peerj_json_files/PeerJ_Json_136.json

{
    "v1_Abstract": "We developed a novel method based on the Fourier analysis of protein molecular surfaces to speed up the analysis of the vast structural data generated in the post--genomic era. This method computes the power spectrum of surfaces of the molecular electrostatic potential, whose three--dimensional coordinates have been either experimentally or theoretically determined. Thus we achieve a reduction of the initial three--dimensional information on the molecular surface to the one--dimensional information on pairs of points at a fixed scale apart. Consequently, the similarity search in our method is computationally less demanding and significantly faster than shape comparison methods. As proof of principle, we applied our method to a training set of viral proteins that are involved in major diseases such as Hepatitis C, Dengue fever, Yellow fever, Bovine viral diarrhea and West Nile fever. The training set contains proteins of four different protein families, as well as a mammalian representative enzyme. We found that the power spectrum successfully assigns a unique signature to each protein included in our training set, thus providing a direct probe of functional similarity among proteins. The results agree with established biological data from conventional structural biochemistry analyses.",
    "v1_col_introduction": "introduction  : The spatial structure of proteins encodes information on their function, which is essential for a successful drug design. In the post\u2013genomic era, the search for functional similarities among proteins is based mostly on identity and/or similarity of genomic sequences rather than on their spatial structure. An approach that has been widely used is the application of self-organizing maps to the protein amino acid sequence in order to predict the protein shape and to infer the protein function [1, 2]. This approach searches for local similarities in the amino acid sequence and is based on the assumption that the proteins have the same size and that the amino acid sequence is a determinant of the protein structure. However, there are many examples of proteins where sequence\u2013based searches are insufficient to describe their biological function [3]. While self-organizing maps can classify proteins into families, they fail at predicting the structure. Since structure is more conserved than sequence, evolutionary relationships among proteins, protein structure\u2013function predictions and comparative modelling should be based on structural information, rather than on primary amino acid or genomic sequence [4].\nOther approaches have been developed that search for functional similarities using the complete three\u2013 dimensional information encoded in the spatial coordinates of all the atoms within the protein structure, which have been derived from X\u2013ray or nuclear magnetic res-\nonance experiments. In these approaches, the three\u2013 dimensional protein structure is modelled by a representation (or descriptor) based on topological characteristics or structure elements (see e.g. Ref. [5] and references therein). Although the structure\u2013based approaches are more informative on the function than the sequence\u2013 based ones, structure comparison methods are too slow and are thus rendered impractical to use in large\u2013scale experiments and real\u2013life applications [6\u20138].\nOther approaches use the protein solvent\u2013accessible surface, since it is a stronger determinant of the protein function than sequence or structure [9]. Shape descriptors have been developed based on spatial symmetries, where the search for similarities consists of shape comparison [10\u201312]. However, surface comparison methods are computationally challenging, largely because they suffer from ambiguity in spatial orientation and require that the surfaces be aligned for an optimal matching (see Ref. [9] and references therein).\nBioinformatics has become the new biomedical informatics bottleneck, as the cost of genome sequencing and the sheer quantity of genomic data has recently skyrocketed. It has been estimated that the unprocessed data generated per sequencing machine can be of order at least 30 Gbs per day, which can scale up by a significant factor in the case of mapped/processed data. There is a clear requirement for fast and efficient analysis of the entire genome/proteome sequencing data in the up\u2013coming era of personalized medicine. Due to the continuous improvements in sequencing technologies and proteomic method-\nPeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013)\nR ev ie w in g M an\nus cr ip t\n2 ologies, the current scaling of available computing, storage and analysis throughput is far lower than the scaling of the data generation rate. The induced lag between the processing potential and the processing requirements already poses problems to researchers and companies in the bioinformatics field. Since it is impossible to constantly upgrade computer hardware to keep up with the increasing data production rate, the only feasible solution is to devise algorithms that can offer a competing processing scaling using the existing hardware at its full potential.\nHere, we propose a new approach to search for functional similarities among proteins using their molecular surfaces [13]. Protein molecular surfaces are determinant of the protein biological activity, with different types of molecular surfaces encoding different information about the protein function. We choose to use surfaces of the molecular electrostatic potential due to the importance of the charge distribution in the protein\u2013protein interactions. Protein\u2013protein interactions are essential for cell signalling and cell function [14, 15]. These processes require a correct and fast molecular recognition, in which interactions among electrostatic charges intervene. Disturbances in these processes are in the origin of almost every major disorder [16] and may lead to severe diseases such as cancer [17\u201319]. Therefore the electrostatic potential distribution on the protein molecular surfaces is crucial to virtually all biological macromolecules involved in key biochemical pathways [20\u201322].\nOnce we calculate the molecular surface for a particular filter, we proceed to measure the signal off of the molecular surface. For our signal analysis, we propose a method based on the Fourier analysis of molecular surfaces. An advantage of Fourier analysis is that it most easily separates large from small scales. The signal at each point can be regarded as a realization of a distribution of fluctuations around an average value of the molecular surface [23, 24]. Instead of measuring information on the individual points over the surface as shape descriptors do, we measure information on the correlations among the points, thus waiving the need that the surfaces be aligned. The simplest statistic is the two\u2013point correlation function in Fourier space, which averages the signal over the whole volume and measures the variance in the distribution. Hence our approach transforms three\u2013 dimensional spatial data into one\u2013dimensional frequency data.\nThe manuscript is organized as follows. First we present the selected proteins and how we synthesise the corresponding molecular surfaces. Then we describe our proposed method to extract functional information, based on the Fourier analysis of molecular surfaces and on a dimensionality reduction of the usable information. Then we present the results and discuss further improvements in the robustness of this method. Finally we outline an integrated solution for a functional similarity search among proteins, which progresses towards a\nFigure 1: Surfaces of the electrostatic molecular potential. Left panel: Hepatitis C helicase protein, Right panel: Hepatitis C polymerase protein. The electrostatic potential is measured in eV, with range as shown in the corresponding colour bar.\ndimensionality increase of the usable information and a reduction of the protein sample size.",
    "v2_Abstract": "We developed a novel method based on the Fourier analysis of protein molecular surfaces to speed up the analysis of the vast structural data generated in the post{genomic era. This method computes the power spectrum of surfaces of the molecular electrostatic potential, whose three-dimensional coordinates have been either experimentally or theoretically determined. Thus we achieve a reduction of the initial three{dimensional information on the molecular surface to the one-dimensional information on pairs of points at a fixed scale apart. Consequently, the similarity search in our method is computationally less demanding and significantly faster than shape comparison methods. As proof of principle, we applied our method to a training set of the Hepatitis C viral proteins with similar and dissimilar functions, as well as to a mammalian representative enzyme. We found that the power spectrum successfully assigns a unique signature to each protein included in our training set, thus providing a direct probe of functional similarity among proteins. The results agree with established biological data from conventional structural biochemistry analyses.",
    "v2_col_introduction": "introduction  : The spatial structure of proteins encodes information on their function, which is essential for a successful drug design. In the post\u2013genomic era, the search for functional similarities among proteins is based mostly on identity and/or similarity of genomic sequences rather than on their spatial structure. There are many examples of proteins where sequence\u2013based searches are insufficient to describe their biological function [1]. Since structure is more conserved than sequence, evolutionary relationships among proteins, protein structure\u2013function predictions and comparative modelling should be based on structural information, rather than on primary amino acid or genomic sequence [2].\nApproaches have been developed that search for functional similarities using the complete three\u2013dimensional information encoded in the spatial coordinates of all the atoms within the protein structure, which have been derived from X\u2013ray or nuclear magnetic resonance experiments. In these approaches, the three\u2013dimensional protein structure is modelled by a representation (or descriptor) based on topological characteristics or structure elements (see e.g. Ref. [3] and references therein). Although the structure\u2013based approaches are more informative on the function than the sequence\u2013based ones, structure comparison methods are too slow and are thus rendered impractical to use in large\u2013scale experiments and real\u2013life applications [4\u20136].\nOther approaches use the protein solvent\u2013accessible surface, since it is a stronger determinant of the protein\nfunction than sequence or structure [7]. Shape descriptors have been developed based on spatial symmetries, where the search for similarities consists of shape comparison [8\u201310]. However, surface comparison methods are computationally challenging, largely because they suffer from ambiguity in spatial orientation and require that the surfaces be aligned for an optimal matching (see Ref. [7] and references therein).\nBioinformatics has become the new biomedical informatics bottleneck, as the cost of genome sequencing and the sheer quantity of genomic data has recently skyrocketed. It has been estimated that the unprocessed data generated per sequencing machine can be of order at least 30 Gbs per day, which can scale up by a significant factor in the case of mapped/processed data. There is a clear requirement for fast and efficient analysis of the entire genome/proteome sequencing data in the up\u2013coming era of personalized medicine. Due to the continuous improvements in sequencing technologies and proteomic methodologies, the current scaling of available computing, storage and analysis throughput is far lower than the scaling of the data generation rate. The induced lag between the processing potential and the processing requirements already poses problems to researchers and companies in the bioinformatics field. Since it is impossible to constantly upgrade computer hardware to keep up with the increasing data production rate, the only feasible solution is to devise algorithms that can offer a competing processing scaling using the existing hardware at its full potential.\nHere, we propose a new approach to search for functional similarities among proteins using their molecular\nPeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013)\nR ev ie w in g M an\nus cr ip t\n2 surfaces [11]. Protein molecular surfaces are determinant of the protein biological activity, with different types of molecular surfaces encoding different information about the protein function. We choose to use surfaces of the molecular electrostatic potential due to the importance of the charge distribution in the protein\u2013protein interactions. Protein\u2013protein interactions are essential for cell signalling and cell function [12, 13]. These processes require a correct and fast molecular recognition, in which interactions among electrostatic charges intervene. Disturbances in these processes are in the origin of almost every major disorder [14] and may lead to severe diseases such as cancer [15\u201317]. Therefore the electrostatic potential distribution on the protein molecular surfaces is crucial to virtually all biological macromolecules involved in key biochemical pathways [18\u201320].\nOnce we calculate the molecular surface for a particular filter, we proceed to measure the signal off of the molecular surface. For our signal analysis, we propose a method based on the Fourier analysis of molecular surfaces. An advantage of Fourier analysis is that it most easily separates large from small scales. The signal at each point can be regarded as a realization of a distribution of fluctuations around an average value of the molecular surface [21, 22]. Instead of measuring information on the individual points over the surface as shape descriptors do, we measure information on the correlations among the points, thus waiving the need that the surfaces be aligned. The simplest statistic is the two\u2013point correlation function in Fourier space, which averages the signal over the whole volume and measures the variance in the distribution. Hence our approach transforms three\u2013 dimensional spatial data into one\u2013dimensional frequency data.\nThe manuscript is organized as follows. First we describe our proposed method to extract functional information, based on the Fourier analysis of molecular surfaces and on a dimensionality reduction of the usable information. Then we present the results and discuss further improvements in the robustness of this method. Finally we outline an integrated solution for a functional similarity search among proteins, which progresses towards a dimensionality increase of the usable information and a reduction of the protein sample size.",
    "v1_text": "results : Power spectrum of the molecular surfaces of the selected proteins To test our method, we used for training set the protein simulations described above, containing four different protein families. For each molecular surface of the electrostatic potential, we computed its power spectrum and the corresponding white-noise power spectrum. The white\u2013noise power spectrum was computed from a surface synthesised as a Gaussian distribution N(0, 1) times the mean value of the corresponding molecular surface. We observe that the power spectra of all molecular surfaces have comparable magnitudes, stabilizing around 10\u22126 for sufficiently large k (not shown), whereas the white\u2013noise power spectra have magnitudes that range from 10\u221211 to 10\u22127 (Fig. 3). This range is populated by the HCV polymerase at the top, followed by the HCV helicaseStrB and HCV helicaseHM in the intermediary range, and finally the 1A1Vs helicase HCV helicaseStrA and its models HCV helicaseEM and HCV helicaseMD at the bottom. Hence the information derived from the mean value alone, assuming an underlining Gaussian distribution, suggests a coarse clustering of the proteins in helicases, polymerases and a mixed PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t 6 Figure 8: Power spectrum of the molecular surfaces of the selected methyltransferase proteins. Power spectra of the molecular surfaces divided by the power spectra of the corresponding white-noise molecular surfaces. The symbols depict the power spectra and the error bars depict the error associated with the measurement. The values of k are measured in nm\u22121. cluster containing helicases and non\u2013helicases. For an easier comparison of the results, we divided the power spectra of molecular surfaces by the mean of the corresponding white\u2013noise power spectra (Figs. 4, 5, 6, 7, 8, 9). For each molecular surface, the power at each k is one realization of a distribution, hence the power spectrum is noisy. This noise was estimated by the uncertainty of the Fourier coefficients at each k, given by \u2206P (k) = P (k) \u221a 2/k2, which we used to compute the error bars. We also included the power spectrum of Mouse kinase in all plots, which shows a nearly flat spectrum punctuated by irregular peaks. First we analyse the HCV helicase protein set, which illustrates how our method performs at distinguishing different treatments and strains of the same protein. We plotted the power spectra of the HCV helicase proteins in Fig. 4. We observe that the power spectra of HCV helicaseStrA, HCV helicaseEM, HCV helicaseMD and HCV helicaseStrB exhibit a similar pattern up to k \u2248 10 nm\u22121 compatible with that of HCV helicaseHM. A further inspection reveals details that distinguish among the helicases. In particular, we observe that the power spectra of the models HCV helicaseEM and HCV helicaseMD exhibit very similar patterns of peaks attesting to their similar binding state. Although HCV helicaseStrA is in a different binding state, its power spectrum exhibits the same level of similarities with both HCV models, with an anticipated HCV-like grouping of peaks specific to our data. For k > 1 nm\u22121, these three helicase proteins exhibit three strong peaks at k \u2248 2.3, 4.6, 7.3 nm\u22121. From the distance between peaks, we infer an average wavelength of \u03bb \u2248 2.5 nm. The power spectrum of HCV helicaseHM follows the same pattern as that of HCV helicaseStrA shifted to smaller k with a varying relative phase which most of the time is close to \u03c0, with strong peaks at k \u2248 1.8, 3.6 nm\u22121. In comparison with the HCV models, the power spectrum of HCV helicaseStrB exhibits differences in the position of the peaks (found at k \u2248 2.7, 3.6, 5.5 nm\u22121) and in their amplitude ratios, which attest to the different treatment in HCV helicaseStrB from that in the HCV models. As k increases, we observe a gradual damping of the power of the helicases and an emerging tail reminiscent of shot noise in a Poisson power spectrum, more prominent in HCV helicaseHM and HCV helicaseStrB, PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t 7 which indicates the damping of the fluctuations about the mean value and thus the vanishing of the structural signal. This damping is most visible for k > 6 nm\u22121. This agrees with the observation above that sets the upper limit of k to the size of a typical cluster of aminoacids and hence sets the minimum distance below which correlations are not of biological interest nor can be reliably probed by X\u2013ray/NMR experiments. We now proceed to analyse the remaining helicase strains, which illustrates how our method performs at distinguishing strains of the same family. We plotted the power spectra of the Dengue virus (DEN) helicase proteins in Fig. 5 and the Yellow fever virus (YF) helicase proteins in Fig. 6. The power spectra of both the YF helicase proteins and the DEN helicase proteins exhibit a similar pattern with a varying relative phase among the proteins of each strain, with the difference between the two strains being in the typical wavelength and amplitude. In particular, we observe that the DEN helicases have an underlying flat spectrum punctuate by peaks at k \u2248 2.0, 3.8, 5.5 nm\u22121 (DEN 2BHR), k \u2248 3.0, 5.0, 6.0 nm\u22121 (DN 2JLQ) and k \u2248 3.5, 5.0, 6.5 nm\u22121 (DN 2JLU), that yield an average \u03bb \u2248 4.2 nm. The DEN 2BMF shows a different pattern characterized by a decreasing power law up to k \u2248 5, with superposed peaks k \u2248 5.5, 7.0, 8.5 nm\u22121. In contrast, the YF helicases have a nearly flat spectrum punctuated by small peaks at k \u2248 1.0, 3.5, 5.5 nm\u22121 (YF 1YKS) and k \u2248 1.5, 5.5 nm\u22121 (YF 1YMF), that yield an average \u03bb \u2248 2.0 nm. The YF 2V80 shows a nearly flat spectrum with barely no peaks, indicating a predominantly isotropic distribution of power. These families have a similar pattern with the HCV helicases but the features have smaller amplitudes. The global pattern attests to the fact that these proteins are also helicases and have the same treatment as the HCV, whereas the differences in amplitude attest to the fact that are of different strains. We now proceed to analyse the non-helicase families, which illustrates how our method performs at distinguishing protein families. We plotted the power spectra of the polymerase proteins in Fig. 7. We observe that all the polimerases have the same pattern characterized by an underlying decreasing power law with superposed peaks. In particular, the West Nile strains have the same pattern at all scales and a peak at k \u2248 8 nm\u22121, i.e. close to the smallest scale accessible. The BVDV strain has a very similar power law behaviour to the WN strains but is punctuated by regular peaks namely at k \u2248 1.5, 3.0, 4.5, 6.0, 8.0 nm\u22121, corresponding to an average \u03bb \u2248 4 nm. The HCV polymerase has the steepest decreasing power law behaviour and peaks at k \u2248 5.5, 7.5 nm\u22121. We plotted the power spectra of the methyltransferase proteins in Fig. 8. We observe that all the YF methyltransferase have similar patterns characterized by a nearly flat, featureless power spectrum punctuated by Figure 10: Power spectra of the molecular surfaces of the HCV helicaseEM after being subject to molecular dynamics simulations for 100 ps. Power spectra of the molecular surfaces divided by the power spectra of the corresponding white-noise molecular surfaces. The symbols depict the power spectra and the error bars depict the error associated with the measurement. The values of k are measured in nm\u22121. irregular low\u2013amplitude peaks. Finally, we plotted the power spectra of the glycoproteins in Fig. 9. We observe that all the BVDV glycoproteins have the same pattern characterized by an underlying a convex quadratic function with superposed peaks. In particular both the strains 4DVN and 4DW3 have a single peak at k \u2248 7.5 nm\u22121, whereas the 4DW4 have peaks at k \u2248 2.0, 4.5, 6.0, 8.0 nm\u22121, corresponding to an average \u03bb \u2248 3.3 nm. Power Spectrum of a dynamical simulation To further test our method, we used the 1A1V template energetically minimized up to a gradient of 10\u22125 to generate ten dynamical realizations captured in ten time frames separated by 10 ps. We then energetically minimized the tenth frame up to a gradient of 10\u22125 [38\u201340] We computed the power spectrum of each frame, generated the corresponding white noise surface and plotted the results in Fig. 10. The purpose of this test is to show how our method behaves when applied to controlled simulations. We observe that there is no significant difference among the different frames. This observation supports the fact that the surfaces do not change over time after energy minimization (EM). Also we observe that the two simulations energetically minimized up to a gradient 10\u22125 are in phase, whereas the simulation with up to a gradient 5 \u00d7 10\u22122 is visibly out of phase with the former. This observation supports the fact that there is a difference between crude and fine EM. PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t 8 conclusions : We presented a new method based on the Fourier analysis of protein molecular surfaces to extract functional information on proteins. For a selected set of proteins of HCV with different structural features, we first produced surfaces of the molecular electrostatic potential, as well as the corresponding white\u2013noise surfaces, and then computed their two-point correlation function in harmonic space (the power spectrum). We found that this method can distinguish different functional protein groups. More specifically, in this manuscript we established a helicase, a polymerase, a methyltransferase and a glycoprotein group. We also tested this method on dynamical simulations after energy minimization. An immediate extension of this work is the application of this method to isolated structural subunits that form larger structures within proteins. Similarly sized subunits will have a strong signal in the same frequency range, which will add up in the protein power spectrum. Hence, we must first measure the contribution of each subunit separately and produce a catalogue of subunit signatures, so we can distinguish them in the combined signal when running similarity searches. By reducing the initial three\u2013dimensional information on the molecular surface to the one\u2013dimensional information on pairs of points at a fixed scale apart, this method allows for a fast similarity search. Further refinements in the similarity search will require methods that use information from higher\u2013order correlation functions, such as the correlation among three points at a fixed triangular configuration or its Fourier\u2013transformed (the bispectrum). (See Fig. 2 right panel for an illustration.) The bispectrum measures phase correlations among the modes and thus deviations from a Gaussian distribution. Our ultimate goal is to integrate higher\u2013order correlations and to apply the resulting method to the RCSB database so as to provide the biopharmaceutical and structural research communities with a novel and easily searchable reference without the three\u2013dimensional information compromising the speed of the calculation. This method aims to coalesce techniques, which have been extensively tested and used in other fields such as cosmology, into a fast and robust pipeline for the analysis and processing of very large, three\u2013dimensional biological datasets in an effort to speed up protein similarity searches. Acknowledgments CSC is funded by the FCT\u2013Lisbon, Grant no. SFRH/BPD/65993/2009. This work was supported in part by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program \u201dEducation and Lifelong Learning\u201d of the National Strategic Reference Framework (NSRF) - Research Funding Program: \u201cThales\u201d. 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[27] www.poissonboltzmann.org/apbs [28] www.rcsb.org PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t 9 [29] Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) J Chem Theory Comput 4: 435\u2013447. [30] Lindahl E, Hess B, van der Spoel D (2001) J Mol Model 7: 306\u2013317. [31] van der Spoel D, Lindahl E, Hess B, Groenhof G, Mark AE, et al. (2005) J Comput Chem 26: 1701\u201318. [32] Sellis D, Vlachakis D, Vlassi M (2009) Bioinform Biol Insights 3: 99\u2013102. [33] S\u0306ali A, Blundell TL (1993) J. Mol. Biol. 234: 779\u2013815. [34] Eswar N, John B, Mirkovic N, Fiser A, Ilyin VA, Pieper U, Stuart AC, Mart\u0301\u0131-Renom MA, Madhusudhan MS, Yerkovich B, S\u0306ali A (2003) Nucl Acids Res 31: 3375\u2013 3380. [35] Laskowski RA, Rullmannn JA, MacArthur MW, Kaptein R, Thornton JM (1996) J. Biomol. NMR 8: 477\u2013486. [36] Connolly ML (1983), J. Appl. Cryst. 16: 548\u2013558. [37] Peacock JA (1999) Cosmological Physics, CUP. [38] Vangelatos I, Vlachakis D, Sophianopoulou V, Diallinas G (2009) Molecular membrane biology 26 (5-7): 356-370 [39] Sellis D, Drosou D, Vlachakis D, Voukkalis D, Gian- nakouros T, Vlassi M (2012) Biochimica et Biophysica Acta 1820 (1): 44\u201355 [40] Vlachakis D, Tsagrasoulis D, Megalooikonomou V, Kossida S (2013) Bioinformatics 29 (1): 126-128 PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t method : selected proteins : For our training set, we selected four distinct protein families, which include twelve helicase proteins, six methyltransferase proteins, four polymerase proteins and four glycoproteins. These proteins are mainly viral components that are involved in major diseases such as Hepatitis C, Dengue fever, Yellow fever, Bovine viral diarrhea and West Nile fever. We use the Mouse kinase protein as a decoy, since it has a very different function from all the other proteins. Helicases are responsible for the unwinding of double stranded DNA or RNA during viral replication. Polymerases are key enzymes that are used for copying the viral genetic material. Methyltransferases or methylases are transferase enzymes that are responsible for transferring methyl groups from a donor to an acceptor. Finally glycoproteins are used for molecular recognition by viruses. Protein treatments vary depending on the needs of each comparison chart. The main treatment is the default X\u2013ray crystallography protein conformation as it is deposited in the RCSB database [28]. The selected unedited proteins were the following. Among the helicases, we selected: a) 1A1V and 8OHM of the Hepatitis C virus (HCV), b) 1YMF, 1YKS and 2V80 of the Yellow fever virus (denoted by YF 1YMF, YF 1YKS and YF 2V80 respectively), and c) 2JLU, 2BHR, 2BMF and 2JLQ of the Dengue fever virus (denoted by DEN 2JLU, DEN 2BHR, DEN 2BMF and DEN 2JLQ respectively). Among the polymerases, we selected 2CJQ, 2HCS and 2HCN of the West Nile fever virus (denoted by WN 2CJQ, WN 2HCS and WN 2HCN respectively). Among the methyltransferase, we selected PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t 3 3EVA, 3EVB, 3EVC, 3EVD, 3EVE and 3EVF of the Yellow fever virus (denoted by YF 3EVA, YF 3EVB, YF 3EVC, YF 3EVD, YF 3EVE and YF 3EVF respectively). Among the glycoproteins, we selected 1NB7, 4DVN, 4DW4 and 4DW3 of the bovine diarrhea virus (denoted by BVDV 1NB7, BVDV 4DVN, BVDV 4DW4 and BVDV 4DW3 respectively). In the Hepatitis C viral protein family, we considered two HCV helicase proteins, namely the HCV helicase strain A (the 1A1V entry, denoted by HCV helicaseStrA) and the HCV helicase strain B (the 8OHM entry, denoted by HCV helicaseStrB), whose three-dimensional coordinates were obtained from the RCSB database [28] of X\u2013ray protein crystallography structures. Furthermore, we generated two simulations of the 1A1V protein crystal, namely the energy\u2013minimized version (denoted by HCV helicaseEM) and the molecular dynamics version (denoted by HCV helicaseMD). Both the HCV helicaseEM and the HCV helicaseMD have been energetically minimized up to a gradient of 0.05. The HCV helicaseMD has additionally been subject to a molecular dynamics simulation. We also established a homology model of the HCV helicase (denoted by HCV helicaseHM) so that the in silico three\u2013dimensional model of HCV was included in our training set. We also included an example of a non\u2013helicase HCV viral protein, namely the 1NB7 structure of the HCV polymerase (the 1NB7 entry, denoted by HCV polymerase). Molecular surfaces of the selected proteins Surfaces of the molecular electrostatic potential follow the nonlinear Poisson\u2013Boltzmann equation [25, 26]. We solved numerically for the electrostatic potential using the finite\u2013difference method as implemented in the APBS Software [27]. The potential was calculated on a regular grid of size (65, 65, 65)1, with the grid\u2013fill\u2013by\u2013 solute parameter set to 80%. The dielectric constants of the solvent and the solute were set to 80.0 and 2.0, respectively. An ionic exclusion radius of 2.0 A\u030a, a solvent radius of 1.4 A\u030a and a solvent ionic strength of 0.145 M were applied. Default APBS charges and atomic radii were used. Energy minimization (EM) removes any residual geometrical strain from each molecular system, whereas molecular dynamics (MD) simulates a periodic cytoplasm\u2013like aqueous environment. Both EM and MD were performed with the Gromacs suite [29\u201331] through 1 The size of the grid was kept small in order to speed up the calculation and reduce the computational load. It was tested to be suitable for this study, as higher detail would not change the surface by much, while it would increase the computational load significantly. our previously developed graphical interface [32]. Molecular dynamics took place in a periodic environment, which was subsequently solvated with the simple point\u2013 charge water model using the truncated octahedron box extending to 7 A\u030a from each molecule. Partial charges were applied and the molecular systems neutralized with counter\u2013ions as required. The temperature was set to 300 K, the pressure to 1 atm and the step size to 2 fs. The total time elapsed at each molecular complex run was 50 ns, using constant number of atoms, volume and temperature (NVT) throughout the calculation in a canonical environment. The results of the MD simulations were collected in a molecular trajectory database for further analysis. The homology model was produced using Modeller [33, 34] and was evaluated using the Procheck utility [35]. This model was designed in order to include a computer modelled structure in our training set, which however shares high sequence identity with its template structure (approximately 90%). The RCSB/PDB entries of the selected proteins are summarized in Table I. In Fig. 1 we show surfaces of the electrostatic molecular potential for two HCV proteins, namely the helicase and the polymerase. The electrostatic potential is measured in eV. In these manuscript, we used the Connolly representation for the molecular surfaces [36]. Power spectrum of molecular surfaces Molecular surfaces contain information on a property of proteins along the three spatial dimensions. This property, in this case the values of the electrostatic potential, can be regarded as a field F (x) defined over points x on the surface. Functional information is encoded not only in the positions of the points but also in the correlations among points. The simplest correlation function that we can measure is that between pairs of points. The twopoint correlation function \u03be of the field F measures the convolution of the field over its complex conjugate (see e.g. Ref. [37]) \u03be(r) \u2261 \u3008F \u2217(x)F (x + r)\u3009 = 1 L3 \u222b d3x F \u2217(x)F (x + r).(1) The angle brackets indicate an averaging over the normalization volume, which here we take as the volume of the molecular surface, L3. We assume that the field has a flat geometry and can be decomposed in a Fourier expansion of plane waves F (x) = \u2211 k Fk exp[\u2212ik \u00b7 x], (2) where the wavenumber k relates with the frequency \u03bd by k = 2\u03c0/\u03bd. If the field has a curved geometry, then a PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t 4 Family Protein Size=[lx, ly, lz] Helicase HCV helicaseStrA [72.4, 64.8, 55.1] HCV helicaseEM [72.8, 65.1, 55.5] HCV helicaseMD [72.3, 65.5, 56.3] HCV helicaseHM [71.5, 65.7, 55.9] HCV helicaseStrB [61.9, 69.6, 61.7] DEN 2BHR [93.5, 101.4, 76.8] DEN 2BMF [84.4, 111.7, 106.0] DEN 2JLQ [66.8, 69.6, 77.0] DEN 2JLU [80.4, 95.0, 85.0] YF 1YKS [62.2, 58.4, 67.8] YF 1YMF [63.6, 58.2, 67.8] YF 2V8O [49.2, 69.6, 67.6] Polymerase HCV polymerase [59.0, 77.7, 65.0] BVDV 2CJQ [74.4, 69.5, 64.5 WN 2HCN [78.5, 75.4, 61.1] WN 2HCS [77.2, 75.2, 63.2] Methyltransferase YF 3EVA [43.9, 56.2, 62.7] YF 3EVB [43.6, 56.4, 62.6] YF 3EVC [43.8, 56.0, 62.2] YF 3EVD [44.1, 55.5, 63.3] YF 3EVE [44.6, 55.9, 65.2] YF 3EVF [43.9, 56.1, 64.2] Glycoproteins BVDV 4DVN [46.2, 67.2, 68.0] BVDV 4DW3 [46.3, 68.5, 67.9] BVDV 4DW4 [46.8, 73.4, 67.6] Kinase Mouse kinase [52.5, 69.0, 48.8] Table I: Input data. Protein families, protein PDB names and sizes of the corresponding molecular surfaces along the [x,y,z]\u2013directions, measured in A\u030a. Fourier expansion in spherical harmonics should be used instead. However, the difference between the two expansions only matters in scales of order the size of the molecular surface, which correspond to the smallest frequency. The smallest frequency is the zero\u2013mode in the Fourier expansion and describes a global offset. The two-point correlation function becomes \u03be(r) = \u2329\u2211 k \u2211 k\u2032 F \u2217kFk\u2032 exp[i(k \u2212 k \u2032) \u00b7 x] exp[\u2212ik\u2032 \u00b7 r] \u232a .(3) Since the molecular surface is closed, the field is periodic within the size of the surface, which restricts the allowed wavenumbers to the harmonic boundary condition kn = (n2\u03c0/L)e\u0302k, where n \u2208 {0, 1, ...} is the order of the Fourier modes. As a consequence, all the cross terms with k\u2032 6= k average to zero and the remaining sum is \u03be(r) = ( L 2\u03c0 )3 \u222b d3k |Fk|2 exp[\u2212ik \u00b7 r]. (4) Hence the correlation function is the Fourier transform of the power spectrum P (k) = |Fk|2. This relationship is known as the Wiener-Khinchin theorem. The power spectrum measures amplitude correlations among the modes, discarding however information on the phase. We proceed to compute the Fourier transform Fk of 3 1 k P 1 PP 2 2 k12 12 k31 k23 P P Figure 2: Schematic representation of point configurations for correlations in harmonic space. Left panel: The configuration of the two-point correlation function contains one free parameter, k12, which is the distance in harmonic space between the two points P1 and P2. Right panel: The configuration of the three-point correlation function contains two free parameters, e.g. k12 and k23, describing the distances in harmonic space respectively between P1 and P2, and between P2 and P3. The third parameter k13 is related to the former two by the triangle condition k12 + k23 + k31 = 0. the molecular surface inferred over a regular grid. The Fourier\u2013transformed surface measures the amplitude of the plane waves whose combination reproduces the information on the original surface. The frequencies of the plane waves range from the frequency corresponding to the extension of the surface (i.e. to n = 1), up to the Nyquist frequency corresponding to twice the bin size of the grid (i.e. to n = N/2, where N is the number of bins along a direction of the grid). The size of the molecular surfaces ranges between 5\u22127 nm (Table I). The smallest spatial scale of biological interest is the size of a typical cluster of aminoacids, which is of order xball \u223c 0.3 nm. We choose this spatial scale for the size of the grid, so that the largest frequency scale that can be probed is of order kball \u223c 10 nm\u22121. Furthermore, we assume that the field is isotropic, i.e. that it does not have a preferential direction, so that the power spectrum depends only on the distance between each pair of points. (See Fig. 2 left panel for an illustration.) By assuming isotropy, we are discarding information on the direction. We proceed to take the ensemble average of P (k) so that the power at the mode k is the sum of the power at all the points on a sphere of radius k from the zero\u2013mode, resulting in a one-dimensional function P (k). In this way, we collapse the information on the three-dimensional field over the molecular surface onto a one-dimensional power spectrum over the wavenumbers of the Fourier\u2013transformed molecular surface. For a given k, we are sampling a distribution, which we assume to be Gaussian with mean value \u3008Fk\u3009 and variance \u2329 |Fk|2 \u232a = P (k), from which the Fourier coefficients Fk are drawn. Hence there is a fundamental uncertainty about the underlying variance, which depends on the number of coefficients sampled at a given k. Since the number of k\u2019s on a sphere of radius k scales as k2 and for any real field it holds that F\u2212k = Fk\u2217, where the asterisk stands for the complex conjugate, then the uncertainty scales as \u2206P (k)/P (k) = \u221a 2/k2. PeerJ reviewing PDF | (v2013:06:567:1:0:NEW 1 Oct 2013) R ev ie w in g M an us cr ip t 5 Figure 4: Power spectrum of the molecular surfaces of the selected HCV helicase proteins. Power spectra of the molecular surfaces divided by the power spectra of the corresponding white-noise molecular surfaces. The symbols depict the power spectra and the error bars depict the error associated with the measurement. The values of k are measured in nm\u22121.",
    "v2_text": "results : To test our method, we used for training set the protein simulations described above, containing helicase and non-helicase proteins. For each molecular surface of the electrostatic potential, we computed its power spectrum and the corresponding white-noise power spectrum. The white\u2013noise power spectrum was computed from a surface synthesised as a Gaussian distribution N(0, 1) times the mean value of the corresponding molecular surface. We observe that the power spectra of all molecular surfaces have comparable magnitudes, stabilizing around 10\u22126 for sufficiently large k (not shown), whereas the white\u2013noise power spectra have magnitudes which range from 10\u221211 to 10\u22127 (Fig. 3). This range is populated by the HCV polymerase at the top, fol- Figure 3: Power spectrum of the molecular surfaces of the selected proteins. Power spectra of the corresponding white-noise molecular surfaces. The values of k are measured in nm\u22121. lowed by the HCV helicaseStrB and HCV helicaseHM in the intermediary range, and finally the 1A1Vs helicase HCV helicaseStrA and its models HCV helicaseEM and HCV helicaseMD at the bottom. Hence the information derived from the mean value alone, assuming an underlining Gaussian distribution, suggests a coarse clustering of the proteins in helicases, polymerases and a mixed cluster containing helicases and non\u2013helicases. For an easier comparison of the results, we divided the power spectra of molecular surfaces by the mean of the corresponding white\u2013noise power spectra (Fig. 4). For each molecular surface, the power at each k is one realization of a distribution, hence the power spectrum is noisy. This noise was estimated by the uncertainty of the Fourier coefficients at each k, given by \u2206P (k) = P (k) \u221a 2/k2, which we used to compute the error bars. We observe that the power spectra of HCV helicaseStrA, HCV helicaseEM, HCV helicaseMD and HCV helicaseStrB exhibit a similar pattern up to k \u2248 10 nm\u22121 compatible with that of HCV helicaseHM, whereas the power spectrum of HCV polymerase exhibits a different pattern from that of the other proteins compatible with that of Mouse kinase. This global pattern attests to the fact that the former proteins are helicases whereas the latter is a polymerase. A further inspection reveals details that distinguish among the helicases. In particular, we observe that the power spectra of the models HCV helicaseEM and HCV helicaseMD exhibit very similar patterns of peaks attesting to their similar binding state. Although HCV helicaseStrA is in a different binding state, its power spectrum exhibits the same level of similarities with both HCV models, with an anticipated HCV-like grouping of peaks specific to our data. For k > 1 nm\u22121, these three helicase proteins exhibit three strong peaks at k \u2248 2.3, 4.6, 7.3 nm\u22121. From the distance between peaks, we infer an average wavelength of \u03bb \u2248 2.5 nm. The power spectrum of HCV helicaseHM follows the same pattern PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t 5 Figure 4: Power spectrum of the molecular surfaces of the selected proteins. Power spectra of the molecular surfaces divided by the power spectra of the corresponding white-noise molecular surfaces. The symbols depict the power spectra and the error bars depict the error associated with the measurement. Top panel: Helicase proteins. Bottom panel: Non\u2013helicase proteins. The values of k are measured in nm\u22121. as that of HCV helicaseStrA shifted to smaller k with a varying relative phase which most of the time is close to \u03c0, with strong peaks at k \u2248 1.8, 3.6 nm\u22121. In comparison with the HCV models, the power spectrum of HCV helicaseStrB exhibits differences in the position of the peaks (found at k \u2248 2.7, 3.6, 5.5 nm\u22121) and in their amplitude ratios, which attest to the different treatment in HCV helicaseStrB from that in the HCV models. As k increases, we observe a gradual damping of the power of the helicases and an emerging tail reminiscent of shot noise in a Poisson power spectrum, more prominent in HCV helicaseHM and HCV helicaseStrB, which indicates the damping of the fluctuations about the mean value and thus the vanishing of the structural signal. This damping is most visible for k > 6 nm\u22121. This agrees with the observation above that sets the upper limit of k to the size of a typical cluster of aminoacids and hence sets the minimum distance below which correlations are not of biological interest nor can be reliably probed by X\u2013ray/NMR experiments. Conversely, the polymerases exhibit a predomi- nantly structureless power spectrum. In particular, Mouse kinase shows a flat spectrum which indicates an isotropic distribution of the power, whereas HCV polymerase shows an unstable area for 2 < k < 4 nm\u22121 and a strong peak at k \u2248 5.5 nm\u22121, then settling in a flat spectrum. conclusions : We presented a new method based on the Fourier analysis of protein molecular surfaces to extract functional information on proteins. For a selected set of proteins of HCV with different structural features, we first produced surfaces of the molecular electrostatic potential, as well as the corresponding white\u2013noise surfaces, and then computed their two-point correlation function in harmonic space (the power spectrum). We found that this method can distinguish between helicases and polymerases, as well as between different treatments in helicases. However, for the same treatment, this method failed to distinguish between different bound states in helicases. An immediate extension of this work is the application of this method to isolated structural subunits that form larger structures within proteins. Similarly sized subunits will have a strong signal in the same frequency range, which will add up in the protein power spectrum. Hence, we must first measure the contribution of each subunit separately and produce a catalogue of subunit signatures, so we can distinguish them in the combined signal when running similarity searches. By reducing the initial three\u2013dimensional information on the molecular surface to the one\u2013dimensional information on pairs of points at a fixed scale apart, this method allows for a fast similarity search. Further refinements in the similarity search will require methods that use information from higher\u2013order correlation functions, such as the correlation among three points at a fixed triangular configuration or its Fourier\u2013transformed (the bispectrum). (See Fig. 2 right panel for an illustration.) The bispectrum measures phase correlations among the modes and thus deviations from a Gaussian distribution. Our ultimate goal is to integrate higher\u2013order correlations and to apply the resulting method to the RCSB database so as to provide the biopharmaceutical and structural research communities with a novel and easily searchable reference without the three\u2013dimensional information compromising the speed of the calculation. This method aims to coalesce techniques, which have been extensively tested and used in other fields such as cosmology, into a fast and robust pipeline for the analysis and processing of very large, three\u2013dimensional biological datasets in an effort to speed up protein similarity searches. Acknowledgments CSC is funded by the FCT\u2013Lisbon, Grant no. SFRH/BPD/65993/2009. This work was sup- PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t 6 ported in part by the European Union (European Social Fund - ESF) and Greek national funds through the Operational Program \u201dEducation and Lifelong Learning\u201d of the National Strategic Reference Framework (NSRF) - Research Funding Program: \u201cThales\u201d. Investing in knowledge society through the European Social Fund. \u2217 Electronic address: cscarvalho@oal.ul.pt \u2020 Electronic address: dvlachakis@bioacademy.gr \u2021 Electronic address: gtsiliki@bioacademy.gr \u00a7 Electronic address: vasilis@ceid.upatras.gr \u00b6 Electronic address: skossida@bioacademy.gr [1] Dobson PD, Cai YD, Stapley BJ, Doig AJ (2004) Curr Med Chem 11: 2135\u20132142 [2] Illerg\u030aard K, Ardell DH, Elofsson A (2009) Proteins 15; 77(3): 499\u2013508. [3] Venkatraman V, Sael L and Kihara D (2009), Cell Biochem Biophys 54: 23\u201332. [4] Kolodny R, Koehl P, Levitt M (2005) J Mol Biol 346: 1173\u20131188. [5] Mayr G, Domingues FS, Lackner P (2007) BMC Struct Biol 7: 50. [6] Berbalk C, Schwaiger CS, Lackner P (2009) Protein Sci 18: 2027\u20132035. [7] Via A, Ferre\u0300 F, Brannetti B and Helmer-Citterich M (2000), Protein surface similarities: a survey methods to describe and compare protein surfaces [8] Kazhdan M, Funkhouser T and Rusinkiewicz S (2003), Proc 2003 Eurographics, 43: 156\u2013164. [9] Ritchie DW, Kozakov D and Vajda S (2008), Bioinformatics 24(17): 1865?1873. [10] Venkatraman V, Chakravarthy PR, and Kihara D (2009), J Cheminformatics 1: 19. [11] Vlachakis D, Tsiliki G, Tsagkrasoulis D, Carvalho CS, Megalooikonomou V, Kossida S (2012) EMBnet J. 18(1): 6\u20139. [12] Przytycka TM, Singh M, Slonim DK (2010) Brief Bioinform. 11 (1): 15\u201329. [13] Berger-Wolf TY, Przytycka TM, Singh M, Slonim DK (2010) Pac Symp Biocomput. 15: 120\u2013122. [14] Gire SK, Stremlau M, Andersen KG, Schaffner SF, Bjornson Z, Rubins K, Hensley L, McCormick JB, Lander ES, Garry RF, Happi C, Sabeti PC (2012) Science 9; 338(6108); 750\u2013752. [15] Elcock AH, Gabdoulline RR, Wade RC, McCammon JA. (1999) J Mol Biol. 291(1): 149\u2013162. [16] Sept D, Elcock AH, McCammon JA. (1999) J Mol Biol. 294(5): 1181\u20131189. [17] Wlodek ST, Shen T, McCammon JA. (2000) Biopolymers. 53(3): 265\u2013271. [18] Honig B, Nicholls A. (1995) Science 268(5214): 1144\u2013 1149. [19] Wong GC, Pollack L. (2010) Annu Rev Phys Chem. 61: 171\u2013189. [20] McCammon JA. (2009) Proc Natl Acad Sci USA. 106(19): 7683\u20137684. [21] Vlachakis D, Champeris\u2013Tsaniras S, Kossida S. (2012) Mol Biochem. 1(3): 144\u2013149. [22] Kandil S, Biondaro S, Vlachakis D, Cummins AC, Coluccia A, Berry C, Leyssen P, Neyts J and Brancale A. (2009) J Bioorg Med Chem Lett. 1; 19(11): 2935\u20132937. [23] Konecny R, Baker NA, McCammon JA (2012) Comput Sci Discov 26; 5(1) 015005. [24] Unni S, Huang Y, Hanson RM, Tobias M, Krishnan S, Li WW, Nielsen JE, Baker NA (2011) J Comput Chem. 32(7): 1488\u20131491. [25] www.poissonboltzmann.org/apbs [26] www.rcsb.org [27] Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) J Chem Theory Comput 4: 435\u2013447. [28] Lindahl E, Hess B, van der Spoel D (2001) J Mol Model 7: 306\u2013317. [29] van der Spoel D, Lindahl E, Hess B, Groenhof G, Mark AE, et al. (2005) J Comput Chem 26: 1701\u201318. [30] Sellis D, Vlachakis D, Vlassi M (2009) Bioinform Biol Insights 3: 99\u2013102. [31] S\u0306ali A, Blundell TL (1993) J. Mol. Biol. 234, 779\u2013815. [32] Eswar N, John B, Mirkovic N, Fiser A, Ilyin VA, Pieper U, Stuart AC, Mart\u0301\u0131-Renom MA, Madhusudhan MS, Yerkovich B, S\u0306ali A (2003) Nucl Acids Res 31, 3375\u2013 3380. [33] Laskowski RA, Rullmannn JA, MacArthur MW, Kaptein R, Thornton JM (1996) J. Biomol. NMR 8, 477\u2013486. [34] Connolly ML (1983), J. Appl. Cryst. 16, 548\u2013558. [35] Peacock JA (1999) Cosmological Physics, CUP. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t Figure 1 Figure 1: Surfaces of the electrostatic molecular po-tential. Left panel: Hepatitis C helicase protein PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t Figure 2 Figure 1: Surfaces of the electrostatic molecular potential. Righ panel: Hepatitis C polymerase protein. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t Figure 3 Figure 2: Schematic representation of point con PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t gu-rations for correlations in harmonic space. Left panel. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t Figure 4 Figure 2: Schematic representation of point con PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t gu-rations for correlations in harmonic space. Right panel. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t Figure 5 Figure 3: Power spectrum of the molecular surfaces ofthe selected proteins. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t Figure 6 Figure 4: Power spectrum of the molecular surfacesof the selected proteins.Upper. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t Figure 7 Figure 4: Power spectrum of the molecular surfacesof the selected proteins. Lower. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t molecular surfaces : Surfaces of the molecular electrostatic potential follow the nonlinear Poisson\u2013Boltzmann equation [23, 24]. We solved numerically for the electrostatic potential using the finite\u2013difference method as implemented in the APBS Software [25]. The potential was calculated on a Figure 1: Surfaces of the electrostatic molecular potential. Left panel: Hepatitis C helicase protein, Righ panel: Hepatitis C polymerase protein. The electrostatic potential is measured in eV, with range as shown in the corresponding colour bar. regular grid of size (65, 65, 65)1, with the grid\u2013fill\u2013by\u2013 solute parameter set to 80%. The dielectric constants of the solvent and the solute were set to 80.0 and 2.0, respectively. An ionic exclusion radius of 2.0 A\u030a, a solvent radius of 1.4 A\u030a and a solvent ionic strength of 0.145 M were applied. Default APBS charges and atomic radii were used. For our training set, we selected Hepatitis C viral (HCV) proteins with similar and dissimilar functions. We considered two HCV helicase proteins, namely the HCV helicase strain A (denoted by HCV helicaseStrA) and the HCV helicase strain B (denoted by HCV helicaseStrB), whose three-dimensional coordinates were obtained from the RCSB database [26] of X\u2013ray protein crystallography structures, with entry codes 1A1V and 8OHM respectively. Furthermore, we generated two simulations of the 1A1V protein crystal, namely the energy\u2013minimized version (denoted by HCV helicaseEM) and the molecular dynamics version (denoted by HCV helicaseMD). We also established a homology model of the HCV helicase (denoted by HCV helicaseHM) so that the in silico three\u2013 dimensional model of HCV were included in our training set. Energy minimization (EM) removes any residual geometrical strain from each molecular system, whereas molecular dynamics (MD) simulates a periodic cytoplasm\u2013like aqueous environment. Both EM and MD were performed with the Gromacs suite [27\u201329] through our previously developed graphical interface [30]. Molecular dynamics took place in a periodic environment, which was subsequently solvated with the simple point\u2013 charge water model using the truncated octahedron box 1 The size of the grid was kept small in order to speed up the calculation and reduce the computational load. It was tested to be suitable for this study, as higher detail would not change the surface by much while it would increase the computational load significantly. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t 3 extending to 7 A\u030a from each molecule. Partial charges were applied and the molecular systems neutralized with counter\u2013ions as required. The temperature was set to 300 K, the pressure to 1 atm and the step size to 2 fs. The total run of each molecular complex was 50 ns, using constant number of atoms, volume and temperature (NVT) throughout the calculation in a canonical environment. The results of the MD simulations were collected in a molecular trajectory database for further analysis. The homology model was produced using Modeller [31, 32] and was evaluated using the Procheck utility [33]. This model was designed in order to include a computer modelled structure in our training set, which however shares high sequence identity with its template structure (approximately 90%). We also included two examples of non\u2013helicase proteins, namely the 1NB7 structure of the HCV polymerase (denoted by HCV polymerase) and the camp\u2013 dependent protein kinase (denoted by Mouse kinase), with RCSB database entry codes 1NB7 and 1ATP respectively. Whereas the HCV polymerase is a virus protein of the same species as the selected helicases, the Mouse kinase is a mouse protein which has a very different function both from the HCV helicase and from the HCV polymerase. In Fig. 1 we show surfaces of the electrostatic molecular potential for two HCV proteins, namely the helicase and the polymerase. The electrostatic potential is measured in eV. In these manuscript, we used the Connolly representation for the molecular surfaces [34]. Power function of the molecular surfaces Molecular surfaces contain information on a property of proteins along the three spatial dimensions. This property, in this case the values of the electrostatic potential, can be regarded as a field F (x) defined over points x on the surface. Functional information is encoded not only in the positions of the points but also in the correlations among points. The simplest correlation function that we can measure is that between pairs of points. The twopoint correlation function \u03be of the field F measures the convolution of the field over its complex conjugate (see e.g. Ref. [35]) \u03be(r) \u2261 \u3008F \u2217(x)F (x + r)\u3009 = 1 L3 \u222b d3x F \u2217(x)F (x + r).(1) The angle brackets indicate an averaging over the normalization volume, which here we take as the volume of the molecular surface, L3. We assume that the field has a flat geometry and can be decomposed in a Fourier expansion of plane waves F (x) = \u2211 k Fk exp[\u2212ik \u00b7 x], (2) where the wavenumber k relates with the frequency \u03bd by k = 2\u03c0/\u03bd. If the field has a curved geometry, then a Fourier expansion in spherical harmonics should be used instead. However, the difference between the two expansions only matters in scales of order the size of the molecular surface, which correspond to the smallest frequency. The smallest frequency is the zero\u2013mode in the Fourier expansion and describes a global offset. The two-point correlation function becomes \u03be(r) = \u2329\u2211 k \u2211 k\u2032 F \u2217kFk\u2032 exp[i(k \u2212 k \u2032) \u00b7 x] exp[\u2212ik\u2032 \u00b7 r] \u232a .(3) Since the molecular surface is closed, the field is periodic within the size of the surface, which restricts the allowed wavenumbers to the harmonic boundary condition kn = (n2\u03c0/L)e\u0302k, where n \u2208 {0, 1, ...} is the order of the Fourier modes. As a consequence, all the cross terms with k\u2032 6= k average to zero and the remaining sum is \u03be(r) = ( L 2\u03c0 )3 \u222b d3k |Fk|2 exp[\u2212ik \u00b7 r]. (4) Hence the correlation function is the Fourier transform of the power spectrum P (k) = |Fk|2. This relationship is known as the Wiener-Khinchin theorem. The power spectrum measures amplitude correlations among the modes, discarding however information on the phase. We proceed to compute the Fourier transform Fk of the molecular surface inferred over a regular grid. The Fourier\u2013transformed surface measures the amplitude of the plane waves whose combination reproduces the information on the original surface. The frequencies of the plane waves range from the frequency corresponding to the extension of the surface (i.e. to n = 1), up to the Nyquist frequency corresponding to twice the bin size of the grid (i.e. to n = N/2, where N is the number of bins along a direction of the grid). The size of the molecular surfaces ranges between 5\u22127 nm (Table I). The smallest spatial scale of biological interest is the size of a typical cluster of aminoacids, which is of order xball \u223c 0.3 nm. We choose this spatial scale for the size of the grid, so that the largest frequency scale that can be probed is of order kball \u223c 10 nm\u22121. Furthermore, we assume that the field is isotropic, i.e. that it does not have a preferential direction, so that the power spectrum depends only on the distance between each pair of points. (See Fig. 2 left panel for an illustration.) By assuming isotropy, we are discarding information on the direction. We proceed to take the ensemble average of P (k) so that the power at the mode k is the sum of the power at all the points on a sphere of radius k from the zero\u2013mode, resulting in a one-dimensional function P (k). In this way, we collapse the information on the three-dimensional field over the molecular surface onto a one-dimensional power spectrum over the wavenumbers of the Fourier\u2013transformed molecular surface. PeerJ reviewing PDF | (v2013:06:567:0:1:NEW 7 Jun 2013) R ev ie w in g M an us cr ip t 4 k P P 1 2 21 1 P P P 1 2 3 21 2 k k k 3 3 Figure 2: Schematic representation of point configurations for correlations in harmonic space. Left panel: The configuration of the two-point correlation function contains one free parameter, k12, which is the distance in harmonic space between the two points P1 and P2. Right panel: The configuration of the three-point correlation function contains two free parameters, e.g. k12 and k23, describing the distances in harmonic space respectively between P1 and P2, and between P2 and P3. The third parameter k13 is related to the former two by the triangle condition k12 + k23 + k31 = 0. HCV helicaseStrA [72.4,64.8,55.1] HCV helicaseEM [72.8,65.1,55.5] HCV helicaseMD [72.3,65.5,56.3] HCV helicaseHM [71.5,65.7,55.9] HCV helicaseStrB [61.9,69.6,61.7] HCV polymerase [59.0,77.7,65.0] Mouse kinase [52.5,69.0,48.8] Table I: Sizes of the molecular surfaces along the [x,y,z]\u2013directions. Sizes are measured in A\u030a. For a given k, we are sampling a distribution, which we assume to be Gaussian with mean value \u3008Fk\u3009 and variance \u2329 |Fk|2 \u232a = P (k), from which the Fourier coefficients Fk are drawn. Hence there is a fundamental uncertainty about the underlying variance, which depends on the number of coefficients sampled at a given k. Since the number of k\u2019s on a sphere of radius k scales as k2 and for any real field it holds that F\u2212k = Fk\u2217, where the asterisk stands for the complex conjugate, then the uncertainty scales as \u2206P (k)/P (k) = \u221a 2/k2. method :",
    "url": "https://peerj.com/articles/186/reviews/",
    "review_1": "Jim Caunt \u00b7 Oct 2, 2013 \u00b7 Academic Editor\nACCEPT\nDear Prof. Niggli,\n\nMany thanks for your response and clarifications. Many congratulations on your interesting and informative paper: I enjoyed reading it. Have an excellent day!",
    "review_2": "Jim Caunt \u00b7 Sep 16, 2013 \u00b7 Academic Editor\nMINOR REVISIONS\nI agree with the reviewers that this submission is largely clearly written and the experiments justify the conclusions, and that it represents an advance of current knowledge. However, there is a consensus view that a few minor experimental and manuscript points would need to be addressed prior to acceptance for publication, which fall under two main categories.\n\n1. Experimental\nThough the data look convincing, I agree with reviewer 2 that the inclusion of another negative control comprising the use of two primary antibodies to proteins that do not interact would increase confidence in the data.\n2. Manuscript\nI also agree with reviewer 1 that, although the manuscript is largely well-written, it could do with a proof-read to weed out minor mistakes. Examples here include the one highlighted by reviewer 2, I also noticed:\nLine 42: remove 'anymore'.\nLine 48: replace 'allows detection also of' with 'also allows detection of'.\nLine 115: replace 'We now investigated' with 'In the present study, we have investigated' or 'Here, we have investigated'.\nI also think some detailed clarification of the image analysis would also be helpful, especially given this is the focus of the paper. For example, in the materials and methods, it says 100 cells per condition were evaluated, but in the text some of the numbers corresponding to total cell number analysed don't tally with this figure (e.g. a total of 261 cells analysed for n=3 in Fig. 4B). Similarly, I think you should indicate if the data are derived from a confocal stack or from a representative optical section (I'm assuming it's the latter, but I'm not sure).",
    "review_3": "Reviewer 1 \u00b7 Sep 13, 2013\nBasic reporting\nNo comments.\nExperimental design\nNo comments.\nValidity of the findings\nNo comments.\nAdditional comments\nBaumann et al. examine pair-wise proximity of proteins, such as flotillin-1 and 2, phosphorylated ERM, PSGL-1 and PIPKI\u03b390, that are important for structuring the uropod during T-cell polarization. Previously, FRET and biochemical approaches have suggested associations among these proteins. However, FRET is based on over-expression while biochemical assays lack spatial information and are prone to post-lysis artifacts. The authors use the Proximity Ligation Assay to investigate associations of the endogenous proteins before and after T-cell stimulation. They find that flotillin-1/flotillin-2, flotillin-2/p-ERM, flotillin-2/PSGL-1 and PIPKI\u03b390/p-ERM complexes pre-exist in un-stimulated cells and become confined in the uropod upon stimulation. The results nicely confirm and extend previous findings.\n\nThe experiments were performed and interpreted well and presented clearly. While studies on the dynamics of these complexes will be needed to reveal the connections between the preformed complexes and the ones confined in the uropod , as it stands the work presented is an important first step. In addition, whether these associations are part of the same complex or separately co-exist represent an important future direction. For the time being, the authors may simply choose to further discuss these points.\nCite this review as\nAnonymous Reviewer (2013) Peer Review #1 of \"Analysis of close associations of uropod-associated proteins in human T-cells using the proximity ligation assay (v0.1)\". PeerJ https://doi.org/10.7287/peerj.186v0.1/reviews/1",
    "review_4": "Reviewer 2 \u00b7 Sep 9, 2013\nBasic reporting\nThe manuscript is generally well presented and easy to follow. I would recommend careful proof-reading since one or two mistakes are still present eg line 152 Fig1C should be 2C.\nExperimental design\nThe use of the proximity ligation assay (PLA) adds information on the co-localisations seen between flotilins, PSGL-1, ERM and PIPKIgamma90 in the uropod of T-cells. The data presented is convincing as far as it goes; the minimum controls are shown for the the PLA assays (leaving out one of the two antibodies) but it's still difficult to really assess what's required for the PLA assay to give a positive signal eg only beta-actin and flotillin2 are shown as an 'irrelevent pair' and they do show significant interaction.\nValidity of the findings\nThe data are robust with the required number of repetitions and statistical analysis.\nAdditional comments\nOverall, I think this manuscript makes a modest advance over previous work published by this group and others but does not move us on much conceptually in terms of how close associations between proteins in the uropod are created.\nCite this review as\nAnonymous Reviewer (2013) Peer Review #2 of \"Analysis of close associations of uropod-associated proteins in human T-cells using the proximity ligation assay (v0.1)\". PeerJ https://doi.org/10.7287/peerj.186v0.1/reviews/2",
    "pdf_1": "https://peerj.com/articles/186v0.2/submission",
    "pdf_2": "https://peerj.com/articles/186v0.1/submission",
    "all_reviews": "Review 1: Jim Caunt \u00b7 Oct 2, 2013 \u00b7 Academic Editor\nACCEPT\nDear Prof. Niggli,\n\nMany thanks for your response and clarifications. Many congratulations on your interesting and informative paper: I enjoyed reading it. Have an excellent day!\nReview 2: Jim Caunt \u00b7 Sep 16, 2013 \u00b7 Academic Editor\nMINOR REVISIONS\nI agree with the reviewers that this submission is largely clearly written and the experiments justify the conclusions, and that it represents an advance of current knowledge. However, there is a consensus view that a few minor experimental and manuscript points would need to be addressed prior to acceptance for publication, which fall under two main categories.\n\n1. Experimental\nThough the data look convincing, I agree with reviewer 2 that the inclusion of another negative control comprising the use of two primary antibodies to proteins that do not interact would increase confidence in the data.\n2. Manuscript\nI also agree with reviewer 1 that, although the manuscript is largely well-written, it could do with a proof-read to weed out minor mistakes. Examples here include the one highlighted by reviewer 2, I also noticed:\nLine 42: remove 'anymore'.\nLine 48: replace 'allows detection also of' with 'also allows detection of'.\nLine 115: replace 'We now investigated' with 'In the present study, we have investigated' or 'Here, we have investigated'.\nI also think some detailed clarification of the image analysis would also be helpful, especially given this is the focus of the paper. For example, in the materials and methods, it says 100 cells per condition were evaluated, but in the text some of the numbers corresponding to total cell number analysed don't tally with this figure (e.g. a total of 261 cells analysed for n=3 in Fig. 4B). Similarly, I think you should indicate if the data are derived from a confocal stack or from a representative optical section (I'm assuming it's the latter, but I'm not sure).\nReview 3: Reviewer 1 \u00b7 Sep 13, 2013\nBasic reporting\nNo comments.\nExperimental design\nNo comments.\nValidity of the findings\nNo comments.\nAdditional comments\nBaumann et al. examine pair-wise proximity of proteins, such as flotillin-1 and 2, phosphorylated ERM, PSGL-1 and PIPKI\u03b390, that are important for structuring the uropod during T-cell polarization. Previously, FRET and biochemical approaches have suggested associations among these proteins. However, FRET is based on over-expression while biochemical assays lack spatial information and are prone to post-lysis artifacts. The authors use the Proximity Ligation Assay to investigate associations of the endogenous proteins before and after T-cell stimulation. They find that flotillin-1/flotillin-2, flotillin-2/p-ERM, flotillin-2/PSGL-1 and PIPKI\u03b390/p-ERM complexes pre-exist in un-stimulated cells and become confined in the uropod upon stimulation. The results nicely confirm and extend previous findings.\n\nThe experiments were performed and interpreted well and presented clearly. While studies on the dynamics of these complexes will be needed to reveal the connections between the preformed complexes and the ones confined in the uropod , as it stands the work presented is an important first step. In addition, whether these associations are part of the same complex or separately co-exist represent an important future direction. For the time being, the authors may simply choose to further discuss these points.\nCite this review as\nAnonymous Reviewer (2013) Peer Review #1 of \"Analysis of close associations of uropod-associated proteins in human T-cells using the proximity ligation assay (v0.1)\". PeerJ https://doi.org/10.7287/peerj.186v0.1/reviews/1\nReview 4: Reviewer 2 \u00b7 Sep 9, 2013\nBasic reporting\nThe manuscript is generally well presented and easy to follow. I would recommend careful proof-reading since one or two mistakes are still present eg line 152 Fig1C should be 2C.\nExperimental design\nThe use of the proximity ligation assay (PLA) adds information on the co-localisations seen between flotilins, PSGL-1, ERM and PIPKIgamma90 in the uropod of T-cells. The data presented is convincing as far as it goes; the minimum controls are shown for the the PLA assays (leaving out one of the two antibodies) but it's still difficult to really assess what's required for the PLA assay to give a positive signal eg only beta-actin and flotillin2 are shown as an 'irrelevent pair' and they do show significant interaction.\nValidity of the findings\nThe data are robust with the required number of repetitions and statistical analysis.\nAdditional comments\nOverall, I think this manuscript makes a modest advance over previous work published by this group and others but does not move us on much conceptually in terms of how close associations between proteins in the uropod are created.\nCite this review as\nAnonymous Reviewer (2013) Peer Review #2 of \"Analysis of close associations of uropod-associated proteins in human T-cells using the proximity ligation assay (v0.1)\". PeerJ https://doi.org/10.7287/peerj.186v0.1/reviews/2\nReview 5: nan\nReview 6: \n",
    "LLM_extracted_review": "[\"1. Review 1: Many congratulations on your interesting and informative paper: I enjoyed reading it.\\n\\n2. Review 2: \\n   - Experimental: The inclusion of another negative control comprising the use of two primary antibodies to proteins that do not interact would increase confidence in the data.\\n   - Manuscript: The manuscript could do with a proof-read to weed out minor mistakes. Specific examples include:\\n     - Line 42: remove 'anymore'.\\n     - Line 48: replace 'allows detection also of' with 'also allows detection of'.\\n     - Line 115: replace 'We now investigated' with 'In the present study, we have investigated' or 'Here, we have investigated'.\\n   - Clarification of the image analysis is needed, especially regarding the total cell number analyzed and whether the data are derived from a confocal stack or a representative optical section.\\n\\n3. Review 3: The experiments were performed and interpreted well and presented clearly. While studies on the dynamics of these complexes will be needed, the work presented is an important first step. Future directions include discussing whether these associations are part of the same complex or separately co-exist.\\n\\n4. Review 4: \\n   - Basic reporting: The manuscript is generally well presented and easy to follow, but careful proof-reading is recommended as one or two mistakes are present (e.g., line 152 Fig1C should be 2C).\\n   - Experimental design: The minimum controls shown for the PLA assays make it difficult to assess what's required for the PLA assay to give a positive signal.\\n   - Validity of the findings: The data are robust with the required number of repetitions and statistical analysis.\\n   - Overall, the manuscript makes a modest advance over previous work but does not significantly enhance our conceptual understanding of how close associations between proteins in the uropod are created.\"]"
}