MOTIVATION: The simultaneous availability of ATAC-seq and RNA-seq experiments allows to obtain a more in-depth knowledge on the regulatory mechanisms occurring in gene regulatory networks. In this article, we highlight and analyze two novel aspects that leverage on the possibility of pairing RNA-seq and ATAC-seq data. Namely we investigate the causality of the relationships between transcription factors, chromatin and target genes and the internal consistency between the two omics, here measured in terms of structural balance in the sample correlations along elementary length-3 cycles. RESULTS: We propose a framework that uses the a priori knowledge on the data to infer elementary causal regulatory motifs (namely chains and forks) in the network. It is based on the notions of conditional independence and partial correlation, and can be applied to both longitudinal and non-longitudinal data. Our analysis highlights a strong connection between the causal regulatory motifs that are selected by the data and the structural balance of the underlying sample correlation graphs: strikingly, >97% of the selected regulatory motifs belong to a balanced subgraph. This result shows that internal consistency, as measured by structural balance, is close to a necessary condition for 3-node regulatory motifs to satisfy causality rules. AVAILABILITY AND IMPLEMENTATION: The analysis was carried out in MATLAB and the code can be found at https://github.com/albertozenere/Multi-omics-elementary-regulatory-motifs. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Complex eukaryotic promoters normally contain multiple cis-regulatory sequences for different transcription factors (TFs). The binding patterns of the TFs to these sites, as well as the way the TFs interact with each other and with the RNA polymerase (RNAp), lead to combinatorial problems rarely understood in detail, especially under varying epigenetic conditions. The aim of this paper is to build a model describing how the main regulatory cluster of the olfactory receptor Or59b drives transcription of this gene in Drosophila. The cluster-driven expression of this gene is represented as the equilibrium probability of RNAp being bound to the promoter region, using a statistical thermodynamic approach. The RNAp equilibrium probability is computed in terms of the occupancy probabilities of the single TFs of the cluster to the corresponding binding sites, and of the interaction rules among TFs and RNAp, using experimental data of Or59b expression to tune the model parameters. The model reproduces correctly the changes in RNAp binding probability induced by various mutation of specific sites and epigenetic modifications. Some of its predictions have also been validated in novel experiments.

In simple organisms like E.coli, the metabolic response to an external perturbation passes through a transient phase in which the activation of a number of latent pathways can guarantee survival at the expenses of growth. Growth is gradually recovered as the organism adapts to the new condition. This adaptation can be modeled as a process of repeated metabolic adjustments obtained through the resilencings of the non-essential metabolic reactions, using growth rate as selection probability for the phenotypes obtained. The resulting metabolic adaptation process tends naturally to steer the metabolic fluxes towards high growth phenotypes. Quite remarkably, when applied to the central carbon metabolism of E.coli, it follows that nearly all flux distributions converge to the flux vector representing optimal growth, i.e., the solution of the biomass optimization problem turns out to be the dominant attractor of the metabolic adaptation process.

MOTIVATION: A gene regulatory network in which the modes (activation/inhibition) of the transcriptional regulations are known and in which gene expression assumes boolean values can be treated as a system of linear equations over a binary field, i.e. as a constraint satisfaction problem for an information code. RESULTS: For currently available gene networks, we show in this article that the distortion associated with the corresponding information code is much lower than expected from null models, and that it is close to (when not lower than) the Shannon bound determined by the rate-distortion theorem. This corresponds to saying that the distribution of regulatory modes is highly atypical in the networks, and that this atypicality greatly helps in avoiding contradictory transcriptional actions. Choosing a boolean formalism to represent the gene networks, we also show how to formulate criteria for the selection of gates that maximize the compatibility with the empirical information available on the transcriptional regulatory modes. Proceeding in this way, we obtain in particular that non-canalizing gates are upper-bounded by the distortion, and hence that the boolean gene networks are more canalizing than expected from null models.

MOTIVATION: Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug. RESULTS: In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling. CONCLUSIONS: The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

MOTIVATION: Given a large-scale biological network represented as an influence graph, in this article we investigate possible decompositions of the network aimed at highlighting specific dynamical properties. RESULTS: The first decomposition we study consists in finding a maximal directed acyclic subgraph of the network, which dynamically corresponds to searching for a maximal open-loop subsystem of the given system. Another dynamical property investigated is strong monotonicity. We propose two methods to deal with this property, both aimed at decomposing the system into strongly monotone subsystems, but with different structural characteristics: one method tends to produce a single large strongly monotone component, while the other typically generates a set of smaller disjoint strongly monotone subsystems. AVAILABILITY: Original heuristics for the methods investigated are described in the article. CONTACT: [email protected]

MOTIVATION: Deciphering the response of a complex biological system to an insulting event, at the gene expression level, requires adopting theoretical models that are more sophisticated than a one-to-one comparison (i.e. t-test). Here, we investigate the ability of a novel reverse engineering approach (System Response Inference) to unveil non-obvious transcriptional signatures of the system response induced by prion infection. RESULTS: To this end, we analyze previously published gene expression data, from which we extrapolate a putative full-scale model of transcriptional gene-gene dependencies in the mouse central nervous system. Then, we use this nominal model to interpret the gene expression changes caused by prion replication, aiming at selecting the genes primarily influenced by this perturbation. Our method sheds light on the mode of action of prions by identifying key transcripts that are the most likely to be responsible for the overall transcriptional rearrangement from a nominal regulatory network. As a first result of our inference, we have been able to predict known targets of prions (i.e. PrP(C)) and to unveil the potential role of previously unsuspected genes. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: ERNEST Reaction Network Equilibria Study Toolbox is a MATLAB package which, by checking various different criteria on the structure of a chemical reaction network, can exclude the multistationarity of the corresponding reaction system. The results obtained are independent of the rate constants of the reactions, and can be used for model discrimination. AVAILABILITY AND IMPLEMENTATION: The software, implemented in MATLAB, is available under the GNU GPL free software license from http://people.sissa.it/ approximately altafini/papers/SoAl09/. It requires the MATLAB Optimization Toolbox. CONTACT: [email protected].

Prion proteins are known to misfold into a range of different aggregated forms, showing different phenotypic and pathological states. Understanding strain specificities is an important problem in the field of prion disease. Little is known about which PrP(Sc) structural properties and molecular mechanisms determine prion replication, disease progression and strain phenotype. The aim of this work is to investigate, through a mathematical model, how the structural stability of different aggregated forms can influence the kinetics of prion replication. The model-based results suggest that prion strains with different conformational stability undergoing in vivo replication are characterizable in primis by means of different rates of breakage. A further role seems to be played by the aggregation rate (i.e. the rate at which a prion fibril grows). The kinetic variability introduced in the model by these two parameters allows us to reproduce the different characteristic features of the various strains (e.g., fibrils' mean length) and is coherent with all experimental observations concerning strain-specific behavior.

BACKGROUND: In the past years devising methods for discovering gene regulatory mechanisms at a genome-wide level has become a fundamental topic in the field of systems biology. The aim is to infer gene-gene interactions in an increasingly sophisticated and reliable way through the continuous improvement of reverse engineering algorithms exploiting microarray data. MOTIVATION: This work is inspired by the several studies suggesting that coexpression is mostly related to 'static' stable binding relationships, like belonging to the same protein complex, rather than other types of interactions more of a 'causal' and transient nature (e.g. transcription factor-binding site interactions). The aim of this work is to verify if direct or conditional network inference algorithms (e.g. Pearson correlation for the former, partial Pearson correlation for the latter) are indeed useful in discerning static from causal dependencies in artificial and real gene networks (derived from Escherichia coli and Saccharomyces cerevisiae). RESULTS: Even in the regime of weak inference power we have to work in, our analysis confirms the differences in the performances of the algorithms: direct methods are more robust in detecting stable interactions, conditional ones are better for causal interactions especially in presence of combinatorial transcriptional regulation. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Inferring a gene regulatory network exclusively from microarray expression profiles is a difficult but important task. The aim of this work is to compare the predictive power of some of the most popular algorithms in different conditions (like data taken at equilibrium or time courses) and on both synthetic and real microarray data. We are in particular interested in comparing similarity measures both of linear type (like correlations and partial correlations) and of non-linear type (mutual information and conditional mutual information), and in investigating the underdetermined case (less samples than genes). RESULTS: In our simulations we see that all network inference algorithms obtain better performances from data produced with 'structural' perturbations, like gene knockouts at steady state, than with any dynamical perturbation. The predictive power of all algorithms is confirmed on a reverse engineering problem from Escherichia coli gene profiling data: the edges of the 'physical' network of transcription factor-binding sites are significantly overrepresented among the highest weighting edges of the graph that we infer directly from the data without any structure supervision. Comparing synthetic and in vivo data on the same network graph allows us to give an indication of how much more complex a real transcriptional regulation program is with respect to an artificial model. AVAILABILITY: Software is freely available at the URL http://people.sissa.it/~altafini/papers/SoBiAl07/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The paper introduces the notion of Riemannian submersion for the modeling and control of certain types of redundant robotic chains. In the robotics literature, the redundant case is normally treated only in numerical terms, as the need to resort to pseudoinversion techniques is usually considered a barrier to the use of analytic or geometric methods. Using Riemannian submersions, however, we can single out a particular type of inverse, the horizontal lift, with distinguished properties with respect to the infinitely many possible others. Quite remarkably, for a wide class of robotic chains, characterized by the vanishing of the curvature tensor, such horizontal lift coincides with the curve obtained from the Moore-Penrose pseudoinverse of the Jacobian.

Kinematically, a mobile manipulator i.e. a robot arm mounted on the top of a mobile platform, is a concatenation of rigid body motions in SE(3), the Special Euclidean group and its subgroups. The formalism of matrix Lie groups is used to generate a smooth curve for the end-effector of the robot. In particular, different closed-form C/sup 2/ curves in SE(3) can be obtained from boundary data with the De Casteljau algorithm. Pseudoinversion techniques applied to the Jacobian of the kinematic chain allow then to transform the path of the end-effector into smooth joint space trajectories via the product of exponentials formula.

A control scheme is proposed for the backward line tracking problem of a truck with trailer. It combines two different regulators, one for backward motion and the other for forward, in a switching scheme that assures convergence to the desired line. The scheme has been implemented and successfully used to reverse a radio-controlled vehicle.

A control scheme is proposed for stabilization of backward driving along simple paths for a miniaturized vehicle composed of a truck and a two-axle trailer. The paths chosen are straight lines and arcs of circles. When reversing, the truck and trailer under examination can be modeled as an unstable nonlinear system with state and input saturations. The simplified goal of stabilizing along a trajectory (instead of a point) allows us to consider a system with controllable linearization. Still, the combination of instability and saturations makes the task impossible with a single controller. In fact, the system cannot be driven backward from all initial states because of the jack-knife effects between the parts of the multibody vehicle; it is sometimes necessary to drive forward to enter into a specific region of attraction. This leads to the use of hybrid controllers. The scheme has been implemented and successfully used to reverse the radio-controlled vehicle.

Sensing the load dynamic in an overhead crane is not a simple task because both load angular position and velocity measurements are not easily attainable and subject to disturbances. A method to reconstruct the dynamic of the load is presented. It is based on the estimate of the torque that the load produces on the drive that governs the translational dynamic of the trolley at which the load is hanging. It requires a minimal sensor equipment, namely measures of the electrical torque and angular velocity of the drive, as both swing angle and load speed are shown to be observable for the linearized model.

Engineers in the underground mining industry have known for a long time that an articulated vehicle is preferable to a normal truck for the navigation in the narrow environments of an underground mine because of its higher manoeuvrability. The two advantages of the articulated configuration can be explained in terms of degrees of freedom in the selection of the directions needed to span the whole tangent space and of the reduced gap between the trajectories followed by the wheels of the truck when steering. Both characteristics can be used in a constructive way for path planning and navigation purposes.