB: 1KXK). We also were able to identify and troubleshoot potentially incorrect regional conformations in the conventionally refined structures of both molecules. For instance, we uncovered three problematic long range distance restraints in the ai5γ-D5 bulge, which when removed generated a smoother backbone trajectory in the bulge region, lower RMSD values, and fewer restraint violations. We also found that in three of the five PL-D5 structures, residue 25 was apparently trapped in a partially extruded conformation that upon heat annealing converted to the stacked conformation having lower RMSD values and fewer restraint violations. Noticing the problematic regions required MD simulations orders of magnitude longer than were previously and typically applied in order to highlight trapped or metastable conformations. Finally, the pairwise RMSD values for the simulation ai5γ_mDAR structures are lower than those for PL_mDAR, which is the reverse of what was found using conventional structure refinement. This is likely due to the greater flexibility in the bulge region of PL-D5 observed during the significantly longer and less-tightly restrained simulations used to re-refine the structure. The need to carefully evaluate the choice of NOE and restraint assignments —coupled with the potential for conformational trapping—suggest that automated NMR refinement of RNA structures remains a challenge. Our results suggest that the refinement of RNA structures requires a careful balance between the strength of the experimental restraints and the influence of the force field, and perhaps most importantly, the resulting structures require careful validation and assessment.The publication of a self-spliced group IIc intron crystal structure Supplementary material 2 (ZIP 194 kb)Below is the link to the electronic supplementary material.


Escherichia coli in suspension in a liquid medium swims by a succession of runs and tumbles, effectively describing a random walk. The tumbles randomize incompletely, i.e. with a directional persistence, the orientation taken by the bacterium. Here, we model these tumbles by an active rotational diffusion process characterized by a diffusion coefficient and a diffusion time. In homogeneous media, this description accounts well for the experimental reorientations. In shallow gradients of nutrients, tumbles are still described by a unique rotational diffusion coefficient. Together with an increase in the run length, these tumbles significantly contribute to the net chemotactic drift via a modulation of their duration as a function of the direction of the preceding run. Finally, we discuss the limits of this model in propagating concentration waves characterized by steep gradients. In that case, the effective rotational diffusion coefficient itself varies with the direction of the preceding run. We propose that this effect is related to the number of flagella involved in the reorientation process.The bacterium  Escherichia coli whose motion is classically described by a succession of runs and tumbles run∼20 µm/sVrun>∼1 s<τ and tumble>∼0.1 s<τt∼Vrun2<τrun>∼100 µm2/sDMicro-organisms living in liquids have developed several strategies to explore their environment and colonize new niches more favorable  for their development E. coli performs a temporal comparison of the molecular concentration via its membrane-bound chemoreceptors  When swimming in a gradient of chemoattractant, However, since runs and tumbles modulations involve the same pathway, it is natural to think that an increase in run durations could go with a variation (a decrease for synergy) of tumble durations (less reorientation meaning longer persistence) leading to a more efficient motion of the bacteria toward favorable niches. This idea has been supported by numerical simulations In the present article, we investigate in details the physical mechanism of tumbling and its apparent resemblance with a process of active rotational diffusion. We first test this idea on bacteria swimming in a homogeneous medium and on tumbler mutants. This description having potentially profound consequences on the chemotaxis of these organisms, we have checked whether a constant diffusion coefficient can account for the differential modulation of the reorientations observed in static shallow nutrient gradients. We end by discussing the limits of this approach in the case of propagating concentration waves where gradients are steeper and imposed locally by the bacteria themselves.The motion of ellipsoidal brownian particles dispersed in a liquid medium at rest consists in both translational and rotational diffusion. We will remind in this section some of the basic aspects of rotational diffusion.p is the probability density distribution for the particle to have an orientation of polar angle θ and azimuthal angle ϕ at a given time t  = δ(θ) , the temporal evolution is given by an expansion in spherical harmonics lP is the Legendre's polynomial of order l.Starting at t = 0, from a Dirac distribution n indicating the orientation (major axis) of the particle describes a random walk on a sphere.A simulation of this rotational diffusion process for a particle is shown in <cosθ>(t) = <n(t)·n(0)> deduced from this distribution is simply given byi.e. the only contribution in Eq.2 is 0 = 1P . The distribution p(θ) of the reorientation angles between successive runs has been studied in θ = 63° meaning that the orientation of the bacteria is not completely randomized during a tumble (<θ> = 69°). There is therefore a persistence in the orientation from one run to the next. The duration of these tumbles is exponentially distributed with a mean value of tumble> = 0.14 s<τWe question here whether tumbles can be described by active rotational diffusion in the reorientation space (tumble)p. The theoretical curve that best fits the experimental data is obtained for a rotational diffusion coefficient r = 3.5±0.3 rad2/sD and the agreement is then very good , a direct comparison with The analysis of bacteria trajectories gives the tumble durations and the corresponding change in orientation (the angle between two successive runs) without details on the evolution of the orientation during a tumble. Moreover, since the tumble durations are exponentially distributed Here, we determine precisely the evolution of the orientation of an ellipse-shaped bacterium as a function of time  by high <cosψ>(τ) = <cos(ψ(t+τ)−ψ(t))> of tumbler mutants in LB and M9 medium. The values obtained for the rotational diffusion coefficients in LB and M9 medium are respectively rLB = 2.4 rad2/sD and rM9 = 1.6 rad2/sD. Again, even though the strains are different, these values are very close to the ones determined by analyzing the trajectories of the motile E. coli and confirm that the reorientation of the bacteria can be described by an active rotational diffusion process.drift = 5.1±0.5 µm/sV of the bacteria along the gradient. We We have described so far the behavior of bacteria in isotropic environments. In a gradient of nutrients , one canr = 2.3±0.3 rad2/sD obtained in the absence of gradient  according to their swimming direction. As a consequence, bacteria swimming up the gradient reorient less which improves the chemotactic drift tumble)<cosψ>, r = 4.4±0.3 rad2/sD in the opposite direction (red), and r = 3.2±0.2 rad2/sD in the perpendicular direction (blue) (r/Dr∼67%ΔD) is more important than the variation of tumble durations (r/τr∼22%Δτ) Here, the correlation functions were clearly different according to the swimming direction, each of them being described by an exponential decay of the reorientation as a function of time. When averaging out the values of the diffusion coefficients over the whole front, we found n (blue) . In this<cosθ>∼0.33The respective effects of run lengthenings and reorientations have been studied in details in Since the tumbles are well decribed by a rotational diffusion process, eq. (3) holds and leads todriftV. The run lengthening effect alone would give a drift velocity drift = 5.1 µm/sV  and equally affect the translational diffusion coefficient. It is possible to quantify more precisely both contributions and to directly compare them with the measured value of 5.1 µm/s . If we iWe note that computer simulations have shown that a small (∼5°) modulation of the reorientation after a tumbles can dramatically affect the mean drift velocity, up to a factor of two i.e. opposing effects of the gradient on run lengthening and tumble shortening), a single diffusion coefficient cannot describes all the tumbles within the wave even though this description holds for subfamilies sorted upon their swimming direction. As proposed in Although the same trend is observed for bacterial waves  and its derivative, a “tumbler” mutant (ΔCheZ) In this study, we have used the Both strains were transformed with a PZE1R-GFP plasmid  Different media were used in this study:−1 Bacto™ Casamino Acids , 4 g·L−1 D-Glucose, and 1 mM MgSO4M9 Minimal Salts, 5× supplemented with 1 g·L“Motility buffer” LB medium (Sigma) was also occasionally used for bacterial culture when specified.600 = 0.5 (∼5×108 bact/cm3). Ampicilin (50 µg/mL) was added to maintain the plasmid when necessary.In all these experiments, cells were cultured at 30°C in 3 mL medium, shaken at 300 rpm up to reach an OD600 = 0.5. A droplet of this solution was entrapped between two coverslips separated by thin PDMS spacers (100 µm). Bacteria were observed at ambient temperature (22°C) under an inverted fluorescence microscope (Zeiss Axiovert 200) with a 100× objective and an intensified camera  at 50 fps, approximately in the middle of the chamber. The resulting images were analyzed with the ImageJ plugin Analyze Particles to extract (best fit by an ellipse ψ of the major axis of the bacteria in the observation plane as a function of time (The tumbler mutant cells (ΔCheZ) were grown either in LB medium or in enriched M9 medium up to an OD of time .The microfluidic channels were placed under a variable zoom fluorescence stereomicroscope  equipped with a CCD camera . The whole set-up was maintained at 30°C, high humidity during the experiments to prevent evaporation through PDMS. Fluorescence mode was used to track the individual fluorescent bacteria. In our setup, the depth of field was ∼100 µm making possible to follow single bacteria over 20 s or more and measure the projections of their actual trajectories.For the traveling wave experiments, low intensity transmission illumination (dark field mode) was superimposed to simultaneously follow the motion of the (mostly non-fluorescent bacteria mixed with fluorescent one at a ratio 500/1) wave Movie S1Movie of a “tumbler” mutant: Motion of the “tumbler” strain (CR33) observed by fluorescence microscopy. This observation is performed at high magnification  and high video rate (50 fps). The orientation of the bacterium in the focal plane is deduced by computing the major axis of the ellipse that best fits the image of the bacterium.(AVI)Click here for additional data file.


Accurate mechanical characterization by the atomic force microscope at the highest spatial resolution requires that topography is deconvoluted from indentation. The measured height of nanoscale features in the atomic force microscope (AFM) is almost always smaller than the true value, which is often explained away as sample deformation, the formation of salt deposits and/or dehydration. We show that the real height of nano-objects cannot be obtained directly: a result arising as a consequence of the local probe-sample geometry.We have modeled the tip-surface-sample interaction as the sum of the interaction between the tip and the surface and the tip and the sample. We find that the dynamics of the AFM cannot differentiate between differences in force resulting from 1) the chemical and/or mechanical characteristics of the surface or 2) a step in topography due to the size of the sample; once the size of a feature becomes smaller than the effective area of interaction between the AFM tip and sample, the measured height is compromised. This general result is a major contributor to loss of height and can amount to up to ∼90% for nanoscale features. In particular, these very large values in height loss may occur even when there is no sample deformation, and, more generally, height loss does not correlate with sample deformation. DNA and IgG antibodies have been used as model samples where experimental height measurements are shown to closely match the predicted phenomena.Being able to measure the true height of single nanoscale features is paramount in many nanotechnology applications since phenomena and properties in the nanoscale critically depend on dimensions. Our approach allows accurate predictions for the true height of nanoscale objects and will lead to reliable mechanical characterization at the highest spatial resolution. The AFM is a powerful surface characterization tool allowing the height and the width of nanoscale features to be measured routinely with nanometer and sub-nanometer resolution c) leading to loss of true height Still, there is a fundamental problem concerned with the 3D information that is obtained at very short length scales. Typical measurements of nanoscale features with an AFM give an apparent height that is almost always lower than their known true height c1 follows. Over a second surface 2 with the same properties as surface 1, and with true height D1 relative to the level surface 1, zc is now zc2  based on a point mass and a spring 0)2. Here the spring constant of the cantilever is k, the natural angular frequency is ω0, the driving force is F0cosωt and Fts is the net tip-sample force. Moreover, z is the instantaneous position of the tip and it is measured from the equilibrium position for the unperturbed cantilever.In (1) the effective mass of the AFM probe is defined For the tip-surface scenario we have,* is the effective elastic modulus as typically defined in contact mechanics 0 is an intermolecular distance introduced to avoid divergence Here E* as the effective distance between the tip and the “sample”. Then d* is defined as the surface distance minus the height of the surface feature, which, in the case of a sphere of radius R2, gives d* = d-2R2. Note that (3) is an approximation to the true sphere-sphere interaction. Nevertheless, it can be shown that this approximation is justified when results are compared to those obtained when using the true, more convoluted, expression (see section 4 and c2−zc1)/2R2<1 (c2−zc1) with decreasing forces is also ruled out. This is because it can be shown both experimentally (c2−zc1 can increases with increasing force or free amplitude A0 and/or deformation (see s) /2R2  whereas for the tip-sample forces (3–4) we use the parameter d1)/2R2<1 . Thus, o1)/2R2<1  that agr1)/2R2<1 . Third, mentally  and withmentally  that zc2 (see s) . Fifth,  (see s) . In Fig.tibodies . Importatibodies  nor in ttibodies . Sixth, tibodies , the valIn summary, we have shown that the geometry of the tip-surface-sample interaction area can induce deviations in the apparent relative to true height of up to 90%. The intrinsic resolution limit in the atomic force microscope causes height information to be spread-out laterally across the tip-sample interaction area resulting in loss of height for features of nanoscale lateral dimensions.Since phenomena occurring in the nanoscale, where the properties of matter vary from those displayed by atoms or macro-objects, are largely dependent on the dimensions of the features, accurate understanding of measurements is paramount. In this respect, the results presented in this article are relevant to all fields of research using the AFM to characterize the dimensions of nanoscale samples. Our results have further shown that the effects of the size of the sample here described are particularly relevant in the nc mode of operation where very small and attractive forces are typically involved. Since this is a common mode of operation when imaging soft matter, and for preserving the sharpness of the tip, special care should be taken in these experiments to interpret data. We have further shown that even with relatively small forces, and as long as the effective area of interaction is larger than the lateral size of the feature, the true apparent height will never be obtained. For example, the forces in the non-contact mode in More generally, predicted heights with this model and future adaptations can be compared with experimental data and used to deduce the real height values. This will therefore enable decoupling of intrinsic height loss from other sources thus allowing local mechanical properties of molecules and surfaces to be more rigorously defined at the nanoscale. This interpretation brings AFM into analogy with other forms of microscopy where there is an intrinsic resolution limit.c1 whereas the sample forces (3–4) have been used to obtain the cantilever-sample separation zc2. One can choose any set of operational parameters and cantilever-surface-sample properties to obtain a difference zc2−zc1. This is the predicted apparent height.The experimental data in this work has been obtained with a Nanoscope Multimode IIIa AFM (Veeco). Only cantilevers for which a Lorentzian response in air could be obtained have been used. Both dsDNA (1074 bp) and Immunoglobulin G (IgG) antibodies samples have been used as model systems where details on sample preparation can be found in the literature Figure S11) to other points inside <Area> (e.g. P2). This is exemplified with differences in contrast where, in the example, the darker the colour the greater the localisation. For example the force per unit area  is larger in (a) d1 than (b) d2 where d2>d1.Scheme of the effective interaction area, <Area>, of a tip in the proximity of a surface and its relationship to sensitivity and proximity of surface features. The force per unit area might change from the point just under the tip (P(TIF)Click here for additional data file.Figure S2c2−zc1) in the non-contact mode for a tip-surface-sample system  for several values of tip radius . The value zc2−zc1/2R2 decreases with R2 and increases with decreasing R even though the characteristic parameters of both sample (i.e. a sphere) and surface are the same, except for the elastic modulus. However, since all measurements are in the nc mode the value of E is irrelevant here. The parameters are: A0 = 3 m, Es = 0.2 GPa, E = 10 GPa, γ = 30 m (surface and sphere) J/m2, H = 6×10−20 J (surface and sphere), Asp/A0 = 0.90. Tip-surface systems. (b) Changes in apparent height (zc2−zc1) due to variations in the local value of H in the nc mode for R = 10 and 30 nm. The parameters are: A0 = 3 m, E = 0.2 GPa, and Asp/A0 = 0.90, γ = 30 m J/m2 (H = 6×10−20 J) and the rest as above. The reference value is H = 10×10−20 J (zc1). (c) Changes in apparent height due to variations in the local values of the E in the repulsive regime. Values for R = 10 nm and R = 30 nm overlap in this case because very large free amplitudes were used except for the case E = 10 MPa and R = 30 nm for which the repulsive regime could not be reached. The parameters are: A0 = 60 nm, Asp/A0 = 0.70 and the rest as above. The reference value is E = 1 GPa (zc1).Simulations where the predicted apparent height of surface samples is shown. (a) Changes in apparent height (z(TIF)Click here for additional data file.Figure S32). The meaning of the markers is also the same as that in Predictions of apparent height as a function of elastic modulus of the sample including viscoelasticity. (a) As (TIF)Click here for additional data file.Figure S42 = 1 nm. The indentations correspond to those in s<2 GPa) both when no viscoelasticity is allowed (squares) and when it is present (rhombuses); less so in the latter. The legends are different to those in Predictions for the normalised deformation (or indentation) for a sample sphere of R(TIF)Click here for additional data file.Figure S5c2−zc1)/2R2 for (a) a compliant sample (Es = 0.1 GPa) and (b) an intermediately compliant sample (Es = 2 GPa) as a function of free amplitude for a constant set-point. Where the markers overlap these are shown explicitly with arrows pointing to the respective points. If no viscoelasticity is allowed total deformation is predicted in some cases (data not shown). The parameters are: Asp/A0 = 0.88, E = 10 GPa, γ = 60 m J/m2, H = 12×10−20 J and η = 1000 Pa•s2.Predictions of apparent height as a function of free amplitude, elastic modulus and Hamaker. Apparent height (z(TIF)Click here for additional data file.Figure S60 corresponding to the same parameters used to obtain 0 but does not correspond to a pattern that might be expected if reduction in apparent height, (zc2−zc1)/2R2 was a consequence of deformation only (c.f. c2−zc1)/2R2 when the repulsive regime is reached on the surface (A0>15 nm) the deformation still increases.Predictions for the Normalised deformation as a function of Anly c.f. , S6. In (TIF)Click here for additional data file.Figure S70 has been systematically increased (1<A0<20 nm) while keeping the set-point high and driving at resonance. All scans have been acquired with Asp/A0∼0.9 except for (o) where Asp/A0 has been slightly reduced compared to (n), in order to allow comparison of apparent heights between the L-state (attractive regime) and H-state (repulsive regime) there. The value of R was approximately 10 nm.Sequence of topographic scans of two 800 Kbp dsDNA molecules. (a–o) A(TIF)Click here for additional data file.Figure S8c2−zc1)/2R2 and phase shift corresponding to c2−zc1)/2R2, where R2 = 1 nm has been taken as the reference value for the true radius of dsDNA molecules. Even though the DNA molecules are certainly not perfectly circular in cross-section, the predicted values can be taken as a first approximation to the phenomenon. Average values and error scales are shown. Note that an extra value is shown at the end for A0 = 4.5 nm. This corresponds to a control scan obtained to compare the values of (zc2−zc1)/2R2 after the sequence (scan not shown). The two values of A0 = 4.5 nm are coloured blue to allow easy comparison. There are also two values for A0 = 19.5 nm corresponding to the attractive and repulsive regions in 0 and, as predicted (c2−zc1)/2R2 is larger in the repulsive regime! This is despite δ also being larger in the repulsive regime. This outcome is also demonstrated in the main text in 0, (zc2−zc1)/2R2 can be larger in the repulsive regime for a given Asp/A0. From this, it does not necessarily follow that (zc2−zc1)/2R2 increases with A0. In particular, the tendency for increasing A0 is that (zc2−zc1)/2R2 decreases with increasing A0 once in the repulsive regime and this is confirmed in simulations for A0>19 nm such as that shown in Experimental values of (zredicted  (zc2−zc1(TIF)Click here for additional data file.Figure S9c2−zc1)/2R2 for Es = 2 GPa (filled) and 5 GPa (outlined) of R2 = 1 (squares) and 2 nm (circles). A value of A0 = 24 nm and set-point of Asp/A = 0.80 has been used throughout. No viscoelastic term has been used (e.g. η = 0 Pa•s2). Here δ is seen to increase with increasing drive frequency while ((zc2−zc1)/2R2) decreases. All values have been obtained in the repulsive regime. There is a clear relationship between increasing δ and decreasing (zc2−zc1)/2R2. The parameters are: H = 10×10−20 J and R = 10 nm and the rest as indicated in the main text.Predictions relative to drive frequency in the repulsive regime. Simulations of (a) Normalized δ and (b) (z(TIF)Click here for additional data file.Figure S101) and a sphere (R2) for (a) R = 10 nm and (b) 20 nm. The forces predicted by the simplified van der Waals equations are shown (filled) against the true values (outlined) for R2 = 1 (squares) and 5 nm (rhombuses) respectively.Comparison between exact and simplified van der Waals expressions for two spheres. Force versus distance between a tip (R = R(TIF)Click here for additional data file.Figure S11Comparison between exact and simplified van der Waals expressions for an infinite surface and an sphere. Comparison between the simplified equations (filled) for the van der Waals force between a sphere of radius R and an infinite and flat surface and the true equations (outlined). The forces are shown as a function of distance d. The relationships are shown for R = 10 (squares) and 20 nm (rhombuses). The simplified form closely follows the true equation even for distances as large as 3 and 4 nm.(TIF)Click here for additional data file.Figure S12c2−zc1)/2R2 for several values of R and R2. The true equations for the van der Waals interactions (filled) have been used against the simplified equations (outlined) for R = 10 and 30 nm respectively. The true values produce only slightly smaller values for the apparent height. All data was achieved in the non contact mode. The parameters are: A0 = 1 nm, Asp/A0 = 0.95, Es = 5 GPa, E = 10 GPa, H = 6.1×10−20 J, γ = 30 m J/m2 and all other parameters as detailed in the main article.Comparison between the results for apparent height between the exact and simplified van der Waals expressions in the nc mode. Simulations showing (z(TIF)Click here for additional data file.


Understanding the processes and conditions under which populations diverge to give rise to distinct species is a central question in evolutionary biology. Since recently diverged populations have high levels of shared polymorphisms, it is challenging to distinguish between recent divergence with no (or very low) inter-population gene flow and older splitting events with subsequent gene flow. Recently published methods to infer speciation parameters under the isolation-migration framework are based on summarizing polymorphism data at multiple loci in two species using the joint site-frequency spectrum (JSFS). We have developed two improvements of these methods based on a more extensive use of the JSFS classes of polymorphisms for species with high intra-locus recombination rates. First, using a likelihood based method, we demonstrate that taking into account low-frequency polymorphisms shared between species significantly improves the joint estimation of the divergence time and gene flow between species. Second, we introduce a local linear regression algorithm that considerably reduces the computational time and allows for the estimation of unequal rates of gene flow between species. We also investigate which summary statistics from the JSFS allow the greatest estimation accuracy for divergence time and migration rates for low (around 10) and high (around 100) numbers of loci. Focusing on cases with low numbers of loci and high intra-locus recombination rates we show that our methods for the estimation of divergence time and migration rates are more precise than existing approaches. Understanding speciation processes is crucial in numerous fields including conservation biology, ecology, host-parasite co-evolution and human evolution Drosophila species Solanum peruvianum and S. chilenseAllopatric population divergence is the classical scenario for isolation between populations Drosophila melanogasterThe most widely used general model of population divergence is the “isolation-migration” model S of dimension (1n+1)×(2n+1)−2 where entry i,jS is the number of polymorphic sites for which the derived state is found i times in the sample from population 1 and j times in the sample from population 2. For example, 2,3S = 10 if 10 polymorphisms are found as doubletons in population 1 and as tripletons in population 2. For parameter estimation, Wakeley and Hey W =  containing the number of private polymorphisms in species 1 and 2, respectively , fixed differences between species (3W), and shared ancestral polymorphisms (4W). Examples of JSFS expectation values are shown in W. Approximate Bayesian Computation (ABC) methods were also developed to estimate parameters of the isolation-migration model from summary statistics such as the amount of private polymorphisms and diversity per population and in the pooled sample  e popABC . A greatS. peruvianum and S. chilense). Not only do these species appear to have recently diverged but gene flow may be on-going W have limited power to distinguish between divergence in isolation and divergence with continuing gene flow. Since we wished to determine whether these two species split recently with no or negligible levels of gene flow, or split less recently, but diverged in the presence of gene flow, we realized that previously described methods were not adequate.The present study was motivated by research on non-model organisms, including, for example, two recently diverged species of wild tomatoes (4W (shared polymorphisms) of the JSFS into further classes for singletons and doubletons shared between species (see W perform better than MIMAR.Our first aim is to show as a proof of concept that refining the summary of the JSFS to more classes results in improved estimates of divergence time and gene flow. For this purpose we decompose the class cies see . The ratcies see . In the cies see . We use eN generations) all methods overestimate divergence time and gene flow, although our more complex summary of the JSFS seems to be more robust than other methods. Importantly, we show that our composite likelihood methods based on the assumption of genealogically independent SNPs are also more accurate than previous methods when estimating parameters at low recombination rates. As a practical conclusion for the use of JSFS statistics, we apply our composite likelihood method to determine which JSFS decompositions yield the highest accuracy for estimating divergence and gene flow parameters. We provide this comparison for the case where 7 loci , which decreases the correlation across polymorphic sites. We neglect these dependencies and employ a composite likelihood approach based on a Poisson point process approximation of the JSFS, which significantly reduces the run time of the simulations. The parameter estimations are realized by local log-linear regression analysis. We demonstrate that this leads to a quantitative improvement of the use of the Wakeley-Hey summary statistics, because it allows the estimation of unequal directional gene flow between populations. Furthermore, computation time is much reduced compared to other methods. We show that our method is faster and gives more accurate estimates of divergence times and rates of gene flow than MIMAR, popABC, and ∂a∂i. However, for very recent divergence times . Following Wakeley and Hey μ is the average mutation rate across loci and can be used to estimate the effective population sizes of the three populations  if the scaled mutation rates Aθ = 4AμN, 1 = θ41μN and 2 = θ42μN can be estimated from the data. Note that as in Wakeley and Hey τ is the estimated time of species divergence (in units of 21N generations). The two migration rates 12m and 21m are defined as follows: 12m is the fraction of population 2 that is replaced by migrants from population 1 each generation, and vice versa for 21m. The migration parameter is rescaled as twice the number of individuals in a population replaced by migrants (backward in time) with 21M = 41m21N and 12M = 42m12N. In the current version, this model assumes that each locus is located on an autosome and follows the infinite-site mutation model with reciprocal recombination c. This value is assumed to be constant and known within a given locus and across all loci, i.e. we do not allow for variable recombination rates in the genome.We consider a neutral IM model in which an ancestral population splits into two populations that may exchange migrants. It is assumed that Aθ, 1θ, 2θ, τ, 12M, 21M, c) isp(Ω | Θ) is the likelihood of the vector of parameter values, Θ, and p(Θ) is its prior probability.Following the description of the IM model by Hey and Nielsen 1n sequences from population 1 to 2n sequences from population 2 i and j take integer values between 0 and 1n and 0 and 2n, respectively. Wakeley and Hey The full JSFS can be used to compare nucleotide sequence data of derived alleles from i.e. different classes of the JSFS are used as summary statistics, and b) in the estimation procedure used to calculate the parameter values. To investigate the benefit of various sets of summary statistics for the joint estimation of divergence time and gene flow, we focus on estimating Θ =  assuming that Aθ, 1θ, 2θ, and c are known.We demonstrate that using additional classes of the JSFS allows us to utilize more information than these original approaches, and improves the estimation of Θ. We present two methods that differ a) in the summary statistics used, τ, 12M, 21M) D, D′, D″, *D. Our simplest summary of the JSFS, D, is a vector of 7 values  expanding the four classes kW  in Eq. 2. Additional classes relative to the Wakeley-Hey set are created by splitting each class of private polymorphisms to each species (1W and 2W) and the fixed differences class (3W), by distinguishing whether the derived allele is fixed or absent in the other species. This results in the following relation between Eq. 2 and elements of D: 1W = 1+D6D, 2W = 2+D7D, 3W = 3+D4D and 4W = 5D  have more elements, 12 for D′ and D″ and 23 for *D, because singletons and doubletons in each population are included as new classes of shared polymorphism (see 4W (Eq. 2) is further divided. The amount of information taken into account from the JSFS increases from D to *D, as shared low frequency and private polymorphisms are counted as separate elements of the summary statistics vector.Our first approach is based on the maximum likelihood inference of the set of parameters Θ = ( W4 = D5 . The othDL(Θ) = p(D | Θ) of the parameter combination Θ, for the given data summaries D  is an integral over all genealogies G  G are scaled in units of 21N generations. Since the probability of the sequence data depends only on G and the mutation rate, we get:p(D | Θ) can be approximated for each locus by generating a set of I genealogies mG, p can be computed explicitly. The number i,jS of polymorphic sites of frequency i in population 1 and j in population 2 is Poisson distributed with mean i,jθ1L/2, where i,jL is the total length of ARG branches leading to i sequences in the first and j sequences in the second sample. Conditional on the genealogies, the probabilities of observing each element kD of the vector D are independent. The likelihood of the data for a given locus is approximated byD, K = 7, but for D′ and D″, K = 12, and for *D, K = 23.Following Eq. 1, the likelihood 1 (using vector D), D2 (using vector D′), D3 (using vector D″) and D4 (using vector D*).A modified version of Hudson's ms is used to calculate the likelihood values for each simulated genealogy, and 10,000 genealogies were randomly drawn for each parameter combination. In the following, the maximum-likelihood methods based on these summaries are called Di.e. τ, 12M and 21M, within a defined range. The maximum likelihood parameter values are obtained by local regression analysis using the locfit function available in the statistical software R . In the initial version of Jaatha, the JSFS is split into 23 elements constituting the vector kĎ, Ď is similar to D* mentioned above as it considers classes of shared polymorphisms that are singletons or doubletons in both populations . We give a detailed description of Ď in Ď of summary statistics was stored.The parameters, ns Ď6 in . HoweverRN for all three parameters. Each region contained RN3 points characterized by the set of summary statistics J. In practice, we chose RN = 5, i.e. we subdivided the parameter space into 8×8×8 blocks each of which contained 5×5×5 different parameter combinations used in the simulation step. For each block and for each of the 23 summary statistics a log-linear Poisson regression model with the three parameters  as explanatory variables was fitted to the simulated data from 5×5×5×10 = 1,250 simulations  and the same holds for y with log and z with log. Fitting the log-linear Poisson model for a certain block b and a certain summary kJ requires the estimation of coefficients  such that the following equation holds for the expected value k,x,y,zd of kĎi,kβ is a transformation of i,kα. Given any parameter values τ, 12M, and 21M in the range of block k, the observed values of the summary statistic kĎ are assumed to be Poisson distributed with expected value 1,ϕd , 2,ϕd , …, 23,ϕd are the expected values of the 23 summary statistics for a certain combination ϕ =  of parameter values and F =  are the observed values, then the Poisson model likelihood of ϕ isi.e. recent divergence time and low gene flow.Next, the three-dimensional space of parameters was divided into sub-regions of size 1, J2, J3 and J4):The first two steps are carried out independently of the observed data, and the most time-consuming part of the method is to fit regression models that describe how the expectation values of the summary statistics depend on the model parameters in the simulated data. The results of these steps can be reused to analyze data with similar sample sizes and parameter ranges. We have tried four different strategies for parameter estimation  using our maximum likelihood methods (D1–D4) and the composite method (J1–J4). For comparison, estimations were also computed using the MCMC-likelihood program MIMAR 1–4 and J1–4 have identical fixed values for population sizes and recombination rate  when estimating divergence and migration. The model underlying our simulation study is motivated by research on sequence variation in genes from non-model organisms for which few loci  are available in two closely related species. However, our methods can also be applied to species for which numerous sequenced loci are available. In this case, the accuracy of the parameter estimates increases  from very low (12 = M21M = 0.5) to intermediate (12M = 21M = 2). Moreover, we investigated how other parameters of the model influence the accuracy of each method. Based on population sizes observed in wild tomatoes Aθ, 1θ, 2θ are assumed to be equal (Aθ = 1 = θ2θ), taking a value of 5 or 10. Similarly, the recombination rate ρ = 41cN takes values of 5 (low c), 10 (intermediate c) or 20 (approximating high recombination). For each set of parameter values, 20 datasets of 7 loci were generated and analyzed using our maximum likelihood methods (D1–4), the composite method (J1–4) and MIMAR. MIMAR was run twice with two and 10 million steps of burn-in, the outputs being calculated based on 100,000 or 500,000 steps, respectively. Convergence to maximum likelihood values was assessed by a high rate of accepted steps, as recommended  by comparing performance with that obtained with MIMAR τ = 0.01) to ancient (τ = 9), migration rates were unequal (12M≠21M) each ranging from very low (M = 0.01) to high (M = 9). The mutation parameters Aθ = 1θ = 2θ and the scaled recombination rate ρ = 41cN were chosen at random between 5 and 20 per locus. The uniform priors for divergence time and migration rates are identical for our composite method (J1–J4), MIMAR, and popABC, and are defined as 0.01<τ<10 and 0.01<12M, 21M<10. Note that all methods have identical fixed values for the population sizes and recombination rate .The second accuracy analysis deals with testing the robustness and speed of the composite method  simulations. Tests with popABC using all 22 possible summary statistics did not lead to reliable estimates. ABC methods can lack statistical power to estimate parameters when the number of summary statistics is too large i.e. for each species: the mean mutation frequency spectrum, an estimate of STF based on segregating sites, and the number of private segregating sites τ, 12M and 21M (fixing ρ and Aθ = 1θ = 2θ) could not be obtained after more than 4 weeks of running. This is probably due to the wide range of priors for τ, 12M and 21M extending over several orders of magnitude (C. Becquet pers. comm.).We used popABC to generate 300,000 simulations for each of the 100 data sets assuming fixed values of i.e. coarsenings D, D′, D″, D* or Ď of the JSFS, to be used for parameter estimation with our fast composite likelihood method. We ran methods J1–4 with these 5 different vectors of summary statistics and compared estimates with those obtained running methods J1–4 with the Wakeley-Hey vector of statistics (W). We analyzed the 100 simulated data sets of 7 loci  with randomly chosen parameter values as described above. In addition, we performed a second analysis with simulated data sets of 100 independent loci of 1,000 bp each with parameters values in the same range as above . The results of this analysis are shown in We looked for the best set of summary statistics, RE) is the relative difference between the estimated parameter value and the true parameter value that was used to simulate the data. For example, for the divergence time (τ), the relative error is τRE:simn data sets) between the estimated value and the simulated value divided by the simulated value, and similarly, for τ:2F) is the proportion of data sets for which the estimated value (of τ or M) is at least half and at most twice the simulated value. Analyses of variance statistics were computed using the glm function, and multiple mean comparisons are based on Tukey's HSD test (confirmed by a Bonferroni test), as implemented in the R software  showed variation in estimates of divergence time and, in particular, migration rates , 2. Howeτ = 0.01) to very old (τ = 9), large overestimations were not common  than for recent population splits  and the recombination rate (ρ). In fact, the relative error of the divergence time depends only on the method chosen and the population mutation rate. A significant interaction between method and θ is analyzed further by calculating the RMSE, in order to find which method performs better for a given value of θ  increases, reflecting the dependence between these parameter estimates  is high, although the median of the relative error rates is similar to results of popABC  tend to over- or underestimate divergence time and migration rates more often than the other maximum likelihood methods  of unequal migration rates between populations (12M≠21M) than do popABC statistics , the population sizes of the two extant populations (1θ and 2θ), the ancestral population size (Aθ), and the migration rates between populations (12M and 21M). The likelihood methods of Nielsen and Wakeley D′, D″, D* and Ď take low-frequency polymorphisms that are shared between populations into account. We show that this provides a significant improvement for estimating the divergence time and gene flow between populations under recent divergence and across a range of intra-locus recombination rates.The JSFS is a summary of polymorphism data that contains information about the parameters of the isolation-migration model Drosophila and wild tomatoes Reliable estimates of migration rate and divergence time are linked to variances in the four classes of the JSFS Our results show in addition that the coverage of the maximum likelihood methods (varying from 64 to 86%) is higher than that of the composite likelihood methods (50%) and MIMAR (around 10%). These results indicate that the MIMAR runs may have converged on local optima and confirm that the chi-square approximation for confidence intervals is applicable to our composite likelihood method e.g., popABC) can also re-use a given simulated parameter space if the data sets to be analyzed have identical prior distributions.A second quantitative improvement is achieved by developing a simulation-based composite likelihood method that considerably reduces the time of computation compared to MIMAR and our maximum likelihood methods. These methods, as well as full likelihood procedures such as IM 2–4 (with coarsenings D* or Ď) provide the most accurate estimates of migration rate. The assumption of independence of sites does not affect the power of these methods over a range of recombination rates (∂a∂i shows a similar behavior). This indicates that methods which take intra-locus recombination into account are also valid when rates of recombination are low W vector .Our methods Jτ<0.1 in 12M (or 21M) is biased under low migration (12M or 21M<0.1), independent of the divergence time. In contrast, when using the composite likelihood methods (J1–4), large relative errors are observed for estimates of the migration rate 12M if the true migration rate is low (12M<0.1) and the divergence time is very recent . For popABC extreme overestimates of the divergence time occur when the true value is very low τ<0.1 in , indepent τ<0.1,  and S9. τ<1 or small migration M<0.1). Estimates obtained with 14 summary statistics are more accurate than those obtained with 11, although they differ only by the inclusion of haplotype diversity in each population and over pooled populations (D* or Ď (in addition to haplotype diversity), would show better inference of recent divergence times and gene flow, and might be robust over a range of recombination rates.We also notice that inaccurate estimation of parameters with popABC following the regression is due to wide posterior distributions. The mode of the posterior estimated by ABCreg ulations . This hi1–4; τ<0.1), but estimations of migration rate are in line with results from our composite methods and popABC . When analyzing data from two or more diverging populations or species, it should be kept in mind that departures from the stringent model assumptions Appendix S1Supplementary information.(PDF)Click here for additional data file.Figure S1Relative error for estimates of (a) the divergence time (τ) and (b) the migration rate (M = 12M = 21M1–D4), MIMAR and the composite-likelihood methods (J1–J4).), for the maximum likelihood methods /simτ where estτ is the estimated value and simτ is the simulated value. Groups with significant differences between means following multiple comparisons (Tukey HSD test at 0.05) are indicated by letters for each method . Values that are more than 1.5 times the nearest interquartile range (25% or 75%) are displayed as diamonds, those more than 3 times are displayed as stars.(TIF)Click here for additional data file.Figure S2Analysis of regression between errors in estimates of migration rate (12 = M21M) and divergence time τ for the 9 methods tested. (a) D1–4 for the maximum likelihood methods, (b) J1–4 for the composite likelihood methods and (c) for MIMAR. Positive (negative) relative error indicates over (under)-estimation of the parameter. Regression coefficients and p-values are calculated using the lm function in the R software. P-values indicate the significance of the test whether the slope of the linear regression is zero.(TIF)Click here for additional data file.Figure S3Factor 2 as a percentage of the estimates of divergence time (τ) in the range simτ/2<estτ<simτ×2 as a function of the population mutation rates (θ), values of simulated migration rates (12 = M21M) and population recombination rates (ρ). The Factor 2 (2F) is the proportion of data sets for which the estimated value (of τ or M) is at least half and at most twice the simulated value: (a) for the four maximum likelihood methods (D1–D4) and MIMAR, (b) for the four composite-likelihood methods (J1–J4) and MIMAR.(TIF)Click here for additional data file.Figure S4Factor 2 as a percentage of the estimates of migration rate (M = 12 = M21M) in the range simM/2<estM<simM×2 as a function of the population mutation rate (θ), values of simulated migration rates (12 = M21M) and population recombination rates (ρ). (a) For the four maximum likelihood methods (D1–D4) and MIMAR, (b) for the four composite-likelihood methods (J1–J4) and MIMAR.(TIF)Click here for additional data file.Figure S5Factor 2 for estimates of the divergence time and migration rates , ∂a∂i and for popABC with 6, 11 and 14 summary statistics (computed over 100 datasets).) for the four composite-likelihood methods (J(TIF)Click here for additional data file.Figure S6Distribution of relative error for (a) divergence time and for (b) migration rate depending on the population mutation rate (θ4.) for composite-likelihood method J For clarity, only relative errors lower than 15 are shown in (b).(TIF)Click here for additional data file.Figure S7Distribution of the relative error of (a) divergence time and of (b) migration rate depending on the population recombination rate (ρ4.) for composite-likelihood method J For clarity, only relative errors lower than 15 are shown in (b).(TIF)Click here for additional data file.Figure S8Relative error for estimation of migration rate depending on the simulated value of the migration rate (12M in blue and 21M2. in red) for composite method J (a) For simulated divergence times less than 0.5, and (b) for simulated divergence times greater than 1. Note the difference in scale of the y-axes between (a) and (b).(TIF)Click here for additional data file.Figure S9Relative error in the estimation of the migration rate (12M in blue and 21M4. in red) depending on the simulated value of the migration rate for composite likelihood method J (a) For simulated divergence times smaller than 0.5, and (b) for simulated divergence times greater than 1. Note the difference in scale of the y-axes between (a) and (b).(TIF)Click here for additional data file.Figure S10Relative error in the estimation of migration rate depending on the simulated value of the migration rate (12M in blue and 21M in red) for popABC estimates with 6 summary statistics. (a) For simulated divergence times smaller than 0.5, and (b) for simulated divergence times greater than 1.(TIF)Click here for additional data file.Figure S11Power analysis of the various JSFS coarsenings to estimate divergence time and migration rates for 100 datasets of 100 loci. RMSE are computed for estimates of the (a) divergence time (τ) and (b) migration rates (12M≠21M) for the four composite-likelihood methods (J1–J4) based on six vectors of summary statistics with different numbers elements. The vector W is defined by the Wakeley-Hey 4 classes from Eq. 2, and other vectors D, D′, D″, D* and Ď are refined decompositions of the JSFS with higher number of classes.(TIF)Click here for additional data file.Table S1ANOVA table of analysis of error in the estimation of divergence times (τ).(PDF)Click here for additional data file.Table S2ANOVA table of analysis of error in the estimation of migration rates (12 = M21M).(PDF)Click here for additional data file.


Alzheimer's disease (AD) is the most common form of dementia and associated with the progressive accumulation of amyloid β-peptides (Aβ) in form of extracellular amyloid plaques in the human brain. A critical role of Aβ in the pathogenesis of AD is strongly supported by gene mutations that cause early-onset familial forms of the disease. Such mutations have been identified in the APP gene itself and in presenilin 1 and 2. Importantly, all the identified mutations commonly lead to early deposition of extracellular plaques likely by increasing the generation and/or aggregation of Aβ. However, such mutations are very rare and molecular mechanisms that might trigger aggregation and deposition of Aβ, in the most common late onset AD are largely unknown. We recently demonstrated that extracellular Aβ undergoes phosphorylation by a cell surface-localized or secreted form of protein kinase A. The phosphorylation of serine residue 8 promotes aggregation by stabilization of β-sheet conformation of Aβ and increased formation of oligomeric Aβ aggregates that represent nuclei for fibrillization. Phosphorylated Aβ was detected in the brains of transgenic mice and human AD brains and showed increased toxicity in Drosophila models as compared with non-phosphorylated Aβ. Together, these findings demonstrate a novel molecular mechanism that triggers aggregation and toxicity of Aβ. Thus, phosphorylation of Aβ could be relevant in the pathogenesis of late onset AD. The identification of extracellular protein kinase A should also stimulate pharmacological approaches to decrease Aβ phosphorylation in the therapy and/or prevention of AD. Alzheimer's disease (AD) is the most common form of dementia in the ageing population and affects millions of people worldwide . At the Aβ is a proteolytically processed fragment of the amyloid precursor protein (APP) ;11. It oAPP is a type I membrane protein and ubiquitously expressed in most cell types. Alternative mRNA splicing leads to several cell type and development-specific isoforms . In addiAβ is produced during normal cellular metabolism and secreted to the extracellular milieu of the human brain and also found in cerebrospinal fluid (CSF) ;16. The The generation of Aβ is initially starts with a cleavage of APP by β-secretase at the N-terminus of the Aβ domain Figure . This clThe mutations within APP that causes early onset AD (EOAD), are all located within or close to the Aβ domain. Notably, a double mutation in APP at the cleavage site for β-secretase that cause EOAD increases the β-secretory cleavage resulting in an overall higher production of Aβ peptides . The stabilization of Aβ by phosphorylation might play a crucial role in AD pathogenesis, because it would eventually result in increased concentrations of this peptide in the brain. Therefore, inhibition of extracellular kinases or stimulation of Aβ dephosphorylation could be pursued as valuable targets to prevent or slow down the progression of AD. Further, the detection of phosphorylated Aβ in biological fluids could also be explored for evaluation as biomarkers. Together, phosphorylation of Aβ might have very important implications for AD pathogenesis and offer novel therapeutic avenues.Increasing evidence suggests that phosphorylation of proteins involved in several neurodegenerative diseases and plays a serious role during the pathogenesis ;112;113.


T. thermophilus allows the generation of new crystal forms and the crystallization of ribosome–GTPase complexes.Truncation of ribosomal protein L9 in  Thermus thermophilus, HB8-MRCMSAW1, in which the ribosomal protein L9 gene has been truncated was constructed by homologous recombination. Mutant 70S ribosomes were used to crystallize and solve the structure of the ribosome with EF-G, GDP and fusidic acid in a previously unobserved crystal form. Subsequent work has shown the usefulness of this strain for crystallization of the ribosome with other GTPase factors.Crystallographic studies of the ribosome have provided molecular details of protein synthesis. However, the crystallization of functional complexes of ribosomes with GTPase translation factors proved to be elusive for a decade after the first ribosome structures were determined. Analysis of the packing in different 70S ribosome crystal forms revealed that regardless of the species or space group, a contact between ribosomal protein L9 from the large subunit and 16S rRNA in the shoulder of a neighbouring small subunit in the crystal lattice competes with the binding of GTPase elongation factors to this region of 16S rRNA. To prevent the formation of this preferred crystal contact, a mutant strain of  These factors have all been visualized on the ribosome by cryo-electron microscopy  gene  according to Fig. 1The L9 truncated mutant was prepared using homologous recombination with a pUC19 plasmid containing the rplI gene were PCR-amplified using the primers L9f1  and L9b1 , and L9f2  and L9b2 , and ligated into pUC19 cleaved using KpnI and HindIII. The resulting plasmid was cleaved using PstI and the HTK gene amplified with the primers Htkf  and Htkb  was inserted into the PstI site. The resulting plasmid pL9_55_htk was transformed into T. thermophilus HB8 cells . The cells were lysed in lysis buffer  using an Emulsiflex  and the cell debris was pelleted by centrifugation for 30 min at 30 000g. The cell lysate was incubated at 338 K for 30 min and denatured E. coli proteins were pelleted by centrifugation. The supernatant was loaded onto an Ni–NTA agarose column (Qiagen) pre-equilibrated in lysis buffer. After washing with lysis buffer containing 20 mM imidazole, EF-G was eluted, dialyzed against TEV buffer  and treated with TEV protease overnight. After the addition of 20 mM imidazole, the untagged EF-G was passed through an Ni–NTA agarose column (Qiagen). EF-G fractions were pooled and applied onto a HiLoad 26/60 Superdex 200 prep-grade column (Amersham Biosciences) in gel-filtration buffer . The EF-G peak was dialyzed against ion-exchange buffer  and subsequently loaded onto a HiPrep QXL column  equilibrated with the same buffer. EF-G was eluted with a linear gradient of 0–0.7 M NaCl in ten column volumes. Finally, EF-G was dialyzed against buffer G  and concentrated to 24.5 mg ml−1 using an Ultra concentrator (Amicon).T. thermophilus HB8-MRCMSAW1 and E. coli tRNAfMet were prepared using previously described methods  and a Phe codon at the A site (underlined bold).70S ribosomes from 2.4.M mRNA were incubated in buffer G at 328 K for 6 min. 16.0 µM tRNAfMet was quickly added and the complex was incubated at 328 K for 6 min. At this point, 500 µM fusidic acid, 20 µM EF-G and 100 µM GTP which had been pre-incubated at room temperature for 20 min were added to the ribosome complex and the resulting mixture was incubated for 20 min at 328 K and for 30 min at room temperature prior to crystallization. 2.3 µM Deoxy Big CHAP  was added to the complex, giving a final concentration of 3.3 µM 70S ribosomes. The complex was subjected to crystallization screening in sitting-drop vapour-diffusion experiments using 200 nl drops . After optimization to improve the crystal size and quality, 3 µl reservoir solution  was mixed with 3 µl complex solution and streak-seeded. Crystals grew in 5–14 d to dimensions of ∼20 × 100 × 500 µm . L9 in a similar conformation extending from the ribosome has also been observed in single-particle cryo-EM studies of 70S complexes with EF-G and GTP . Despite the similarity, the exact interactions are not conserved: the hidden surface area varies between 140 and 460 Å2 and the relative position of the C-terminal domain of L9 differs by up to 20 Å. In the three most extensive packing interactions, with more than 400 Å2 hidden surface area (Table 1b).Even though the crystal forms belong to different space groups and are from different species, a Table 1, the posa Table 1b.et al., 2005et al., 2007et al., 2009et al., 2009et al., 2007et al., 2007et al., 2007et al., 2009et al., 2005The L9 contact occurs in the area of the 30S subunit where domains II of IF-2 (Myasnikov Our observations suggested to us that the preferred contact between L9 and the 30S shoulder could be one of the main causes of the lack of success in crystallizing complexes of 70S ribosomes from several different species with different ribosomal GTPases.3.2.E. coli is viable when the chromosomal L9 gene is truncated or deleted and that the peptidyl-transferase activity of 50S subunits lacking L9 is indistinguishable from that of the wild type (Lieberman et al., 2000et al., 2001T. thermophilus have produced well diffracting crystals of 30S subunits (Wimberly et al., 2000et al., 2006T. thermophilus strain in which ribosomal protein L9 is truncated after the N-terminal domain in order to eliminate its potential crystal contact with a neighbouring 30S subunit. The truncation was designed based on the L9 structure within the T. thermophilus 70S ribosome (Selmer et al., 2006It has previously been shown that T. thermophilus HB8-MRCMSAW1 strain was constructed using homologous recombination and has a stop codon after L9 residue 55 followed by a kanamycin-resistance cassette.The 3.3.T. thermophilus strain HB8-MRCMSAW1, mRNA and P-site tRNA were grown in MES buffer pH 6.5–6.6 using PEG 20K as a precipitant (Fig. 2et al., 2009Diffraction-quality crystals of the fusidic acid-locked complex of EF-G with 70S ribosomes from nt Fig. 2. There iT. thermophilus 70S ribosomes with mRNA and tRNA (Selmer et al., 2006et al., 2009et al., 2010et al., 2011The DOBC detergent, which was added to the complex solution prior to crystallization, was critical for crystal growth in the above condition. Interestingly, the same detergent was also used in the crystallization of wild-type et al., 2009et al., 20092 and the position of domain II of the two factors differs by 3–5 Å relative to 16S rRNA. For EF-Tu, this interaction has been implicated in GTPase activation in response to correct decoding (Schmeing et al., 2009et al., 2009In the crystal structures of EF-G (Gao This work shows that there are situations in which fortuitous crystal contacts in the ribosome can be so strong that they can displace normal binding of factors and lead to crystallization without the factors present. We had previously been unable to obtain alternative crystal forms that included the factor, presumably because crystallization of the factorless forms was favoured by the L9 contact and drove the equilibrium in this direction. The fact that a deletion mutant unable to form the L9 contact could be used to crystallize three different GTPase ribosome complexes shows that engineering ribosomes to remove favourable contacts can allow the crystallization of completely new forms. It is possible that this strategy may be of use in the crystallization of other macromolecular complexes.