Cyclone: open-source package for simulation and analysis of finite dynamical systems.

MOTIVATION: While there are software packages that analyze Boolean, ternary, or other multi-state models, none compute the complete state space of function-based models over any finite set. Results: We propose Cyclone, a simple light-weight software package which simulates the complete state space for a finite dynamical system over any finite set. AVAILABILITY AND IMPLEMENTATION: Source code is freely available at https://github.com/discretedynamics/cyclone under the Apache-2.0 license.

Geometric Characterization of Data Sets with Unique Reduced Gröbner Bases.

Model selection based on experimental data is an important challenge in biological data science. Particularly when collecting data is expensive or time-consuming, as it is often the case with clinical trial and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models. We identify geometric properties of input data that result in an unique algebraic model, and we show that if the data form a staircase, or a so-called linear shift of a staircase, the ideal of the points has a unique reduced Gröbner basis and thus corresponds to a unique model. We use linear shifts to partition data into equivalence classes with the same basis. We demonstrate the utility of the results by applying them to a Boolean model of the well-studied lac operon in E. coli.

The Patterns of Non-vitamin K Antagonist Oral Anticoagulants (NOACs) Use in Patients with Atrial Fibrillation in Seven Balkan Countries: a Report from the BALKAN-AF Survey.

INTRODUCTION: Data on management of atrial fibrillation (AF) in the Balkan Region are scarce. To capture the patterns in AF management in contemporary clinical practice in the Balkan countries a prospective survey was conducted between December 2014 and February 2015, and we report results pertinent to the use of non-vitamin K antagonist oral anticoagulants (NOACs). METHODS: A 14-week prospective, multicenter survey of consecutive AF patients seen by cardiologists or internal medicine specialists was conducted in Albania, Bosnia and Herzegovina, Bulgaria, Croatia, Montenegro, Romania, and Serbia (a total of about 50 million inhabitants). RESULTS: Of 2712 enrolled patients, 2663 (98.2%) had complete data relevant to oral anticoagulant (OAC) use (mean age 69.1 ± 10.9 years, female 44.6%). Overall, OAC was used in 1960 patients (73.6%) of whom 338 (17.2%) received NOACs. Malignancy [odds ratio (OR), 95% confidence interval (CI) 2.06, 1.20-3.56], rhythm control (OR 1.64, 1.25-2.16), and treatment by cardiologists were independent predictors of NOAC use (OR 2.32, 1.51-3.54) [all p < 0.01)], whilst heart failure and valvular disease were negatively associated with NOAC use (both p < 0.01). Individual stroke and bleeding risk were not significantly associated with NOAC use on multivariate analysis. CONCLUSIONS: NOACs are increasingly used in AF patients in the Balkan Region, but NOAC use is predominantly guided by factors other than evidence-based decision-making (e.g., drug availability on the market or reimbursement policy). Efforts are needed to establish an evidence-based approach to OAC selection and to facilitate the optimal use of OAC, thus improving the outcomes in AF patients in this large region.

Stroke prevention in atrial fibrillation and 'real world' adherence to guidelines in the Balkan Region: The BALKAN-AF Survey.

Data on the management of atrial fibrillation (AF) in the Balkan Region are limited. The Serbian AF Association (SAFA) prospectively investigated contemporary 'real-world' AF management in clinical practice in Albania, Bosnia&Herzegovina, Bulgaria, Croatia, Montenegro, Romania and Serbia through a 14-week (December 2014-February 2015) prospective, multicentre survey of consecutive AF patients. We report the results pertinent to stroke prevention strategies. Of 2712 enrolled patients, 2663 (98.2%) with complete data were included in this analysis (mean age 69.1 ± 10.9 years, female 44.6%). Overall, 1960 patients (73.6%) received oral anticoagulants (OAC) and 762 (28.6%) received antiplatelet drugs. Of patients given OAC, 17.2% received non-vitamin K antagonist oral anticoagulants (NOACs). CHA2DS2-VASc score was not significantly associated with OAC use. Of the 'truly low-risk' patients (CHA2DS2-VASc = 0 [males], or 1 [females]) 56.5% received OAC. Time in Therapeutic Range (TTR) was available in only 18.7% of patients (mean TTR: 49.5% ± 22.3%). Age ≥ 80 years, prior myocardial infarction and paroxysmal AF were independent predictors of OAC non-use. Our survey shows a relatively high overall use of OAC in AF patients, but with low quality of vitamin K antagonist therapy and insufficient adherence to AF guidelines. Additional efforts are needed to improve AF-related thromboprophylaxis in clinical practice in the Balkan Region.

Molecular network control through boolean canalization.

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This work studies the role of canalization in the control of Boolean molecular networks. It provides a method for identifying the potential edges to control in the wiring diagram of a network for avoiding undesirable state transitions. The method is based on identifying appropriate input-output combinations on undesirable transitions that can be modified using the edges in the wiring diagram of the network. Moreover, a method for estimating the number of changed transitions in the state space of the system as a result of an edge deletion in the wiring diagram is presented. The control methods of this paper were applied to a mutated cell-cycle model and to a p53-mdm2 model to identify potential control targets.

Difference equation for tracking perturbations in systems of Boolean nested canalyzing functions.

This paper studies the spread of perturbations through networks composed of Boolean functions with special canalyzing properties. Canalyzing functions have the property that at least for one value of one of the inputs the output is fixed, irrespective of the values of the other inputs. In this paper the focus is on partially nested canalyzing functions, in which multiple, but not all inputs have this property in a cascading fashion. They naturally describe many relationships in real networks. For example, in a gene regulatory network, the statement "if gene A is expressed, then gene B is not expressed regardless of the states of other genes" implies that A is canalyzing. On the other hand, the additional statement "if gene A is not expressed, and gene C is expressed, then gene B is automatically expressed; otherwise gene B's state is determined by some other type of rule" implies that gene B is expressed by a partially nested canalyzing function with more than two variables, but with two canalyzing variables. In this paper a difference equation model of the probability that a network node's value is affected by an initial perturbation over time is developed, analyzed, and validated numerically. It is shown that the effect of a perturbation decreases towards zero over time if the Boolean functions are canalyzing in sufficiently many variables. The maximum dynamical impact of a perturbation is shown to be comparable to the average impact for a wide range of values of the average sensitivity of the network. Percolation limits are also explored; these are parameter values which generate a transition of the expected perturbation effect to zero as other parameters are varied, so that the initial perturbation does not scale up with the parameters once the percolation limits are reached.

Probabilistic polynomial dynamical systems for reverse engineering of gene regulatory networks.

Elucidating the structure and/or dynamics of gene regulatory networks from experimental data is a major goal of systems biology. Stochastic models have the potential to absorb noise, account for un-certainty, and help avoid data overfitting. Within the frame work of probabilistic polynomial dynamical systems, we present an algorithm for the reverse engineering of any gene regulatory network as a discrete, probabilistic polynomial dynamical system. The resulting stochastic model is assembled from all minimal models in the model space and the probability assignment is based on partitioning the model space according to the likeliness with which a minimal model explains the observed data. We used this method to identify stochastic models for two published synthetic network models. In both cases, the generated model retains the key features of the original model and compares favorably to the resulting models from other algorithms.

Discretization of time series data.

An increasing number of algorithms for biochemical network inference from experimental data require discrete data as input. For example, dynamic Bayesian network methods and methods that use the framework of finite dynamical systems, such as Boolean networks, all take discrete input. Experimental data, however, are typically continuous and represented by computer floating point numbers. The translation from continuous to discrete data is crucial in preserving the variable dependencies and thus has a significant impact on the performance of the network inference algorithms. We compare the performance of two such algorithms that use discrete data using several different discretization algorithms. One of the inference methods uses a dynamic Bayesian network framework, the other-a time-and state-discrete dynamical system framework. The discretization algorithms are quantile, interval discretization, and a new algorithm introduced in this article, SSD. SSD is especially designed for short time series data and is capable of determining the optimal number of discretization states. The experiments show that both inference methods perform better with SSD than with the other methods. In addition, SSD is demonstrated to preserve the dynamic features of the time series, as well as to be robust to noise in the experimental data. A C++ implementation of SSD is available from the authors at http://polymath.vbi.vt.edu/discretization .