Fast Gr\"obner Basis Computation for Boolean Polynomials

We introduce the Macaulay2 package BooleanGB, which computes a Gr\"obner basis for Boolean polynomials using a binary representation rather than symbolic. We compare the runtime of several Boolean models from systems in biology and give an application to Sudoku

Inferring Biologically Relevant Models: Nested Canalyzing Functions

Inferring dynamic biochemical networks is one of the main challenges in systems biology. Given experimental data, the objective is to identify the rules of interaction among the different entities of the network. However, the number of possible models fitting the available data is huge and identifying a biologically relevant model is of great interest. Nested canalyzing functions, where variables in a given order dominate the function, have recently been proposed as a framework for modeling gene regulatory networks. Previously we described this class of functions as an algebraic toric variety. In this paper, we present an algorithm that identifies all nested canalyzing models that fit the given data. We demonstrate our methods using a well-known Boolean model of the cell cycle in budding yeast

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

Background: Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, with the goal to gain a better understanding of the system. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. Although there exist sophisticated algorithms to determine the dynamics of discrete models, their implementations usually require labor-intensive formatting of the model formulation, and they are oftentimes not accessible to users without programming skills. Efficient analysis methods are needed that are accessible to modelers and easy to use. Method: By converting discrete models into algebraic models, tools from computational algebra can be used to analyze their dynamics. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Results: A method for efficiently identifying attractors, and the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness, i.e., while the number of nodes in a biological network may be quite large, each node is affected only by a small number of other nodes, and robustness, i.e., small number of attractors

Applicability of literature values for green–ampt parameters to account for infiltration in hydrodynamic rainfall–runoff simulations in ungauged basins

This study aimed to evaluate the suitability of literature parameter values for the Green–Ampt infiltration model to be used in hydrodynamic rainfall–runoff simulations. The outcome of this study supports to decide which literature values should be taken if observed data for model calibration is not available. Different laboratory experiments, a plot-scale experiment in the Thiès catchment in Senegal, and a flash flood in the region of El Gouna in Egypt, have been simulated with the 2D shallow water model Hydroinformatics Modeling System (hms) incorporating the Green–Ampt model. For four test cases with available runoff data, the results of the calibrated models were compared to those obtained from average values after Rawls et al. (Journal of Hydraulic Engineering 1:62–70, 1) and Innovyze (Help documentation of XPSWMM and XPStorm, 2). The results showed a clear underestimation of infiltration in two of three considered laboratory experiments, while for a field experiment in Senegal, average values after Rawls et al. (Journal of Hydraulic Engineering 1:62–70, 1) led to a strong overestimation and the ones after Innovyze (Help documentation of XPSWMM and XPStorm, 2) to an underestimation of infiltration. In a case study on flash floods in an ungauged region in Egypt, the values of both sources led to a strong overestimation of infiltration, when the simulation results are compared to observed flooding areas. It can be concluded, that the values after Innovyze (Help documentation of XPSWMM and XPStorm, 2) lead to overall better results than the ones after Rawls et al. (Journal of Hydraulic Engineering 1:62–70, 1). According to the results, the hydraulic conductivity in ungauged areas with bare sandy soil should be reduced by about 90–100 % compared to the value after Rawls et al. (Journal of Hydraulic Engineering 1:62–70, 1).TU Berlin, Open-Access-Mittel – 2021DFG, 248198858, GRK 2032: Grenzzonen in urbanen Wassersysteme

ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

Abstract Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on mathematical algorithms as a web-based tool for several different input formats, and it makes analysis of complex models accessible to a larger community, as it is platform independent as a web-service and does not require understanding of the underlying mathematics

A Mathematical Framework for Agent Based Models of Complex Biological Networks

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog

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.Comment: Web interface of the software is available at http://polymath.vbi.vt.edu/polynome

Steady state analysis of Boolean molecular network models via model reduction and computational algebra.

BACKGROUND: A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. RESULTS: This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. CONCLUSIONS: The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate connectivity. The problem for large Boolean networks with high average connectivity remains an open problem. BMC Bioinformatics 2014; 15:221

Shallow Water Flow Based Simulation of Flash Floods in Small Catchments

The Second International Symposium on Flash Floods in Wadi Systems: 25-27 October 2016. Technische Universität Berlin, Campus El Gouna, Egypt

Mineralizing Gelatin Microparticles as Cell Carrier and Drug Delivery System for siRNA for Bone Tissue Engineering

The local release of complexed siRNA from biomaterials opens precisely targeted therapeutic options. In this study, complexed siRNA was loaded to gelatin microparticles cross-linked (cGM) with an anhydride-containing oligomer (oPNMA). We aggregated these siRNA-loaded cGM with human mesenchymal stem cells (hMSC) to microtissues and stimulated them with osteogenic supplements. An efficient knockdown of chordin, a BMP-2 antagonist, caused a remarkably increased alkaline phosphatase (ALP) activity in the microtissues. cGM, as a component of microtissues, mineralized in a differentiation medium within 8–9 days, both in the presence and in the absence of cells. In order to investigate the effects of our pre-differentiated and chordin-silenced microtissues on bone homeostasis, we simulated in vivo conditions in an unstimulated co-culture system of hMSC and human peripheral blood mononuclear cells (hPBMC). We found enhanced ALP activity and osteoprotegerin (OPG) secretion in the model system compared to control microtissues. Our results suggest osteoanabolic effects of pre-differentiated and chordin-silenced microtissues