Gene locations may contribute to predicting gene regulatory relationships

Gene locations may contribute to predicting gene regulatory relationships 基因位置可以用于预测基因调控关系 1 corresp first-author ‡Corresponding Author ‡Corresponding Author †E-mail:junmeng@zju.edu.cn †E-mail:junmeng@zju.edu.cn junmeng@zju.edu.cn 1 1 2 1 Department of System Science and Engineering, School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China Department of System Science and Engineering, School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China Laboratory of Machine Learning and Optimization, École Polytechnique Fédérale de Lausanne (EPFL), Route Cantonale, 1015 Lausanne 999034, Switzerland Laboratory of Machine Learning and Optimization, École Polytechnique Fédérale de Lausanne (EPFL), Route Cantonale, 1015 Lausanne 999034, Switzerland We propose that locations of genes on chromosomes can contribute to the prediction of gene regulatory relationships. We constructed a time-based gene regulatory network of zebrafish cardiogenesis on the basis of a spatio-temporal neighborhood method. Through the network, specific regulatory pathways and order of gene expression during zebrafish cardiogenesis were obtained. By comparing the order with locations of these genes on chromosomes, we discovered that there exists a reversal phenomenon between the order and order of gene locations. The discovery provides an inherent rule to instruct exploration of gene regulatory relationships. Specifically, the discovery can help to predict if regulatory relationships between genes exist and contribute to evaluating the correctness of discovered gene regulatory relationships. 目的 2 证明基因位置顺序与基因调控顺序的关系,说明利用基因位置顺序信息可以作为预测基因调控关系的先验知识. 创新点 2 通过研究与斑马鱼心脏发育阶段有关的基因和miRNA,利用时空邻域法,建立了一个基于时间的基因调控网络.通过这个基因调控网络,我们获得了一些特殊的基因调控通路和基因之间调控的时间顺序.通过研究斑马鱼心脏发育阶段有关的基因在染色体上的位置,将基因位置顺序与基因调控时间顺序比较,我们发现了这两个顺序具有逆转现象.这个逆转现象的存在,可以帮助我们利用基因位置顺序来预测基因调控关系和调控的时间顺序. 方法 2 采用时空邻域法研究了斑马鱼心脏发育阶段的基因和miRNA,建立基因调控网络(图5),并通过进一步比较,得到了基因位置顺序和基因调控时间顺序的联系. 结论 2 基因位置顺序信息可以用于预测基因调控关系. Prediction Gene regulatory relationships Order of gene location Spatio-temporal neighborhood method Zebrafish cardiogenesis 预测 基因调控关系 基因位置顺序信息 时空邻域法 斑马鱼心脏发育期 Introduction 1 To avoid uncertainty which may be generated from the construction of gene regulatory relationships, some inherent rules are necessary to instruct the construction. Probabilistic integrated gene networks, where linkages between genes indicate their likelihood of being involved in the same biological process, are based on functional genomics, proteomics, and comparative genomics (Lee et al., 2008 2008 ). Common methods of exploration on gene regulatory relationships include high-throughput biological experiments and computational methods (Zhong and Sternberg, 2006 2006 ; Lee et al., 2007 2007 , 2008 2008 , 2010 2010 ; Ma et al., 2007 2007 ; Huttenhower et al., 2009 2009 ; Bassel et al., 2011 2011 ; Kourmpetis et al., 2011 2011 ). Although functional genomics, proteomics, and comparative genomics contain much valuable data, they are incomplete and error-prone (Lee et al., 2008 2008 ). In addition, exploration methods of regulatory relationships between genes also contain some blindness. This blindness together with the incompleteness of databases leads to the conclusion that a constructed gene regulatory network may have uncertainties. Therefore, we need some inherent features of gene regulatory relationships to instruct constructions. Existing creatures are results of evolution; the embryogenesis of creatures should contain a certain amount of evolutionary information. During evolution, length and complexity of genes increase in the space due to the addition of new genes, with conservation of “good” genes in the creatures under natural selection. Conserved genes in creatures are sequentially expressed during embryogenesis to development into mature individuals. Take the evolution of heart and cardiogenesis of human as an example (Olson, 2006 2006 ; Nemer, 2008 2008 ). Beginning with cardiac muscle cells of Cnideria to the pharynx of Nematodes, the pharynx preliminarily contracts like a heart. It is believed that the first heart-like organ appeared over 4 billion years ago, which resembled the simple tubular vessel-like organs of tunicates (Romer, 1967 1967 ; Moorman and Christoffels, 2003 2003 ; Bishopric, 2005 2005 ; Simões-Costa et al., 2005 2005 ; Lee et al., 2010 2010 ). The first heart-like organ evolves from a single-layered tube with peristaltic contractility to a more efficient and powerful pump with thick muscular chambers dedicated to receiving and pumping blood (Moorman and Christoffels, 2003 2003 ; Simões-Costa et al., 2005 2005 ; Olson, 2006 2006 ). To transit from an aquatic to a terrestrial environment, the hearts of fish contain a single atrial and a single ventricle (Olson, 2006 2006 ), while the hearts of amphibians have two atria and a single ventricle, and amniotes have a four-chambered heart (Olson, 2006 2006 ). Consistent with the evolution of the heart, formation of a human heart starts at early stages of embryogenesis with commitment of anterior lateral plate mesoderm cells to the cardiogenic lineage and their migration and organization into the cardiac crescent which later forms into a beating linear heart tube (Nemer, 2008 2008 ). The linear heart tube contains a single atrial and a single ventricle, which underdoes chamber specification, septation, and trabeculation to form the definitive four-chambered heart (Nemer, 2008 2008 ). During chamber specification, the atrial of the linear heart tube is specified before the ventricle. This example demonstrates that there probably exists some correlation between evolution and embryogenesis. Therefore, if we can find the correlation, we may discover some inherent features to instruct construction of gene regulatory relationships. If the correlation between evolution and embryogenesis exists, there should be a correlation between spatial features and temporal features of genes. Length and complexity of genes increase in the space due to addition of new genes during evolution. The addition leads to formation of orders of gene locations on chromosomes. Although chromosomal rearrangement occurs during evolution, orders of some genes on the partial chromosomes are conserved. The conserved gene locations have been discovered to determine or reflect a mechanism of genetic control (Anchel et al., 2016 2016 ). During embryogenesis, genes are sequentially expressed by time, where there exists time order. Through comparison of orders of gene locations on chromosomes and the time order, we can deduce that if there exists some correlation between evolution and embryogenesis, and this helps us to determine that whether evolution can instruct the construction of regulatory relationships between genes. To simplify study, we only compare spatial features and temporal features of genes on the same chromosome, without consideration of chromosomal rearrangement during evolution. Materials and methods 1 Prior knowledge of zebrafish cardiogenesis 2 The specific progress of zebrafish cardiogenesis is as follows (Stainier, 2001 2001 ; Glickman and Yelon, 2002 2002 ). Just before gastrulation, 5 h post fertilization (hpf), the heart progenitor cells are located throughout the ventral and lateral regions of the embryo. After involution, these cells converge towards the embryonic axis and reach their destination at the level of the future hindbrain by the five-somite stage (about 12 hpf). Three rows of cells are represented at this stage. The myocardial precursors lie mostly laterally and the endocardial precursors mostly medially (Alexander and Stainier, 1999 1999 ). By the 13-somite stage (15.5 hpf), the myocardial precursors have segregated into preatrial and preventricular groups, although this segregation might well happen earlier (Yelon et al., 1999 1999 ). Starting at 19 hpf, the myocardial precursors merge posteriorly to form a horseshoe-shaped structure (Yelon et al., 1999 1999 ). By 19.5 hpf, as anterior cells migrate medially, the horseshoe transforms into a cone with the ventricular cells at its center and apex, and the atrial cells at its base. The endocardial cells line the inside of the cone. Next, the cone telescopes out to form a tube. The ventricular end of the heart tube assembles first, followed by the atrial end. By 24 hpf, the tube lies along the anterioposterior axis with the atrial end to the left of the midline. Subsequently, by 30 hpf, visibly distinct ventricular and atrial chambers form. By 36 hpf, the heart undergoes looping morphogenesis. By 48 hpf, functional valves are formed. Based on the time, we divide the process of cardiogenesis of zebrafish into developmental stages (Table 1 1 ).  Time (hpf) Developmental stages of cardiogenesis 0–5 Involution of heart progenitor cells 12–15.5 Heart progenitor cells differentiate into myocardial precursors 15.5–24 Proliferation of myocardial precursors and morphogenesis of heart 24–30 Morphological development of heart and development of ventricle 30–36 Development of ventricle and atrial 36–48 Looping morphogenesis ≥48 Formation of functional valves After clarifying the developmental stages of the cardiogenesis of zebrafish, we have arranged functions of related genes (Table 2 2 ) and microRNAs (miRNAs) (Table 3 3 ), preparing for the construction of a gene regulatory network. Gene Functions of the gene Fgf8a Fgf8 is expressed in cardiac precursors and later in the heart ventricle (Reifers et al., 2000 2000 ). Fgf8 is expressed in and required for development of the zebrafish heart precursors, particularly during initiation of cardiac gene expression (Reifers et al., 2000 2000 ) Gata4 There are interactions between Gata4 and Nkx2.5 . Gata4 first functions in the early development of cardiac precursor cells (Serbedzija et al., 1998 1998 ). Gata4 is regulators of proliferation of myocardial precursors (Kikuchi et al., 2010 2010 ). Gata4 is an important regulator of cardiac hypertrophy, which functions together with SRF , Nkx2.5 , Tbx5 , and Gata6 (Akazawa and Komuro, 2003 2003 ) Tbx20 Tbx20 expression is enriched in the atrioventricular canal (AVC), the outflow tract and right ventricle but is reduced in the left ventricle (Plageman and Yutzey, 2004 2004 ; Ataliotis et al., 2005 2005 ). Tbx1 interacts with the Tbx20 during cardiac development, especially during the development of the outflow tract. Tbx20 physically interacted with cardiac transcription factors Nkx2-5 , Gata4 , and Gata5 , collaborating to synergistically activate cardiac gene expression (Kloosterman et al., 2006 2006 ). Tbx20 regulates development in myocardial and acts in synergy with other cardiac transcription factors of the homeodomain and zinc finger families, including Nkx2.5 , Gata 4 , and Gata5 (Stennard et al., 2003 2003 ) Nkx2.5 Nkx2.5 is expressed in early cardiac mesoderm and in heart muscle lineage throughout life. Targeted disruption is lethal to embryos and arrests cardiac development at the linear heart tube stage (Benson et al., 1999 1999 ) Has2 Has2 is a crucial component of the cardiac jelly matrix, which requires Bmp2 for myocardial expression (Ma et al., 2005 2005 ) Tbx5a Increased expression of Tbx5 leads to an increase in Ndrg4 expression, which promotes proliferation of cardiomyocytes and formation of atrioventricular canal (Qu et al., 2008 2008 ; Ghosh et al., 2009 2009 ). Maintenance of Tbx5 expression and cmlc2 -expressing are indispensable for myocardial differentiation (Yelon et al., 2000 2000 ) Hand2 Hand2 is important for maintenance of Tbx5 expression, vmhc expression, and heart tube formation (Yelon et al., 2000 2000 ) Bmp2b Bmp2b expresses during the early stages of heart development. Bmp2b has important relations with cardiac differentiation in anterior medial mesoderm and expressions of some important genes related with cardiac development, such as Nkx2.5 , Gata4/5/6 (Schultheiss et al., 1997 1997 ; Schlange et al., 2000 2000 ) Tbx2a Tbx2a is essential for chamber differentiation, patterning the atrioventricular canal and morphogenesis of the outflow tract during heart development (Harrelson et al., 2004 2004 ) Cx43 Defects of Cx43 lead to hindrance of cardiac looping morphogenesis (Liu et al., 2008 2008 ) Tbx1 With a 20% decrease of Tbx1 , abnormal cardiac morphogenesis occurs due to hindrance of cardiac looping morphogenesis, including no-looping or wrong looping direction (Zhang et al., 2010 2010 ). Decrease of Tbx1 impairs myocardial function and leads to decrease of cardiac contraction and heart rate miRNA Functions of the miRNA dre-miR-143 miR-143 is required for chamber morphogenesis through direct repression of adducin3 . Knockdown of miR-143 leads to ventricular collapse and decreased contractility (Moulton, 2010 2010 ) dre-miR-138 miR-138 is expressed in ventricular cardiomyocyte and regulates formation of single-ventricle during cardiac development (Morton et al., 2008 2008 ). Disruption of miR-138 function leads to ventricular expansion of gene expression normally restricted to the atrio-ventricular valve region and, ultimately, to disrupted ventricular cardiomyocyte morphology and cardiac function (Morton et al., 2008 2008 ) dre-miR-145 Loss of miR-145 results in defects of heart and gut. In early zebrafish development between 16 and 24 hpf, miR-145 is expressed ubiquitously at very low levels with increasingly specific expression in the heart, ear, and pharyngeal arches between 24 and 72 hpf (Zeng et al., 2009 2009 ) dre-miR-218 miR-218 regulates heart morphogenesis through miR-218 during formation of ventricle (Chiavacci et al., 2012 2012 ). Down-regulation of miR-218 is able to rescue the heart defects generated by Tbx5 over-expression supporting the notion that miR-218 is a crucial mediator of Tbx5 in heart development and suggesting its possible involvement in the onset of heart malformations (Chiavacci et al., 2012 2012 ) dre-miR-499 miR-499 is expressed in the ventricle and atrium, the muscles of the head, and the somitic muscles (Kloosterman et al., 2006 2006 ). The temporal expression of miR-499 in situ is from 48 h to adult (Kloosterman et al., 2006 2006 ) Regulatory relationships between miRNAs and RNAs 2 We deduce that the function of mRNA against miRNA is that the transcription of mRNA promotes the generation of miRNA. Details of this deduction are shown as follows. miRNAs are produced from either their own genes or from introns. miRNA is divided into two categories according to sources, intergenic miRNA and intronic miRNA. Intergenic miRNA generates from non-protein coding genes. Thus miRNAs are initially transcribed as part of one arm of a RNA stem-loop (about 80 nucleotide (nt)) that in turn forms part of a several hundred nucleotides-long miRNA precursor termed a primary miRNA (Cai et al., 2004 2004 ; Lee et al., 2004 2004 ). Precursor miRNAs, about 70 nt hairpin structures, are in turn excised from a primary miRNA transcript by the enzyme Drosha. Finally, mature miRNAs are cleaved from pre-mRNAs by the enzyme Dicer (Esquela-Kerscher and Slack, 2006 2006 ; Chen and Rajewsky, 2007 2007 ; Okamura et al., 2007 2007 ). The intronic miRNA is defined as small RNAs, derived from introns, processed by splicing and pre-miRNA degradations, and targets the intracellular mRNA for silencing of that gene expression (Ying and Lin, 2006 2006 ). In consideration of the reliability of DNA data resources and clarity of DNA regionalism, we only take intronic miRNAs into account in this research. A corollary of this deduction is that we can deduce whether a miRNA derives from an mRNA through comparison of matching degree between the miRNA and introns of the mRNA. The probability of the miRNA deriving from the mRNA increases with the growth of matching times between the miRNA and introns of the mRNA. Hence, translation of mRNA, which means production of more introns, promotes generation of miRNA. With respect to the effect of miRNA on mRNA, we mainly consider the effect of the regulation of miRNA on the translation of mRNA. The deduction is that miRNA will promote the translation of target mRNA. The specific reasoning process is as follows. It has been demonstrated that if there is complete complementation between the miRNA and target mRNA sequence, Ago2 can cleave the mRNA and lead to direct mRNA degradation. Yet, if there is not complete complementation the silencing is achieved by preventing translation (Lim et al., 2005 2005 ). During the development of creatures, the level of receptor proteins remains relatively stable, and thus the number of receptor proteins expressed through mRNAs remains relatively stable. In the case that the number of receptor proteins expressed through mRNAs remains relatively stable, complete complementation between the miRNA and target mRNA sequence will lead to direct mRNA degradation, and therefore promote the translation of the target mRNA to keep the number of target mRNA relatively stable. In conclusion, if receptor proteins during development remain stable, complete complementation between the miRNA and target mRNA sequence will promote the translations of mRNAs. A corollary of the deduction is that we can deduce whether a miRNA promotes translation of an mRNA through comparison of matching degree between the miRNA and extrons of the mRNA. The more times the miRNA matches with extrons of the mRNA, which means more probability of complete complementation, the more mRNA will be degraded. The degradation will in turn promote translation of the mRNA. Hence, miRNA can promote the translation of mRNA, while the expression of protein is relatively stable. In summary, some mRNAs produce mature miRNAs, which will lead to degradation of target mRNAs of miRNAs. Since receptor proteins during development remain stable, the degradation of target mRNAs promotes translations of the target mRNAs, and this will in turn promote productions of miRNAs. The conclusion is that introns of genes translate to form miRNAs, which in turn regress function of mRNA through complementary base pairing with extrons of genes. This process includes mutual regulations of introns, extrons, and miRNAs, based on which we can construct gene regulatory relationships through miRNAs. The following constructions of network will be based on this deduction. Spatio-temporal neighborhood method 2 The nonlinear spatio-temporal neighborhood method is a data mining method which attempts to acquire casual links between dynamic data by clustering the data. The main notions and procedures of the method are presented as follows. The spatio-temporal neighborhood method is a method dedicated to exploring relations between spatial features and temporal features during the process of development. Assume there are n points e 1 t , e 2 t , e 3 t ,…, e n t in space at time t and mapping parameter from e i t to e j t is λ ij t . Due to differences of parameters, these points form into clusters C 1 t , C 2 t ,…, C m t , $$C_k^t = \{ c_{k1}^te_1^t,\;c_{k2}^te_2^t,\; \cdots ,\;c_{kn}^te_n^t\}$$ at time t ,where $$c_{kl}^t = \left\{ {\begin{array}{*{20}{c}}{0,\;e_l^t \notin C_k^t} \\{1,\;e_l^t \in C_k^t}\end{array}} \right.$$ . When time changes, clusters will change owing to changes of mapping parameters. The temporal neighborhood that spatio-temporal neighborhood method takes research into includes t 1 , t 2 ,…, t p , while the spatial neighborhood includes clusters of all the points in the space at time t , such as C 1 t , C 2 t , C 3 t ,…, C m t . By analyzing temporal changes of clusters in the spatial neighborhood, the evolutionary rule $$F = \{ {f_1},\;{f_2},\; \cdots ,\;{f_l}\}$$ can be obtained based on changes of mapping parameters. The rule F between clusters at time t and t +Δ t is shown as follows: $$\begin{gathered}\left[ \begin{gathered}C_1^{(t + \Delta t)}\{ c_{11}^{(t + \Delta t)}e_1^{(t + \Delta t)},\;c_{12}^{(t + \Delta t)}e_2^{(t + \Delta t)},\; \cdots ,\;c_{1n}^{(t + \Delta t)}e_n^{(t + \Delta t)}\} \\C_2^{(t + \Delta t)}\{ c_{21}^{(t + \Delta t)}e_1^{(t + \Delta t)},\;c_{22}^{(t + \Delta t)}e_2^{(t + \Delta t)},\; \cdots ,\;c_{2n}^{(t + \Delta t)}e_n^{(t + \Delta t)}\} \\\quad \vdots \\C_m^{(t + \Delta t)}\{ c_{m1}^{(t + \Delta t)}e_1^{(t + \Delta t)},\;c_{m2}^{(t + \Delta t)}e_2^{(t + \Delta t)},\; \cdots ,\;c_{mn}^{(t + \Delta t)}e_n^{(t + \Delta t)}\} \\\end{gathered} \right] \\= F\left( {\left[ \begin{gathered}C_1^t\{ c_{11}^te_1^t,\;c_{12}^te_2^t,\; \cdots ,\;c_{1n}^te_n^t\} \\C_2^t\{ c_{21}^te_1^t,\;c_{22}^te_2^t,\; \cdots ,\;c_{2n}^te_n^t\} \\\quad \vdots \\C_m^t\{ c_{m1}^te_1^t,\;c_{m2}^te_2^t,\; \cdots ,\;c_{mn}^te_n^t\} \\\end{gathered} \right]} \right). \\\end{gathered}$$ . Through the rule F , we can obtain $$\left[ \begin{gathered}c_i^{(t + \Delta t)}e_i^{(t + \Delta t)} \\c_j^{(t + \Delta t)}e_j^{(t + \Delta t)} \\\end{gathered} \right] = {f_l}\left( {\left[ \begin{gathered}c_i^te_i^t \\c_j^te_j^t \\\end{gathered} \right]} \right)$$ by analyzing e i t , which can contribute to predictions of e i t+Δt . Based on the predictions, clusters of t +Δ t can be predicted, where some important bifurcations can be discovered by comparing with clusters formed at time t . Take an example to demonstrate procedures of spatio-temporal neighborhood method (Fig. 1 1 ). There are eight points e 1 , e 2 , e 3 , e 4 , e 5 , e 6 , e 7 , e 8 in space. The eight points form into two clusters $$C_1^{{t_1}},\;C_2^{{t_1}}$$ at time t 1 , while these points form into new clusters $$C_1^{{t_2}},\;C_2^{{t_2}},\;C_3^{{t_2}}$$ under rules f 1 , f 2 , f 3 at time t 2 , respectively. At time t 3 , new clusters are formed under rules f 1 , f 2 , and f 3 , respectively. We can observe that there exists a strong correlation between clusters $$C_1^{{t_1}}$$ , $$C_1^{{t_2}}$$ and $$C_1^{{t_3}}$$ , which is shown as follows: (1) If $$e \in C_1^{{t_1}}$$ when t = t 1 and $$e \in C_1^{{t_2}}$$ when t = t 2 , then $$e \in C_1^{{t_2}}$$ can be obtained when t = t 3 ; (2) If $$e \in C_1^{{t_1}}$$ when t = t 1 and $$e \in C_2^{{t_2}}$$ when t = t 2 , then $$e \in C_2^{{t_3}}$$ can be obtained when t = t 3 . e ij t represents a point in the space at the time of t , wherein t represents time, i represents clusters that the point belongs to and j represents label of the point. For example, represents the point labeled two at the time of t 1 belongs to cluster one. C j t represents a cluster, wherein t represents time and j represents label of the cluster. For example, represents the first cluster at the time of t 1 . f j represents different rules for different j , which leads to formation of new clusters In addition, we observe $${e_1},\;{e_2},\;{e_3},\;{e_4},\;{e_5}\; \in C_1^{{t_1}}$$ when t = t 1 , while influenced by changes of rule f which result from changes of mapping parameters, $${e_1},\;{e_3},\;{e_4}\; \in C_1^{{t_2}}$$ and $${e_2},\;{e_5} \in C_2^{{t_2}}$$ at time t = t 2 , $${e_1},\;{e_3} \in C_1^{{t_3}}$$ and $${e_2},\;{e_5} \in C_2^{{t_3}}$$ at time t = t 3 . Through changes of clusters that points belong to, we can obtain temporal bifurcations which contain significant information that represents the generation of new functions during evolution in the biology. Multi-layer sub-network construction method 2 The multi-layer sub-network construction method obeys specific rules, which are: (1) When we construct sub-network n+ 1 on the base of sub-network n at stage m , ignore regulatory relationships in the sub-network n , and only consider regulation of gene in the sub-network n on the added miRNAs of the sub-network n +1 and regulation of added genes in the sub-network n +1 on miRNAs of the sub-network n . In this case, we presume that the sub-network n already exists at stage m and regulatory relationships have been formed at stage m− 1. (2) When we construct regulatory relations between stages m and m +1, ignore existed regulatory relationships between stages m− 1 and m , and only take newly added regulatory relationships between stages m and m +1 into consideration. (3) When a newly added miRNA at stage m regulates a gene of the sub-network n at stage m +1, we deduce that the miRNA promotes the formation of mRNA corresponding to the gene. In this case, the gene particularly refers to a newly added gene of the sub-network n with respect to the sub-network n− 1. (4) When a miRNA of sub-network n +1 is regulated by a gene of sub-network n , we deduce that the sub-network n has regulated the miRNA. In this case, the gene particularly refers to a newly added gene of the sub-network n with respect to the sub-network n− 1. (5) If a gene or a miRNA does not belong to sub-network n and has no relations with other genes or miRNAs, then we deduce that the gene or miRNA does not participate in the regulation at this time. Results 1 To prove that orders of gene locations on chromosomes can instruct exploration on gene regulatory relationships, the time order that genes express in during cardiogenesis of zebrafish and location of genes on the same chromosome were compared. Also a reversal phenomenon was discovered to exist between the time order and order of gene locations on chromosomes (Fig. 2 2 ). Through a constructed time-based gene regulatory network, we found that Tbx5a first expresses during morphogenesis of heart (12–24 hpf), Tbx2a first expresses during development of ventricle and atrial (24–36 hpf), and Tbx1 first expresses during looping morphogenesis (36–48 hpf). Therefore, the time order form beginning to end between these genes is Tbx5a , Tbx2a , Tbx1 . These genes are all located on the chromosome 5 of zebrafish, and the order of locations from begin to end is Tbx1 , Tbx2a , Tbx5a . Obviously, the order of locations of these genes is exactly the reverse of their time order Based on spatio-temporal concentrates of miRNAs and expressing genes during zebrafish cardiogenesis (Schultheiss et al., 1997 1997 ; Serbedzija et al., 1998 1998 ; Alexander and Stainier, 1999 1999 ; Benson et al., 1999 1999 ; Yelon et al., 1999 1999 , 2000 2000 ; Schlange et al., 2000 2000 ; Reifers et al., 2000 2000 ; Stainier, 2001 2001 ; Glickman and Yelon, 2002 2002 ; Akazawa and Komuro, 2003 2003 ; Stennard et al., 2003 2003 ; Harrelson et al., 2004 2004 ; Plageman and Yutzey, 2004 2004 ; Ataliotis et al., 2005 2005 ; Ma et al., 2005 2005 ; Kloosterman et al., 2006 2006 ; Prall et al., 2007 2007 ; Liu et al., 2008 2008 ; Morton et al., 2008 2008 ; Qu et al., 2008 2008 ; Ghosh et al., 2009 2009 ; Zeng et al., 2009 2009 ; Kikuchi et al., 2010 2010 ; Moulton, 2010 2010 ; Zhang et al., 2010 2010 ; Chiavacci et al., 2012 2012 ), time was introduced into the construction of the gene regulatory network (Fig. 3 3 ). miRNAs are endogenous about 23 nt RNAs that play important gene-regulatory roles in animals by paring to the mRNAs of protein-coding genes to direct their posttranscriptional repression (Cai et al., 2004 2004 ; Lee et al., 2004 2004 ; Chen and Rajewsky, 2007 2007 ; Chen et al., 2015 2015 ). Through variations of miRNAs’ spatio-temporal concentrates, the expression time of genes can be determined. The construction of a time-based gene regulatory network is achieved through a spatio-temporal neighborhood method. The spatio-temporal neighborhood method connects every sub-network that centers on a specific miRNA. From the constructed time-based gene regulatory network, the time order that genes express during the cardiogenesis of zebrafish can be obtained. Determination of up-stream and down-stream mRNAs of miRNAs 2 Based on the deduction of regulatory relationships between miRNAs and mRNAs, we explore relationships between miRNA and mRNA by MATLAB. The deduction is that introns of mRNAs translate to generate miRNAs, while the generation regresses functions of mRNAs through complementary base pairing with extrons of mRNAs (Cai et al., 2004 2004 ; Lee et al., 2004 2004 ; Lim et al., 2005 2005 ; Esquela-Kerscher and Slack, 2006 2006 ; Ying and Lin, 2006 2006 ; Chen and Rajewsky, 2007 2007 ; Okamura et al., 2007 2007 ). Using a matching algorithm which takes only complete complementation as a match, we obtain relationships between miRNAs and introns of mRNAs (Fig. 4a 4a ), which determines the up-stream of miRNAs. Based on the same method, we acquire relationships between miRNAs and extrons of mRNAs (Fig. 4b 4b ), which determines the down-stream of miRNAs. To clarify the up-stream and down-stream of miRNAs, we have visualized matching results of Fig. 4a 4a and Fig. 4b 4b in terms of miRNAs and mRNAs (Fig. 5 5 ). (a) Y -axis represents miRNAs of related genes, X -axis refers to introns of related genes and colors represent times that a miRNA matches with introns of an mRNA. Based on prior knowledge of regulatory relationships between miRNAs and mRNAs, we recognize an mRNA whose introns match with a miRNA at least one time as up-stream of the miRNA. (b) Y -axis represents miRNAs of related genes, X -axis represents extrons of related genes and colors represent times that a miRNA matches with extrons of an mRNA. According to prior knowledge of regulatory relationships between miRNAs and mRNAs, we obtain an mRNA whose extrons match with a miRNA at least one time as down-stream of the miRNA Black lines represent up-stream of miRNAs and red lines represent down-stream of miRNAs. The number on black lines represents times that a miRNA matches with introns of an mRNA, while the number on red lines refers to times that a miRNA matches with extrons of an mRNA (Note: for interpretation of the references to color in this figure legend, the reader is referred to the web version of this article) Construction of a time-based gene regulatory network 2 Based on prior knowledge of zebrafish cardiogenesis and determination of up-stream and down-stream of miRNAs, we adopt a spatio-temporal neighborhood method to construct a time-based gene regulatory network. The constructed time-based gene regulatory network (Fig. 6 6 ) demonstrates procedures of the morphological evolution of a zebrafish’s heart, which have guiding significance on the research of morphological evolution of zebrafish’s heart. Although we know that Bmp2b and Gata4 probably occur earliest at stage 5 hpf, the constructed time-based gene regulatory network shows that Bmp2b participates in the regulation at time 24 hpf instead of 5 hpf. Although the inconsistency reduces completeness of the network, it cannot impact on the correctness of the regulatory network. Overall, the constructed time-based gene regulatory network is consistent with current work. Y -axis is the time axis. On the time axis, hpf means hours post-fertilization. Words at time points or between time points explain developmental stages. X -axis is occurrence of miRNA and gene. Black lines between miRNA and gene demonstrate that intron series of the gene matches with the miRNA and can translate into miRNA; the numbers on lines are times that miRNAs match with introns; the possibility of translation of introns into miRNAs increases with the times that miRNAs match with introns. Red lines between miRNA and gene indicate that extrons of the gene match with the miRNA and can regress or degrade mRNA; the numbers on lines are times that miRNAs match with extrons; the possibility of regression or degradation of mRNA, which will in turn promote the production of mRNA, increases with the times that miRNAs match with extrons. To clarify the constructed time-based gene regulatory network, we have simplified the network based on a multi-layer sub-network construction method (Note: for interpretation of the references to color in this figure legend, the reader is referred to the web version of this article) Through the time-based gene regulatory network (Fig. 6 6 ), we have obtained the time order of main functioning genes during cardiogenesis. The time order from beginning to the end is Fgf8a , Gata4 , Tbx20 , Nkx2.5 , Has2 , Tbx5a , Hand2 , Bmp2b , Tbx2a , Cx43 , Tbx1 . Comparison of spatial feature and temporal feature of genes 2 In order to compare the time order with the order of gene locations on chromosomes, we have arranged locations of these genes according to the National Center for Biotechnology Information (NCBI) database (Table 4 4 ). The arrangement shows that Tbx5a , Tbx2a , and Tbx1 are all on the same chromosome 5 and the location order is Tbx1 , Tbx2a , and Tbx5a . Since the time order we have from the time-based gene regulatory network is Tbx5a , Tbx2a , and Tbx1 , a reverse is found between location order and time order. The reverse is also found between Tbx20 and Has2 , as well as Gata4 , Bmp2b , and Cx43 . Related chromosome where gene is located Gene Location of gene on the chromosome Danio rerio strain Tuebingen chromosome 13, Zv9 (NC_007124.6) Fgf8a 28 365 067–28 371 535 Danio rerio strain Tuebingen chromosome 16, Zv9 (NC_007127.6) Tbx20 Has2 42 605 255–42 619 962 15 481 299–15 497 339 Danio rerio strain Tuebingen chromosome 5, Zv9 (NC_007116.6) Tbx5a Tbx2a Tbx1 71 474 708–71 505 188 55 834 959–55 843 728 14 701 844–14 716 157 Danio rerio strain Tuebingen chromosome 20, Zv9 (NC_007131.6) Gata4 Bmp2b Cx43 53 146 771–53 162 461 45 989 447–45 995 178 40 818 053–40 823 343 Danio rerio strain Tuebingen chromosome 14, Zv9 (NC_007125.6) Nkx2.5 23 943 996–23 946 789 Danio rerio strain Tuebingen chromosome 1, Zv9 (NC_007112.6) Hand2 37 473 969–37 475 834 Discussion 1 To avoid the uncertainty which can be generated from the construction of gene regulatory relationships, some inherent rules are necessary to instruct the construction. By comparing the time order of the main functioning genes during cardiogenesis of a zebrafish and their locations on chromosomes, we find that there exists a reverse between time order that genes express in and the order of gene locations on the same chromosome. For example, genes Tbx1 , Tbx2a , and Tbx5a express in the order of Tbx5a , Tbx2a , and Tbx1 , while locations of these genes on chromosome is in the order of Tbx1 , Tbx2a , and Tbx5a . Based on this reversal phenomenon, orders of gene locations can help to predict gene regulatory relationships. For example, if gene A’s location on a chromosome is before gene B’s location on the same chromosome, then during embryogenesis, gene A will probably express after gene B. Through the prediction, the number of genes to be selected can be much reduced when researchers try to determine the following expressing gene in a gene regulatory network. For example, if gene C’s express time has been determined in a gene regulatory network, then genes expressing after gene C’s are mostly located before gene C. Furthermore, the prediction can contribute to evaluating the correctness of discovered regulations between genes. For example, if gene D’s location on a chromosome is before gene E’s location on the same chromosome, and gene D expresses before gene E in a gene regulatory network, then work is needed to verify the correctness of the gene regulatory network. Although the reverse between time order that genes express in and order of gene locations on the same chromosome has been found during the cardiogenesis of zebrafish, there still needs to be more research to establish whether this reversal also exists in other species. In another paper, we have studied the correlation between time order and order of gene locations in the development of Arabidopsis thaliana and we have a conclusion consistent with this paper (data not shown). The reverse we have obtained between time order that genes express in and order of gene locations on the same chromosome provides a rule for construction of a gene regulatory network. Based on the rule, the uncertainty generated from construction of gene regulatory relationships will be decreased, and this will increase the correctness of gene regulatory network and save much research efforts. Most importantly, the paper has not only provided an easier way to construct a gene regulatory network with gene locations on the chromosome determining the basic structure of a network, but has also shown a dynamic relationship between genes since miRNAs can determine the expression of genes and the time at which they express. References H Akazawa , I Komuro . Roles of cardiac transcription factors in cardiac hypertrophy . Circ Res , 2003 . 92 ( 10 ): 1079 - 1088 . 12775656 DOI: 10.1161/01.RES.0000072977.86706.23 http://doi.org/10.1161/01.RES.0000072977.86706.23 . 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We are particularly grateful to Shu ZHENG in the Second Affiliated Hospital, School of Medicine, Zhejiang University (Hangzhou, China) for valuable advice on miRNAs and embryogenesis, Zhao-lin WANG for instructing the writing of this manuscript. Compliance with ethics guidelines Jun MENG, Wen-yuan XU, Xiao CHEN, Tao LIN, and Xiao-yu DENG declare that they have no conflict of interest. All institutional and national guidelines for the care and use of laboratory animals were followed. 10.1631/jzus.B1700303 Project supported by the National Natural Science Foundation of China (Nos. 60574079, 30872957, and 30572129) 2017-06-08 2017-11-19 2022-01-05 Copyright © Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2018 2018 Journal of Zhejiang University-SCIENCE B (Biomedicine and Biotechnology) 01 19