Maximum Number of Fixed Points in Regulatory Boolean Networks

Boolean networks (BNs) have been extensively used as mathematical models of genetic regulatory networks. The number of fixed points of a BN is a key feature of its dynamical behavior. Here, we study the maximum number of fixed points in a particular class of BNs called regulatory Boolean networks, where each interaction between the elements of the network is either an activation or an inhibition. We find relationships between the positive and negative cycles of the interaction graph and the number of fixed points of the network. As our main result, we exhibit an upper bound for the number of fixed points in terms of minimum cardinality of a set of vertices meeting all positive cycles of the network, which can be applied in the design of genetic regulatory networks.     

Mathematical Conditions for Induced Cell Differentiation and Trans-differentiation in Adult Cells

We present a theoretical framework for the analysis of the effect of a fully differentiated cell population on a neighboring stem cell population in Multi-Cellular Organisms (MCOs). Such an organism is constituted by a set of different cell populations, each set of which converges to a different cycle from all possible options, of the same Boolean network. Cells communicate via a subset of the nodes called signals. We show that generic dynamic properties of cycles and nodes in random Boolean networks can induce cell differentiation. Specifically we propose algorithms, conditions and methods to examine if a set of signaling nodes enabling these conversions can be found. Surprisingly we find that robust conversions can be obtained even with a very small number of signals. The proposed conversions can occur in multiple spatial organizations and can be used as a model for regeneration in MCOs, where an islet of cells of one type (representing stem cells) is surrounded by cells of another type (representing differentiated cells). The cells at the outer layer of the islet function like progenitor cells (i.e. dividing asymmetrically and differentiating). To the best of our knowledge, this is the first work showing a tissue-like regeneration in MCO simulations based on random Boolean networks. We show that the probability to obtain a conversion decreases with the log of the node number in the network, showing that the model is relevant for large networks as well. We have further checked that the conversions are not trivial, i.e. conversions do not occur due to irregular structures of the Boolean network, and the converting cycle undergoes a respectable change in its behavior. Finally we show that the model can also be applied to a realistic genetic regulatory network, showing that the basic mathematical insight from regular networks holds in more complex experiment-based networks.     

A mathematical design of vector vaccine against autoimmune disease

Viruses have been implicated in the initiation, progression, and exacerbation of several human autoimmune diseases. Evidence also exists that viruses can protect against autoimmune disease. Several proposed mechanisms explain the viral effects. One mechanism is “molecular mimicry” which represents a shared immunologic epitope with a microbe and the host. We consider, using a simple mathematical model, whether and how a viral infection with molecular mimicry can be beneficial or detrimental for autoimmune disease. Furthermore, we consider the possibility of development of a vector therapeutic vaccine that can relieve autoimmune disease symptoms. Our findings demonstrate that vaccine therapy success necessitates (i) appropriate immune response function, (ii) appropriate affinities with self and non-self antigen, and (iii) a replicative vector vaccine. Moreover, the model shows that the viral infection can cause autoimmune relapses.     

A novel generalized design methodology and realization of Boolean operations using DNA

The biological deoxyribonucleic acid (DNA) strand has been increasingly seen as a promising computing unit. A new algorithm is formulated in this paper to design any DNA Boolean operator with molecular beacons (MBs) as its input. Boolean operators realized using the proposed design methodology is presented. The developed operators adopt a uniform representation for logical 0 and 1 for any Boolean operator. The Boolean operators designed in this work employ only a hybridization operation at each stage. Further, this paper for the first time brings out the realization of a binary adder and subtractor using molecular beacons. Simulation results of the DNA-based binary adder and subtractor are given to validate the design.     

A deoxyribozyme-based molecular automaton

We describe a molecular automaton, called MAYA, which encodes a version of the game of tic-tac-toe and interactively competes against a human opponent. The automaton is a Boolean network of deoxyribozymes that incorporates 23 molecular-scale logic gates and one constitutively active deoxyribozyme arrayed in nine wells (3x3) corresponding to the game board. To make a move, MAYA carries out an analysis of the input oligonucleotide keyed to a particular move by the human opponent and indicates a move by fluorescence signaling in a response well. The cycle of human player input and automaton response continues until there is a draw or a victory for the automaton. The automaton cannot be defeated because it implements a perfect strategy.     

The progress of DNA analyzing techniques and its impact on plant molecular systematics

Recent advances in manipulating nucleic acids have opened a new research field called plant molecular systematics. This short review provides an overview of molecular techniques which have been used in the analysis of DNA molecules for the study of plant systematics, with a special emphasis on PCR. The early application of DNA analysis, DNA/DNA hybridization, has not become popular with plant systematists, because of several disadvantages inherent in the method. The survey of restriction fragment length polymorphisms (RFLPs), on the contrary, has become one of the preferred methods used by plant molecular systematists, since the method is relatively easy to perform. Although unambiguous data can be obtained by both long-range restriction mapping and nucleotide sequencing, these approaches may have limited use in plant molecular systematics because of their laborious experimental procedures relying on conventional molecular cloning techniques. To date, PCR based analyses of the DNA molecule seem to be the most suitable experimental approach for plant molecular systematics. Several advantages of the method have changed both the quality and quantity of the DNA data. Further application of PCR to plant molecular systematics will open up a new era in the field. The present paper is based on the contribution which was read in a symposium entitled “Organellar DNA Variations in Higher Plants and their Taxonomic Significance”, at the 50th Annual Meeting of the Botanical Society of Japan in Shizuoka on October 2, 1990, under the auspices of the Japan Society of Plant Taxonomists.     

Intervention in context-sensitive probabilistic Boolean networks

MOTIVATION: Intervention in a gene regulatory network is used to help it avoid undesirable states, such as those associated with a disease. Several types of intervention have been studied in the framework of a probabilistic Boolean network (PBN), which is essentially a finite collection of Boolean networks in which at any discrete time point the gene state vector transitions according to the rules of one of the constituent networks. For an instantaneously random PBN, the governing Boolean network is randomly chosen at each time point. For a context-sensitive PBN, the governing Boolean network remains fixed for an interval of time until a binary random variable determines a switch. The theory of automatic control has been previously applied to find optimal strategies for manipulating external (control) variables that affect the transition probabilities of an instantaneously random PBN to desirably affect its dynamic evolution over a finite time horizon. This paper extends the methods of external control to context-sensitive PBNs. RESULTS: This paper treats intervention via external control variables in context-sensitive PBNs by extending the results for instantaneously random PBNs in several directions. First, and most importantly, whereas an instantaneously random PBN yields a Markov chain whose state space is composed of gene vectors, each state of the Markov chain corresponding to a context-sensitive PBN is composed of a pair, the current gene vector occupied by the network and the current constituent Boolean network. Second, the analysis is applied to PBNs with perturbation, meaning that random gene perturbation is permitted at each instant with some probability. Third, the (mathematical) influence of genes within the network is used to choose the particular gene with which to intervene. Lastly, PBNs are designed from data using a recently proposed inference procedure that takes steady-state considerations into account. The results are applied to a context-sensitive PBN derived from gene-expression data collected in a study of metastatic melanoma, the intent being to devise a control strategy that reduces the WNT5A gene's action in affecting biological regulation, since the available data suggest that disruption of this influence could reduce the chance of a melanoma metastasizing.     

Algorithms for identifying Boolean networks and related biological networks based on matrix multiplication and fingerprint function.

Due to the recent progress of the DNA microarray technology, a large number of gene expression profile data are being produced. How to analyze gene expression data is an important topic in computational molecular biology. Several studies have been done using the Boolean network as a model of a genetic network. This paper proposes efficient algorithms for identifying Boolean networks of bounded indegree and related biological networks, where identification of a Boolean network can be formalized as a problem of identifying many Boolean functions simultaneously. For the identification of a Boolean network, an O(mnD+1) time naive algorithm and a simple O (mnD) time algorithm are known, where n denotes the number of nodes, m denotes the number of examples, and D denotes the maximum in degree. This paper presents an improved O(momega-2nD + mnD+omega-3) time Monte-Carlo type randomized algorithm, where omega is the exponent of matrix multiplication (currently, omega < 2.376). The algorithm is obtained by combining fast matrix multiplication with the randomized fingerprint function for string matching. Although the algorithm and its analysis are simple, the result is nontrivial and the technique can be applied to several related problems.     

酶催化反应驰豫时间的布尔函数图解法

证明可使用布尔函数图论方法＾「１」来研究酶反应驰豫时间问题,所用方法与解决酶催化反应驰豫时间的Ｋｉｎｇ－Ａｌｔｍａｎ法＾「２」相比,具有图形鲜明、绘法简易、使用方便（不需画出支撑入树之类的图形,不需代数运算）、结果可靠（不易发生遗漏或错算）等优点。列举一类酶反应体系（Ｅ等价于ＥＳ等价于ＥＳ＾＊）作为此图形方法求解的实例。     

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.     

Boolean analysis of cell regulation networks

A comparison is made between the predictions of the Boolean and continuous analysis of a regulation model when the formation of two mediators interacting by cross-inhibition is stimulated by one or two specific signals. For such a system, the Boolean analysis reproduces the characteristics of behaviour previously predicted by continuous analysis (multiple stable states of opposite type, discontinuous transition, and associated hysteresis phenomenon). The qualitative agreement between the two methods allows a qualitative but rigorous treatment of regulation systems in which the Boolean analysis is applicable. From a general schematic representation of interaction in bidirectional control systems, we analyse by the Boolean method a large range of possible systems of increasing complexities which could theoretically apply. Previously unforeseen consequences of some systems are described. After that, we give a logical analysis of a well-known system (negative loop grafted with additional external controls) and discuss the application of such a system to explain certain oscillatory phenomena in the cell, showing the disrupting role of an additional control on the expected behaviour. Thus, when the analysis of a model including a negative loop does not indicate the possibility of experimentally suggested oscillations, we propose other simple logical structures which can predict this behaviour. Finally, we show a logical analysis of an opposite type of example of cell regulation where the biochemical observations can be accounted for simply by a negative loop grafted with one input variable.     

Improved agarose gel electrophoresis method and molecular mass calculation for high molecular mass hyaluronan

The molecular mass of the polysaccharide hyaluronan (HA) is an important determinant of its biological activity and physicochemical properties. One method currently used for the analysis of the molecular mass distribution of an HA sample is gel electrophoresis. In the current work, an improved agarose gel electrophoresis method for analysis of high molecular mass HA is presented and validated. HA mobility in 0.5% agarose minigels was found to be linearly related to the logarithm of molecular mass in the range from approximately 200 to 6000 kDa. A sample load of 2.5 μg for polydisperse HA samples was employed. Densitometric scanning of stained gels allowed analysis of the range of molecular masses present in the sample as well as calculation of weight-average and number-average values. The method was validated for a polydisperse HA sample with a weight-average molecular mass of approximately 2000 kDa. Excellent agreement was found between the weight-average molecular mass determined by electrophoresis and that determined by rheological measurement of the solution viscosity. The revised method was then used to show that heating solutions of HA at 100 °C, followed by various cooling procedures, had no effect on the HA molecular mass distribution.     

Identification of control targets in Boolean molecular network models via computational algebra

Background

Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system.

Results

This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg.

Conclusions

This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.

     

Boolink: a graphical interface for open access Boolean network simulations and use in guard cell CO2 signaling

Signaling networks are at the heart of almost all biological processes. Most of these networks contain large number of components, and often either the connections between these components are not known or the rate equations that govern the dynamics of soluble signaling components are not quantified. This uncertainty in network topology and parameters can make it challenging to formulate detailed mathematical models. Boolean networks, in which all components are either on or off, have emerged as viable alternatives to detailed mathematical models that contain rate constants and other parameters. Therefore, open-source platforms of Boolean models for community use are desirable. Here, we present Boolink, a freely available graphical user interface that allows users to easily construct and analyze existing Boolean networks. Boolink can be applied to any Boolean network. We demonstrate its application using a previously published network for abscisic acid (ABA)-driven stomatal closure in Arabidopsis spp. (Arabidopsis thaliana). We also show how Boolink can be used to generate testable predictions by extending the network to include CO₂ regulation of stomatal movements. Predictions of the model were experimentally tested, and the model was iteratively modified based on experiments showing that ABA effectively closes Arabidopsis stomata at near-zero CO₂ concentrations (1.5-ppm CO₂). Thus, Boolink enables public generation and the use of existing Boolean models, including the prior developed ABA signaling model with added CO₂ signaling components.

An open-source, graphical interface for the simulation of Boolean networks is presented, applied to an abscisic acid signaling network in guard cells, and extended to include input from CO₂.     

Médicaments radiopharmaceutiques : du diagnostic au théranostique des tumeurs neuroendocrines

Neuroendocrine tumors (NET) are a heterogeneous group originating from endocrine cells, which have the ability to develop themselves on various organs. Most of NET are well differentiated and have the capacity to produce different hormones and biogenic amines. NETs usually appear sporadically and can also be associated with different syndromes (multiple endocrine neoplasia). For the majority of NETs, surgical resection is the treatment of choice requiring the precise location of the tumor before surgery as well as the determination of the stage, followed by monitoring the progression of the disease. In the diagnostic process, nuclear medicine with molecular imaging plays a fundamental role. The secretory functions of these tumors enable the use of molecular imaging by targeting specific metabolic pathways or receptors. In addition, nuclear medicine also plays an important role in the field of therapy by replacing in one radiopharmaceutical drugs, the imaging suited radionuclide by replacing with a radionuclide emitting radiation suitable for therapy, also called vectorized internal radiotherapy. The activity of nuclear medicine, which enables diagnosis and treatment to be carried out using the same structures specific to the molecular targets of neuroendocrine tumors, is fully integrated into the new theragnostic approach, and constitutes one of its main pillars. The objective of this work is to describe the molecular targets expressed by NETs and corresponding radiopharmaceuticals, validated for human use (diagnosis and therapy).     

A method for molecular phylogeny construction by direct use of nucleotide sequence data

Summary A method for molecular phylogeny construction is newly developed. The method, called the stepwise ancestral sequence method, estimates molecular phylogenetic trees and ancestral sequences simultaneously on the basis of parsimony and sequence homology. For simplicity the emphasis is placed more on parsiomony than on sequence homology in the present study, though both are certainly important. Because parsimony alone will sometimes generate plural candidate trees, the method retains not one but five candidates from which one can then single out the final tree taking other criteria into account.The properties and performance of the method are then examined by simulating an evolving gene along a model phylogenetic tree. The estimated trees are found to lie in a narrow range of the parsimony criteria used in the present study. Thus, other criteria such as biological evidence and likelihood are necessary to single out the correct tree among them, with biological evidence taking precedence over any other criterion. The computer simulation also reveals that the method satisfactorily estimates both tree topology and ancestral sequences, at least for the evolutionary model used in the present study.