A computational model of gene expression in an inducible synthetic circuit

Synthetic biology aims to the rational design of gene circuits with predictable behaviours. Great efforts have been done so far to introduce in the field mathematical models that could facilitate the design of synthetic networks. Here we present a mathematical model of a synthetic gene-circuit with a negative feedback. The closed loop configuration allows the control of transcription by an inducer molecule (IPTG). Escherichia coli bacterial cells were transformed and expression of a fluorescent reporter (GFP) was measured for different inducer levels. Computer model simulations well reproduced the experimental induction data, using a single fitting parameter. Independent genetic components were used to assemble the synthetic circuit. The mathematical model here presented could be useful to predict how changes in these genetic components affect the behaviour of the synthetic circuit

Approximated Perspective Relaxations: a Project&Lift Approach

The Perspective Reformulation (PR) of a Mixed-Integer NonLinear Program with semi-continuous variables is obtained by replacing each term in the (separable) objective function with its convex envelope. Solving the corresponding continuous relaxation requires appropriate techniques. Under some rather restrictive assumptions, the Projected PR (P^2R) can be defined where the integer variables are eliminated by projecting the solution set onto the space of the continuous variables only. This approach produces a simple piecewise-convex problem with the same structure as the original one; however, this prevents the use of general-purpose solvers, in that some variables are then only implicitly represented in the formulation. We show how to construct an Approximated Projected PR (AP^2R) whereby the projected formulation is "lifted" back to the original variable space, with each integer variable expressing one piece of the obtained piecewise-convex function. In some cases, this produces a reformulation of the original problem with exactly the same size and structure as the standard continuous relaxation, but providing substantially improved bounds. In the process we also substantially extend the approach beyond the original P^2R development by relaxing the requirement that the objective function be quadratic and the left endpoint of the domain of the variables be non-negative. While the AP^2R bound can be weaker than that of the PR, this approach can be applied in many more cases and allows direct use of off-the-shelf MINLP software; this is shown to be competitive with previously proposed approaches in some applications

A branch-and-price algorithm for the temporal bin packing problem

We study an extension of the classical Bin Packing Problem, where each item consumes the bin capacity during a given time window that depends on the item itself. The problem asks for finding the minimum number of bins to pack all the items while respecting the bin capacity at any time instant. A polynomial-size formulation, an exponential-size formulation, and a number of lower and upper bounds are studied. A branch-and-price algorithm for solving the exponential-size formulation is introduced. An overall algorithm combining the different methods is then proposed and tested through extensive computational experiments

Casting Light on the Hidden Bilevel Combinatorial Structure of the Capacitated Vertex Separator Problem

Given an undirected graph, we study the capacitated vertex separator problem that asks to find a subset of vertices of minimum cardinality, the removal of which induces a graph having a bounded number of pairwise disconnected shores (subsets of vertices) of limited cardinality. The problem is of great importance in the analysis and protection of communication or social networks against possible viral attacks and for matrix decomposition algorithms. In this article, we provide a new bilevel interpretation of the problem and model it as a two-player Stackelberg game in which the leader interdicts the vertices (i.e., decides on the subset of vertices to remove), and the follower solves a combinatorial optimization problem on the resulting graph. This approach allows us to develop a computational framework based on an integer programming formulation in the natural space of the variables. Thanks to this bilevel interpretation, we derive three different families of strengthening inequalities and show that they can be separated in polynomial time. We also show how to extend these results to a min-max version of the problem. Our extensive computational study conducted on available benchmark instances from the literature reveals that our new exact method is competitive against the state-of-the-art algorithms for the capacitated vertex separator problem and is able to improve the best-known results for several difficult classes of instances. The ideas exploited in our framework can also be extended to other vertex/edge deletion/ insertion problems or graph partitioning problems by modeling them as two-player Stackel- berg games and solving them through bilevel optimization

A combinatorial flow-based formulation for temporal bin packing problems

We consider two neighboring generalizations of the classical bin packing problem: the temporal bin packing problem (TBPP) and the temporal bin packing problem with fire-ups (TBPP-FU). In both cases, the task is to arrange a set of given jobs, characterized by a resource consumption and an activity window, on homogeneous servers of limited capacity. To keep operational costs but also energy consumption low, TBPP is concerned with minimizing the number of servers in use, whereas TBPP-FU additionally takes into account the switch-on processes required for their operation. Either way, challenging integer optimization problems are obtained, which can differ significantly from each other despite the seemingly only marginal variation of the problems. In the literature, a branch-and-price method enriched with many preprocessing steps (for TBPP) and compact formulations (for TBPP-FU), benefiting from numerous reduction methods, have emerged as, currently, the most promising solution methods. In this paper, we introduce, in a sense, a unified solution framework for both problems (and, in fact, a wide variety of further interval scheduling applications) based on graph theory. Any scientific contributions in this direction failed so far because of the exponential size of the associated networks. The approach we present in this article does not change the theoretical exponentiality itself, but it can make it controllable by clever construction of the resulting graphs. In particular, for the first time all classical benchmark instances (and even larger ones) for the two problems can be solved – in times that significantly improve those of the previous approaches

A fast ILP-based Heuristic for the robust design of Body Wireless Sensor Networks

We consider the problem of optimally designing a body wireless sensor network, while taking into account the uncertainty of data generation of biosensors. Since the related min-max robustness Integer Linear Programming (ILP) problem can be difficult to solve even for state-of-the-art commercial optimization solvers, we propose an original heuristic for its solution. The heuristic combines deterministic and probabilistic variable fixing strategies, guided by the information coming from strengthened linear relaxations of the ILP robust model, and includes a very large neighborhood search for reparation and improvement of generated solutions, formulated as an ILP problem solved exactly. Computational tests on realistic instances show that our heuristic finds solutions of much higher quality than a state-of-the-art solver and than an effective benchmark heuristic.Comment: This is the authors' final version of the paper published in G. Squillero and K. Sim (Eds.): EvoApplications 2017, Part I, LNCS 10199, pp. 1-17, 2017. DOI: 10.1007/978-3-319-55849-3\_16. The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-55849-3_1

The role of the multidisciplinary evaluation of interstitial lung diseases: Systematic literature review of the current evidence and future perspectives

The opportunity of a multidisciplinary evaluation for the diagnosis of interstitial pneumonias highlighted a major change in the diagnostic approach to diffuse lung disease. The new American Thoracic Society, European Respiratory Society, Japanese Respiratory Society, and Latin American Thoracic Society guidelines for the diagnosis of idiopathic pulmonary fibrosis have reinforced this assumption and have underlined that the exclusion of connective tissue disease related lung involvement is mandatory, with obvious clinical and therapeutic impact. The multidisciplinary team discussion consists in amoment of interaction among the radiologist, pathologist and pulmonologist, also including the rheumatologist when considered necessary, to improve diagnostic agreement and optimize the definition of those cases in which pulmonary involvement may represent the first or prominent manifestation of an autoimmune systemic disease. Moreover, the proposal of classification criteria for interstitial lung disease with autoimmune features (IPAF) represents an effort to define lung involvement in clinically undefined autoimmune conditions. The complexity of autoimmune diseases, and in particular the lack of classification criteria defined for pathologies such as anti-synthetase syndrome, makes the involvement of the rheumatologist essential for the correct interpretation of the autoimmune element and for the application of classification criteria, that could replace clinical pictures initially interpreted as IPAF in defined autoimmune disease, minimizing the risk of misdiagnosis. The aim of this review was to evaluate the available evidence about the efficiency and efficacy of different multidisciplinary team approaches, in order to standardize the professional figures and the core set procedures that should be necessary for a correct approach in diagnosing patients with interstitial lung disease

Rational design of modular circuits for gene transcription: A test of the bottom-up approach

BACKGROUND: Most of synthetic circuits developed so far have been designed by an ad hoc approach, using a small number of components (i.e. LacI, TetR) and a trial and error strategy. We are at the point where an increasing number of modular, inter-changeable and well-characterized components is needed to expand the construction of synthetic devices and to allow a rational approach to the design. RESULTS: We used interchangeable modular biological parts to create a set of novel synthetic devices for controlling gene transcription, and we developed a mathematical model of the modular circuits. Model parameters were identified by experimental measurements from a subset of modular combinations. The model revealed an unexpected feature of the lactose repressor system, i.e. a residual binding affinity for the operator site by induced lactose repressor molecules. Once this residual affinity was taken into account, the model properly reproduced the experimental data from the training set. The parameters identified in the training set allowed the prediction of the behavior of networks not included in the identification procedure. CONCLUSIONS: This study provides new quantitative evidences that the use of independent and well-characterized biological parts and mathematical modeling, what is called a bottom-up approach to the construction of gene networks, can allow the design of new and different devices re-using the same modular parts