This involves extracting a self-contained flavonoid subnetwork from the AraCyc database and calculating feasible metabolic routes or elementary modes (EMs) for it. Those EMs leading to anthocyanin compounds are taken to constitute the anthocyanin biosynthetic pathway (ABP) and their interplay with the rest of the EMs is used to study the minimal cut sets (MCSs), which are different combinations of reactions to block for eliminating colour pigmentation. By relating the reactions to their corresponding genes, the MCSs are used to explore the phenotypic roles of the ABP genes, their relevance to the ABP and the impact their eliminations would have on other processes in the cell.The numerous diverse metabolic pathways by which plant compounds can be produced make it difficult to predict how colour pigmentation is lost for different tissues and plants. This study employs mathematical and Aquilegia and; ii) the impact of another MCS requiring CHS suppression, corresponds to findings where the suppression of the early gene CHS eliminated nearly all flavonoids but did not affect the production of volatile benzenoids responsible for floral scent.Simulation and prediction results of the effect of different MCSs for eliminating colour pigmentation correspond with existing experimental observations. Two examples are: i) two MCSs which require the simultaneous suppression of genes DFR and ANS to eliminate colour pigmentation, correspond to observational results of the same genes being co-regulated for eliminating floral pigmentation in in silico analyses methods in the design of experiments. The methods could be used to prioritize target enzymes for different objectives to achieve desired outcomes, especially for less understood pathways.From the various MCSs identified for eliminating colour pigmentation, several correlate to existing experimental observations, indicating that different MCSs are suitable for different plants, different cells, and different conditions and could also be related to regulatory genes. Being able to correlate the predictions with experimental results gives credence to the use of these mathematical and  Flavonoids ,2 are ubAquilegia, the particular subset of genes that were suppressed, was strongly correlated. They also observed that the genes concerned (DFR and ANS) were co-regulated, one of similar findings of co-regulation in the anthocyanin biosynthetic pathway (ABP) genes, another example of which is made by Durbin et al. [Because of their role in pigmentation, changes in the expression of anthocyanins are easily observed. One example is where flowers have been found to lose their colour in response to different insect pollinators . It is rn et al.  who showin silico perspective. Rather than observing genes and inferring network properties, we start from a known self-contained metabolic network containing all reactions necessary for the synthesis of flavonoid compounds. As reactions are catalyzed by enzymes which are coded by genes, the reactions can be correlated to their corresponding genes; without needing knowledge about the genes involved, metabolic pathway analysis (MPA) [This study complements the biological investigations from a mathematical and is (MPA) ,8 tools In their work, Whittal et al remarked that the DFR and ANS enzymes corresponded to steps that were late in the ABP. This led them to interpret their finding as a consequence of pleiotropic functions for enzymes such as CHS and CHI that occur earlier in the ABP. While this explanation seems plausible enough in terms of a linear pathway, it needs to be recognized that, like all empirical pathways, the ABP is in fact embedded in a complex biochemical network. This raises additional questions, for example, even if the early enzymes perform other functions, would their loss destroy those functions or are there alternative paths available? Instead of blocking a "late" gene, would it not be more efficient to block an "early" gene and eliminate the subsequent reactions? Is the number of reactions in which an enzyme participate an adequate measure of whether it is essential, or can more refined measures be employed?In order to answer such questions, a more quantitative approach based on the biochemical network analysis methods is clearly needed. The MPA methods are based on elementary modes (EMs) which are non-decomposable pathways or routes that lead from an external substrate to an external product with the network maintained at steady state. The EMs consist of minimal sets of reactions that allow the system to operate at steady state ,10; theyEMs can be used to compute minimal cut sets (MCSs) . MCSs arBy performing a comprehensive mathematical analysis of the extracted subnetwork structure, the study enables the prediction of all possible EMs and MCSs compatible with the network structure. Such exhaustive characterization is very hard to achieve experimentally because, regardless of how many examples of a phenomenon one has observed, there might always be others not yet observed. However, the mathematical analysis provides a complete set of all possible EMs and MCSs. It is this aspect of completeness, subject only to a complete knowledge of the network itself, that makes it possible to make quantitative assessments e.g. of the relative importance of reactions and their corresponding enzymes/genes.Hence, the study provides an interesting look at all the possible target genes for anthocyanin suppression and how they fit into different situations. For example, although it is possible to target one single enzyme in order to suppress anthocyanin production, the question is whether that would be best? In nature, the absence of more than one enzyme is often observed and the reasons for pigmentation loss are numerous: it can be a single mutation in CHS, as described for a specific white flowering Matthiola line  or petunArabidopsis network. Next, the set of EMs for it are calculated. For the main focus of the study, which is the role of anthocyanin genes in the loss of colour pigmentation, the EMs that directly lead to the formation of anthocyanin compounds are identified and taken to constitute the ABP. MCSs and other methods designed for EM-based network structural analysis are then applied to identify and compare candidate genes (through their associated reactions) that could be targeted for eliminating colour pigmentation. Finally, we also use flux balance analysis (FBA) to investigate how each MCS candidate would affect the rate of production of associated metabolites. Where possible, the analysis results are compared and related to results from biological studies.The study proceeds through a number of stages: First, a self-contained flavonoid subnetwork is extracted from the full Arabidopsis, is used for the study because of its fully sequenced genome and the actively curated metabolic data (AraCyc) [Arabidopsis network formed by collecting all known metabolic reactions and enzymes from the AraCyc database version 8.0 [AC8_subnet.sbml, metabolites, prelim_constr_influx.val, and reactions, constitute input files for CNA).The standard model plant, (AraCyc)  availablsion 8.0 . A set osion 8.0  scripts sion 8.0  performssion 8.0  network sion 8.0 , a softwFrom the MPA perspective, a metabolic network is a (hyper-) graph where the nodes represent compounds and the edges chemical reactions. The boundary nodes are external biochemical inputs (substrates) or outputs (products) while the internal nodes are intermediate compounds with associated stoichiometric constraints to guarantee mass conservation. Full specification of the network also requires identification of the compounds to be taken as external. As part of the parsing process, a preliminary classification of 'external' is applied to all compounds that consistently appear as either substrates or products in all reactions.While many previous MPA studies, particularly on microbes, have been directly applied to genome scale networks, our approach is to first isolate a self-contained functional subnetwork to which FBA methods are then applied. This is motivated, both by:Arabidopsis network (2719 compounds in 2418 reactions), which would entail a combinatorial explosion of the number of EMs [i) the large size of the r of EMs  and timer of EMs ,27; andii) the fact that only a limited subset of the secondary metabolism is relevant to flavonoid production.For the approach to be viable, the subnetwork needs to be both self-contained  and complete .To achieve that, we note that a subnetwork is created by cutting through some internal network nodes, in effect removing the corresponding stoichiometric constraints. That is justifiable for compounds that are known to be of sufficient supply or that are buffered by an external reservoir in the cell, such as carrier compounds like ATP and ADP. The fact that this maintains the integrity of all EMs involving such compounds, is intuitively obvious but has been more formally demonstrated using null space analysis in .The following heuristic approach  has beenFirst, a list of external compounds plausibly buffered for the purposes of flavonoid metabolism is drawn up. Guidelines for this is taken from the catabolism-anabolism interface as described, for example, by Palsson : fig thrThe preliminary classification of nodes in the network mentioned above, is augmented by taking all those that correspond to compounds on this list, as external as well. The connectivity (i.e. the number of reactions in which it participates) for each node in the network is also recorded.Next, a prototype subnetwork for flavonoid production is compiled from all reactions participating in empirically known pathways explicitly listed in the AraCyc pathways table as flavonoid related, for example, anthocyanin, flavonol, and flavanone biosynthetic pathways.This prototype is then extended by comparing node classification and connectivity for the full and prototype networks:Arabidobsis network, where it is involved, on the one hand, in the formation of cyanidin and 2,3-trans-catechin, but itself is formed by dihydroquercetin. The related compounds and their corresponding reactions are added to the prototype and leucocyanidin becomes internal in both the revised prototype and the full network.1. If a node is external in the prototype but internal in the full network, its links in the full network are traced back and forwards to an acceptable external and the node becomes internal in the prototype. For example, taking the anthocyanin biosynthetic pathway as one of the starting pathways for the prototype, consider one of its starting substrates- the compound leucocyanidin. Leucocyanidin is external in the anthocyanin pathway but internal in the full AraCyc f in the full network than its connectivity Cs in the subnetwork, then:2. If a node is internal in both, but has larger connectivity Cf >>Cs, the node is be reclassified as external in the prototype because there are many processes in the full network outside the subnetwork to account for buffering it. In effect, this refers to ubiquitous compounds and if we had not already recognized compounds like malonyl coA, Erythrose-4P as ubiquitous earlier in the process, they would have been classified here as external in the prototype, although they are internal, but highly connected, in the full network. A highly connected node in the full network qualifies the node to be external in the prototype.• If C• Otherwise, all its connections are traced back as in 1 above.3. All reactions encountered in the traceback are added to the prototype, thus transforming a node initially not in the prototype, into an internal or an external node according to its status in the full network.O-sophoroside and malonylshisonin, which are external or highly connected in the full network.4. Classification, comparison and traceback steps 1- 3 are repeated until no reaction is added and no node is reclassified. For example, starting from our initial compound, leucocyanidin, the iterated traceback steps eventually lead to external nodes that include substrates like cinnamyl-alc or products like 2,3-trans-catechin, 2,3-cis-epicatechin, cyanidin 3-The prototype becomes a self contained subnetwork when the nodes connecting it to the rest of the full network are either external nodes in the full network, or boundary nodes that represent plausible reservoirs. Furthermore, the set of links emanating from each internal node in the subnetwork is identical in both the full network and the subnetwork. This is termed a coherent subnetwork.Arabidopsis flavonoid subnetwork, convergence was obtained for a subnet of 180 compounds and 164 reactions . However, these methods do not claim any knowledge of enzymes/genes or situations in which reactions occur. So, although it is necessary to discuss MCS in terms of enzymes for relating to experimental observations, the MCSs are based on the reactions themselves which are considered independently of their corresponding enzymes/genes. A consequence of this is that the same enzymes are considered separately in relation to their different reactions. This is especially important in the MCS study and will be explained further under that section and the explanations for the third table.Three different criteria were used to prioritize enzymes targeted for suppression of colour pigmentation:The pleiotropic considerations such as those used by Whittal et al. can be quantified by counting the number of pathways or EMs in which each reaction and its associated ABP enzyme/gene participates. The result quantitatively shows the importance of the genes in terms of their link with other reactions and processes.Escherichia coli [Arabidopsis.MPA provides a more specific tool for investigating loss of function than mere participation counting: this is the concept of minimal cut sets (MCSs). The concept of MCSs was introduced in 2004  and has hia coli  using thThe MCSs are calculated using the concept  where a Although recent studies  have shoThe "objective reactions" for our study are those that directly form the anthocyanin compounds responsible for the function of colour pigmentation. In effect, these MCSs provide the full set of ABP reactions to block, which are related to the subsequent gene candidates for genetic changes for loss-of-function, thereby preventing anthocyanin production. Because a complex network provides many alternate pathways, there are generally several different MCSs for a single collection of objective reaction(s). All of these MCSs would be effective; however, their efficiency would differ.Because the mathematics guarantees that the collection of MCSs is complete, we can use quantitative analysis to compare and investigate the effect that each MCS has on the remaining non-target set of EMs. Along with other different MPA methods, these effects are utilized in exploring the MCSs that would achieve loss-of-function most efficiently, and whether this was related to the position ("early" versus "late") of the genes in the ABP.fc) provide a measure of how essential reactions are for a specific objective. The number of EMs that a gene is involved in is a good indication of its importance but it is also conceivable that a gene involved in only a small number of EMs may nevertheless be crucial for those modes. In effect, if a gene is part of a larger MCS, its fc will be lower as its malfunction will be less crucial for the objective reaction(s).Another method used in considering the best candidates for loss of colour pigmentation is the fragility coefficient calculated using the MCSs. The fragility coefficients  is often used to identify the most realistic representation of the metabolic state of a cell within the constrained region of flux space. This is not applicable for flavonoids because they are secondary metabolites not needed for basic life functions in a cell. Fortunately, however, the chosen subnetwork also supplies the ingredients for synthesizing the lignin macromolecule, which is a significant constituent of plant biomass. This allows us to relate some flux values to the well-measured overall biomass growth rate.• Literature values for lignin monomer ratios show some variation according to plant species, tissue, developmental state and environmental stress, and similarly the lignin fraction of the biomass is variable. We make the following assumptions based on a survey of the literature -37:• The lignin composition is taken as:370 CONIFERYL-ALCOHOL + 238 SINAPYL-ALCOHOL + 60 COUMARYL-ALCOHOL-1 [-1 of the primary growth of the plant.• Taking the lignin biomass constituent as 15% ,35 of th-1 , the lig• In the absence of measured rates for flavonoid reactions, we estimate values based on measured concentrations. We assume that the rates are proportional to the concentrations; as we only evaluate ratios between rates with and without an MCS imposed, the unknown proportionality constant cancels.• Rates are compiled in this way for one type of plant: grapes ,40. InfoTable Taking these constraints as well as the fixed lignin biomass production rate, CNA is allowed to calculate a feasible state of the network and this is taken as the reference state. The values of all input fluxes calculated in this state are listed in Table Due to the varying origins of the constraints used and the arbitrary selection of a single feasible state, results based on this reference state is only expected to be indicative, not quantitatively significant. Some reassurance is obtained from the fact that the resulting flux balance system does have feasible solutions, so that the constraints are at least not mutually contradictive. A further measure to reduce reliance on details of the reference state is that only flux ratios are considered, not absolute values. It is also noted that the reference state is not meant to represent any particular physiological state, but rather a generic representation of all the capabilities of the flavonoid subnetwork. In the final analysis, the results themselves as reported in the next section gives further support to the appropriateness of this approach.The MCS states are simulated by constraining the fluxes through the reactions constituting each MCS to zero, while maintaining the initial constraints and external inputs at the same values as for the reference state. It is conceivable that blocking the reactions in a MCS might change the fluxes exchanged with the full network, provided that such changes are compatible with flux balances in the full network. If we did allow changes to these inputs, we could not test their feasibility with just the subnet. So while we have only studied a specific case, to extend that would necessitate dealing with the complete network which does not seem practical. By keeping the influx into the network constant, the reaction rates for each MCS can be compared against the reference state. The MCS simulated fluxes are normalized to their values in the reference state by dividing each MCS reaction rate by its rate from the reference state. This cancels out the units so we are looking at the relative impact of the MCSs on a typical (reference) state of a plant cell. A similar analysis was done without the constraints, to check that the relative impact is not just specific to the chosen reference state; it was found that the flux ratios were generally the same whether the preliminary constraints were used or not.To represent the results the external metabolite products are grouped into seven flavonoid groups and four non-flavonoid groups. The flavanoid groups are flavanols, flavanones, flavones, proanthocyanidins, leucoanthocaynidins, anthocyanins and flavonols which is further split into two groups: flavonols1 consisting of kaempferol derivatives and flavonols2 consisting of quercetin derivatives. The average relative fluxes through the end reactions of the EMs producing these external products enable us to study the impact that the MCSs have on other processes.The extracted flavonoid subnetwork shown in Figure The flavonoid subnetwork has more metabolites than reactions; it consists of 180 metabolites and 164 reactions. This illustrates a common feature of plant secondary metabolites where "decorating"  enzymes are of low substrate specificity, enabling a single reaction to utilize multiple substrates to produce different products ,17.In addition, the 359 EMs calculated from the flavonoid network is quite low compared to previous studies that concentrated on the primary metabolism of microbes ,9. TheseFrom the 359 EMs calculated from the subnetwork, 203 lead to non-flavonoid products, whilst 156 lead to flavonoid compounds of which there are seven subclasses. These are: i) anthocyanins; (ii) flavanols; iii) flavanones; iv) flavones; v) flavonols; vi) leucoanthocyanidin and vii) proanthocyanidins. Details of these flavonoids can be seen in -47. FourFigure The focus of this study is on the anthocyanin compounds and their role in plant colour pigmentation. As shown in Figure A detailed part of the subnetwork showing the subset of nodes or metabolites involved in the 24 EMs relevant for the ABP is shown in Figure Arabidopsis contains two anthocyanin compounds responsible for colour pigmentation: pelargonidin-3-O-glucoside (Pg) and cyanidin-3-O-glucoside (Cy). The number of EMs (routes) is higher for Cy-type anthocyanin than Pg-type anthocyanin because EM calculation depends on the structure of the metabolic network and how the compounds are linked by reactions. As shown in Figure O-glucoside than there are post pelargonidin-3-O-glucoside.As shown in Figure Further modification of the anthocyanin compounds  is illustrated in Figure For the metabolic reactions in the ABP, the main related genes/enzymes to be studied are: CHS, CHI, F3H, F3'H, DFR, LDOX/ANS ,60, and Genes such as FLS  are not The first network property looked at is the connectivity of the anthocyanin genes as shown in Figure The results in Figure Table The reactions directly forming the anthocyanin compounds (PELUDP-RXN and RXN1F-775) are identified as the objective functions for which the MCSs are determined.The 22 MCSs shown in Table At the top of the list is MCS15 which does not affect any other mode except the 24 anthocyanin EMs. As shown in Figure The MCS result illustrated in Figure On the other hand, it could be more efficient to block an 'early' gene, which argues for MCSs 11 (ANS(cy) & 3-UGT(pg)) and 14 (DFR(pg) & 3-UGT(cy)) with 135 non-affected EMs. While these eliminate 3 additional modes, they may compensate for it by moving the cut higher up the pathway, although these MCSs contain at least one objective function gene. The next five MCSs that do not contain any objective function genes but still make good candidates are: MCS8 (ANS(pg) & ANS(cy)) with 132 non-affected EMs, MCS9 (DFR(pg) & ANS(cy)) and MCS10 (DFR(cy) & 3-UGT(pg)) with 129 non-affected EMs, MCS5 (ANS(pg) & DFR(cy)) with 126 non-affected EMs, and MCS6 (DFR(pg) & DFR(cy)) with 123 non-affected EMs. The number of non-affected EMs then drops to the 60 s or lower.fc) could provide further information on target genes by looking at how essential they are to the pathway.The above analysis gives independent insight into the reasons for the observed molecular convergence in the evolution of colour pigmentation losses by providing a complete listing of all options open to the plant for suppressing anthocyanin production, as well as characterization of the impact each mutation has on the production of other compounds. It shows a more quantitative and therefore more differentiated characterization of the enzyme roles through the exhaustive nature of the mathematical analysis of network structure. Fragility coefficients  than other earlier genes. This supports the observation by Whittall et al [Aquilegia.Considering all the issues highlighted in the analyses so far, the genes ANS/LDOX and DFR corresponding to MCSs 5 and 9 could be considered as having favourable characteristics: they participate in a low number of EMs so don't affect the production of too many compounds; they occur earlier in the pathway and; they are more essential for anthocyanin production  but increase fluxes of kaempferol related flavonols.In general, the reaction rates show that non-flavonoid compounds are not much affected by the elimination of anthocyanins. Even for MCSs 1 and 2 which require the elimination of the early ABP genes that result in the elimination of most of the flavonoids, benzenoid production is not affected. This provides a quantified explanation of experimental observations such as that by Spitzer et al  where thThe above FBA provides a quantified measure of the impact that the different MCSs would have on the production and processes of other flavonoids and related compounds. They provide a more informative way of considering favourable target genes for eliminating colour pigmentation, and show that MCS options that appear similar in terms of structural measures, can have opposite quantitative impacts. For example, looking at genes ANS & DFR (MCSs 5 & 9) that were considered favourable target genes for eliminating colour pigmentation from the previous network structural analysis, the FBA shows that the effect of their MCSs on reaction fluxes is mainly to decrease PA. MCSs 13 & 15, on the other hand, lead to an increase in fluxes through the reactions mainly producing PAs and flavonols. Both effects have been observed in different systems. This additional information suggests that different MCSs suit different cell types or environmental conditions and could be utilized to identify which MCS would work best to achieve a certain outcome.While the reference state used for the reaction rate analysis is admittedly only one out of a possible range of feasible states, the general principle demonstrated by the results is that various MCSs that are by construction equivalent regarding a set of target products, can have quite different repercussions on the flux distribution in the rest of the network.In the main focus of the study, three methods  are employed to consider target ABP reactions and their corresponding genes for eliminating colour pigmentation. On their own, gene participation and reaction rates cannot be used as a basis for identifying the genes to target but they do provide an idea of the importance of, and interplay between, genes from a whole cell perspective. This information, along with MCSs, proves very useful in considering target genes for blocking colour pigmentation.The MCS method is the most important because it offers a list of the set of loss-of-function target genes that would eliminate anthocyanin production. By using the other methods to investigate these MCSs, we are able to analyze the properties of the corresponding genes and the impact that their suppression would have on other processes in the network. The fact that the impacts we demonstrate do coincide with actually observed distinct patterns of flavonoid production supports the simplifying assumption about our reference state and the analysis using reaction rates.The first two methods analyze the structure of the network to determine EMs and make predictions on the capability of the genes in terms of the network structure. When considering the MCS results and initially looking at the impact that each MCS had on other EMs, MCS 15 stands out as containing the best set of genes to target. However, looking at the different MCSs in relation to gene participation and fragility coefficients, the case arises that it might not be so good in certain circumstances and the argument develops for the possibility of other MCSs making better candidates for different situations related to loss of colour pigmentation in plants.Aquilegia [The third method takes the analysis a step further by looking at the functionality of the genes in terms of simulated reaction rates for different MCSs. By using all the three methods together, we are able to consider different possibilities and relate these to experimental observations that have been made. For example, MCSs 5 and 9 that respectively require the simultaneous suppression of genes DFR(cy)/ANS(pg) and DFR(pg)/ANS(cy) to eliminate colour pigmentation, correspond to observational results of the co-regulation of the DFR and ANS genes for eliminating floral pigmentation in quilegia  that shoquilegia  in whichThe results of this study provide a comprehensive list of all the different MCSs possible, according to metabolic network information available to date. It is obvious that these different MCSs would be best for different plants, different cells, and different conditions and may correspond to regulatory genes. From the results we are also able to understand more about the interplay between the MCSs and other metabolic processes in the cell; knowledge which enables us to relate which MCS would correspond best with which plant, cell or condition. Being able to relate the different MCSs to experimental observations, not only provides credence to the mathematical approach, but could also assist with the design of experiments that would more quickly achieve the required results. It also gives credibility to use MCSs to analyse and predict the metabolic functionality of less understood pathways.f: Connectivity in the full network; Cs: Connectivity in the subnetwork; CHI: Chalcone isomerise; CHS: Chalcone synthase; CNA: CellNetAnalyzer; Cy, cy: cyanidin-3-O-glucoside; DFR: Dihydroflavonol reductase; EM: Elementary Mode; F3H: Flavanone 3-hydroxylase; F3'H: Flavanone 3'-hydroxylase; FBA: Flux Balance Analysis; fc: fragility coefficient; FLS: Flavonol synthase; LDOX: Leucoanthocyanidin dioxygenase; MCS: Minimal Cut Set; MPA: Metabolic Pathway Analysis; Pg, pg: pelargonidin-3-O-glucoside; UDPG: UDP-glycosyltransferase.3-UGT: Anthocyanidin 3-O-glucosyltransferase; ABP: Anthocyanin Biosynthetic Pathway; ANS: Anthocyanidin synthase; CThe authors declare that they have no competing interests.STC participated in the design of the study, carried out the analysis and drafted the manuscript. WSV helped in the design of the study, the analysis, and the draft of the manuscript. All authors read and approved the final manuscript.AC8_subnet.sbml. This is an sbml [ an sbml  file repClick here for filemetabolites. A file containing the metabolites and their attributes, downloaded from the AraCyc database [database . Each roClick here for fileprelim_constr_influx.val. A file specifying the preliminary constraints. This can be uploaded and displayed in the CellNetAnalyzer flavonoid network project using the 'Scenario' feature under the 'CellNetAnalyzer' menu. Click here for filereactions. A file containing details of the reactions in the flavonoid subnetwork, downloaded from AraCyc. Each row in the file defines a reaction and its properties: <reaction identifier> <reaction equation> | <default value: # if unknown> <Par1: rate minimum> <Par2: rate maximum> <Par3: objective function coefficient 1- exclude, 0- include> <x-Pos: pixel coordinates> <y-Pos: pixel coordinates> <map number: network map where the box appears> <text box type: 1- editable, 2- noneditable >. Click here for file


The purpose of this paper is to report the noninvasive imaging of hepatic tumors without contrast agents. Both normal tissues and tumor tissues can be detected, and tumor tissues in different stages can be classified quantitatively. We implanted BEL-7402 human hepatocellular carcinoma cells into the livers of nude mice and then imaged the livers using X-ray in-line phase-contrast imaging (ILPCI). The projection images' texture feature based on gray level co-occurrence matrix (GLCM) and dual-tree complex wavelet transforms (DTCWT) were extracted to discriminate normal tissues and tumor tissues. Different stages of hepatic tumors were classified using support vector machines (SVM). Images of livers from nude mice sacrificed 6 days after inoculation with cancer cells show diffuse distribution of the tumor tissue, but images of livers from nude mice sacrificed 9, 12, or 15 days after inoculation with cancer cells show necrotic lumps in the tumor tissue. The results of the principal component analysis (PCA) of the texture features based on GLCM of normal regions were positive, but those of tumor regions were negative. The results of PCA of the texture features based on DTCWT of normal regions were greater than those of tumor regions. The values of the texture features in low-frequency coefficient images increased monotonically with the growth of the tumors. Different stages of liver tumors can be classified using SVM, and the accuracy is 83.33%. Noninvasive and micron-scale imaging can be achieved by X-ray ILPCI. We can observe hepatic tumors and small vessels from the phase-contrast images. This new imaging approach for hepatic cancer is effective and has potential use in the early detection and classification of hepatic tumors. Malignant hepatic tumors are tumors that result in high rates of morbidity and mortality. Improvement of therapeutic efficacy and the survival rate from hepatic tumors is an important problem, and the key issue is early diagnosis of hepatic tumors. Conventional methods of imaging diagnosis for hepatic tumors, such as sonography There are many other areas of research in the early detection of hepatic tumors. For example, gold nanoparticles in material science are studied as a hepatic tumor contrast agent As a new imaging method, X-ray phase-contrast imaging (XPCI) has high spatial resolution and density resolution, which can provide high contrast images by using the phase shift of the X-ray. The density resolution for C, H, O and other light elements is approximately 1,000 times higher than that of traditional X-ray absorption imaging. This technique can greatly improve the image quality of soft tissues, particularly at the interface of tissues, where the refractive index changes significantly Texture is the visual perception of local features on an image. Texture analysis of medical images is a sophisticated computer-aided technique that allows the detection of mathematical modes in the gray level distribution of pixels in digital images. It provides an objective characterization of the signal behavior of anatomical structures or pathological processes. The texture features of an image reflect the spatial distribution of the pixel properties, and they usually have irregular local and regular macroscopic characteristics. The texture features of a part of an image are closely related to the gray value changes in this region. A smooth region of an image contains pixels whose gray values are similar to one another, whereas the gray values of the pixels in a rough region differ dramatically Nude mice are usually considered to be the laboratory animal offering the closest approximation to human chromosomes. Animal grouping and transplanting: male nude mice, weighing approximately 18 g, were obtained from the Institute of Laboratory Animal Sciences, Cancer Institute and Hospital, Chinese Academy of Medical Sciences. A total of 24 nude mice were grouped randomly into 4 groups. Each group (consisting of 6 mice) was sacrificed after either 6, 9, 12, or 15 days after inoculation with hepatocellular carcinoma cells.Each nude mouse was anesthetized with an injection of 0.81 mg (45 mg/kg) pentobarbital sodium. After it was anesthetized, we opened the abdominal cavity of the mouse and implanted BEL-7402 human hepatocellular carcinoma cells X-ray ILPCI is called propagation-based imaging or in-line holography, and it is based on the principle of Fresnel diffraction. The Fresnel diffraction formula can be expressed as follows:2 indicates the distance from the source to the detector. The incident wave arriving at the front surface of the object is assumed to be a plane wave. If the amplitude is not taken into account, The formula is usually shown approximately in actual diffraction problems because of the complex integrand. In addition, the work of many researchers is based on the Wigner distribution theory. First, in the coaxial or paraxial approximation, the inclination factor for the Fresnel integral equation can be set equal to 1 without considering the impact of integration. Second, the distance from a point to the reference point on the viewing screen has a minimal effect on coherence, so the impact of the spherical sub-wave on the reference point can be ignored. After the initial approximation above, the Fresnel diffraction From the spatial intensity expression, we can see that image visibility is proportional to the Laplacian operator of the X-ray phase shift after passing through an object. Phase variation will be produced when the internal density of an object changes dramatically, and a second-order partial differential equation applied to the phase shift will greatly impact the image contrast. After the X-rays have traveled a certain distance, the intensity distribution received by the detector will reflect the edge enhancement of an object.The schematic diagram of the synchrotron radiation in X-ray ILPCI is shown in The X-ray ILPCI experiments were carried out at the BL13W1 beamline of Shanghai Synchrotron Radiation Facility (SSRF). The X-ray ILPCI facility is shown in To simulate an actual human environment, the hepatic samples were placed in a 10% formalin solution; the projection imaging results are not ideal. The blood vessels of the liver are not clear. However, when we take the sample out of the formalin solution and image directly without any other substances, we find that the results clearly show the texture and the presence of tumors and blood vessels.Specifically, nude mouse hepatic specimens containing the transplanted BEL-7402 human hepatocellular carcinoma cells were wrapped with insulating material and were placed on the sample table. The specimens were vertically and horizontally adjusted to allow matrix scanning and the capture of projection images.To further investigate the texture features, the textures of X-ray ILPCI projection images were quantified using the GLCM method The formula for the angular second moment can be expressed as follows:The formula for the inertia can be expressed as follows:The formula for the inverse difference moment can be expressed as follows:The formula for the entropy can be expressed as follows:The formula for the correlation can be expressed as follows:The formula for the sum average can be expressed as follows:The formula for the difference average can be expressed as follows:The formula for the sum entropy can be expressed as follows:The formula for the difference entropy can be expressed as follows:The nine texture parameters reflect the uniformity, randomness or other features of an image. A total of 20 square regions of interest (ROIs) were selected in each tumor region of different stage hepatic refraction image. In addition, the 20 ROIs were placed within each normal region of the same stage hepatic refraction image. Each ROI had a size of 60×60 pixels. Subsequently, the texture features of the normal tissue and tumor tissue regions were extracted separately.The principles of PCA can be expressed as follows: first, we perform standardization processing on the matrix consisting of the nine texture parameters of the 20 ROIs. Then, the correlation coefficient matrix of the texture matrix, the eigenvalues denoted as  of the correlation coefficient matrix, and the eigenvector denoted as  of λi, are solved. The new component can be expressed as follows:The contribution rate (CR) of Fi can be expressed as follows:If the CR of Fi is greater than some threshold, we use Fi as the principal component.PCA was carried out on the texture parameters we acquired above. The components with the CR up to 80% were used as the principal components. Subsequently, the means and standard deviations of the principal components were computed to discriminate the normal and tumor regions.We used DTCWT to decompose the images into two levels and chose ROIs. DTCWT was carried out on each ROI. After the deccomposition, we acquired two low-frequency coefficient images and two high-frequency coefficient images. The texture features of the four images in In this paper, SVM is used to classify hepatic tumors into different stages. The low-frequency coefficients of wavelet decomposition carry abundant information about the tumor tissue, so the first-level texture parameters of the low-frequency decomposition are used as the basis for classification. The acuqired texture features of the ROIs for each tumor stage were analyzed by PCA, and the components with the CR greater than 80% were used as the PCs.The traditional X-ray absorption imaging of normal hepatic tissue is shown in Experimental samples of hepatic tumors were imaged using a CCD detector with an image resolution of 9 μm. The livers were removed from 10% formalin.The PCA of the texture features based on GLCM was carried out on the four images in ROIs are randomly selected by the operator. Each time, it is different F1 and CR values when operator calculates the different ROIs. However, this selection does not change the positive or negative value of F1 for a normal or tumor region. If F1 is greater than zero, it indicates a normal region. If F1 is less than zero, it indicates a tumor region. Thus, randomly selecting ROIs does not directly impact the detection of tumors. The selection of different ROIs does not directly affect the diagnosis of early hepatic tumors.The PCA of the texture features based on DTCWT was carried out on the projection images of the 6-, 9-, 12- and 15-day-old samples. Because of the high CR, we also simply took the first PC F1 as the basis for the classification of normal regions and tumor regions. The means, standard deviations and CRs of F1 for different samples are shown in In this paper, we randomly selected 20 ROIs from each image of a 6-, 9-, 12- or 15-day-old hepatic tumor. The DTCWT decomposition was carried out on each ROI. We extracted the texture features of the decomposition of coefficient matrix on a low-frequency level 1 and analyzed the PC. The CR of the first PC F1 was 89.02%. The experimental result shows that the maximum classification accuracy for classifying hepatic tumors into different stages was 83.33%.Cancer diagnosis is the result of a comprehensive diagnosis, and biopsy remains the gold standard for the diagnosis of tumors. The analysis method of texture features reported in the paper is one of the auxiliary means of the tumor diagnosis. Texture features of these suspected cancer cases have the same texture features reported in this article, but other diagnostic tests such as blood tests and biopsies are still needed. Biopsy is a necessary and sufficient test for early diagnosis of hepatic tumors. In this article, hepatic tumors of samples have been known to exist before the X-ray ILPCI experiments were performed.The lesion can been observed in a X-ray ILPCI projection image, and the texture characteristics have the same features as those reported in this article, but the final diagnosis of hepatic cancer still requires a biopsy. This paper presents a noninvasive auxiliary method for the early diagnosis of hepatic cancer.From the above results, we can see that X-ray ILPCI has high contrast resolution and spatial resolution and that the subtle structure of tissues can be observed with X-ray ILPCI. The spatial resolution of images is improved from the millimeter level to the micron or even sub-micron level by X-ray ILPCI, which has a potential application in the early diagnosis of hepatic tumors. The range of substances that X-ray imaging can detect extends from highly absorbing heavy elements to weakly absorbing light elements, which has some potential clinical applications. Compared with conventional imaging, X-ray ILPCI has greater advantages.In this paper, we study the morphological changes of early hepatic tumors. Phase-contrast images show that the development of tumors may cause a change in the density of tissues or coarseness in tissue texture, and the seriousness degree of tumor can be discriminated by these morphological features. Using quantitative texture analysis, normal regions and diseased regions in the projection image can be distinguished. The low-frequency coefficient images of DTCWT carry abundant information about biological tissues, whereas GLCM only describes the distribution of pixel pairs in a comprehensive image. Thus, DTCWT is better than GLCM in terms of feature extraction. We also use the SVM method for the first time to classify different stages of hepatic tumors. However, because the number of samples is too small and lacks a certain degree of statistical significance, the accuracy of the classification is not high. In the future, we will increase the number of samples to solve this issue.X-ray ILPCI is still in the experimental stages, and experiment samples are limited to static samples. There is still no good way to process live samples. The X-ray ILPCI device of SSRF has a small field of view. It takes us approximately half an hour to acquire images from 0 degrees to 180 degrees. Samples must not move within that half an hour. Movement of the sample has a direct impact on the image and may even lead to vision disappeared. It is difficult to solve the problem of movement from the breathing of living samples in vivo experiments. These movements lead directly to artifacts in the final projection images.It is good effect for a single sample. The image effect may be still clear if the sample has been placed in a water or formalin solution to simulate physiological conditions. We obtained a total of more than 1000 2D projection images using X-ray ILPCI of a nude mouse hepatic tumor sample by rotating it by 180 degrees, and we subsequently used image processing technology such as a filtered back-projection reconstruction imaging algorithm or another reconstruction imaging algorithm. Tomography images can be reconstructed. The overlapping details of 2D projection images can be more clearly observed in 3D tomography images. It can be observed every internal detail in the reconstruction images of the diffraction CT of X-ray ILPCI. Thus, the thickness of the sample does not affect the imaging result.X-ray ILPCI presents a micron-scale imaging method. X-ray ILPCI requires further research before its clinical application. It will be a qualitative leap, once X-ray ILPCI is used clinically. X-ray ILPCI is an innovation from current millimeter-scale to micron-scale image resolution, and it may represent a new noninvasive auxiliary imaging technique for diagnosing hepatic tumors.


Metagenomic assembly is a challenging problem due to the presence of genetic material from multiple organisms. The problem becomes even more difficult when short reads produced by next generation sequencing technologies are used. Although whole genome assemblers are not designed to assemble metagenomic samples, they are being used for metagenomics due to the lack of assemblers capable of dealing with metagenomic samples. We present an evaluation of assembly of simulated short-read metagenomic samples using a state-of-art de Bruijn graph based assembler.We assembled simulated metagenomic reads from datasets of various complexities using a state-of-art de Bruijn graph based parallel assembler. We have also studied the effect of k-mer size used in de Bruijn graph on metagenomic assembly and developed a clustering solution to pool the contigs obtained from different assembly runs, which allowed us to obtain longer contigs. We have also assessed the degree of chimericity of the assembled contigs using an entropy/impurity metric and compared the metagenomic assemblies to assemblies of isolated individual source genomes.Our results show that accuracy of the assembled contigs was better than expected for the metagenomic samples with a few dominant organisms and was especially poor in samples containing many closely related strains. Clustering contigs from different k-mer parameter of the de Bruijn graph allowed us to obtain longer contigs, however the clustering resulted in accumulation of erroneous contigs thus increasing the error rate in clustered contigs. Advances in sequencing technologies have equipped researchers with the ability to sequence collective genomes of entire microbial communities, commonly referred to as metagenomics, in an inexpensive and high-throughput manner. Microbes are omnipresent within the human body and environments across the world. As such, characterizing and understanding their roles is crucial for improving human health and the environment. Metagenomics provides an unbiased view of the diversity and biological potential of microbial communities  and analOne of the major challenges related to metagenomic processing is the assembly of short reads obtained from community samples. Due to the lack of specific assemblers to handle metagenomes, researchers continue to use assemblers originally developed for whole genome assembly.We have evaluated the performance of a state-of-the-art Eulerian-path based sequence assembler on simulated metagenomic datasets using a read length of 36 base pairs (bp), as produced by the Solexa/Illumina sequencing technology. The datasets were meant to reflect the different complexities of real metagenomic samples . They inThe assembled contigs were evaluated based on several quality measures for contig length and assembly accuracy. To improve the quality of the contigs, we clustered the results of different parameter runs of the assembler. We used efficient local alignment to quickly and accurately map the assembled contigs to the input source genomes. We also used a short read mapping algorithm to align the input reads to the assembled contigs to compute the homogeneity of the assembled contigs using entropy as a metric. Finally, we assessed the coverage of the source genomes by the produced contigs.Short-read assembly of metagenomes performed better than our initial expectation in some aspects such as accuracy of the contigs and coverage of the source genomes. However, fragmentation of the contigs was more severe in metagenomic datasets than in the isolate assemblies. The assembly of a smaller dataset consisting of reads from 30 EColi strains showed that the contigs obtainable through co-assembly of related strains are considerably shorter than those generated using isolate assemblies. We also observed that by clustering results from assembly runs for different k-mer size values of de Bruijn graph, we were able to obtain a greater number of longer contigs .Traditionally, microbial genomics has relied primarily on pure cultures of microbes for sequencing. In recent years, researchers have developed a new approach known as metagenomics wherein the genetic material is obtained by directly sequencing the complex microbial communities without prior culturing. This presents an unbiased view of the diversity and biological potential of these communities .The heterogeneous nature of the genetic material contained in metagenomic samples presents significant challenges for metagenomic assembly and analysis. Metagenomic samples have genomic content from many organisms which can not be easily separated. The genetic material of individual organisms in these samples is roughly proportional to the abundance of these organisms in the communities, which varies significantly. The dominant organisms are over-represented whereas the organism at low levels of abundance are not sequenced at sufficient depth. Also, the polymorphism between related members of the communities may lead to incorrect estimation of the repeat structures .bp. In addition to binning and assembly, several other tools have been developed for gene prediction  and  and bp. ediction 17]. We . We bp. ediction  for a reSanger’s method  has beenTo study the extent of errors in metagenomic assemblies in comparison to single genome assembly, we performed a set of experiments on simulated datasets. Although, simulated datasets do not completely capture the characteristics of real metagenomes , simulatWe have evaluated metagenomic assemblies based on the accuracy of the generated contigs using alignment-based similarity to the source genomes, contig length statistics, and the proportions of the source genomes recovered by the contigs. As the k-mer size of de Bruijn graph plays a crucial role in ABYSS’s assembly, we have also tried to assess the impact of k-mer size on metagenomic assemblies by comparing the contigs produced from different runs of the k-mer parameter. We also provide comparisons of metagenomics assemblies to the isolate assemblies of the constituent genomes.k to obtain longer contigs changes from 29 for simLC (a single dominant genome at a very high coverage) to 21 and 23 for simHC, which does not have any distinctly dominant genomes. As seen from Figure k = 25 seems to produce the longer contigs. The clustered results effectively pool the contigs produced from different runs of assembly by varying the k-mer parameter values across the different datasets. Figure N50 (weighted median) values.Figure k and pooled the results using the clustering algorithm. Figure As a benchmark for our metagenomic assemblies we separated the reads by their source sequence and performed isolate assemblies. We assembled the reads from each individual sequence separately and combined the final contigs from all the source sequences. We performed the isolate assemblies with different values of k=21. Further, the accuracy of the clustered contigs was lowest, due to the accumulation of errors from all the contig sets. This is due to our clustering approach, which tries to retain all the unique sequences. An alternative clustering strategy could be designed that takes the consensus of contigs obtained from different runs. This strategy would improve the accuracy of the results while reducing the total number of bases recovered.Even assemblies of isolate genomes are not completely error free. In the case of metagenomes, the presence of multiple genomes at different coverage depths causes additional problem and the contigs are expected to have more mis-assemblies compared to the contigs from isolate genome assemblies. To assess the accuracy of the assembly we aligned the contigs back to the source genomes. Table In an ideal case of metagenomic assembly, all the reads forming a contig would come from the same source sequence. In metagenomes the reads from different sources may be co-assembled, resulting in chimeric assemblies. Therefore, to estimate the degree of chimericity, we evaluated the homogeneity of contigs using their read composition. Essentially, greater the number of sources from which a contig is assembled, the higher its entropy will be. The methods section describes the alignment of reads to the assembled contigs and entropy calculations.Figure Figure k=27 and 29 produced the longest contigs. Figure k=27 and 29. The contigs in metagenomic assembly are considerably shorter than the isolate assembly, suggesting a severe degradation in assembly quality resulting from the presence of multiple strains. Figure Since the collection of DNA sequences for metagenomic experiments does not involve cloning, the reads could come from strains which are highly similar, with very little sequence variation. In this case, even though the effective read coverage of the species is high, due to minor differences in the sequences of the strains, the quality of assembly might not be as good as an isolate genome assembly. To evaluate the performance of co-assembly of reads from related strains, we created the EColiStrains dataset consisting of 10 million reads from 30 strains of Escherichia Coli. For comparing the assembly performance, we created another dataset with the same number of reads from a single strain, E.Coli strain 536 (represents the isolate assembly), and assembled it using the different k-mer size values used for assembly of the strains dataset. For isolate assembly, To evaluate the improvement in assembly quality with mate-pairs information we generated and assembled datasets similar to simHC, simLC and simMC with paired-ended reads of insert length 2000 bases. However we observed that only a small fraction (less than 2 %) of the contigs being produced were using mate pairs information. In addition, most of these contigs were assembled with gaps. For our analysis we broke those contigs at the gaps and treated them as separate contigs. Therefore, because to these two factors, we did not observe a significant improvement in the assembly quality of paired ended reads in metagenomic samples.In this paper we have presented the results of assembly and analysis of some simulated metagenomic datasets. Short-read assembly of metagenomes performed better than our initial expectations in some aspects such as accuracy of the contigs and coverage of the source genomes. Although a large fraction of the contigs were assembled accurately, fragmentation of the contigs was more severe in metagenomic datasets when compared to the isolate assemblies. Further, assembling the high complexity dataset was more difficult in comparison to the the low complexity dataset as well as the medium complexity datasets. We also observed that ABYSS was able to utilize the mate pairs information to assemble only a small fraction of the contig with gaps. Therefore, using mate-pairs did not improve the results significantly in our case. The assembly of a smaller dataset consisting of reads from 30 EColi strains showed that the contigs obtainable through co-assembly of related strains are considerably shorter than those generated using isolate assemblies.We also observed that by simple clustering of the results from various assembly runs  we were able to obtain a greater number of longer contigs, as optimal contigs are distributed across the k-mer space. However, due to our simple approach towards clustering which retains all unique contigs, most mis-assembled contigs made their way into the clustered results, increasing their error rate. Further improvements in clustering technique may be required to improve the quality of the clustered results.We created our simulated datasets using Metasim . It is asimLC (low complexity), simMC (medium complexity), and simHC (high complexity) simulate the composition of real metagenomic datasets. In the low complexity simLC dataset, a sizable portion of the reads belong to a single dominant organism. The high complexity dataset simHC has no distinctly dominant organism and all organisms are present in approximately equal concentrations. The simMC dataset has more than one dominant organism, but their concentrations in the samples are considerably lower than the concentration of the dominant sequence in simLC. We also produced datasets similar to each of the three datasets described above with paired-end reads with an insert size of 2 kb, to evaluate the performance of paired-ended assembly.Metagenomes vary considerably in their compositions depending on the environment from which the reads were sampled. Therefore, to assess the assembly quality as a function of metagenome’s complexity, we constructed three datasets using the profiles described in . These dEcoliStrains consisting of 10 million reads sampled uniformly from 30 different strains of Escherichia coli. The coverage of each strain was approximately 2.3x. This dataset was constructed to study the extent of co-assembly when reads from very similar organisms are assembled together.Figure Due to the high computational requirements for the assembly of our metagenomic datasets, we used ABYSS  assembleWe also performed paired-ended assemblies using ABYSS on datasets generated with mate-pairs information. ABYSS performs paired-ended assembly in two stages, first it assembles the reads without using the mate-pair information and in the second stage it utilizes the paired reads information to merge the contigs. We set the minimum number of pairs required to merge the contigs at 10.Due to the presence of sequencing errors and repeat regions in the source genome, assemblies are usually not completely error free, even in the context of a single genome. We assembled the reads from the individual source genomes by separating them first and combined all the produced contigs. In this study, the assembly performed in this manner is referred to as isolate assembly and provides us a comparative baseline to the metagenomic assembly.We observed that the contigs of optimal length were distributed across the k-mer space. Therefore, we pooled the assembled contigs from different contig sets  and clustered them to remove duplicate or suboptimal contigs which were contained in another longer contig. We clustered the contigs using Cd-hit , which ulocalAcc) produced by NUCMER using the ratio of length of the alignment  to the length of the contig (contigLen), as given by (1).To estimate the assembly accuracy we aligned the contigs to the source genomes. Accurate contigs are expected to match at least one source sequence with high accuracy. Therefore, to speed up the alignment process we used NUCMER pipeline of MUMMER . NUCMER Some contigs, especially the shorter ones, produced multiple alignments, either to the same or to a different genome. Therefore, we used the best accuracy among all the alignments as the contig’s assembly accuracy. For contig coverage calculations (discussed later on) we consider only the contigs that were assembled with a threshold accuracy of at least 95%. We would like to note that this threshold is rather arbitrary and in many cases, the acceptable accuracy threshold would be dependent on particular application. Our choice was motivated by a similar threshold used by the authors of ABYSS  for evalWe estimated the homogeneity of contigs by observing the source genome of reads used to assemble a contig. This was done by performing a read-to-contig alignment using a fast short read aligner. We used BWA , which pUsing the counts of reads from each source sequence mapped to a given contig, we calculated the entropy of the contigs as shown in (2).ip is the fraction of total reads coming from source genome i. At different phylogenetic levels, organisms generally display a greater sequence similarity within their group when compared with the organisms belonging to a different group. Due to this sequence similarity, the assemblers are more likely to make the mistake of mis-assembling reads belonging to the same phylogenetic class. We also compute the entropy at two higher phylogenetic levels, genus and phylum, in addition to the entropy at sequence and strain level, to see if there is a significant decrease in entropy at higher phylogenetic levels.where The need for a short-read aligner arises because, for Eulerian path based assemblers, it is difficult to determine the actual read composition of the contigs. The input reads are not used directly but are broken down into smaller k-mers and the original read information is lost.k, we calculated the extent to which the source sequences are recovered by the contigs. This is determined by aligning the contigs to the source sequences. We considered only the accurate alignments of the contigs, i.e. the alignments which accurately cover at least 95% of the contig. For each such alignment, we marked all the positions of the source genomes which were part of the alignments. The collection of all such positions of the source genome covered by the contigs, represents the contig coverage of the genome. The contig coverage described here is different from the read coverage which is approximate coverage of the genome from the sampled reads and represents the sequencing depth of the source sequences in the datasets. The contig coverage represents the fraction of the source sequence recovered by the contigs and can be at most 1. We refer to this contig coverage as the source coverage ratio.For different assemblies generated by varying the values of assembly parameter In cases where contigs had multiple accurate alignments, possibly due to repeat regions or shared sequences between genomes, we counted each contig’s contribution for all the alignments. Therefore, our contig mapping to source genomes is not unique, and our source coverage ratio calculation may have over-counted a little. As it is not possible to prefer one particular alignment over another, we believe this is a better option than randomly choosing a particular alignment of the contig.AC performed the experiments and wrote all the programs needed for this study. Both, AC and HR conceptualized this study and setup the different experiments. All authors wrote the manuscript, read the manuscript, and approved for final submission.The authors declare that they have no competing interests.


We present an approach for identifying genes under natural selection using polymorphism and divergence data from synonymous and non-synonymous sites within genes. A generalized linear mixed model is used to model the genome-wide variability among categories of mutations and estimate its functional consequence. We demonstrate how the model's estimated fixed and random effects can be used to identify genes under selection. The parameter estimates from our generalized linear model can be transformed to yield population genetic parameter estimates for quantities including the average selection coefficient for new mutations at a locus, the synonymous and non-synynomous mutation rates, and species divergence times. Furthermore, our approach incorporates stochastic variation due to the evolutionary process and can be fit using standard statistical software. The model is fit in both the empirical Bayes and Bayesian settings using the lme4 package in R, and Markov chain Monte Carlo methods in WinBUGS. Using simulated data we compare our method to existing approaches for detecting genes under selection: the McDonald-Kreitman test, and two versions of the Poisson random field based method MKprf. Overall, we find our method universally outperforms existing methods for detecting genes subject to selection using polymorphism and divergence data. Drosophila and human-chimp data.We present a new methodology, SnIPRE, for identifying genes under natural selection. SnIPRE is a “McDonald-Kreitman” type of analysis, in that it is based on MK table data and has an advantage over other types of statistics because it is robust to demography. Similar to the MKprf method, SnIPRE makes use of genome-wide information to increase power, but is non-parametric in the sense that it makes no assumptions (and does not require estimation) of parameters such as mutation rate and species divergence time in order to identify genes under selection. In simulations SnIPRE outperforms both the MK statistic and the two versions of MKprf considered. We then apply our method to  Populations evolve over time and how they evolve is the product of different evolutionary forces. Population genetic theory gives us mathematical descriptions of how each of these forces is thought to affect the patterns of genetic variability within and between species. However, if the goal is not to start with an evolutionary model and see what happens, but rather to start with the data and understand what caused it one usually encounters an identifiability issue. For this reason, most population genetic data analyses looking for mutations under selection start by assuming a neutral population genetics model , and test for deviations from this model. Commonly used examples of such procedures include tests based on summary statistics of the site frequency spectrum (distribution of mutation frequencies), such as Tajima's D One class of tests which is generally robust to demography are those tests commonly referred to as “McDonald-Kreitman-type tests” Selection Inference using Poisson Random Effects, works by modeling the variation within and between species as a combination of four types of “effects”, one for each class of variation. These effects are functions of unknown population parameters of interest, including the selection coefficients.Unlike many of the tests mentioned above, the method we present here assumes no particular population genetic model - in other words it is a non-parametric approach. Similar to the MK statistic, it is also generally robust to demography. Our method, which we call SnIPRE for Previously, we have developed a suite of powerful approaches that can estimate the average strength of selection operating on a locus and/or the distribution of fitness effects under a specified population genetic setting for MK polymorhism and divergence data see . A main There are two main advantages of SnIPRE over MK and MKprf, which we highlight here. The first is that it can reliably identify genes under weak and strong negative as well as positive selection without needing to specify a population genetic model a priori. Nonetheless, because it “borrows information” from the rest of the genome regarding the average and variance in polymorphism to divergence, it outperforms the one-at-time MK test. This gain in power is attributable to SnIPRE's use of a “James-Stein” class of estimator. The second advantage is that if one is willing to assume a particular population genetic model, it is possible to view the SnIPRE parameters as a re-parameterization of the population genetic model. With these additional assumptions, we can extend our inference beyond idenfication of genes that are not evolving according to the neutral theory, to quantification of strength and directionality of the selection forces.Drosophila comparison and human-chimp comparison.In this paper we will develop the model and the interpretation of its terms, and then describe how that model can be fit in both the empirical Bayes (SnIPRE) and fully Bayesian (B SnIPRE) settings. We also show how this model is robust to demographic history and recombination using standard coalescent simulations. Furthermore, we demonstrate how the Poisson Random Field estimates of average selection intensity, species-split time, mutation rate, and degree of selective constraint at the locus can be “extracted” directly from the SnIPRE estimates. We then compare the SnIPRE methods to the MK statistic and MKprf methods in detecting and estimating selection and other population parameters in simulations, and apply SnIPRE to data from a Because SnIPRE works by picking up on the same type of signature of selection as the MK statistic, we will start with a review of this method and the theory behind it. While most techniques to identify loci under selection require assumptions about demography (particularly constant population size and no substructure), the MK statistic does not. Like the HKA statistic, it works by comparing divergence information between inferred neutral sites (such as synonymous sites in a protein-coding gene) and sites potentially under selection (such as non-synonymous sites at the same gene). Strictly speaking, the test is a test of the neutral protein evolution hypothesis which states that the vast majority of evolutionary changes at the molecular level are caused by random drift of selectively neutral mutants (not affecting fitness) PN) to divergent non-synonymous (DN) mutations, In its traditional form the MK table consists of counts for four categories of mutations which occur in the coding region of a gene: polymorphic synonymous, divergent synonymous, polymorphic non-synonymous, and divergent non-synonymous, see McDonald and Kreitman Motivated by the MK statistic, the SnIPRE framework uses the MK table polymorphism and divergence data for identifying genes under selection. Using generalized linear mixed models we incorporate genome wide effects into our analysis as fixed effects, and individual gene effects as random effects. This method allows us to pool information across genes which increases our power to detect those under selection.MKprf is another method that was developed by us which directly estimates the posterior distributions of genomic parameters, such as the species divergence time, based on the MK tables' synonymous cell entries. The posterior of the selection coefficients for each gene are then calculated conditional on these genomic parameters and the non-synonymous cell entries in the MK table, see The data consists of MK table counts for each gene, as well as the total number of synonymous sites and non-synonymous sites surveyed. Incorporating the number of sites into our model allows us to extend our inference beyond non-synonymous and divergent interaction effects to include effects due to changes in the mutation rate, both in the synonymous and non-synonymous sites.Let By using fixed and random effects in the model we are assuming that these gene-specific effects come from some distribution, and that distribution is estimated from the data. The use of mixed effects is particularly relevant in this setting where it capitalizes on the fact that genes share a phylogeny. Thus, even though the mutation rate, coalescent times, constraint and selection forces will vary across genes, the distribution of the influence of these forces across genes can be well estimated by viewing the data set as a whole. From this perspective we estimate the fixed effect terms (genome-wide average estimates) of our model, as well as the variability in the distribution in of the random (gene-specific) effect terms of the model. The random effects, or gene-specific parameters, are then estimated given this context. Below we describe how the terms in this model allow us to estimate for any given gene the average effect of mutation, divergence, constraint and selection levels over time.selection effect for the Of primary interest is identifying genes under selection, either positive or negative. Identification of these genes can be done quite easily in the SnIPRE framework with only the assumptions of the MK test: i. synonymous and non-synonymous sites sampled are interspersed; ii. synonymous sites are not under selection. The non-synonymous-divergent interaction effects, gene effect. Similarly, divergence effect. The proportion of non-synonmyous mutations that are non-lethal are reflected in constraint effect. These relationships are summarized in The other terms in the SnIPRE model are also quite interpretable. The interecept and the gene specific effect, We fit this model in R For the Bayesian model the fixed effects have Normal priors with mean An alternative formulation of the Bayesian model using hierarchical centering maybe be preferable as it results in quicker convergence In standard coalescent theory we have Our model also works well in the Poisson random field (PRF) framework which assumes i. mutations arise at exponentially distributed times, ii. each mutation occurs at a new site, and iii. each mutant follows and independent Wright-Fisher process (no linkage)The gene effect The divergence effect, The selection effect The non-synonymous effect, It is interesting to note that these are the relationships used by Sawyer and Hartl (1992) to fit their single locus PRF models to To assess and compare the performance of the SnIPRE methods against the MK statistic and MKprf method we simulated data using 3 different methods. The first method, based on coalescent theory, was implemented in R. The second method, PRFREQ, simulates data based on the PRF framework. The third method is a forward simulation method, SFS_CODE. In these simulations our first goal was to compare the false positive rates of the methods using simulations under neutrality. Additionally, we simulated data with selective constraint but without selection which illustrates SnIPRE's ability to distinguish between mutational constraint and selection. Using PRFREQ, we were also able to simulate data sets with a distribution of selection coefficients and use this to compare the methods in a litany of non-neutral settings.For the results reported below, the MK test (Fisher's exact test) was applied and the resulting p-value left unadjusted for multiple testing, significance was determined by an To assess false positive rate FPR for each of the methods, we simulated data using standard coalescent theory. In Next we investigated the impact of demographic history as well as recombination on the FPR of the methods using the forward simulator SFS_CODE. In The key point from all these simulations is that SnIPRE performs just as conservatively as the MK test and better than MKprf under a litany of neutral scenarios that might be cause for concern in analyses for inference of selection.A particularly interesting application of SnIPRE is to identify regions of the human (or a new genome) that show very low levels of variation based on both polymorphism and divergence data. These might be interpretable as regions of high selective constraint either at the amino acid or non-coding level  and may represent biologically meaningful sequences, see To quantify the power of SnIPRE to identify constrained loci, we used the coalescent method to simulate three different scenarios with varying degree of selective constraint, or A comparison can also be made when selection is present, and there is no constraint . SnIPRE, however, found significant evidence of negative selection, as well as mutational constraint. The SnIPRE estimated selection effect for this particular gene was Odf2, The application to humans in particular illustrates nicely the improved power in the SnIPRE model to detect genes under strong negative selection (constraint) and recurrent negative selection on mildly deleterious mutations. Because of the relatively low mutation rate in humans, genes under varying degrees of negative selection usually have such low mutation counts in the MK table that the MK test is unable to achieve significance. For example, consider the spermatogenic BRC2 gene, associated with breast cancer and important for DNA repair, is another illustration of a case where examining the individual MK table we are unable to find significant evidence of selection. However the SnIPRE model indicates a significant amount of mutational constraint, indicating strong negative selection. The MK table for this gene has PS = 13, DS = 16, PN = 9, and DN = 17. While there is little evidence of negative selection  require further assumptions. The parameters of the SnIPRE model are easily interpreted and can be effectively used to estimate the affects of selection, constraint, divergence time, and mutation rate on genome-wide patterns of variation on a gene-by-gene basis. Effects may be readily evaluated in the absolute, or relative to the genome-wide estimates.Drosophila and human-chimp results with other findings corroborates the legitimacy of this methodology in this setting.The simulations provided here illustrate the significant increase in power over the traditional MK test that the SnIPRE model provides, while maintaining a low false positive rate. This makes sense since we are using genome-wide data to improve our estimate of the influence of mutation rate, species divergence time, constraint, and selection effects. The fixed effects reflect genome-wide averages of these effects; the random effects reflect the gene-by-gene variation in the influence of these forces and provide estimates of this variation with James-Stein-type shrinkage. Both the empirical Bayes and fully Bayesian implementation borrow strength across genes to improve estimates of the parameters of interest. The success of the method in simualtions, as well as the consistency of the When the assumptions of the PRF are met, our simulations indicate the method provides estimates of the selection coefficient as un-biased as the more parametric method MKprf, and with generally smaller confidence intervals. While in this paper we have focused on the interpretation of SnIPRE parameters in the PRF framework, we believe an extension of the model could be used in another framework which allows for arbitrary dominance. One such framework is described in Williamson et al In the future, we will explore the impact of varying recombination rate on the accuracy of parameter estimates and, in turn, the efficacy of natural selection in weeding out deleterious alleles while promoting favorable mutations to high frequency.


High-frequency (HF) stimulation has been shown to block conduction in excitable cells including neurons and cardiac myocytes. However, the precise mechanisms underlying conduction block are unclear. Using a multi-scale method, the influence of HF stimulation is investigated in the simplified FitzhHugh-Nagumo and biophysically-detailed Hodgkin-Huxley models. In both models, HF stimulation alters the amplitude and frequency of repetitive firing in response to a constant applied current and increases the threshold to evoke a single action potential in response to a brief applied current pulse. Further, the excitable cells cannot evoke a single action potential or fire repetitively above critical values for the HF stimulation amplitude. Analytical expressions for the critical values and thresholds are determined in the FitzHugh-Nagumo model. In the Hodgkin-Huxley model, it is shown that HF stimulation alters the dynamics of ionic current gating, shifting the steady-state activation, inactivation, and time constant curves, suggesting several possible mechanisms for conduction block. Finally, we demonstrate that HF stimulation of a network of neurons reduces the electrical activity firing rate, increases network synchronization, and for a sufficiently large HF stimulation, leads to complete electrical quiescence. In this study, we demonstrate a novel approach to investigate HF stimulation in biophysically-detailed ionic models of excitable cells, demonstrate possible mechanisms for HF stimulation conduction block in neurons, and provide insight into the influence of HF stimulation on neural networks. Electrical signaling is fundamental to the physiological function of excitable cells such as neurons and cardiac myocytes. Irregular electrical patterns in the brain and heart can lead to life-threatening conditions including epileptic seizures and ventricular fibrillation. External stimulation can terminate these irregular rhythms In the 1960s, it was shown that kilohertz-range high frequency (HF) sinusoidal stimulation could reversibly block conduction in neurons averaged model, which accounts for the HF stimulus but does not contain a high-frequency term Alternatively, one can apply a multi-scale method, separating the fast time scale dynamics—due to the HF stimulus—and the slow dynamics of the excitable cell, and derive an In this study, we first illustrate the multi-scale method to derive the averaged FHN (AFHN) model equations and use phase-plane analysis to determine critical HF stimulus thresholds above which the model cannot exhibit repetitive firing or elicit a single action potential. We then extend this approach to simulate the dynamics of the classical Hodgkin-Huxley (HH) neuron model We begin by deriving and analyzing a simplified model of spiking which accounts for the influence of HF stimulation. We consider the FitzHugh-Nagumo (FHN) model where and the dot indicates differentiation with respect to time If the period of the fast HF stimulus is much smaller than all characteristic times of the FHN model, according to the method of averaging whereandThe AFHN model is very similar to the FHN model, with the only difference being the modification of the cubic function Repetitive firing in the AFHN model. In the parameter region considered in this study, the cell is excitable, that is, in the absence of an external stimulus, the cell is at rest, and the addition of a stimulus can induce a single or multiple action potentials. In this study, we will consider two types of applied current stimuli: a constant applied current and a brief applied current pulse, in addition to the HF stimulation.We first consider the case of a constant applied current For the parameters chosen, the AFHN model has a single steady-state and shown in Using standard techniques from linear stability analysis Hopf bifurcation. Many previous studies have shown that in the FHN model  neuron model of the giant squid axon where HF stimulus parameters Assuming that the period of the fast HF stimulation is much shorter than the characteristic times of the dynamics of whereandfor As with the FHN model, we plot or  and  . Below aRepetitive firing in the AHH model. As in the previous section, we consider the influence of an applied current We plot the ncreases .Excitability in the AHH model. We next consider excitability in the AHH model following brief applied current pulses. Here, we consider both positive  and negative  applied current stimuli. As with the FHN model, the HH model is known to not exhibit a strict all-or-none firing threshold. However, especially for brief (0.1 ms) pulses, the HH model demonstrates a threshold-like response. In post-inhibitory rebound. In the classical HH model  . For smaAs ncreases .  when  As ulation  .  when  The AHH model suggests that there are different mechanisms of conduction block, depending on the strength of the HF stimulus. For small In summary, the influence of the HF stimulation parameter Finally, we consider the influence of HF stimulation on a random network of 100 neurons, each with, on average, 10 connections, coupled via both excitatory and inhibitory synapses  following a single initial applied current at the simulation onset. The network response to a constant, repetitive, or random (Poissonian) applied current, in addition to the HF stimulation, may be significantly different. We additionally only consider sparsely connected random network architectures. In this study, we found that the specific network architecture was highly important in determining the response to HF stimulation, and thus it is reasonable to speculate that the network response in highly connected and/or directed neural networks could be different from our findings. Several studies of models including more detailed network architecture and specific cell types have suggested mechanisms underlying deep brain stimulation treatment using HF stimulation in the 100–200 Hz range. Rubin and Terman demonstrated that HF stimulation of the subthalamic nucleus can regularize globus pallidus firing and eliminate pathological thalamic rhythmicity In this study, we investigate a simple network with a random architecture and consider the influence of HF stimulation as function of the relative fraction of excitatory synaptic connections. We illustrate a general approach to study HF stimulation in a large neural network which does not require simulation of the HF stimulation term and thus does not require a prohibitively small simulation time step. Here, we consider HF stimulation in the context of only a few network parameters. However, neural networks can exhibit rich and complex dynamics, and much work has demonstrated that the local network architecture can have significant influence on global behavior, e.g., the small-world phenomenon The critical values for repetitive firing and evoking action potentials are defined in terms of the HF stimulus frequency-to-amplitude ratio; that is, as the HF stimulus frequency increases, so must the HF stimulus amplitude for the same response. In a therapeutic device, it is ideal to minimize the amplitude of an applied stimulus, to minimize power consumption and mitigate safety issues for both the patient and device. Thus, determining the optimal frequency regime to minimize the amplitude for optimal HF stimulation is an important and practical issue. Future work will consider these complications, which must also include analysis of HF stimulation at frequencies approaching the same time scales as cellular dynamics.In most clinical settings of interest, HF stimulation is applied in the form of an external electrical field stimulus. In this study, we do not account for the influence of an external electrical field nor account for the spatial extent of the nerve axon. Such levels of details are significant for studies of local neural conduction block The HH model of the giant squid nerve axon is a classical model of an excitable cell, highly studied and well-characterized, and thus it was a reasonable biophysically-detailed ionic model to characterize the influence of HF stimulation using the method of averaging approach. However, several more detailed neuronal models relevant to mammalian physiology have been described, incorporating more detailed and multiple sodium, potassium, and calcium currents Finally, the simulation results presented here are deterministic and do not account for stochastic fluctuations inherent in neuronal signaling at both the cellular and subcellular levels. Indeed, studies have shown that noise-induced firing can be enhanced by HF stimulation for sufficiently large noise levels, termed vibrational resonance We derive the AFHN model equations, following the approach in and derive the following equations for Mathematically, we are interested in the limit The variables After calculating the integrals and returning to the original time scale, the averaged system is as given above in Eqs. 2a and 2b. Importantly, we note that the assumption implicit in stating Eq. 13a, specifically that the original system voltage Following a similar approach as described in and  see . The minThe locations of  the transmembrane potential averaged over all neurons. The frequency-domain representation of the pEEG is computed by the Fast Fourier Transform.The synchrony of the electrical activity in the network is given by the synchrony measure where the variance of the time fluctuations of the average transmembrane potential, the variance of the time fluctuations of the individual transmembrane potentials and All numerical simulations were performed in MATLAB. For simulations of the AHH model, the modified gating variable rate functions (Eqs. 12e–12f) were pre-calculated for a given value of