Boolean Models of Bistable Biological Systems

This paper presents an algorithm for approximating certain types of dynamical systems given by a system of ordinary delay differential equations by a Boolean network model. Often Boolean models are much simpler to understand than complex differential equations models. The motivation for this work comes from mathematical systems biology. While Boolean mechanisms do not provide information about exact concentration rates or time scales, they are often sufficient to capture steady states and other key dynamics. Due to their intuitive nature, such models are very appealing to researchers in the life sciences. This paper is focused on dynamical systems that exhibit bistability and are desc ribedby delay equations. It is shown that if a certain motif including a feedback loop is present in the wiring diagram of the system, the Boolean model captures the bistability of molecular switches. The method is appl ied to two examples from biology, the lac operon and the phage lambda lysis/lysogeny switch

An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring $R$, i.e., a ring with an explicit algorithm to solve one-sided (in)homogeneous linear systems over $R$. For a finitely generated maximal ideal $\mathfrak{m}$ in a commutative ring $R$ we show how solving (in)homogeneous linear systems over $R_{\mathfrak{m}}$ can be reduced to solving associated systems over $R$. Hence, the computability of $R$ implies that of $R_{\mathfrak{m}}$. As a corollary we obtain the computability of the category of finitely presented $R_{\mathfrak{m}}$-modules as an Abelian category, without the need of a Mora-like algorithm. The reduction also yields, as a by-product, a complexity estimation for the ideal membership problem over local polynomial rings. Finally, in the case of localized polynomial rings we demonstrate the computational advantage of our homologically motivated alternative approach in comparison to an existing implementation of Mora's algorithm.Comment: Fixed a typo in the proof of Lemma 4.3 spotted by Sebastian Posu

The Historical Context of the Gender Gap in Mathematics

This chapter is based on the talk that I gave in August 2018 at the ICM in Rio de Janeiro at the panel on "The Gender Gap in Mathematical and Natural Sciences from a Historical Perspective". It provides some examples of the challenges and prejudices faced by women mathematicians during last two hundred and fifty years. I make no claim for completeness but hope that the examples will help to shed light on some of the problems many women mathematicians still face today

The Influence of Canalization on the Robustness of Boolean Networks

Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by $k$-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to $c$-sensitivity and provides formulas for the activities and $c$-sensitivity of general $k$-canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the $c$-sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally efficient way to obtain Derrida values of Boolean networks, deterministic or stochastic, that does not involve simulation.Comment: 16 pages, 2 figures, 3 table

Impact of combined 18F-FDG PET/CT in head and neck tumours

To compare the interobserver agreement and degree of confidence in anatomical localisation of lesions using 2-[fluorine-18]fluoro-2-deoxy-D-glucose (18F-FDG) positron emission tomography (PET)/computed tomography (CT) and 18F-FDG PET alone in patients with head and neck tumours. A prospective study of 24 patients (16 male, eight female, median age 59 years) with head and neck tumours was undertaken. 18F-FDG PET/CT was performed for staging purposes. 2D images were acquired over the head and neck area using a GE Discovery LS™ PET/CT scanner. 18F-FDG PET images were interpreted by three independent observers. The observers were asked to localise abnormal 18F-FDG activity to an anatomical territory and score the degree of confidence in localisation on a scale from 1 to 3 (1=exact region unknown; 2=probable; 3=definite). For all 18F-FDG-avid lesions, standardised uptake values (SUVs) were also calculated. After 3 weeks, the same exercise was carried out using 18F-FDG PET/CT images, where CT and fused volume data were made available to observers. The degree of interobserver agreement was measured in both instances. A total of six primary lesions with abnormal 18F-FDG uptake (SUV range 7.2–22) were identified on 18F-FDG PET alone and on 18F-FDG PET/CT. In all, 15 nonprimary tumour sites were identified with 18F-FDG PET only (SUV range 4.5–11.7), while 17 were identified on 18F-FDG PET/CT. Using 18F-FDG PET only, correct localisation was documented in three of six primary lesions, while 18F-FDG PET/CT correctly identified all primary sites. In nonprimary tumour sites, 18F-FDG PET/CT improved the degree of confidence in anatomical localisation by 51%. Interobserver agreement in assigning primary and nonprimary lesions to anatomical territories was moderate using 18F-FDG PET alone (kappa coefficients of 0.45 and 0.54, respectively), but almost perfect with 18F-FDG PET/CT (kappa coefficients of 0.90 and 0.93, respectively). We conclude that 18F-FDG PET/CT significantly increases interobserver agreement and confidence in disease localisation of 18F-FDG-avid lesions in patients with head and neck cancers

Modeling Stochasticity and Variability in Gene Regulatory Networks

Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used successfully. This paper contributes an approach as an alternative to these classical settings. Within the discrete paradigm, where genes, proteins, and other molecular components of gene regulatory networks are modeled as discrete variables and are assigned as logical rules describing their regulation through interactions with other components. Stochasticity is modeled at the biological function level under the assumption that even if the expression levels of the input nodes of an update rule guarantee activation or degradation there is a probability that the process will not occur due to stochastic effects. This approach allows a finer analysis of discrete models and provides a natural setup for cell population simulations to study cell-to-cell variability. We applied our methods to two of the most studied regulatory networks, the outcome of lambda phage infection of bacteria and the p53-mdm2 complex.Comment: 23 pages, 8 figure

Casual Compressive Sensing for Gene Network Inference

We propose a novel framework for studying causal inference of gene interactions using a combination of compressive sensing and Granger causality techniques. The gist of the approach is to discover sparse linear dependencies between time series of gene expressions via a Granger-type elimination method. The method is tested on the Gardner dataset for the SOS network in E. coli, for which both known and unknown causal relationships are discovered

Mining and state-space modeling and verification of sub-networks from large-scale biomolecular networks

<p>Abstract</p> <p>Background</p> <p>Biomolecular networks dynamically respond to stimuli and implement cellular function. Understanding these dynamic changes is the key challenge for cell biologists. As biomolecular networks grow in size and complexity, the model of a biomolecular network must become more rigorous to keep track of all the components and their interactions. In general this presents the need for computer simulation to manipulate and understand the biomolecular network model.</p> <p>Results</p> <p>In this paper, we present a novel method to model the regulatory system which executes a cellular function and can be represented as a biomolecular network. Our method consists of two steps. First, a novel scale-free network clustering approach is applied to the large-scale biomolecular network to obtain various sub-networks. Second, a state-space model is generated for the sub-networks and simulated to predict their behavior in the cellular context. The modeling results represent <it>hypotheses </it>that are tested against high-throughput data sets (microarrays and/or genetic screens) for both the natural system and perturbations. Notably, the dynamic modeling component of this method depends on the automated network structure generation of the first component and the sub-network clustering, which are both essential to make the solution tractable.</p> <p>Conclusion</p> <p>Experimental results on time series gene expression data for the human cell cycle indicate our approach is promising for sub-network mining and simulation from large-scale biomolecular network.</p