Luis Mendoza - Academia.edu (original) (raw)

Papers by Luis Mendoza

Research paper thumbnail of Dynamics of the Genetic Regulatory Network for Arabidopsis thaliana Flower Morphogenesis

Journal of Theoretical Biology, 1998

We present a network model and its dynamic analysis for the regulatory relationships among 11 gen... more We present a network model and its dynamic analysis for the regulatory relationships among 11 genes that participate inArabidopsis thalianaflower morphogenesis. The topology of the network and the relative strengths of interactions among these genes were based on published genetic and molecular data, mainly relying on mRNA expression patterns under wild type and mutant backgrounds. The network model is made of binary elements and we used a particular dynamic implementation for the network that we call semi-synchronic. Using this method the network reaches six attractors; four of them correspond to observed patterns of gene expression found in the floral organs ofArabidopsis(sepals, petals, stamens and carpels) as predicted by the ABC model of flower morphogenesis. The fifth state corresponds to cells that are not competent to flowering, and the sixth attractor predicted by the model is never found in wild-type plants, but it could be induced experimentally. We discuss the biological implications and the potential use of this network modeling approach to integrate functional data of regulatory genes of plant development.

Research paper thumbnail of Genetic Regulation of Root Hair Development in Arabidopsis Thaliana: A Network Model

Journal of Theoretical Biology, 2000

The root epidermis of Arabidopsis thaliana is formed by alternate "les of hair and non-hair cells... more The root epidermis of Arabidopsis thaliana is formed by alternate "les of hair and non-hair cells. Epidermal cells overlying two cortex cells eventually develop a hair, while those overlying only one cortex cell do not. Here we propose a network model that integrates most of the available genetic and molecular data on the regulatory and signaling pathways underlying root epidermal di!erentiation. The network architecture includes two pathways; one formed by the genes ¹¹G, R homolog, G¸2 and CPC, and the other one by the signal transduction proteins ETR1 and CTR1. Both parallel pathways regulate the activity of AXR2 and RHD6, which in turn control the development of root hairs. The regulatory network was simulated as a dynamical system of eight discrete state variables. The distinction between epidermal cells contacting one or two cortical cells was accounted for by "xing the initial states of CPC and ETR1 proteins. The model allows for predictions of mutants and pharmacological e!ects because it includes the ethylene receptor. The dynamical system reaches one of the six stable states depending upon the initial state of the CPC variable and the ethylene receptor. Two of the stable states describe the activation patterns observed in mature trichoblasts (hair cells) and atrichoblasts (non-hair cells) in the wild-type phenotype and under normal ethylene availability. The other four states correspond to changes in the number of hair cells due to experimentally induced changes in ethylene availability. This model provides a hypothesis on the interactions among genes that encode transcription factors that regulate root hair development and the proteins involved in the ethylene transduction pathway. This is the "rst e!ort to use a dynamical system to understand the complex genetic regulatory interactions that rule Arabidopsis primary root development. The advantages of this type of models over static schematic representations are discussed.

Research paper thumbnail of An Efficient Method for Dynamic Analysis of Gene Regulatory Networks and in silico Gene Perturbation Experiments

With the increasing availability of experimental data on gene-gene and protein-protein interactio... more With the increasing availability of experimental data on gene-gene and protein-protein interactions, modeling of gene regulatory networks has gained a special attention lately. To have a better understanding of these networks it is necessary to capture their dynamical properties, by computing its steady states. Various methods have been proposed to compute steady states but almost all of them suffer from the state space explosion problem with the increasing size of the networks. Hence it becomes difficult to model even moderate sized networks using these techniques. In this paper, we present a new representation of gene regulatory networks, which facilitates the steady state computation of networks as large as 1200 nodes and 5000 edges. We benchmarked and validated our algorithm on the T helper model from [8] and performed in silico knock out experiments: showing both a reduction in computation time and correct steady state identification.

Research paper thumbnail of Synchronous versus asynchronous modeling of gene regulatory networks

Bioinformatics/computer Applications in The Biosciences, 2008

In silico modeling of gene regulatory networks has gained some momentum recently due to increased... more In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. Results: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software.

Research paper thumbnail of A method for the generation of standardized qualitative dynamical systems of regulatory networks

Theoretical Biology and Medical Modelling, 2006

Background Modeling of molecular networks is necessary to understand their dynamical properties. ... more Background Modeling of molecular networks is necessary to understand their dynamical properties. While a wealth of information on molecular connectivity is available, there are still relatively few data regarding the precise stoichiometry and kinetics of the biochemical reactions underlying most molecular networks. This imbalance has limited the development of dynamical models of biological networks to a small number of well-characterized systems. To overcome this problem, we wanted to develop a methodology that would systematically create dynamical models of regulatory networks where the flow of information is known but the biochemical reactions are not. There are already diverse methodologies for modeling regulatory networks, but we aimed to create a method that could be completely standardized, i.e. independent of the network under study, so as to use it systematically. Results We developed a set of equations that can be used to translate the graph of any regulatory network into a continuous dynamical system. Furthermore, it is also possible to locate its stable steady states. The method is based on the construction of two dynamical systems for a given network, one discrete and one continuous. The stable steady states of the discrete system can be found analytically, so they are used to locate the stable steady states of the continuous system numerically. To provide an example of the applicability of the method, we used it to model the regulatory network controlling T helper cell differentiation. Conclusion The proposed equations have a form that permit any regulatory network to be translated into a continuous dynamical system, and also find its steady stable states. We showed that by applying the method to the T helper regulatory network it is possible to find its known states of activation, which correspond the molecular profiles observed in the precursor and effector cell types.

Research paper thumbnail of Dynamics of the Genetic Regulatory Network for Arabidopsis thaliana Flower Morphogenesis

Journal of Theoretical Biology, 1998

We present a network model and its dynamic analysis for the regulatory relationships among 11 gen... more We present a network model and its dynamic analysis for the regulatory relationships among 11 genes that participate inArabidopsis thalianaflower morphogenesis. The topology of the network and the relative strengths of interactions among these genes were based on published genetic and molecular data, mainly relying on mRNA expression patterns under wild type and mutant backgrounds. The network model is made of binary elements and we used a particular dynamic implementation for the network that we call semi-synchronic. Using this method the network reaches six attractors; four of them correspond to observed patterns of gene expression found in the floral organs ofArabidopsis(sepals, petals, stamens and carpels) as predicted by the ABC model of flower morphogenesis. The fifth state corresponds to cells that are not competent to flowering, and the sixth attractor predicted by the model is never found in wild-type plants, but it could be induced experimentally. We discuss the biological implications and the potential use of this network modeling approach to integrate functional data of regulatory genes of plant development.

Research paper thumbnail of Genetic Regulation of Root Hair Development in Arabidopsis Thaliana: A Network Model

Journal of Theoretical Biology, 2000

The root epidermis of Arabidopsis thaliana is formed by alternate "les of hair and non-hair cells... more The root epidermis of Arabidopsis thaliana is formed by alternate "les of hair and non-hair cells. Epidermal cells overlying two cortex cells eventually develop a hair, while those overlying only one cortex cell do not. Here we propose a network model that integrates most of the available genetic and molecular data on the regulatory and signaling pathways underlying root epidermal di!erentiation. The network architecture includes two pathways; one formed by the genes ¹¹G, R homolog, G¸2 and CPC, and the other one by the signal transduction proteins ETR1 and CTR1. Both parallel pathways regulate the activity of AXR2 and RHD6, which in turn control the development of root hairs. The regulatory network was simulated as a dynamical system of eight discrete state variables. The distinction between epidermal cells contacting one or two cortical cells was accounted for by "xing the initial states of CPC and ETR1 proteins. The model allows for predictions of mutants and pharmacological e!ects because it includes the ethylene receptor. The dynamical system reaches one of the six stable states depending upon the initial state of the CPC variable and the ethylene receptor. Two of the stable states describe the activation patterns observed in mature trichoblasts (hair cells) and atrichoblasts (non-hair cells) in the wild-type phenotype and under normal ethylene availability. The other four states correspond to changes in the number of hair cells due to experimentally induced changes in ethylene availability. This model provides a hypothesis on the interactions among genes that encode transcription factors that regulate root hair development and the proteins involved in the ethylene transduction pathway. This is the "rst e!ort to use a dynamical system to understand the complex genetic regulatory interactions that rule Arabidopsis primary root development. The advantages of this type of models over static schematic representations are discussed.

Research paper thumbnail of An Efficient Method for Dynamic Analysis of Gene Regulatory Networks and in silico Gene Perturbation Experiments

With the increasing availability of experimental data on gene-gene and protein-protein interactio... more With the increasing availability of experimental data on gene-gene and protein-protein interactions, modeling of gene regulatory networks has gained a special attention lately. To have a better understanding of these networks it is necessary to capture their dynamical properties, by computing its steady states. Various methods have been proposed to compute steady states but almost all of them suffer from the state space explosion problem with the increasing size of the networks. Hence it becomes difficult to model even moderate sized networks using these techniques. In this paper, we present a new representation of gene regulatory networks, which facilitates the steady state computation of networks as large as 1200 nodes and 5000 edges. We benchmarked and validated our algorithm on the T helper model from [8] and performed in silico knock out experiments: showing both a reduction in computation time and correct steady state identification.

Research paper thumbnail of Synchronous versus asynchronous modeling of gene regulatory networks

Bioinformatics/computer Applications in The Biosciences, 2008

In silico modeling of gene regulatory networks has gained some momentum recently due to increased... more In silico modeling of gene regulatory networks has gained some momentum recently due to increased interest in analyzing the dynamics of biological systems. This has been further facilitated by the increasing availability of experimental data on gene-gene, protein-protein and gene-protein interactions. The two dynamical properties that are often experimentally testable are perturbations and stable steady states. Although a lot of work has been done on the identification of steady states, not much work has been reported on in silico modeling of cellular differentiation processes. Results: In this manuscript, we provide algorithms based on reduced ordered binary decision diagrams (ROBDDs) for Boolean modeling of gene regulatory networks. Algorithms for synchronous and asynchronous transition models have been proposed and their corresponding computational properties have been analyzed. These algorithms allow users to compute cyclic attractors of large networks that are currently not feasible using existing software.

Research paper thumbnail of A method for the generation of standardized qualitative dynamical systems of regulatory networks

Theoretical Biology and Medical Modelling, 2006

Background Modeling of molecular networks is necessary to understand their dynamical properties. ... more Background Modeling of molecular networks is necessary to understand their dynamical properties. While a wealth of information on molecular connectivity is available, there are still relatively few data regarding the precise stoichiometry and kinetics of the biochemical reactions underlying most molecular networks. This imbalance has limited the development of dynamical models of biological networks to a small number of well-characterized systems. To overcome this problem, we wanted to develop a methodology that would systematically create dynamical models of regulatory networks where the flow of information is known but the biochemical reactions are not. There are already diverse methodologies for modeling regulatory networks, but we aimed to create a method that could be completely standardized, i.e. independent of the network under study, so as to use it systematically. Results We developed a set of equations that can be used to translate the graph of any regulatory network into a continuous dynamical system. Furthermore, it is also possible to locate its stable steady states. The method is based on the construction of two dynamical systems for a given network, one discrete and one continuous. The stable steady states of the discrete system can be found analytically, so they are used to locate the stable steady states of the continuous system numerically. To provide an example of the applicability of the method, we used it to model the regulatory network controlling T helper cell differentiation. Conclusion The proposed equations have a form that permit any regulatory network to be translated into a continuous dynamical system, and also find its steady stable states. We showed that by applying the method to the T helper regulatory network it is possible to find its known states of activation, which correspond the molecular profiles observed in the precursor and effector cell types.