arXiv subjects

Elena Dimitrova

Publications and source records attributed to Elena Dimitrova.

6 recordsLinked to original sources

arXiv2024

Modular control of Boolean network models

The concept of control is crucial for effectively understanding and applying biological network models. Key structural features relate to control functions through gene regulation, signaling, or metabolic mechanisms, and computational models need to encode these. Applications often focus on model-based control, such as in biomedicine or metabolic engineering. In a recent paper, the authors developed a theoretical framework of modularity in Boolean networks, which lead to a canonical semidirect product decomposition of these systems. In this paper, we present an approach to model-based control that exploits this modular structure, as well as the canalizing features of the regulatory mechanisms. We show how to identify control strategies from the individual modules, and we present a criterion based on canalizing features of the regulatory rules to identify modules that do not contribute to network control and can be excluded. For even moderately sized networks, finding global control inputs is computationally challenging. Our modular approach leads to an efficient approach to solving this problem. We apply it to a published Boolean network model of blood cancer large granular lymphocyte (T-LGL) leukemia to identify a minimal control set that achieves a desired control objective.

q-bio.MN↗

arXiv2021

Revealing the canalizing structure of Boolean functions: Algorithms and applications

Boolean functions can be represented in many ways including logical forms, truth tables, and polynomials. Additionally, Boolean functions have different canonical representations such as minimal disjunctive normal forms. Other canonical representation is based on the polynomial representation of Boolean functions where they can be written as a nested product of canalizing layers and a polynomial that contains the noncanalizing variables. In this paper we study the problem of identifying the canalizing layers format of Boolean functions. First, we show that the problem of finding the canalizing layers is NP-hard. Second, we present several algorithms for finding the canalizing layers of a Boolean function, discuss their complexities, and compare their performances. Third, we show applications where the computation of canalizing layers can be used for finding a disjunctive normal form of a nested canalizing function. Another application deals with the reverse engineering of Boolean networks with a prescribed layering format. Finally, implementations of our algorithms in Python and in the computer algebra system Macaulay2 are available at https://github.com/ckadelka/BooleanCanalization.

cs.CC↗

arXiv2019

Quantifying the Total Effect of Edge Interventions in Discrete Multistate Networks

Developing efficient computational methods to assess the impact of external interventions on the dynamics of a network model is an important problem in systems biology. This paper focuses on quantifying the global changes that result from the application of an intervention to produce a desired effect, which we define as the total effect of the intervention. The type of mathematical models that we will consider are discrete dynamical systems which include the widely used Boolean networks and their generalizations. The potential interventions can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. We use a class of regulatory rules called nested canalizing functions that frequently appear in published models and were inspired by the concept of canalization in evolutionary biology. In this paper, we provide a polynomial normal form based on the canalizing properties of regulatory functions. Using this polynomial normal form, we give a set of formulas for counting the maximum number of transitions that will change in the state space upon an edge deletion in the wiring diagram. These formulas rely on the canalizing structure of the target function since the number of changed transitions depends on the canalizing layer that includes the input to be deleted. We also present computations on random networks to compare the exact number of changes with the upper bounds provided by our formulas. Finally, we provide statistics on the sharpness of these upper bounds in random networks.

q-bio.MN↗

arXiv2017

Small Groebner Fans of Ideals of Points

In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this property. Moreover, we provide methodologies for constructing such ideals. We then relax the condition of uniqueness. The second and most relevant topic discussed here is to consider and identify pairs of ideals with the same number of reduced Groebner bases, that is, with the same cardinality of their associated Groebner fan.

math.AC↗

arXiv2011

Nested canalyzing depth and network stability

We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and sensitivities of the variables. This analysis quantifies how canalyzation leads to higher stability in Boolean networks. It generalizes the notion of nested canalyzing functions (NCFs), which are precisely the functions with maximum depth. NCFs have been proposed as gene regulatory network models, but their structure is frequently too restrictive and they are extremely sparse. We find that functions become decreasingly sensitive to input perturbations as the canalyzing depth increases, but exhibit rapidly diminishing returns in stability. Additionally, we show that as depth increases, the dynamics of networks using these functions quickly approach the critical regime, suggesting that real networks exhibit some degree of canalyzing depth, and that NCFs are not significantly better than functions of sufficient depth for many applications of the modeling and reverse engineering of biological networks.

q-bio.MN↗

arXiv2009

Parameter estimation for Boolean models of biological networks

Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web service, that helps users construct Boolean network models based on experimental data and biological input. The key feature is a discrete analog of parameter estimation for continuous models. With only experimental data as input, the software can be used as a tool for reverse-engineering of Boolean network models from experimental time course data.

q-bio.MN↗