Arabidopsis thaliana. Model parameters were estimated based on expression time-courses for relevant genes, and a consistent set of flowering times for plants of various genetic backgrounds. Validation was performed by predicting changes in expression level in mutant backgrounds and comparing these predictions with independent expression data, and by comparison of predicted and experimental flowering times for several double mutants. Remarkably, the model predicts that a disturbance in a particular gene has not necessarily the largest impact on directly connected genes. For example, the model predicts that SUPPRESSOR OF OVEREXPRESSION OF CONSTANS (SOC1) mutation has a larger impact on APETALA1 (AP1), which is not directly regulated by SOC1, compared to its effect on LEAFY (LFY) which is under direct control of SOC1. This was confirmed by expression data. Another model prediction involves the importance of cooperativity in the regulation of APETALA1 (AP1) by LFY, a prediction supported by experimental evidence. Concluding, our model for flowering time gene regulation enables to address how different quantitative inputs are combined into one quantitative output, flowering time.Various environmental signals integrate into a network of floral regulatory genes leading to the final decision on when to flower. Although a wealth of qualitative knowledge is available on how flowering time genes regulate each other, only a few studies incorporated this knowledge into predictive models. Such models are invaluable as they enable to investigate how various types of inputs are combined to give a quantitative readout. To investigate the effect of gene expression disturbances on flowering time, we developed a dynamic model for the regulation of flowering time in  Flowering at the right moment is crucial for the reproductive success of flowering plants. Hence, plants have evolved genetic and molecular networks integrating various environmental cues with endogenous signals in order to flower under optimal conditions . VariousThe complexity of flowering time regulation is enormous, even when focusing on the network involved in integrating the various signals. To understand how gene disturbances influence flowering time, it is not only important to know which genes regulate each other, but also how strongly these genes influence each other. Hence, quantitative aspects of flowering time changes upon perturbations of input signals cannot be understood by merely assessing qualitatively which interactions are present. To this end, a quantitative model describing how different genes in the network regulate each other is needed. Indeed, other complex plant developmental processes have been subject to extensive modeling efforts . This inArabidopsis thaliana. Substantial qualitative information is available about the factors involved and how these interact genetically. However, the information that is needed for quantitative and dynamic modelling is missing to a large extent. This includes comprehensive and standardized quantitative data on flowering time under various conditions and in different genetic backgrounds [Arabidopsis thaliana has been scarcely studied using modeling approaches. Recently a few promising mathematical modeling approaches appeared aimed at modeling the floral transition in various plant species [Arabidopsis halleri [Arabidopsis thaliana flowering time did not take genetic regulation into account or used a mainly qualitative approach [Arabidopsis thaliana flowering time integration network was presented [Flowering time regulation has been extensively studied experimentally in the plant model species kgrounds , and tim species –21. Dong species , and Satapproach . Only veresented .Arabidopsis thaliana flowering time integration network, by investigating a core gene regulatory network composed of eight genes (SHORT VEGETATIVE PHASE (SVP), FLOWERING LOCUS C (FLC), AGAMOUS-LIKE 24 (AGL24), SUPPRESSOR OF OVEREXPRESSION OF CONSTANS 1 (SOC1), APETALA1 (AP1), FLOWERING LOCUS T (FT), LEAFY (LFY) and FD. Although certainly more genes are involved in integrating the various signals influencing the timing of the floral transition [FT [SOC1 [AP1 expression [FLC and SVP are also expressed in the SAM, where they repress the expression of SOC1 [SOC1 integrates signals from multiple pathways and transmits the outcome to LFY [AGL24 is involved upon dimerizing with SOC1 [AP1 [AP1 and LFY. Once the expression of AP1 is initiated, this transcription factor orchestrates the floral transition by specifying floral meristem identity and regulating the expression of genes involved in flower development [SOC1, SVP and AGL24 in our model.We aimed to obtain a mechanistic understanding of the ht genes : SHORT Vansition , we focution [FT . FT is ption [FT ,29. FT htion [FT ,31 and cFT [SOC1  and AP1 pression ,33. FLC  of SOC1 –36. SOC1e to LFY ,38, whicith SOC1 . In turnOC1 [AP1  and of FOC1 [AP1 . The comelopment . Importaelopment  we incluAP1 as orchestrator of floral meristem identity specification, the moment at which the AP1 expression level starts to rise is used as a proxy for flowering time in the model.The above introduced interactions between the flowering time integration genes and the floral meristem identity genes at the end of the pathway allow to derive a set of Ordinary Differential Equations (ODEs) describing how genes in the network regulate each other. ODEs were chosen because they arise from continuum modelling of molecular interactions and allow quantitative analysis of the effect of perturbations on expression levels and finally on flowering time. Because of the above mentioned role of i and ii). We validated our model by comparing predicted expression time-courses for mutants in components of the network with experimental data (dataset iii). Finally, we obtained detailed understanding of how genes are affected by perturbation in other genes, via the regulatory interactions that constitute the network.In order to build and validate an ODE model describing the network constituted by the eight selected genes, we obtained three quantitative datasets: i) gene expression time-courses of the selected eight genes in wild type; ii) flowering time of plants of different genetic backgrounds; and iii) expression data of the selected genes in the plants of these different genetic backgrounds. A key aspect of our approach is that we estimate model parameters using the dynamic gene expression time-course data for the components of the model, in combination with flowering time data , which describe how the expression level of each gene is influenced by the other genes. This regulation is described by Hill functions , which rmeristem , we assuAP1 [AP1 expression and fine tuning of flowering time in response to different environmental cues. In wild type Arabidopsis, the AP1 level remains barely detectable in the SAM until about day 13 after germination and then sharply increases  was obtained. For SOC1, the overall fit was good, but does not capture the data point at day 9, which deviates from the general trend in the time series, resulting in a nrmse of 19%. For AP1 and FD the value of the nrmse was around 14%, and for AGL24 and LFY it was 7%. The FLC and SVP expression data were used directly as input to the model; these are shown in Figure B in AP1, we could only obtain a good fit by introducing a particular value of one parameter describing how AP1 is regulated by LFY. As further discussed below, this parameter indicates DNA binding cooperativity for which indeed experimental evidence exists.A total of 35 parameters in six equations were estimated from the time series data containing 13 datapoints (expression levels) per gene . Besides this exception, there is considerable agreement between data and predictions. Indeed, comparison of the Pearson correlation  with correlation obtained using randomized data demonstrates the significance of this result (p<0.005), indicating a satisfactory model fit.Simulated flowering times in various genetic backgrounds are shown in soc1, agl24, fd and flc). In these experiments, a flowering inducing shift from short-day to long-day conditions was used [SOC1, FD and AGL24 mutations, but not for FLC mutation. The latter could be due to the low expression and limited role of FLC in the Col-0 background due to the FRIGIDA (FRI) mutation [A key issue in our model is the mechanism by which the network is able to give a quantitative response to specific perturbations. How are changes in a given gene expression level transferred to other components of the network, and how does this impact flowering time? In order to validate model predictions of how changes in expression propagate through the network, we simulated the expression time-courses for mutants and obtained independent experimental data for comparison. For that, microarray experiments were used, which were carried out for wild type and four mutant backgrounds  for the influence of SOC1 on LFY (β7) is much smaller than that for the influence of LFY on AP1  in yeast-two-hybrid assay, AGL24 and SOC1 form a heterodimer [LFY is expressed only in those tissues where SOC1 and AGL24 expression overlap [soc1 and agl24 mutants  SOerodimer ; (III) L overlap . Neverth mutants . If thesLFY. We tested an alternative model version in which AGL24 and SOC1 only regulated LFY as a dimer and not separately from each other. This resulted in a decreased goodness-of-fit in particular for LFY (nrmse 43% instead of 7%) and in this alternative model, indeed the effect of agl24 and soc1 mutation on LFY and on flowering time were comparable, which contradicts available experimental data.Based on these considerations, in our final model, AGL24 and SOC1 have independent roles in regulating LFY, the simulated LFY expression is reduced by only ~25% in the agl24 knockout mutant relative to its time-course expression in wild type. In contrast, LFY expression is predicted to be reduced by ~65% in the soc1 mutant  and expression activation strength (parameter β). A difference in any of these two parameters between SOC1 and AGL24 could lead to a difference in the effect of SOC1 versus AGL24 mutation. In the set of parameter values we obtained for our model, the DNA binding efficiency for AGL24 (K10) and SOC1 (K11) binding to the LFY promoter is quite similar. However, there is a substantial difference in activation strength (β7 vs β6), with SOC1 being much more able to activate LFY, resulting in a much larger effect of soc1 mutation compared to agl24 mutation. Analysis of predicted flowering times for a range of values of β for SOC1 and AGL24 confirms the dependency on the SOC1 activation strength . In agreement with this observation, the model simulation predicts a small additional reduction in LFY expression for the soc1/agl24 double mutant , which is a stronger activator. In the case of the different effect of the soc1 mutation compared to the agl24 mutation, it is important to consider that both SOC1 and AGL24 are known to form additional complexes, and such dimers might also play a role in their differential functioning [An important reason to apply computational models to a biological system, such as the floral integration network, is that it allows investigating how the various interactions that together constitute the network, transmit perturbations into a final readout. Indeed, by integrating experimental data with modeling we analyse how different components of the flowering time regulation network react to changes in other components, finally leading to a specific flowering time. We specifically analysed the regulation of ctioning . In addiIn a recently published review, an overview is given of attempts to model plant reproduction Gene Regulatory Networks, including networks involved in flowering time regulation . PreviouSVP overexpression mutant and an FT knock-out mutant on flowering time were predicted less accurately compared to other mutants (including SVP knock-out and FT overexpression mutants). FT and SVP are connected to each other in the network, which could indicate that in this part of the network the model needs refinement. In particular, given that SVP overexpression results in lower FT expression, the fact that both SVP overexpression and FT knock-out were not well predicted indicates that the effect of lower FT levels, either directly on AP1 or more indirect via SOC1, is not perfectly captured. It is however also important to consider that the FT levels used as input in our model are relatively low, which is related to the fact that they are not measured at the peak of diurnal expression of FT. Another aspect to consider is that FLC and SVP are present as external inputs in the model and are not directly modelled; if a mutation in one of these impacts the other as well, the model would miss such effect, which would deteriorate prediction performance. This might indeed be the case, according to ChIP-seq data [When analysing for which genes the model predictions were of better quality, the effects of an seq data ,36.soc1 vs. agl24 mutation, for which we provide an explanation in terms of a difference in a specific parameter in the model, difference in protein levels in spite of similarity in RNA levels could also be relevant, although there is currently no experimental data that indicates this.Clearly, there are several directions to expand our work. We do not specifically represent protein and RNA separately; currently the state of the art in the proteomics field does not allow high-throughput and precise quantification of protein levels during the vegetative phase of plant development. Recent evidence indicates however that for at least one component in the model, SVP, the effect of protein stability is important . In theoIn general, the amount of detail in the model will always be a compromise. This holds as well for the type of interactions in the network. Currently, regulatory interactions are modelled, whereas protein-protein interactions are not explicitly included. Nevertheless, the way in which regulatory inputs are combined gives an implicit representation of the way in which proteins interact with each other. Although the importance of complex formation for the components of the network is clear ,53, one SVP decay parameter; for FLM, additional equations describing the two isoforms would be needed. As for the modelling of upstream pathways, in a recent overview of known effects of mutations, ~150 genes were listed as being currently known to impact flowering time [Currently, we focused on a core set of genes involved in integrating various flowering time signals. Given that input from the environment converges on various components of the flowering integration network, an exciting follow-up step will be to incorporate environmental cues as the next layer of information in the gene regulatory network. This could include both direct environmental effects on some of the model components, or modelling complete upstream pathways. As an example of direct environmental influence that could be modelled, recent data indicates that the above mentioned effects of SVP protein stability as well alternative splicing of the flowering time regulator Flowering Locus M (FLM) depend on temperature . To incling time . It remaing time –6 and thTo conclude, we present a dynamic and predictive model for flowering time regulation. Our work presents a framework for studying the mechanisms of flowering time regulation, by addressing how different quantitative inputs are combined into a single quantitative output, the timing of flowering.For the time-course gene expression studies Arabidopsis Col-0 wild type plants were grown under long-day conditions  on rockwool and received 1 g/L Hyponex plant food solution two times per week. Rosette leaves and shoot apical meristem enriched material was harvested daily at ZT3 from seven plants per sample in duplicate.-2 s1. For flowering time measurements, the total number of primary rosette leaves was scored at visual bolting. The position of the plants from the different genotypes were randomized in the trays, and the flowering time phenotype was recorded without prior knowledge of the genotype. Plants for microarray experiments were grown on soil in growth chambers  under short-day conditions  for 25 days , agl24 (SALK_095007), flc-3) or 28 days (fd-3). Flowering was induced by shifting plants to long-day conditions .Plants for flowering time analysis were grown in growth chambers with controlled environment  under long-day conditions . Plants were raised on soil under a mixture of Cool White and Gro-Lux Wide Spectrum fluorescent lights, with a fluorescence rate of 125 to 175 mmol mYELLOW-LEAF-SPECIFIC GENE8 (YLS8) was implemented as reference gene for the analyses.RNA was isolated from the plant samples  using the InviTrap Spin Plant RNA Mini Kit. Subsequently, a DNAse (Invitrogen) treatment was performed, which was stopped with 1μL of a 20 mM EDTA solution and 10 minutes incubation at 65°C. Total RNA concentration was measured, and 1 μg RNA was used to perform cDNA synthesis by the Taqman MultiScribe Reverse Transcriptase kit (LifeTechnologies). qRT-PCR was performed with the SYBR green mix from BioRad using the gene specific oligonucleotides indicated in Table D in Etarget = 2CtΔ, where Ct stands for the threshold cycle and ΔCt = Cttarget—Ctreference. From that, the absolute abundance was estimated by Atarget = Etarget × s, where s stands for a scaling factor obtained by dividing the average abundance that a transcript reaches in a cell by the highest Etarget value among all samples, and multiplying by an assumed maximal protein abundance. Since a linear relationship between abundances of RNA and protein is assumed in the model, the average transcript abundance was adjusted based on average abundance of a protein in cell. An available estimate for the range of protein abundance is between 400nM and 1400nM [The relative gene expression was given by d 1400nM . From thsoc1–6, agl24, and fd-3. Briefly, biotinylated probes were prepared from 1 μg of total RNA using the MessageAmp II-Biotin Enhanced Kit (Ambion) following the manufacturer’s instructions and hybridized to Arabidopsis ATH1–121501 gene expression array (Affymetrix). Arrays were washed on a GeneChip Fluidics Station 450 (affymetrix) and scanned on an Affymetrix GeneChip Scanner 7G using default settings. Expression data for Col-0, soc-6, agl24, and fd-3 have been deposited with ArrayExpress (E-MEXP-4001). Expression data for flc-3 (ArrayExpress: E-MEXP-2041) have previously been published [Microarray time series experiments were performed as previously described  using RNublished . The proublished .FLC and SVP, gene expression is represented in the leaves  and meristem . For all the other genes, the variables correspond to expression in the meristem. Note that for SVP and FLC there are no equations; they act as external inputs in the model, and their regulation is not explicitly modelled. The parameters in the equations have the following meaning  FD requires dimerization with FT in order to activate SOC1 expression. (III) FD can activate AP1 as a monomer. (IV) Recently it was shown that in rice the interaction between FT and FD is bridged by a 14–3–3 protein [AP1, the degree of cooperativity (n) for the LFY-mediated regulation of AP1 was set to n = 3. Model source code is available as Equations –6 are ba protein  and probxi of a gene i depends on the parameter values associated to i. To independently fit an equation i in the right-hand side of the equation were taken from the data, and interpolated with a polynomial fit. This decoupling method has previously been described in full detail [MultiStart solver implemented in MATLAB . The parameters were then input in the whole systems of equations as starting point for a second optimization step. In this second step, the equations were solved as a system and the expressions of the direct regulators of i were taken from their associated ordinary differential equation solutions. This was carried out by the lsqnonlin solver (implemented in MATLAB) to fine-tune the fitting obtained by the first optimization step.In the model, the expression dynamics l detail . By applxmax, xmin are the maximum and minimum observed expression value; xiexp and xipred are the experimental and predicted values at time i; and the sum is over all n timepoints.To assess the goodness of fit for each gene, the normalized root mean square error (NRMSE) was used, which equalsode23s. For simulations of gene expressions of Arabidopsis wild type grown at 23°C/LD, the initial gene abundances were taken equal to the first expression time-points and the parameters were the same as described in Table C in i was fixed to a constant value xi = kmut. For the knock-out null mutants , the values of kmut were adjusted to zero; and for the knockdown mutants (not null mutations), kmut values were adjusted to a small percentage of the expression of i observed in the first time-point from wild type Col-0 .The equations were solved using MATLAB, integrated with the stiff solver trapz function in MATLAB. Subsequently, these values were scaled by subtracting the wild type value and then dividing by the wild type value. Similarly, the experimental relative change was calculated based on the microarray data. Note that comparing these values focusses on the effect of a mutation on dynamics of genes in the network over the complete time-course and as such takes into account the fact that the experimental conditions of the microarray experiment cannot directly be simulated (flowering-inducing shift from short-day to long-day conditions).To assess the model predictions of changes in gene expression we compared predicted relative changes with relative changes obtained with microarray data. To do so, we calculated the predicted total amount of expression  using the AP1 expression. For that it was assumed that, at a molecular level, Arabidopsis undergoes the floral transition in the moment that AP1 expression initiates. Therefore, according to our experimental AP1 time series, for wild type Col-0, the floral transition takes place between days 12 and 13 after germination. For simplification, we take the exact day 12.6 because it corresponds to the average number of rosette leaves (RLs) observed at the onset of flowering for wild type Col-0. To estimate the flowering time from mutant simulations, we use the time in which AP1 expression reaches the same simulated expression value as obtained at day 12.6 for wild type Col-0. This implies that the AP1 expression threshold for triggering the floral transition is the same for different plant growth conditions and mutants. Because flowering times are usually reported in number of rosette leaves (RLs) we subsequently scaled the predicted days to RLs by assuming a linear relationship between the number of RLs observed at the onset of flowering and the time in days after germination that Arabidopsis thaliana undergoes the floral transition at a molecular level.The predictions of flowering time were based on In addition to the set of mutants obtained in consistent conditions in this work, we also included existing mutant data. Wild type Col-0 flowering time in these experiments is somewhat different from that observed in our experiments. In addition, flowering times in literature are mostly reported in rosette leaves (RL), and not directly in days. To be able to integrate these data, we scaled existing mutant data with a linear factor which is chosen in such a way as to scale the wild type Col-0 flowering time to 12.6 RL.S1 File(DOCX)Click here for additional data file.S1 DatasetContains model source code (MATLAB) and RT-PCR data used for parameter estimation. Main model file is “ode_application_final.m”. This uses two files (LoadParametersFromFile_Leaf.m and LoadParametersFromFile_Meristem.m) to read the parameter values; two files that contain the RT-PCR data  and two files with ODEs (ode_equation_FT_leaf.m and ode_equations.m).(ZIP)Click here for additional data file.


Objective: Cyanotic congenital heart diseases (CCHDs) are a series of cardiac anomalies that have long been recognized as a potential cause of nephropathy. There have been few reports on renal impairment in patients with CCHD before and after corrective cardiac surgery. The aim of this study was to evaluate the prevalence of renal dysfunction before and after cardiac surgery and the impact of some risk factors on final renal outcome.Methods: Thirty children with CCHD who had done corrective cardiac surgery in the previous 6 months were enrolled in this study. All data prior to surgery were collected from the charts. Post-operation data including blood and spot urine samples were taken simultaneously for CBC, Cr, and uric acid and 24 hour urine was collected for microalbumin and Cr during the follow up visits. Pre- and post-operation parameters were compared to study the impact of cardiac surgery on renal function.Findings: Pre- and post-operative GFRs were not significantly different. Final GFR was significantly and inversely associated with pre- and post-operation age . Three (10%) patients had microalbuminuria. The prevalence of microalbuminuria in children older than 10 years was 30%. There was no link between microalbuminuria and age, GFR, and hematocrit . Patients with preoperation hematocrit >45 had a significantly lower final GFR compared to children with HCT <45 . The mean uric acid fraction (FEua) excretion was 8.21±4.75. Pre-operative HCT was inversely associated to FEua . There was no relationship between FEua and age, serum uric acid, and GFR .Conclusion: Children with CCHD are at increased risk of renal injury which is related more to the duration of cyanosis and higher degree of hematocrit level. To lower the risk, corrective cardiac surgery is recommended to be done as soon as possible to improve renal function and stop more renal impairment. Several studies have revealed that nephropathy is a prominent feature and a potential complication of CCHD[3-6]. Disorders of renal function in CCHD take the form of abnormal glomerular and tubular function. Regarding glomerular dysfunction, decreased GFR and macro or microalbuminuria have been reported[7]. Congenital cyanotic heart diseases (CCHDs) are a series of cardiac anomalies that can induce severe impairment of various organs including kidneys, respiration, vascular bed, hemostasis, red blood mass, central nervous system, digits, and long bones[8]. The structural integrity and function of proximal tubules have also been studied, indicating tubular dysfunction and loss of its integrity in patients with CCHD[9]. The hallmarks of glomerular changes in CCHD are glomerulomegaly, capillary dilatation, mesangial cell proliferation, and glomerulosclerosis[10]. Duration of cyanosis and an elevated hematocrit are suspected to be involved as the major risk factors for the development of cyanotic nephropathy in patients with CCHD[11]. The aim of the present study was to evaluate the prevalence of renal impairment in patients with CCHD before and after cardiac surgery, and to clarify the impact of several risk factors for nephropathy on the post-operative course. Most studies have investigated the risk factors for nephropathy in patients with CCHD, but few have analyzed the extent of nephropathy after corrective cardiac surgery and its comparison with preoperative valuesIn a cross-sectional study over a period of 8 months (September 2011- April 2012), 30 patients with CCHD who referred to the Pediatric Cardiology Clinic affiliated with Shiraz University of Medical Sciences, and at least 6 months had passed from their corrective cardiac surgery were selected . The stuP<0.05 was considered statistically significant. Statistical analysis was performed using SPSS, version 16. The parametric variables were presented as mean±SD and analyzed by paired t-test and Pearson correlation test as appropriate. Chi-square was used for non-parametric variables. The study population comprised 30 patients with CCHD with a mean age of 11.47±6.7 years. The mean age at the time of surgery was 7.16±4.93 years and the mean duration of follow up after cardiac surgery was 5.3±1 years. Fifteen patients were diagnosed as Tetralogy of Fallot and underwent total correction, 8 had pulmonary atresia and ventricular septal defect, in whom total correction with homograph was done. The remaining 7 patients who had double outlet right ventricle and pulmonary stenosis had also underwent total correction with homograph.P=0.001, r=0.58). Pre- and post-operative GFRs were not significantly different . Pre-operation GFRs were as follows: 41% had GFR>90, 53% 60-90, and 6% <60%. After  There was a significant decrease in hematocrit after cardiac surgery  . corrective surgery, these figures changed to: GFR>90 in 76%, 60-90 in 18%, and <60 in 6% of the patients. Final GFR was significantly and inversely associated with pre- and post-operation age (r=-0.38) . Three (P=0.001)  . The meaP=0.01 r=-0.44). There was no relationship between FEua and age, serum uric acid, and GFR .Pre-operative HCT was inversely associated to FEua  after cardiac surgery. It seems that reduction of GFR prior to operation is related more to the hemodynamic changes in glomerulus rather than structural derangements. In agreement with the result of our study, Awad et al showed a significant improvement in glomerular and tubular functions after palliative cardiac surgery in children with CCHD[11]. Severe hypoxia and secondary erythropoiesis can affect renal function through failure of maximum compensatory hyperfiltration to overcome the reduction of renal plasma flow. It has been shown previously that reduction in hematocrit is accompanied by an increase in renal blood and plasma flow, and a decrease in efferent glomerular arteriolar resistance.  Our study revealed that more than half of the patients had GFR lower than 90cc/min/1.73m. In Martinez et al.’s study, the majority of the adult patients had GFR lower than 90 cc/min/1.73m2, but the proportion with GFR lower than 60 was higher than that of the present study (23% vs 6%)[14]. Dittrich et al identified that the duration of cyanosis is one of the major risk factors for the development of glomerulopathy, and the risk rises sharply during the second decade of life in patients with CCHD[10]. Our results were in accordance with the mentioned study in that 86% (6 out of 7) of children with more than ten years CCHD, had GFR 60-90 and 14% had GFR less than 15[1]. Our study revealed that older children had more renal impairment in comparison with younger patients. Therefore, the present study is supported by other reports indicating that duration of cyanosis is one of the most important predisposing factors for renal dysfunction. Krull et al reported proteinuria in 44% of patients with CCHD mostly in the second decade of life, and only one of nine children under 10 years of age had microalbuminuria[15]. Akita et al assessed 16 patients with CCHD and documented proteinuria and albuminuria in the six oldest patients (aged 15-28 years)[16]. Zheng et al investigated glomerular and tubular damage in 58 children ≤3 years and despite showing higher normalized microalbumin in children with CCHD in comparison to the control group, only one of the children with severe cyanosis had glomerular injury[17]. These studies along with the present study reiterate that the microalbuminuria as a marker of glomerular injury does not commonly occur in early stage in children with CCHD; therefore, patients with CCHD might be followed by microalbuminuria, at least after the second decade of life.  In addition to hemodynamic changes, longstanding cyanosis can proceed to structural damage including tubules and glomerules. One of the early markers of glomerular damage is microalbuminuria. There is no data related to preoperative microalbuminuria, but 10% (3 out of 30) of our patients had microalbuminuria after surgery and all of them were more than 10 years old. No association between microalbuminuria and duration of cyanosis was found, which might be due to the younger age of our patients (mean age 7.16±4.93 years) in comparison to other reports[18-20]. Second, the reduction of peritubular blood flow secondary to hyperviscosity might be responsible for the increase in intra-glomerular pressure and the resulting proteinuria[21]. Third, podocyte stress induced by increase in glomerular capillary surface area results in podocyte hypertrophy and consequent dysfunction[22]. What is the cause of microalbuminuria? There are several hypotheses. First, the erythrocytosis of CCHD is accompanied by intraglomerular shear stress and release of nitric oxide (NO), which leads to dilated, engorged, and enlarged glomeruli with selective dilatation of afferent arterioles that increase intraglomerular pressure and alteration of permeability of the glomerular basement membrane and consequent proteinuria[18]. Howenstine et al showed that noncardiac polycythemia such as polycythemia vera and erythrocytosis resulting from intrinsic lung disease can lead to glomerular lesions similar if not identical to the previously mentioned histology[23]. We found that children with higher hematocrit had a significantly lower post-operative GFR than children with lower hematocrit. Although we had no tissue diagnosis to determine the cause of reduction of GFR, Perloff et al have documented that high viscosity can induce endothelial shear stress and resulting NO release, subsequent glomerular enlargement, mesangial cell proliferation and matrix expansion, and subsequent hyalinized glomeruli, atrophic tubules, and interstitial fibrosis. One limitation of the present study was the lack of data on O2 saturation to be able to detect the impact of hypoxia on GFR, but previous studies have confirmed that polycythemia rather than hypoxia is a risk factor for cyanotic nephropathy. According to several studies, tubular injury occurs in the early stage of CCHD[17]. Agras et al detected increased urinary tubular markers in a study population aged 0-13 years within the first decade of life[9]. Zheng et al showed that tubular injury can occur in very early course of CCHD, even before glomerular damage Urinary N-acetyl-β-D-glucosaminidase (NAG) and α1-microglobulin (α1-MG) are commonly used for evaluation of early tubular dysfunction. We could not measure these biomarkers due to our financial limitations; instead, we calculated fraction excretion of uric acid as a less accurate marker of tubular injury. The mean fraction excretion of uric acid was relatively low (8.21± 4.75) and it was, inversely, more closely related to hematocrit rather than to the age, GFR, and serum uric acid. This result is in accordance with the report of Awad et al who demonstrated that hematocrit was significantly correlated with urinary parameters of tubular damage including NAG and α1microglobulin. He also demonstrated that acute changes in renal hemodynamics are the result of acute changes in hematocrit induced by palliative cardiac surgery and can lead to significant improvement of functional and structural tubular integrity.Children with CCHD are at increased risk of renal injury which is related more to the duration of cyanosis and higher degrees of hematocrit level. To lower the risk, corrective cardiac surgery should be done as soon as possible to improve the renal function and prevent further renal impairment.


MFSelector considers various time stages in stage order  and computes DEtotal of each gene. MFSelector can successfully identify genes with monotonic characteristics.Identification of genes with ascending or descending monotonic expression patterns over time or stages of stem cells is an important issue in time-series microarray data analysis. We propose a method named Monotonic Feature Selector (MFSelector) based on a concept of total discriminating error  and embryonic stem cell vasculogenesis (ESCV) data sets. We have also performed extensive quantitative comparisons of the three monotonic gene selection approaches. Some of the monotonic marker genes such as http://microarray.ym.edu.tw/tools/MFSelector/.We have developed a novel system, easy to use even with no pre-existing knowledge, to identify gene sets with monotonic expression patterns in multi-stage as well as in time-series genomics matrices. The case studies on ESCN and ESCV have helped to get a better understanding of stemness and differentiation. The novel monotonic marker genes discovered from a data set are found to exhibit consistent behavior in another independent data set, demonstrating the utility of the proposed method. The MFSelector R function and data sets can be downloaded from:  In many biological experiments, we analyze regulation of gene or protein expression over time and in some other cases we examine how the expression pattern changes as the grade/stage of a disease progresses, including over time.These biomarkers are "Monotonic" because their pattern ascends or descends with time (or stage/grade), important in time-series studies ,2. For eMany approaches are used to find differentially expressed biomarkers from microarray data -8. By stz-score/p-value. Therefore, an approach without statistical assumptions and not affected by outliers, and able to identify the degree of monotonicity between genes with the same z-score/p-value, is needed. Our method proposed herein, MFSelector (Monotonic Feature Selector) based on the total discriminating error , is quite effective in discovering genes with monotonic attributes. It identifies gradually increasing or decreasing genes irrespective of any heterogeneity in the array data. Furthermore, MFSelector, eliminates the subjectivity required in seed/template selection and also provides assessments of confidence . This new approach is user-friendly as we integrate our algorithm into a simple R function. Users with no proficiency in programming can generate a monotonic gene list and related scatter plots.Some methods to discover monotonic expression patterns are correlation-based, where a seed feature or template is chosen to find genes with good correlation. But the choice of the template plays a critical role, and this is time-consuming, requiring experienced bioinformaticians. In addition, the Cuzick-test  can be uhttp://www.bioconductor.org[http://www.r-project.org. See Materials S1 in Additional file All microarray data sets were downloaded from the NCBI GEO public archive, generated in Affymetrix Human Genome U133 Plus 2.0 platform with 54675 probe sets on chips. The raw data (CEL file) were normalized by RMA algorithm using the 'affy' package of the Bioconductor uctor.org softwareThis data set contains 27 samples over five periods of human embryonic development: three embryonic stem cell (ESC) samples, three embryoid body (EB) samples, six primitive ectoderm cell (PEL) samples, six neural tube-like rosette cell samples, and nine post-natal neural stem cell (NSC) samples.In this data set, there are 13 samples over four periods of human embryonic stem cell differentiation into human mature (vascular) endothelial cells: three undifferentiated embryonic stem cell (ESC) samples, three mesodermal progenitor cell (MPC) samples, four embryoid body (EB) samples, and three human mature vascular endothelial cell (VEC) samples. The results and discussion of application of MFSelector to this data set are exhibited in Materials S1  and a set with ascending trends (denoted 'Asc'). These synthetic data sets are named 's50_Asc' and 's50_Des', respectively. In addition, each data set has 120 genes which are classified into 9 types of monotonic genes (or monotonic-like genes): 'Good (distinct)', 'Good (close)', 'Slightly', 'Outliers (slight)', 'Outliers (severe)', 'Moderately', 'Severely', 'Partially ordered (far)', and 'Partially ordered (close)'. There are 20 genes for each of 'Slightly', 'Moderately', and 'Severely' types and 10 genes for each of 'Good (distinct)', 'Good (close)', 'Outliers (slight)', 'Outliers (severe)', 'Partially ordered (far)', and 'Partially ordered (close)'. If most of the samples follow a trend over time/stages but only a few do not, we call those few samples as outliers. In this study the number of outliers for the synthetic data sets is restricted to less than 6% of total samples.Here we use genes with a monotonic ascending trend to illustrate these nine types of genes used in the synthetic data as shown in Figure The 'Good' category has two subcategories, 'Good (distinct)' and 'Good (close)'. 'Good (distinct)' genes indicate they have the strongest monotonic ascending trend and samples have distinct separation between stages; while 'Good (close)' genes indicate they still have the strongest monotonic trend but samples between stages are close. 'Partially ordered' type genes are also further separated into 'Partially ordered (far)', and 'Partially ordered (close)'. The 'Partially ordered (far)' means that the samples in one of the stages are significantly far from the monotonic trend in a gene expression profile while 'Partially ordered (close)' means that the samples in one of the stages are close to the monotonic trend but it is still out of monotonic order in the gene expression profile. The genes of type 'Outliers (severe)' represent genes where at most six percent of the samples are relatively away from the monotonic trend, and type 'Outliers (slight)' indicates that at most six percent of the samples are slightly away from the monotonic trend. The results on these synthetic data sets by our proposed method (MFSelector) and other two methods are presented in the Results section.total , used to identify genes/biomarkers with stronger monotonic features which may bear a correlation to stem cell development. DEtotal does not make any distributional assumption about the data. MFSelector also provides the related statistical information  for each monotonic gene. Moreover, in order to distinguish among monotonic genes with the same DEtotal, MFSelector also offers an additional novel index, called SVDE (sample variance for discriminating error). Users can download MFSelector from the web site: http://microarray.ym.edu.tw/tools/MFSelector/. Figure total, p- and q- values, and SVDE.In this study, we propose a novel tool, Monotonic Feature Selector (MFSelector) which includes a novel index, called DEN stages. For example, when a monotonic gene has an ascending profile, first we assume samples in Stage One have the lower expression values and samples in other stages have higher expression values. We use a sample in Stage One to draw a horizontal discriminating line to determine how many samples in Stage One have higher expression values than the discriminating line and how many samples in other stages have lower expression values than the discriminating line. The number of samples on the wrong side of the discriminating line is referred to as "discriminating errors". Distinguishing Stage One from all other stages is called the "Level One" process. In addition, since every sample in Stage One can be used to draw a discriminating line, we select the discriminating line with the smallest number of discriminating errors for this level. Note that, when more than one discriminating line for Stage One have the same number of discriminating errors, we can choose any one of the lines; here we use the discriminating line corresponding to the lowest sample number. Secondly, again for the same gene, as a "Level Two" process, we assume samples in Stages One and Two have lower expression patterns than samples in other stages. Therefore, we use each sample from Stages One and Two taken together to draw a discriminating line and determine discriminating error as in Level One. When more than one sample from Stages One and Two together result in the same smallest number of discriminating errors, we consider: (a) when the samples are from the same stage, then we select the line (hence the sample) corresponding to the lowest sample number; (b) when the samples are from different stages, we give priority to the lowest sample number from the highest stage, in this case, Stage Two. This entire process is repeated N-1 times, each time adding one stage . The discriminating line is selected in the same manner for each of the N-1 levels . It is interesting to note that, if the number of distinct discriminating lines is equal to N-1, the corresponding gene is more likely to be a good monotonic gene.Here we use several steps to examine genes with monotonically ascending or descending profiles, which are distributed over M process. This outlier is very likely to add a discriminating error in later levels, i.e., "Level M+1" to "Level N-1"). But we count the outlier's discriminating error only once at Level M. We compare the results for the Cuzick-test and ours in the Results section.Our outlier strategy is different from that used by rank-based statistical tests , where an outlier's deviation in expression value influences its rank, often adversely affecting the statistical calculation. MFSelector does not count samples on the wrong side of the discriminating line more than once. Suppose an outlier adds a discriminating error in the Level N-1 times, though in this case, in descending direction. The discriminating line for each level is also selected in the same manner as that for the ascending case.For a monotonic gene with a descending profile, samples in Stage One should have the higher expression values than the samples in other stages. Thus, we can get the "discriminating errors" for "Level One" process by drawing a discriminating line through one of the samples in Stage One to determine the number of samples in Stage One that have lower expression values than the discriminating line and the number of samples in other stages having higher expression values than the discriminating line. As with an ascending profile, this process is repeated N-1 level processes  denoted by "DEtotal". For instance, when DEtotal=k, k discriminating errors exist over N-1 level processes. Here, the smaller DEtotal of a gene, the fewer the number of discriminating errors and the stronger the monotonicity of the gene. DEtotal is an evaluation index to determine monotonic genes. We sort the DEtotal values for all genes in increasing order to select genes with stronger monotonic features for multi-stage and time-series array data. Note that, in this study we separately consider the DEtotal for monotonically ascending or descending cases. In addition, we also develop another strategy using sample variance for discriminating error (SVDE) to further determine the gene with stronger monotonic feature when several genes have the same DEtotal value. This is explained later.In order to evaluate monotonicity of a gene , we use the sum of its discriminating errors over all We now demonstrate our algorithm using a synthetic gene profile with five stages as shown in Figure nd sample in Stage One to draw the discriminating line, resulting in two discriminating errors. In addition, since two discriminating lines  from Stage One have the same number of discriminating errors, we choose the sample with the lowest sample number  and get two discriminating errors in this level.First, for the "Level One" process, every sample in Stage One is used to draw a discriminating line to determine its associated number of discriminating errors . In this case, we obtain 7, 2, and 2 discriminating errors taking each of three samples in order from Stage One to draw the discriminating lines. For example, one sample from Stage One and another sample from Stage Four are on the wrong side of the discriminating line when considering the 2th sample from Stage One and Two) and get no discriminating errors in this level.Second, for the "Level Two" process, every sample in Stages One and Two is used to draw a discriminating line to determine its associated number of discriminating errors. In this level, we obtain 3, 3, 4, 0, 2, and 1 discriminating errors taking each of six samples in order from Stages One and Two to draw the discriminating lines. Note that, to compute the discriminating errors for the "Level Two" process, we do not consider the samples which have already caused discriminating errors in "Level One". Such samples are masked pink in Figure th sample is selected as the discriminating line because its discriminating error is the lowest, and it has the lowest sample number of the two Level Three samples with the same discriminating error of one.Third, for the "Level Three" process, every sample in Stages One, Two, and Three is used to draw a discriminating line to determine its associated number of discriminating errors. We get 3, 9, 10, 6, 8, 7, 2, 4, 5, 1, 3, and 1 discriminating errors taking each of 12 samples in order from Stage One to Stage Three. The 10th sample with no discriminating error. Finally, we add up all discriminating errors for each selected discriminating line from every level and get the DEtotal = 2 + 0 + 1 + 0 = 3.Similarly, the process is continued for the "Level Four". In this case we determine the 16total index associated with the identified genes in ascending and descending profiles, a permutation test has been performed in Figure p-values and adjusted q-values for multiple comparisons are computed as in our previous studies [G be the total number of genes and S be the total number of sample points. The procedure followed is summarized below.To assess the statistical significance of the DE studies ,8. Let GX  with class labels , we compute the DEtotal,g for ascending case and denotes it by g afor notational simplicity. Similarly, for the descending case also we compute DEtotal,g and denote it by gd.Step 1. Given a gene expression matrix s yB times (500 times in this study). In the th bpermutation (1 ≤ b ≤ B), compute g using the gene expression matrix X and the permuted labels Step 2. Randomly permute the class labels p-value of the observed DEtotal,g with ascending characteristic, ga, for gene g isStep 3. The I(·) is an indicator function that takes the value one when true and takes the value zero when false. Similarly, the p-value of the observed DEtotal,g with descending nature, gd, iswhere G genes, q-values of the observed g aand g dare calculated asStep 4. To account for the multiple tests being performed for the andtotal may exhibit different monotonicities. Therefore, we develop SVDE to address the degree of monotonicity of a gene. This can also help to differentiate between genes with the same DEtotal value.Statistical tests are unable to distinguish which genes with the same level of statistical significance are better. Two genes with the same DELOC100506013 and FAM60A are monotonically descending genes and have the same DEtotal = 0  and of LOC100506013 from Stages One to Four are highly distinguished, and only the expression values of the samples from Stages Four and Five are somewhat close. For these two genes with the same DEtotal, LOC100506013 should have a higher degree of monotonicity , all samples for each of the genes are slightly altered in expression values to examine whether the DEtotal of the altered expression values has changed significantly or not. To evaluate this, we propose an index, called Sample Variance for Discriminating Error (SVDE). We perturb a dataset and evaluate the extent of confidence on the monotonicity properly by adding noise to all samples , and get M new DEtotal values for each gene. We denote the new DEtotal value as the DEi, i = 1, 2, ..., M. Next we compute the variance of these DEi values with respect to original DEtotal for this gene. We denote the original DEtotal as DEorg. Hence for these new DEtotal values we can calculate the variance asTo perturb a dataset with total values are spread around the original DEtotal (DEorg). If each DEi is equal to or close to DEorg, the SVDE will be very small. Figure total of a highly confident monotonic gene even after randomly altering the expression values of all samples. The smaller the SVDE, the stronger the monotonicity of the gene. Figure total is equal to zero, but the SVDE is high. The reason is that separation between adjacent stages for Stages One to Four is not sufficiently distinct. Consequently, genes with a smaller SVDE can be considered more strongly monotonic than genes with a larger SVDE.The SVDE is a measure of how far the set of the new DEOne may think that the time interval between observations should be given importance in defining any index for finding such stemness markers. This is not so because here our objective is to discover monotonic stemness marker genes which are associated with stages of stem cell differentiation. These stages are clinical stages which depend on pathology/clinical phenotypes and are not defined taking observations with arbitrary/equal time interval, but the biological process here dictates the time interval between observations. However, our method would be equally applicable to other experimental scenario where the researchers design experiments to take observations with equal time interval for some scientific reasons. It does not matter if the required time interval is large or small.n be the total number of samples from all classes, i rbe the rank of the th isample determined by the order of its expression value among all samples, N be the number of stages, and i pbe the proportion of samples from class i. Each stage has a weight kw, k = 1,...,N. We associate a weight i zto a sample i, i z= jw, if the th isample is from the th jstage. The Cuzick statistic is computed asIn order to further validate the ability of our method to identify monotonic genes, we have made a comparison with the Cuzick-test , an extewherei w= i, i = 1, ..., N; while for descending genes, we use i w= N-i+1, i = 1, ..., N. The Cuzick statistic above is obtained as a z-score, hence, we can determine a p-value for each gene and identify whether a gene is monotonic and the extent of its monotonicity  by referring to the z-score table. In this study, we compare the performance of the Cuzick-test approach and our MFSelector approach (shown in the Results section).To find ascending genes, we use K stages, respectively. The modified M statistic test and several other statistical tests are further integrated into an R package called IsoGene [We have also performed a comparison with the modified M statistic test . The mod IsoGene . Howevertotal or p-value in ascending order to identify those genes with stronger monotonic patterns, and decide the threshold for the gene list based on monotonicity. In addition, we further sort these monotonic genes with the same DEtotal values according to their associated SVDE. The resulting gene list is fed into the web service tool DAVID Bioinformatics Resources http://david.abcc.ncifcrf.gov/ to identify correspondingly enriched biological processes by cross-referencing to the gene ontology database http://www.geneontology.org/.After getting the list of monotonic genes, we can sort them by DEAs mentioned in the Materials and Methods section, we use two microarray data sets, i.e., embryonic stem cell neurogenesis (ESCN) and embryonic stem cell vasculogenesis (ESCV), to demonstrate the effectiveness of our algorithm in identifying monotonic genes during different stages of stem cell differentiation. The results of application of MFSelector to the ESCV data set are exhibited in Materials S1  clearly distinguishes embryonic stem cells (ESCs) from post-natal neural stem cells (NSCs). It also shows that embryoid bodies (EB), primitive ectoderm cells (PEL) and neural rosette cells are differentiated along the neural lineage as evidenced by moving toward post-natal neural stem cells. Figure S2 , we get 857 ascending and 1,117 descending monotonic genes. The lists of these genes and correlated gene information are shown in Table S1 . Since there are too many monotonic genes whose p-value is less than 1.0E-5, we illustrate approximately one hundred top ranked ascending and descending genes from Table S1  are delineated in a heatmap in Figure total order. The gene expression values change gradually from the blue band  into the red band  in Figure By applying our algorithm for the ESCN data set, we create gene lists for the ascending and descending nature respectively and sort these genes by the DEPNMA2, one of the top three ascending monotonic genes with DEtotal = 0 for the ESCN data set. For PNMA2, the samples from each stage are well distinguished from the samples from other stages sequentially because there is no discriminating error for every level of the process. A preliminary study indicates that PNMA2  is homologous to a recently cloned gene, MA1, which is a novel neuron- and testis-specific protein, and is recognized by the serum of patients with paraneoplastic neurological disorders [PCDH9 and NPAS3) also have correlation with neuronal receptor and neurogenesis [SOX1 , a famous marker for neural lineage cells [Biomarkers for a specific cell type exhibit high expression values when the stem cell is differentiated to this cell at the later stage of differentiation. This is a kind of stemness markers. Figure isorders . Anotherogenesis ,22. Hencge cells .DNMT3B, one of the top 12 descending genes with DEtotal = 0. Here, samples from all stages are also well separated by discriminating lines for each level. DNMT3B is associated with embryonic stem cell development [EPCAM and DPPA4) [Similarly, there are another kind of stemness markers which exhibit high expression at early stages of development and are monotonically descending during embryonic stem cell differentiation into the other cells/tissues . Figure elopment . Some ofd DPPA4) ,26. Thustotal <= 3  in the ESCN dataset are reported in the literature to be related to some stem cell characteristics, including stemness, differentiation, reprogramming, or induced pluripotent stem cell (iPS). Here we find that 54 (40%) monotonically descending genes related to some stem cell characteristics: stemness (44 genes), reprogramming (6 genes), and iPS (4 genes). Thirty-four (25%) genes are related to differentiation and some of them are related to embryogenesis. We could regard some of identified descending genes as stemness or embryo biomarkers. On the other hand, 30 (31%) monotonically ascending genes are found to be related to differentiation and most of them are related to neurogenesis . We could also regard some of identified ascending genes as biomarkers of specific cell types in the differentiated cells. Please see Table S2  ascending genes and 17 (12.5%) descending genes are likely to have bi-stable switches. In the Table S2 . These four genes are distinguished by the SVDE values obtained by adding noise to the expression value and repeating the process 100 times. Figure SOX6, with SVDE = 0.37, is the most monotonic gene compared to the other three genes in Figure total is not easily changed  after adding noise to each sample. Figure STMN4 with SVDE = 0.91 is the second most monotonic gene, because the expression values of two samples, one from Stage Three and another from Stage Four, are very close. Therefore, the number of misclassified samples  for STMN4 is changed more frequently than SOX6 during the 100 experiments after adding noise to each sample. Visual inspection of the figures also suggests that STMN4 is the next monotonic gene in the list of four. Figure ARID5B with SVDE = 2.03 is the third most monotonic gene. This is indeed the case because every two adjacent stages contain samples which have close expression values. Finally, Figure SCD5 with SVDE = 2.95 the least monotonic of the four genes. A careful inspection of the figures also reveals the same and this is so because samples from Stage Three and Stage Four have expression values which are too close to avoid misclassification during the SVDE process.To differentiate genes with the same DESince the Cuzick-test can find many monotonic genes with the same rank, for preliminary comparison we have decided to use ascending genes with rank up to 20 as determined by the Cuzick-test as an example. For Cuzick-test, the number of genes selected with ranks 1~20 is 145. Then we use the top 145 monotonic ascending genes identified by each of the other methods, to find the number of common and unique identified genes. From Table S3  are out of the monotonic trend. Figure S3(A) and (B)  by examining whether we can determine their N-1 distinct discriminating lines.First, although the Cuzick-test can identify monotonic genes, the Cuzick-test results contain some non-monotonic genes  at or near the top of the gene lists. Figure S3 . Actually, many monotonic genes ranked by the Cuzick-test have the same p-value. For example, all of those genes with DEtotal = 0 always belong to the Cuzick-test top level. Figures S4(A) and (B)  and (D)  and both are ranked 10th in the list generated by the Cuzick-test.Second, MFSelector uses SVDE to further determine different levels of monotonicity of genes with the same DEZNF302 is 164th in the list generated by MFSelector, but is 105th  in the list generated by the Cuzick-test because two samples from Stage One and Four, respectively, are significantly distant from its stage . This situation arises because this gene's ranking is significantly affected by the weight assigned to the anomalous expression value for these samples from Stage One and Four, causing the poor ranking for this gene under the Cuzick-test. Figure S5(A)   by examining the number of distinct discriminating lines. Therefore, genes having slight/severe outliers or having partially ordered patterns with the level 'far' or 'close' should be given the similar significance/rank. For the synthetic data set, we find that the ranks of the pseudo genes g46 (with slight outlier characteristics) and g53 (with severe outlier characteristics) discovered by MFSelector are not different  but their ranks are significantly different for the Cuzick-test and the modified M statistic test. The ranks of the pseudo genes g102  and g111  identified by MFSelector are also not different  but the ranks suggested by the Cuzick-test and the modified M statistic test are significantly different ' (20 genes), 'Slightly' (20 genes), and 'Outliers (slight/severe)' (20 genes), and that is what MFSelector does. The results using the Cuzick-test are the approximately the same as that by MFSelector, but the modified M statistic test always selects about fifteen percent of genes in the type 'Partially ordered' which are worse cases and are out of monotonic trend , NANOG, and BLBP (FABP7)  is a well-known transcription factor for maintaining and introducing stemness into embryonic stem cells [POU5F1 is also important for pluripotency of embryonic stem cells [NANOG , is a well-known transcription factor critically involved with self-renewal of undifferentiated embryonic stem cells, and BLBP  is a neuroepithelial progenitor marker [BLBP is always expressed during development in radial glia by the activation of Notch receptors [BLBP is usually induced in neural progenitor cells via Notch-1 activation [HES5 with some ascending monotonic characteristics. This is a neuroepithelial progenitor marker [HES5 has been characterized as a monotonic ascending gene by their microarray data analysis, but in our study, Figure HES5 expression for stages 1-4 is up-regulated and it is down-regulated for stage 5. Our finding is consistent with that of the previous study [HES5 it has a very high DEtotal = 15. In future studies we may consider redefining DE values to include partial monotonicity.Among the top ascending and descending monotonic genes for the ESCN data set  that can serve as markers for human embryonic stem cells and may also contribute to the stemness phenotype. Of particular interest in that study is the strong monotonic descending pattern of DNMT3B  in our study during embryonic stem cell differentiation. LIN28A is without N-1 distinct discriminating lines because its expression is tightly grouping from Stage One to Stage Three. It has a small number of discriminating errors  though. Additional transcription factors that were also highly expressed in human embryonic stem cells include BTF3 and ERH. These genes are marker genes for embryonic stem cell, which show high expressions only in human embryonic stem cells [ERH over different stage is not clearly separated and is not monotonically descending during the neurogenesis process ). We make a hypothesis that ERH does not clearly exhibit monotonic expression during neurogenesis even though it is an embryonic stem cell specific marker gene. This new biomarker needs to be surveyed and studied further both in wet- and dry- laboratory experiments.Another research  has alsoem cells . We depiem cells . HoweverThe genes expressed in an early stage of stem cells or in undifferentiated cells (or precursor cells) of stem cells are often regarded as stem cell biomarkers, which are thought to maintain the pluripotency of embryonic stem cells. Based on the concept of pluripotency, cell growth or proliferation and the self-renewal activity are the most representative characteristics of stem cells which are known to be sustained by multiple genes in both stem cells and precursor cells . DiffereLogically, the differentiation program of stem cells and precursor cells is not only driven by gene regulation but also manipulated by the circumstances of differentiation . Combinahttp://david.abcc.ncifcrf.gov/. This helps us find distinct genes expressed in certain organogenesis with different processes.To validate our inferences, we corroborate the biological processes for those monotonic genes identified from the two data sets by Gene Ontology analysis on the DAVID web tool total = 0~7) found by MFSelector are subjected to Gene Ontology analysis. Some of the biological processes those genes are involved in are neuron differentiation , regulation of neurogenesis , regulation of nervous system development , regulation of neuron differentiation , neuron development , neuron projection development , cell morphogenesis involved in neuron differentiation , axonogenesis , neuron projection morphogenesis , and regulation of axonogenesis . These biological processes very likely play important roles in differentiation of ESC neurogenesis and the development of the organs or the tissues of the nervous system. There are other ascending genes involved in neurotransmission, such as regulation of axon extension , axon guidance , transmission of nerve impulse , and neuron migration . These monotonic genes directly indicate their importance during the development of the nervous system and the process of neurogenesis.For the ESCN data set, the top 857 ascending monotonic genes  found by MFSelector are involved in basic DNA/RNA biological processes, such as translation , RNA processing , ribosome biogenesis , ribonucleoprotein complex biogenesis , rRNA processing , and ncRNA metabolic process . According to the common understanding about the characteristics of undifferentiated or early stage stem cells, basic cellular processes are crucial for maintaining the capacity of self-renewal and proliferation. In addition, these monotonic genes may be responsible for the basic metabolisms and the stability of chromosome structures in cells. Proliferation of cells must undergo the process of cell cycle, and genes involved in the mechanism of cell cycle are able to imply the progress of proliferation. In conformity with this, we notice that genes for M phase , DNA replication , M phase of mitotic cell cycle , mitotic cell cycle , nuclear division , mitosis , cell cycle process , and cell cycle phase  are in the descending monotonic list. This evidence suggests that the stem cell features in the early stage exist during neurogenesis.Similarly, some of the top 1,117 descending monotonic genes (DEPOU5F1 (Oct4)), while many other genes have not been linked to stem cell neurogenesis or vasculogenesis before. In the ESCN and ESCV data sets monotonic features could be found even from heterogeneous gene expression profiles. In addition, we have used monotonic markers discovered from one data set to analyze another data set and obtained very interesting results. An R package implementing our algorithm and data sets can be found at: http://microarray.ym.edu.tw/tools/MFSelector/.We have developed a novel and robust scheme to identify genes with monotonic patterns in multi-stage as well as in time-series genomic data. Our method is based on a concept of total discriminating error practically without requiring any assumption. Using our proposed scheme we have been able to reveal genes with gradually increasing or decreasing expression patterns during stem cell differentiation. Some of these genes are known stemness genes  of the ESCN data set. The DEtotal is four after running a simulation with added noise.Figure S1. Illustration of adding noise to original expression values of 223038_s_at  identified by MFSelector along with information from the literature in support of the facts that those genes are related to some stem cell characteristics, including stemness, differentiation, reprogramming or induced pluripotent stem cells.Table S2. Details for the top monotonic genes (DEClick here for fileTable S3. The lists of the number of common or unique genes from the monotonic ascending gene set (the top 145 genes with ascending profiles) of the ESCN data set identified by MFSelector, the Cuzick-test, and the modified M statistic test.Click here for fileTable S4. The lists of the number of common or unique genes from the monotonic descending gene set (the top 163 genes with descending profiles) of the ESCN data set identified by MFSelector, the Cuzick-test, and the modified M statistic test.Click here for fileDAZAP2); (B) 229824_at (SHC3); (C) 206424_at (CYP26A1); (D) 209122_at (PLIN2).Figure S3. Scatter plots of the four false positive monotonic genes identified by the Cuzick-test from the ESCN data set. (A) 200794_x_at  1559280_a_at (LOC100506013); (B) 223000_s_at (F11R); (C) 230896_at (BEND4); (D) 202234_s_at (SLC16A1).Figure S4. Scatter plots of the four monotonic genes with the same DEClick here for fileEFNB2); (B) 228393_s_at (ZNF302).Figure S5. Scatter plots of the two monotonic genes for the ESCN data set ranked low by the Cuzick-test but high by MFSelector. (A) 202668_at (Click here for fileKIAA1715); (B) 226907_at (PPP1R14C); (C) 229126_at (TMEM19); (D) 244040_at (KCNN3).Figure S6. Scatter plots of the four ascending monotonic genes from the ESCN data set ranked high by the Cuzick-test but low by MFSelector. (A) 225717_at (Click here for fileARHGEF5); (B) 201930_at (MCM6); (C) 219786_at (MTL5); (D) 225359_at (DNAJC19).Figure S7. Scatter plots of the four descending monotonic genes from the ESCN data set ranked high by the Cuzick-test but low by MFSelector. (A) 204765_at  of the ESCN data set identified by MFSelector and the modified M statistic test, respectively. (A) The top hundred monotonic ascending gene set chosen by MFSelector; (B) The top hundred ascending gene set chosen by the modified M statistic test.Click here for fileFigure S9. Heatmaps of the monotonic descending gene set (the top 100 genes with descending profiles) of the ESCN data set identified by MFSelector and the modified M statistic test, respectively. (A) The top hundred monotonic descending gene set chosen by MFSelector; (B) The top hundred descending gene set chosen by the modified M statistic test.Click here for fileTable S5. The lists of the ranks of monotonic genes for the synthetic data sets identified by MFSelector, the Cuzick-test, and the modified M statistic test.Click here for fileTable S6. The list of the number of top genes identified by MFSelector, the Cuzick-test, and the modified M statistic test, in each type of monotonic genes of the synthetic data sets.Click here for fileDNMT3B); (B) 219823_at (LIN28A); (C) 214800_x_at (BTF3); (D) 200043_at (ERH).Figure S10. Scatter plots of the four genes of the ESCN data set reported in the previous study (A) 2206Click here for file


Toxoplasma gondii, Herpes simplex virus type 1, Cytomegalovirus, Human Herpes Virus 6 and the food antigen gliadin as well as measurements of C-reactive protein (CRP), a peripheral marker of inflammation. The subjects are SZ cases, BP cases, parents of cases and screened controls. We look for higher levels of our immunity/infection variables and interactions between them and common genetic variation genome-wide. We find many of the antibody measurements higher in both disorders. While individual tests do not withstand correction for multiple comparisons, the number of nominally significant tests and the comparisons showing the expected direction are in significant excess (permutation p=0.019 and 0.004 respectively). We also find CRP levels highly elevated in SZ, BP and the mothers of BP cases, in agreement with existing literature, but possibly confounded by our inability to correct for smoking or body mass index. In our genome-wide interaction analysis no signal reached genome-wide significance, yet many plausible candidate genes emerged. In a hypothesis driven test, we found multiple interactions among SZ-associated SNPs in the HLA region on chromosome 6 and replicated an interaction between CMV infection and genotypes near the CTNNA3 gene reported by a recent GWAS. Our results support that inflammatory processes and infection may modify the risk for psychosis and suggest that the genotype at SZ-associated HLA loci modifies the effect of these variables on the risk to develop SZ.Inflammation and maternal or fetal infections have been suggested as risk factors for schizophrenia (SZ) and bipolar disorder (BP). It is likely that such environmental effects are contingent on genetic background. Here, in a genome-wide approach, we test the hypothesis that such exposures increase the risk for SZ and BP and that the increase is dependent on genetic variants. We use genome-wide genotype data, plasma IgG antibody measurements against  Schizophrenia (SZ) and bipolar disorder (BP) are debilitating chronic psychiatric diseases, each affecting approximately 1% of the world’s population. Both disorders are clinically and etiologically heterogeneous. Studies have demonstrated significant heritability estimated to be around 80% ,3 therefGWAS have now begun to identify specific variants and genes that increase the risk for SZ  and poinToxoplasma gondii (TOXO), Herpes simplex virus type 1 (HSV1), cytomegalovirus (CMV) and human herpes virus 6 (HHV6) [Infection and immune response have been studied in SZ across two centuries , and thr6 (HHV6) . In more6 (HHV6) . The div6 (HHV6) . Additio6 (HHV6)  includin6 (HHV6)  and pati6 (HHV6) . In addi6 (HHV6) , includi6 (HHV6) –23, alth6 (HHV6) . The inv6 (HHV6)  but, to 6 (HHV6) . That stThe most recent published SZ GWAS has now reported on over 100 SZ-associated loci . The mosThe Epidemiology-Genetics program in psychiatry (EpiGen) at Johns Hopkins University under the leadership of AEP has been collecting individuals affected with SZ and BP and their families for the last 30 years. Since 1996, recruitment has focused on Ashkenazi Jewish (AJ) individuals in the U.S affected with SZ or BP, their families and screened controls. In addition to the extensive information available for the research participants, plasma collected at the time of examination was available for a significant fraction of this sample. Genome wide genotype data was also previously obtained and available. Here we report on our analyses of the plasma of these individuals for anti-TOXO, anti-HSV1, anti-HHV6, anti-CMV and anti-GLD, as well as for CRP. For details on each measurement see Subjects included research participants with a diagnosis of SZ (including schizoaffective) or BP diagnosis recruited over a 15-year period (1996–2011) through advertisements, talks, letters to leaders service providers of the Jewish community and a study web site. The patients were interviewed in-person and diagnosed through a consensus procedure described in detail elsewhere ,31. ApprThe Johns Hopkins institutional review board approved the recruitment methods, protocols and informed consent documents. All participating human subjects provided written informed consent to participate in this study. If the subject was a minor, written informed consent was obtained from both the subject and his/her parent or legal guardian (if subject was age 15–18) or written informed consent was obtained from the parent or legal guardian and an assent procedure was completed with the subject. (if the subject was under age 15). If the subject was not capable of consent, written informed consent was obtained by a legal guardian.For the current study we had plasma samples and successfully obtained antibody (Ab) and CRP data (which we refer to collectively as serology data) for 580 AJ SZ probands, 262 fathers of SZ probands, 266 mothers of SZ probands, 489 AJ BP probands, 314 fathers of BP probands, 314 mothers of BP probands, and 362 AJ controls.We measured plasma IgG class Abs anti-HSV1, anti-HHV6, anti-CMV, anti-TOXO, and anti-GLD using previously described immunoassay methods . BrieflySZ and BP cases, parents and controls were randomly distributed on 32 plates. Ab in the plasma specimen was quantified by the measurement of colorimetric substrate by means of a microplate colorimeter and converted into a ratio by dividing the amount of color generated in the sample wells by the amount of color generated from reaction with a weakly positive sample provided by the manufacturer. For comparison of quantitative results among the different Ab assays, this ratio was standardized to a value of 1.0 on each microtiter plate.2 transform of each of the 6 assay variables, and residuals from each were saved for analysis. The density plots for all residuals are shown in Data for analyses included 2660 records of subjects’ plasma sample assay results. One of the 32 plates showed significant measurement distribution differences from the rest and was excluded as a technical failure. The R Statistical software package “lme4” was used to run linear mixed effect models on the 6 assay variables controlling for the effects of assay processing plate and plasma storage years (with plate as the random effect and storage years as the fixed effect). Assay variable values of zero were removed as failed assays, the model was applied to the logwww.bioconductor.org) package, implements a multilevel model for genotype calls that adjusts for batch effects, avoiding biases and errors from processing different batches of samples at different times.DNA from blood was extracted with the Gentra Puregene Kit or the QIAGEN DNeasy Blood and Tissue Kit. Genotyping was performed with the Affymetrix Human Genome-Wide SNP Array 6.0 at Emory University and has been previously described . Genotyp-6 to account for the multiple tests. We further excluded SNPs with minor allele frequency < 0.05 as underpowered in our relatively small sample, likely to introduce artifacts in the presence of even small deviations of the traits from normality. The final dataset included data on 516,638 SNPs for 460 SZ cases, 397 BP cases and 241 controls with serology data.Genotype data cleaning was performed using the software package PLINK . We follStatistical analyses were performed using R. The serology outcomes were first tested for correlations with sex and age at the time of blood draw. As these variables, and in particular the age at the time of blood draw, showed significant correlations with multiple measurements they were included as covariates in all further analyses. Comparisons between case control and parent groups were made using generalized linear models with serology as the outcome and predictors that included group status, age at blood draw and sex in linear or logistic models depending on the outcome variable.GWAS analyses were performed using PLINK. Gene x infection interaction tests were performed with the respective disease phenotype (SZ or BP) as outcome and genotype, sex, age at blood draw, serology result and the genotype x serology interaction factor as predictors. The results for the interaction factor were then explored for significant signals. The results for associations of genotypes with the disease phenotype will be reported separately.Permutation tests to determine the significance of the excess of signals and their direction were performed using scripts in perl and followed by analysis in R under identical parameters as the primary analysis. The scripts randomized the link between "status"  and Ab variables keeping the parameter "age at blood draw" linked to the Ab variables, where it is relevant. Specifically the data table was separated vertically in two, one retaining the Ab variables together with age at blood draw and the other the "status". One of the two sub-tables was randomly re-ordered and they were merged again for analysis. Additionally, because sex is relevant to both the Ab variables and status before the randomization described above we separated the dataset horizontally into male and female subsets and merged it again before analysis, thus performing a within-sex randomization where a females' Ab measurements always come from other females and all status categories retain their sex distribution. We performed 3,000 permutations to test the significance of signal enrichment in -9 would be necessary to declare significance. In comparing the case and parent groups with controls . We also found a trend for lower levels in males, however this was only statistically significant for anti-HHV6 and anti-CMV (p = 2.45x10-10 and p = 0.016 respectively). Sex and age at blood draw were subsequently used as covariates in all analyses.We first investigated the effects of the age of the individual at the time the blood sample was drawn and of the subject's sex on the Ab and CRP measurements. For this analysis we used the entire sample correcting for diagnostic category or parent status. We found a strong positive correlation with age at the time of blood draw for all the measurements with the exception of anti-HHV6 where a strong negative correlation was observed  than controls for any of our serology measurements. Our results are summarized in In contrast to the individually modest results for infectious agents and gliadin, the comparisons for CRP showed highly significant differences . CRP levWe performed a genome wide association analysis for interactions between each plasma variable and genotype by including an interaction term in the logistic regression model. The aim of this GWAS was not to identify loci predisposing to SZ or BP, for which we knew the sample size was underpowered, but to identify genetic variants that modify the relationship between infection or immune reaction to an antigen and the risk for psychosis. While the effect sizes of common risk variants is expected to be small, due in part to the negative selection of stronger effect alleles, this might not be the case for interactions. The results on the interaction terms are shown in -5 for anti-CMV and anti-HSV1 in both disorders and for anti-TOXO in SZ, shown in -5 under the null hypothesis.None of the 6 tested variables in either disease phenotype provided a genome wide significant result after accounting for multiple testing. However, we identified suggestive associations at p < 10We examined in our GWAS results the SNP rs7902091 recently reported to show interactions with CMV in the only other published genotype by infection interaction GWAS for SZ by Borglum et al . In our -8) from the largest meta-analysis recently reported by the PGC [Due to the importance of HLA in immune responses and the strong associations of DNA variation in the HLA region with SZ, we explored these SZ-associated variants in our data for evidence of interactions between genotype and Ab titer or positivity. We selected the SZ-associated markers (p < 10 the PGC  and idenCRP gene whose genotype influences CRP levels [-4). The same SNP showed no association with SZ in the PGC or in our dataset, or interaction with CRP in our dataset.A recent GWAS has identified a strong signal close to the P levels . We testIt must be noted that another interesting candidate that we did not examine is the IgG1 heavy chain locus on chromosome 14 whose allotypes have been associated with both HSV1 and gliadin ,40. UnfoWe tested the hypothesis that there are increased rates of infection and inflammation in patients with SZ or BP and their parents, which might suggest a role in disease. While individual tests were underpowered for reliable individual comparisons, the excess of nominally significant results and the almost consistent direction toward higher levels of seropositivity or Ab titers in patients and their parents support for this hypothesis. The increased seropositivity in the parents might either reflect a shared family environment or a genetically driven increase in susceptibility to infection, or Ab production, persistence or affinity.Possible reasons for the reduced power to support individual infectious agents possibly include small sample size and perhaps noise introduced by the interval between the blood draw and the presumed relevant time point. Infection is most likely to be important during gestation, perinatally, or close to the disease onset ,41, rathThe strongest results came from the comparisons of CRP levels and agree with previous studies, including studies of drug free patients ,42,43. NIn this study we confirmed the reported association of SNP rs2794520  with CRPSGK1 on chromosome 6, far from the HLA region, which emerged for an interaction with anti-TOXO. It encodes an mTORC2-dependent regulator of the differentiation and function of T cells [NFIL3 on chromosome 9 and anti-CMV titers is intriguing. This gene encodes for an interleukin 3 regulated transcription factor known as E4BP4 thought to act downstream of IL-15 signaling [CLTA coding for Clathrin Light Chain. Clathrin is a major player in endocytosis, important both for neuronal and immune cells [Our genome wide analysis for interactions between infection and genetic variation provided modest results, not reaching genome wide statistical significance. The top hits, however, likely contain true signals, particularly those within or near genes of strong biologically plausibility. With regard to interactions increasing the risk for SZ, the most interesting is  T cells , which a T cells  and acts T cells . With reignaling . Nfil3-dignaling . Its expignaling  and it hignaling , making ne cells  and likeCTNNA3 locus first reported by Borglum et al [While not all these signals are true positives and some of the functional evidence is likely coincidental, it is intriguing that many identified regions contain genes important for both the nervous and the immune system. Our goal in reporting these interactions is not to claim the discovery of variants interacting with inflammation or infection to cause disease, but to trigger replication attempts in additional samples. In the same line, we provide the first replication of a genotype by infection interaction locus in SZ, the interaction with CMV infection at the um et al . It shouum et al  gene-envThe link between infection and SZ is further strengthened by the multiple interactions we observed between HSV1 seropositivity and SZ risk alleles in the HLA region. We find multiple significant interactions with SZ-associated SNPs and our permutations suggest that they are significantly more than the null expectation and not solely due to LD, a result that easily withstands correction for the number of tests. These SZ-associated SNPs span 3.8 Mb and include multiple histone genes. Although SZ-associated SNPs were tested across the HLA region (25.4–33.5 Mb on chromosome 6), the interaction signals stop 50 Kb short of the first HLA gene, HLA-F at 29.7 Mb. As only 9 of the 116 SZ-associated SNPs overlapping between studies were located after 29.7 Mb, it is unclear whether this result should be interpreted as pointing to the specific sub-region or a consequence incomplete testing beyond that location.In this manuscript we support the possible role of infection/inflammation in BP and SZ and we report on a GWAS for interactions with genetic variation. Further, we replicate a reported GWAS signal for CRP levels and another for an interaction between CMV infection and SNP rs7902091. Finally, we find that multiple SZ-associated SNPs in the HLA region show interactions with HSV1. These results are important and encouraging. The low statistical power of individual tests does not allow pointing to specific antibodies and the estimated effect sizes should be interpreted with caution. The results instead make evident the need to study the role of infection and inflammation in SZ and BP. Further explorations to that end could include modeling the genetic overlap between SZ and BP as it relates to infection and multivariate analyses. Further collecting materials at birth or at onset when possible, and developing large datasets through collaborative consortia would be instrumental to appropriately address these questions.S1 Dataset(TXT)Click here for additional data file.S1 Dataset Info(TXT)Click here for additional data file.S1 FigThe software Haploview was used to generate this image and the color and numbers in the diamonds are the r-squared between pairs of SNPs. The 46 SNPs that showed interactions at p<0.05 are marked with a red dot (more details are shown in (TIF)Click here for additional data file.S1 Tablebp location corresponds to hg19; N: number informative individuals; OR: odds ratio. Many but not all of these SNPs are in strong LD see .(XLSX)Click here for additional data file.