Citation Context

...ten recognize a chain effect as a real interaction, thus yielding False Positive results - interactions that do not exist in reality, but are reported by the method. The more advanced algorithms, such as [11] and [18] use so called graph transitive reduction algorithms to remove the edges, wrongly predicted due to this issue. We are using similar techniques as a part of our method. • GRN structure appears to be neither random nor strictly hierarchical, but scale-free [6]. This means that the probability that i regulates k other genes follows a power law, i.e. is p(k) ≈ k−λ , where usually λ ∈ [2,3] [2]. Example of a scale-free network is presented in Figure 1.2. Figure 1.2: Random network versus scale-free network: highlighted are the highest-degree nodes, i.e. hubs. Adapted from [8] The main property in a scale-free network is the relative occurrence frequency of vertices with a degree that greatly exceeds the average, i.e. most genes are regulated by only a few others in the GRN. The highest-degree nodes are called hubs and though there are very few such nodes, they influence almost all other nodes, hence, one can capitalize on this by developing a method, which treats the hubs in a s...

Citation Context

...as well as guidelines for their practical application can be found in [13]. The effectiveness of the state of the art methods is not optimal, as they are not 2 Algorithms for gene regulatory networks reconstruction CHAPTER 1. INTRODUCTION able to solve the following issues, arising when reconstructing the network: • Perturbation experiments only provide indirect information on gene interaction, thus the effect observed may not always be due to the direct causal effect, but due to the existence of motifs - the recurring patterns in a graph that occur more often in GRNs than expected at random. [10]. The most naive approaches are blind to this problem and often recognize a chain effect as a real interaction, thus yielding False Positive results - interactions that do not exist in reality, but are reported by the method. The more advanced algorithms, such as [11] and [18] use so called graph transitive reduction algorithms to remove the edges, wrongly predicted due to this issue. We are using similar techniques as a part of our method. • GRN structure appears to be neither random nor strictly hierarchical, but scale-free [6]. This means that the probability that i regulates k other genes ...

Citation Context

...ithmic transformation shows the best results. So this work takes these methods as a reference and tries to achieve a better scores by improving old algorithms and introducing new. 14 Algorithms for gene regulatory networks reconstruction Chapter 4 REHub The state of the art methods, based on statistics, are all vulnerable to the fact that the inferred GRNs come from real organisms. The underlying networks are not random, but include motifs - the recurring patterns in a graph that occur more often in GRNs than expected at random [10]. There are two main reasons for hubs existence, as stated in [1]: • Growth: thanks to the growing nature of real networks, older nodes had greater opportunities to acquire links. • Preferential attachment: as new nodes appear, they tend to connect to the more connected sites, and these popular locations thus acquire more links over time than their less connected neighbors. These two mechanisms - growth and preferential attachment can be both informally summarized as ”rich get richer”. From the genetical point of view, it can also be explained as conserving the ”richest” structures in the process of evolution: the same motifs are found in different organism...

Citation Context

...a-FFLs” and the second level hubs can be called ”meta-hubs”. These ”meta-FFLs” and ”meta-hubs”, could not have been detected with the LTR algorithm and the simpler version of REHub respectively, because they do not consist of vertices, but of groups of vertices. 4.4.3 Graph clustering In this section, we provide a definition of the graph clustering, that can be used in our desired generalized REHub. The general idea of clustering can be formulated as follows: Divide a data set into clusters such that the elements assigned to a particular cluster are similar or connected in some predefined way [20]. If the structure of the graph is completely uniform, with the edges evenly distributed over the set of vertices, the clustering computed by any algorithm will be rather arbitrary. Figure 4.6 shows two graphs of the same order and size, one of them is a uniform random graph and the other has a clearly clustered structure. Figure 4.6: Random graph and graph with structure. To formalize a cluster concept, we provide the properties, which cluster should have: • Each cluster should intuitively be connected: there should be at least one, preferably several paths connecting each pair of vertices wi...

Citation Context

...genes) in a cell, interacting with each other by the transcription of the messenger RNA (mRNA), which is translated to a protein, capable of influencing the activity of other genes. This activity, also known as gene expression, indicates rates at which genes in the network are transcribed into mRNA, which can transitively lead to a new gene regulation [7]. The process of gene interaction is schematically given in Figure 1.1. While the topology of such networks could be reconstructed, mainly from so called omics studies (genomics, proteomics, transcriptomics) in great detail for many organisms [17], it is still incomplete even for the simplest species. The only way to find out the topology is to reverse-engineer GRNs i.e. to identify interactions between the involved players (genes, proteins, etc.) by analysing the data of systematic and controlled perturbation experiments [11]. Modern technologies, such as microarrays experiments and RNA sequencing, allow biologists to perform such perturbational experiments either by knocking out (making completely inoperative) or knocking down (significantly suppressing the activity) genes and observing the change in the expression levels of other ge...

Citation Context

...• Growth: thanks to the growing nature of real networks, older nodes had greater opportunities to acquire links. • Preferential attachment: as new nodes appear, they tend to connect to the more connected sites, and these popular locations thus acquire more links over time than their less connected neighbors. These two mechanisms - growth and preferential attachment can be both informally summarized as ”rich get richer”. From the genetical point of view, it can also be explained as conserving the ”richest” structures in the process of evolution: the same motifs are found in different organisms [22]. The best scoring methods, analysed in Chapter 3 implicitly use these facts to find the paths, which better explain the knock-out and knock-down observations, than the direct single edge connection. For example, LTR method, following DR-FFL and TRANSWESD apply the principle of Transitive Reduction to identify and eliminate edges reflecting indirect effects [18], better explained by a certain motif (Feed Forward Loop). Our idea is to explicitly incorporate biological motifs in the approach by recognizing certain patterns in a given graph. After recognizing these patterns we perform a technique...

Citation Context

... 8 9 10 N u m b e r o f g e n e s 0 20 40 60 80 100 120 140 160 Hubs Figure 4.1: Distribution of degrees of the nodes in the challenge. 4.2 REHub algorithm A vertical line in Figure 4.1 is an example of a threshold, which is needed to distinguish hubs. The definition of hub is not precise, hence there is no single right way to calculate the threshold value. There is a biological cause for this: the major hubs are closely followed by smaller ones. These smaller hubs, in turn, are followed by other nodes with an even smaller degree and so on. This hierarchy allows for a fault tolerant behavior. [23] 4.2.1 General algorithm We propose the following algorithm to cope with the hubs of different degree. 1. Define a measure of hub majority, classifying the node according to its degree, e.g., the hub, influencing 10 vertices is more major, than the hub, influencing 3 vertices; 2. Measure hub majority for each vertex; 3. Apply a function, which, with respect to hub majority of a vertex finds a set of edges to promote; 4. Promote edges dynamically changing the intensity of promotion, with respect to the parameter of the hub majority of the influencing vertex. These algorithms require an addition...

Citation Context

...egree nodes, i.e. hubs. Adapted from [8] The main property in a scale-free network is the relative occurrence frequency of vertices with a degree that greatly exceeds the average, i.e. most genes are regulated by only a few others in the GRN. The highest-degree nodes are called hubs and though there are very few such nodes, they influence almost all other nodes, hence, one can capitalize on this by developing a method, which treats the hubs in a special way. This fact was noted in [5], but no solution was proposed. Another important property of a scale-free network is their hierarchical nature[9]. This allows to search the patterns on different levels and to use such a techniques, as hierarchical clustering. We research both of this properties in this work. • Inferring large scale cellular networks is computationally challenging and only a limited number of computational tools have been developed to address it. Scalability of algorithms is very important, since the ultimate goal is to reconstruct GRNs of full genomes, consisting of more than 10,000 genes. We solve this issue by preferring the light-weighted methods, such as probabilistic algorithms, over the complex ones, such as supe...

Citation Context

... a graph that occur more often in GRNs than expected at random. [10]. The most naive approaches are blind to this problem and often recognize a chain effect as a real interaction, thus yielding False Positive results - interactions that do not exist in reality, but are reported by the method. The more advanced algorithms, such as [11] and [18] use so called graph transitive reduction algorithms to remove the edges, wrongly predicted due to this issue. We are using similar techniques as a part of our method. • GRN structure appears to be neither random nor strictly hierarchical, but scale-free [6]. This means that the probability that i regulates k other genes follows a power law, i.e. is p(k) ≈ k−λ , where usually λ ∈ [2,3] [2]. Example of a scale-free network is presented in Figure 1.2. Figure 1.2: Random network versus scale-free network: highlighted are the highest-degree nodes, i.e. hubs. Adapted from [8] The main property in a scale-free network is the relative occurrence frequency of vertices with a degree that greatly exceeds the average, i.e. most genes are regulated by only a few others in the GRN. The highest-degree nodes are called hubs and though there are very few such no...

Citation Context

... inference algorithms. 20 Algorithms for gene regulatory networks reconstruction CHAPTER 4. REHUB Figure 4.3: A flowchart of the framework. Algorithms for gene regulatory networks reconstruction 21 CHAPTER 4. REHUB 4.4 Generalization of the method A potential direction to generalize REhub algorithm is presented in this section, leading to a novel approach of motifs identification using the knowledge about hierarchical structure of a graph. 4.4.1 Biological aspects of scale-free graphs It is known that interactions between genes have certain structure that can be described by scale-free graphs [16]. Module extraction techniques are used to generate such a graph. Analysis of gene structure shows that hierarchical representation can be used to explain gene dependencies. Figure 4.4 shows the artificial gene network constructed from motif of four-genes structure. Figure 4.4: Modules of a hierarchical scale-free network. Under the assumption of the hierarchical structure of graph we want to search for generating motifs on different levels of the hierarchy. It is stated in [15] that the best models of GRNs are based on these generating motifs. That is why extending statistical approaches with...

Citation Context

...ten recognize a chain effect as a real interaction, thus yielding False Positive results - interactions that do not exist in reality, but are reported by the method. The more advanced algorithms, such as [11] and [18] use so called graph transitive reduction algorithms to remove the edges, wrongly predicted due to this issue. We are using similar techniques as a part of our method. • GRN structure appears to be neither random nor strictly hierarchical, but scale-free [6]. This means that the probability that i regulates k other genes follows a power law, i.e. is p(k) ≈ k−λ , where usually λ ∈ [2,3] [2]. Example of a scale-free network is presented in Figure 1.2. Figure 1.2: Random network versus scale-free network: highlighted are the highest-degree nodes, i.e. hubs. Adapted from [8] The main property in a scale-free network is the relative occurrence frequency of vertices with a degree that greatly exceeds the average, i.e. most genes are regulated by only a few others in the GRN. The highest-degree nodes are called hubs and though there are very few such nodes, they influence almost all other nodes, hence, one can capitalize on this by developing a method, which treats the hubs in a s...

Citation Context

...s an output to the DREAM4 framework to evaluate the effectiveness, but to improve the result, the further steps are performed. 4 Algorithms for gene regulatory networks reconstruction CHAPTER 1. INTRODUCTION • A classifier identifies the edges to include in the predicted GRN graph. • The graph is transformed to remove and/or add the edges according to an algorithm. • The ranking tool creates an improved edge list, which serves as an output to the DREAM4 framework. We are following the same workflow, exploiting a combination of the best working methods from the previous approaches, reported in [11, 18, 5, 4, 12] We analyse these approaches, identify the best elements, and propose the improvements to them. In addition to the improvement of the existing techniques, we present REHub (Reverse Engineering with Hubs) - a novel method, distinguishing the influential genes (hubs) and promoting the genes these hubs interact with, i.e. increasing their position in the ranking. In the workflow used, REHub is performing a transformation after the graph is generated. The main idea is to incorporate biological motifs in the approach by recognizing certain patterns in a given graph under the assumption of scale-fre...

Citation Context

...rk is presented in Figure 1.2. Figure 1.2: Random network versus scale-free network: highlighted are the highest-degree nodes, i.e. hubs. Adapted from [8] The main property in a scale-free network is the relative occurrence frequency of vertices with a degree that greatly exceeds the average, i.e. most genes are regulated by only a few others in the GRN. The highest-degree nodes are called hubs and though there are very few such nodes, they influence almost all other nodes, hence, one can capitalize on this by developing a method, which treats the hubs in a special way. This fact was noted in [5], but no solution was proposed. Another important property of a scale-free network is their hierarchical nature[9]. This allows to search the patterns on different levels and to use such a techniques, as hierarchical clustering. We research both of this properties in this work. • Inferring large scale cellular networks is computationally challenging and only a limited number of computational tools have been developed to address it. Scalability of algorithms is very important, since the ultimate goal is to reconstruct GRNs of full genomes, consisting of more than 10,000 genes. We solve this iss...

Citation Context

...hoosing the topic Gene regulatory network inference is a central problem in systems biology, hence it attracts a lot of researchers from year to year. A gene regulatory network (GRN) or genetic regulatory network is a collection of DNA segments (genes) in a cell, interacting with each other by the transcription of the messenger RNA (mRNA), which is translated to a protein, capable of influencing the activity of other genes. This activity, also known as gene expression, indicates rates at which genes in the network are transcribed into mRNA, which can transitively lead to a new gene regulation [7]. The process of gene interaction is schematically given in Figure 1.1. While the topology of such networks could be reconstructed, mainly from so called omics studies (genomics, proteomics, transcriptomics) in great detail for many organisms [17], it is still incomplete even for the simplest species. The only way to find out the topology is to reverse-engineer GRNs i.e. to identify interactions between the involved players (genes, proteins, etc.) by analysing the data of systematic and controlled perturbation experiments [11]. Modern technologies, such as microarrays experiments and RNA seque...

Citation Context

...ising when reconstructing the network: • Perturbation experiments only provide indirect information on gene interaction, thus the effect observed may not always be due to the direct causal effect, but due to the existence of motifs - the recurring patterns in a graph that occur more often in GRNs than expected at random. [10]. The most naive approaches are blind to this problem and often recognize a chain effect as a real interaction, thus yielding False Positive results - interactions that do not exist in reality, but are reported by the method. The more advanced algorithms, such as [11] and [18] use so called graph transitive reduction algorithms to remove the edges, wrongly predicted due to this issue. We are using similar techniques as a part of our method. • GRN structure appears to be neither random nor strictly hierarchical, but scale-free [6]. This means that the probability that i regulates k other genes follows a power law, i.e. is p(k) ≈ k−λ , where usually λ ∈ [2,3] [2]. Example of a scale-free network is presented in Figure 1.2. Figure 1.2: Random network versus scale-free network: highlighted are the highest-degree nodes, i.e. hubs. Adapted from [8] The main property in a...