Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development

Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.Comment: 24 pages, 6 figures, 1 tabl

Computational Complexity of Minimal Trap Spaces in Boolean Networks

Trap spaces of a Boolean network (BN) are the sub-hypercubes closed by the function of the BN. A trap space is minimal if it does not contain any smaller trap space. Minimal trap spaces have applications for the analysis of dynamic attractors of BNs with various update modes. This paper establishes computational complexity results of three decision problems related to minimal trap spaces of BNs: the decision of the trap space property of a sub-hypercube, the decision of its minimality, and the decision of the belonging of a given configuration to a minimal trap space. Under several cases on Boolean function specifications, we investigate the computational complexity of each problem. In the general case, we demonstrate that the trap space property is coNP-complete, and the minimality and the belonging properties are $\Pi_2^{\text P}$-complete. The complexities drop by one level in the polynomial hierarchy whenever the local functions of the BN are either unate, or are specified using truth-table, binary decision diagrams, or double-DNF (Petri net encoding): the trap space property can be decided in P, whereas the minimality and the belonging are coNP-complete. When the BN is given as its functional graph, all these problems can be decided by deterministic polynomial time algorithms

SYNTHESIS OF COMPOSITE LOGIC GATE IN QCA EMBEDDING UNDERLYING REGULAR CLOCKING

Quantum-dot Cellular Automata (QCA) has emerged as one of the alternative technologies for current CMOS technology. It has the advantage of computing at a faster speed, consuming lower power, and work at Nano- Scale. Besides these advantages, QCA logic is limited to its primitive gates, majority voter and inverter only, results in limitation of cost-efficient logic circuit realization. Numerous designs have been proposed to realize various intricate logic gates in QCA at the penalty of non-uniform clocking and improper layout. This paper proposes a Composite Gate (CG) in QCA, which realizes all the essential digital logic gates such as AND, NAND, Inverter, OR, NOR, and exclusive gates like XOR and XNOR. Reportedly, the proposed design is the first of its kind to generate all basic logic in a single unit. The most striking feature of this work is the augmentation of the underlying clocking circuit with the logic block, making it a more realistic circuit. The Reliable, Efficient, and Scalable (RES) underlying regular clocking scheme is utilized to enhance the proposed design’s scalability and efficiency. The relevance of the proposed design is best cited with coplanar implementation of 2-input symmetric functions, achieving 33% gain in gate count and without any garbage output. The evaluation and analysis of dissipated energy for both the design have been carried out. The end product is verified using the QCADesigner2.0.3 simulator, and QCAPro is employed for the study of power dissipation

Regulatory patterns in molecular interaction networks

Understanding design principles of molecular interaction networks is an important goal of molecular systems biology. Some insights have been gained into features of their network topology through the discovery of graph theoretic patterns that constrain network dynamics. This paper contributes to the identification of patterns in the mechanisms that govern network dynamics. The control of nodes in gene regulatory, signaling, and metabolic networks is governed by a variety of biochemical mechanisms, with inputs from other network nodes that act additively or synergistically. This paper focuses on a certain type of logical rule that appears frequently as a regulatory pattern. Within the context of the multistate discrete model paradigm, a rule type is introduced that reduces to the concept of nested canalyzing function in the Boolean network case. It is shown that networks that employ this type of multivalued logic exhibit more robust dynamics than random networks, with few attractors and short limit cycles. It is also shown that the majority of regulatory functions in many published models of gene regulatory and signaling networks are nested canalyzing.Comment: gene regulation; signaling; mathematical model; nested canalyzing function; robustnes

Identification and analysis of patterns in DNA sequences, the genetic code and transcriptional gene regulation

The present cumulative work consists of six articles linked by the topic ”Identification and Analysis of Patterns in DNA sequences, the Genetic Code and Transcriptional Gene Regulation”. We have applied a binary coding, to efficiently findpatterns within nucleotide sequences. In the first and second part of my work one single bit to encode all four nucleotides is used. The three possibilities of a one - bit coding are: keto (G,U) - amino (A,C) bases, strong (G,C) - weak (A,U) bases, and purines (G,A) - pyrimidines (C,U). We found out that the best pattern could be observed using the purine - pyrimidine coding. Applying this coding we have succeeded in finding a new representation of the genetic code which has been published under the title ”A New Classification Scheme of the Genetic Code” in ”Journal of Molecular Biology” and ”A Purine-Pyrimidine Classification Scheme of the Genetic Code” in ”BIOForum Europe”. This new representation enables to reduce the common table of the genetic code from 64 to 32 fields maintaining the same information content. It turned out that all known and even new patterns of the genetic code can easily be recognized in this new scheme. Furthermore, our new representation allows us for speculations about the origin and evolution of the translation machinery and the genetic code. Thus, we found a possible explanation for the contemporary codon - amino acid assignment and wide support for an early doublet code. Those explanations have been published in ”Journal of Bioinformatics and Computational Biology” under the title ”The New Classification Scheme of the Genetic Code, its Early Evolution, and tRNA Usage”. Assuming to find these purine - pyrimidine patterns at the DNA level itself, we examined DNA binding sites for the occurrence of binary patterns. A comprehensive statistic about the largest class of restriction enzymes (type II) has shown a very distinctive purine - pyrimidine pattern. Moreover, we have observed a higher G+C content for the protein binding sequences. For both observations we have provided and discussed several explanations published under the title ”Common Patterns in Type II Restriction Enzyme Binding Sites” in ”Nucleic Acid Research”. The identified patterns may help to understand how a protein finds its binding site. In the last part of my work two submitted articles about the analysis of Boolean functions are presented. Boolean functions are used for the description and analysis of complex dynamic processes and make it easier to find binary patterns within biochemical interaction networks. It is well known that not all functions are necessary to describe biologically relevant gene interaction networks. In the article entitled ”Boolean Networks with Biologically Relevant Rules Show Ordered Behavior”, submitted to ”BioSystems”, we have shown, that the class of required Boolean functions can strongly be restricted. Furthermore, we calculated the exact number of hierarchically canalizing functions which are known to be biologically relevant. In our work ”The Decomposition Tree for Analysis of Boolean Functions” submitted to ”Journal of Complexity”, we introduced an efficient data structure for the classification and analysis of Boolean functions. This permits the recognition of biologically relevant Boolean functions in polynomial time

Energy-Efficient Digital Circuit Design using Threshold Logic Gates

abstract: Improving energy efficiency has always been the prime objective of the custom and automated digital circuit design techniques. As a result, a multitude of methods to reduce power without sacrificing performance have been proposed. However, as the field of design automation has matured over the last few decades, there have been no new automated design techniques, that can provide considerable improvements in circuit power, leakage and area. Although emerging nano-devices are expected to replace the existing MOSFET devices, they are far from being as mature as semiconductor devices and their full potential and promises are many years away from being practical. The research described in this dissertation consists of four main parts. First is a new circuit architecture of a differential threshold logic flipflop called PNAND. The PNAND gate is an edge-triggered multi-input sequential cell whose next state function is a threshold function of its inputs. Second a new approach, called hybridization, that replaces flipflops and parts of their logic cones with PNAND cells is described. The resulting \hybrid circuit, which consists of conventional logic cells and PNANDs, is shown to have significantly less power consumption, smaller area, less standby power and less power variation. Third, a new architecture of a field programmable array, called field programmable threshold logic array (FPTLA), in which the standard lookup table (LUT) is replaced by a PNAND is described. The FPTLA is shown to have as much as 50% lower energy-delay product compared to conventional FPGA using well known FPGA modeling tool called VPR. Fourth, a novel clock skewing technique that makes use of the completion detection feature of the differential mode flipflops is described. This clock skewing method improves the area and power of the ASIC circuits by increasing slack on timing paths. An additional advantage of this method is the elimination of hold time violation on given short paths. Several circuit design methodologies such as retiming and asynchronous circuit design can use the proposed threshold logic gate effectively. Therefore, the use of threshold logic flipflops in conventional design methodologies opens new avenues of research towards more energy-efficient circuits.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Tackling Universal Properties of Minimal Trap Spaces of Boolean Networks

Minimal trap spaces (MTSs) capture subspaces in which the Boolean dynamics is trapped, whatever the update mode. They correspond to the attractors of the most permissive mode. Due to their versatility, the computation of MTSs has recently gained traction, essentially by focusing on their enumeration. In this paper, we address the logical reasoning on universal properties of MTSs in the scope of two problems: the reprogramming of Boolean networks for identifying the permanent freeze of Boolean variables that enforce a given property on all the MTSs, and the synthesis of Boolean networks from universal properties on their MTSs. Both problems reduce to solving the satisfiability of quantified propositional logic formula with 3 levels of quantifiers ($\exists\forall\exists$). In this paper, we introduce a Counter-Example Guided Refinement Abstraction (CEGAR) to efficiently solve these problems by coupling the resolution of two simpler formulas. We provide a prototype relying on Answer-Set Programming for each formula and show its tractability on a wide range of Boolean models of biological networks.Comment: Accepted at 21st International Conference on Computational Methods in Systems Biology (CMSB 2023

Inferring Networks with Gene Knockouts and Computational Algebra

The network inference problem is a significant problem in systems biology. In this paper, we will describe an approach to this problem involving computational algebra. Specifically, given an unknown Boolean function, we can create a square-free monomial or pseudomonomial ideal whose primary decomposition encodes the possible sets of variables that the function can depend on, and whether those interactions are activations or inhibitions. We apply this problem to time series data generated from a non-linear ODE, built over unknown feed-forward loops, and subject to gene knockouts