On the asymptotic behavior of the Douglas-Rachford and proximal-point algorithms for convex optimization.

Banjac et al. (J Optim Theory Appl 183(2):490-519, 2019) recently showed that the Douglas-Rachford algorithm provides certificates of infeasibility for a class of convex optimization problems. In particular, they showed that the difference between consecutive iterates generated by the algorithm converges to certificates of primal and dual strong infeasibility. Their result was shown in a finite-dimensional Euclidean setting and for a particular structure of the constraint set. In this paper, we extend the result to real Hilbert spaces and a general nonempty closed convex set. Moreover, we show that the proximal-point algorithm applied to the set of optimality conditions of the problem generates similar infeasibility certificates.

In silico analysis of DNA re-replication across a complete genome reveals cell-to-cell heterogeneity and genome plasticity.

DNA replication is a complex and remarkably robust process: despite its inherent uncertainty, manifested through stochastic replication timing at a single-cell level, multiple control mechanisms ensure its accurate and timely completion across a population. Disruptions in these mechanisms lead to DNA re-replication, closely connected to genomic instability and oncogenesis. Here, we present a stochastic hybrid model of DNA re-replication that accurately portrays the interplay between discrete dynamics, continuous dynamics and uncertainty. Using experimental data on the fission yeast genome, model simulations show how different regions respond to re-replication and permit insight into the key mechanisms affecting re-replication dynamics. Simulated and experimental population-level profiles exhibit a good correlation along the genome, robust to model parameters, validating our approach. At a single-cell level, copy numbers of individual loci are affected by intrinsic properties of each locus, in cis effects from adjoining loci and in trans effects from distant loci. In silico analysis and single-cell imaging reveal that cell-to-cell heterogeneity is inherent in re-replication and can lead to genome plasticity and a plethora of genotypic variations.

Data-enabled predictive control for quadcopters.

We study the application of a data-enabled predictive control (DeePC) algorithm for position control of real-world nano-quadcopters. The DeePC algorithm is a finite-horizon, optimal control method that uses input/output measurements from the system to predict future trajectories without the need for system identification or state estimation. The algorithm predicts future trajectories of the quadcopter by linearly combining previously measured trajectories (motion primitives). We illustrate the necessity of a regularized variant of the DeePC algorithm to handle the nonlinear nature of the real-world quadcopter dynamics with noisy measurements. Simulation-based analysis is used to gain insights into the effects of regularization, and experimental results validate that these insights carry over to the real-world quadcopter. Moreover, we demonstrate the reliability of the DeePC algorithm by collecting a new set of input/output measurements for every real-world experiment performed. The performance of the DeePC algorithm is compared to Model Predictive Control based on a first-principles model of the quadcopter. The results are demonstrated with a video of successful trajectory tracking of the real-world quadcopter.

A Probabilistic Model of the Germinal Center Reaction.

Germinal centers (GCs) are specialized compartments within the secondary lymphoid organs, where B cells proliferate, differentiate, and mutate their antibody genes. Upon exit from the GC, B cells terminally differentiate into plasma cells or memory B cells. While we have a good comprehension of plasma cell differentiation, memory B cell differentiation is still incompletely understood. In this paper, we extend previous models of the molecular events underlying B cell differentiation with new findings regarding memory B cell formation, and present a quantitative stochastic model of the intracellular and extracellular dynamics governing B cell maturation and exit from the GC. To simulate this model, we develop a novel extension to the Gillespie algorithm that enables the efficient stochastic simulation of the system, while keeping track of individual cell properties. Our model is able to explain the dynamical shift from memory B cell to plasma cell production over the lifetime of a GC. Moreover, our results suggest that B cell fate selection can be explained as a process that depends fundamentally on antigen affinity.

Assessment of the Brain's Macro- and Micro-Circulatory Blood Flow Responses to CO2 via Transfer Function Analysis.

OBJECTIVES: At present, there is no standard bedside method for assessing cerebral autoregulation (CA) with high temporal resolution. We combined the two methods most commonly used for this purpose, transcranial Doppler sonography (TCD, macro-circulation level), and near-infrared spectroscopy (NIRS, micro-circulation level), in an attempt to identify the most promising approach. METHODS: In eight healthy subjects (5 women; mean age, 38 ± 10 years), CA disturbance was achieved by adding carbon dioxide (CO2) to the breathing air. We simultaneously recorded end-tidal CO2 (ETCO2), blood pressure (BP; non-invasively at the fingertip), and cerebral blood flow velocity (CBFV) in both middle cerebral arteries using TCD and determined oxygenated and deoxygenated hemoglobin levels using NIRS. For the analysis, we used transfer function calculations in the low-frequency band (0.07-0.15 Hz) to compare BP-CBFV, BP-oxygenated hemoglobin (OxHb), BP-tissue oxygenation index (TOI), CBFV-OxHb, and CBFV-TOI. RESULTS: ETCO2 increased from 37 ± 2 to 44 ± 3 mmHg. The CO2-induced CBFV increase significantly correlated with the OxHb increase (R (2) = 0.526, p < 0.001). Compared with baseline, the mean CO2 administration phase shift (in radians) significantly increased (p < 0.005) from -0.67 ± 0.20 to -0.51 ± 0.25 in the BP-CBFV system, and decreased from 1.21 ± 0.81 to -0.05 ± 0.91 in the CBFV-OxHb system, and from 0.94 ± 1.22 to -0.24 ± 1.0 in the CBFV-TOI system; no change was observed for BP-OxHb (0.38 ± 1.17 to 0.41 ± 1.42). Gain changed significantly only in the BP-CBFV system. The correlation between the ETCO2 change and phase change was higher in the CBFV-OxHb system [r = -0.60; 95% confidence interval (CI): -0.16, -0.84; p < 0.01] than in the BP-CBFV system (r = 0.52; 95% CI: 0.03, 0.08; p < 0.05). CONCLUSION: The transfer function characterizes the blood flow transition from macro- to micro-circulation by time delay only. The CBFV-OxHb system response with a broader phase shift distribution offers the prospect of a more detailed grading of CA responses. Whether this is of clinical relevance needs further studies in different patient populations.

Elucidation of Genetic Interactions in the Yeast GATA-Factor Network Using Bayesian Model Selection.

Understanding the structure and function of complex gene regulatory networks using classical genetic assays is an error-prone procedure that frequently generates ambiguous outcomes. Even some of the best-characterized gene networks contain interactions whose validity is not conclusively proven. Founded on dynamic experimental data, mechanistic mathematical models are able to offer detailed insights that would otherwise require prohibitively large numbers of genetic experiments. Here we attempt mechanistic modeling of the transcriptional network formed by the four GATA-factor proteins, a well-studied system of central importance for nitrogen-source regulation of transcription in the yeast Saccharomyces cerevisiae. To resolve ambiguities in the network organization, we encoded a set of five interactions hypothesized in the literature into a set of 32 mathematical models, and employed Bayesian model selection to identify the most plausible set of interactions based on dynamic gene expression data. The top-ranking model was validated on newly generated GFP reporter dynamic data and was subsequently used to gain a better understanding of how yeast cells organize their transcriptional response to dynamic changes of nitrogen sources. Our work constitutes a necessary and important step towards obtaining a holistic view of the yeast nitrogen regulation mechanisms; on the computational side, it provides a demonstration of how powerful Monte Carlo techniques can be creatively combined and used to address the great challenges of large-scale dynamical system inference.

Iterative experiment design guides the characterization of a light-inducible gene expression circuit.

Systems biology rests on the idea that biological complexity can be better unraveled through the interplay of modeling and experimentation. However, the success of this approach depends critically on the informativeness of the chosen experiments, which is usually unknown a priori. Here, we propose a systematic scheme based on iterations of optimal experiment design, flow cytometry experiments, and Bayesian parameter inference to guide the discovery process in the case of stochastic biochemical reaction networks. To illustrate the benefit of our methodology, we apply it to the characterization of an engineered light-inducible gene expression circuit in yeast and compare the performance of the resulting model with models identified from nonoptimal experiments. In particular, we compare the parameter posterior distributions and the precision to which the outcome of future experiments can be predicted. Moreover, we illustrate how the identified stochastic model can be used to determine light induction patterns that make either the average amount of protein or the variability in a population of cells follow a desired profile. Our results show that optimal experiment design allows one to derive models that are accurate enough to precisely predict and regulate the protein expression in heterogeneous cell populations over extended periods of time.

Inference of protein kinetics by stochastic modeling and simulation of fluorescence recovery after photobleaching experiments.

MOTIVATION: Fluorescence recovery after photobleaching (FRAP) is a functional live cell imaging technique that permits the exploration of protein dynamics in living cells. To extract kinetic parameters from FRAP data, a number of analytical models have been developed. Simplifications are inherent in these models, which may lead to inexhaustive or inaccurate exploitation of the experimental data. An appealing alternative is offered by the simulation of biological processes in realistic environments at a particle level. However, inference of kinetic parameters using simulation-based models is still limited. RESULTS: We introduce and demonstrate a new method for the inference of kinetic parameter values from FRAP data. A small number of in silico FRAP experiments is used to construct a mapping from FRAP recovery curves to the parameters of the underlying protein kinetics. Parameter estimates from experimental data can then be computed by applying the mapping to the observed recovery curves. A bootstrap process is used to investigate identifiability of the physical parameters and determine confidence regions for their estimates. Our method circumvents the computational burden of seeking the best-fitting parameters via iterative simulation. After validation on synthetic data, the method is applied to the analysis of the nuclear proteins Cdt1, PCNA and GFPnls. Parameter estimation results from several experimental samples are in accordance with previous findings, but also allow us to discuss identifiability issues as well as cell-to-cell variability of the protein kinetics. IMPLEMENTATION: All methods were implemented in MATLAB R2011b. Monte Carlo simulations were run on the HPC cluster Brutus of ETH Zurich. CONTACT: lygeros@control.ee.ethz.ch or lygerou@med.upatras.gr SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Fast variance reduction for steady-state simulation and sensitivity analysis of stochastic chemical systems using shadow function estimators.

We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest, these systems are analytically intractable, and one has to resort to computational methods to estimate stationary values of cost functions. In this work, we introduce a novel variance reduction algorithm for stochastic chemical kinetics, inspired by related methods in queueing theory, in particular the use of shadow functions. Using two numerical examples, we demonstrate the efficiency of the method for the calculation of steady-state parametric sensitivities and evaluate its performance in comparison to other estimation methods.

Designing experiments to understand the variability in biochemical reaction networks.

Exploiting the information provided by the molecular noise of a biological process has proved to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single-cell measurements. However, quantifying this additional information a priori, to decide whether a single-cell experiment might be beneficial, is currently only possible in systems where either the chemical master equation is computationally tractable or a Gaussian approximation is appropriate. Here, we provide formulae for computing the information provided by measured means and variances from the first four moments and the parameter derivatives of the first two moments of the underlying process. For stochastic kinetic models for which these moments can be either computed exactly or approximated efficiently, the derived formulae can be used to approximate the information provided by single-cell distribution experiments. Based on this result, we propose an optimal experimental design framework which we employ to compare the utility of dual-reporter and perturbation experiments for quantifying the different noise sources in a simple model of gene expression. Subsequently, we compare the information content of a set of experiments which have been performed in an engineered light-switch gene expression system in yeast and show that well-chosen gene induction patterns may allow one to identify features of the system which remain hidden in unplanned experiments.

Steady-state simulation of metastable stochastic chemical systems.

We address the problem of steady-state simulation for metastable continuous-time Markov chains with application to stochastic chemical kinetics. Such systems are characterized by the existence of two or more pseudo-equilibrium states and very slow convergence towards global equilibrium. Approximation of the stationary distribution of these systems by direct application of the Stochastic Simulation Algorithm (SSA) is known to be very inefficient. In this paper, we propose a new method for steady-state simulation of metastable Markov chains that is centered around the concept of stochastic complementation. The use of this mathematical device along with SSA results in an algorithm with much better convergence properties, that facilitates the analysis of rarely switching stochastic biochemical systems. The efficiency of our method is demonstrated by its application to two genetic toggle switch models.

Moment-based inference predicts bimodality in transient gene expression.

Recent computational studies indicate that the molecular noise of a cellular process may be a rich source of information about process dynamics and parameters. However, accessing this source requires stochastic models that are usually difficult to analyze. Therefore, parameter estimation for stochastic systems using distribution measurements, as provided for instance by flow cytometry, currently remains limited to very small and simple systems. Here we propose a new method that makes use of low-order moments of the measured distribution and thereby keeps the essential parts of the provided information, while still staying applicable to systems of realistic size. We demonstrate how cell-to-cell variability can be incorporated into the analysis obviating the need for the ubiquitous assumption that the measurements stem from a homogeneous cell population. We demonstrate the method for a simple example of gene expression using synthetic data generated by stochastic simulation. Subsequently, we use time-lapsed flow cytometry data for the osmo-stress induced transcriptional response in budding yeast to calibrate a stochastic model, which is then used as a basis for predictions. Our results show that measurements of the mean and the variance can be enough to determine the model parameters, even if the measured distributions are not well-characterized by low-order moments only--e.g., if they are bimodal.

High-speed multiresolution scanning probe microscopy based on Lissajous scan trajectories.

A novel scan trajectory for high-speed scanning probe microscopy is presented in which the probe follows a two-dimensional Lissajous pattern. The Lissajous pattern is generated by actuating the scanner with two single-tone harmonic waveforms of constant frequency and amplitude. Owing to the extremely narrow frequency spectrum, high imaging speeds can be achieved without exciting the unwanted resonant modes of the scanner and without increasing the sensitivity of the feedback loop to the measurement noise. The trajectory also enables rapid multiresolution imaging, providing a preview of the scanned area in a fraction of the overall scan time. We present a procedure for tuning the spatial and the temporal resolution of Lissajous trajectories and show experimental results obtained on a custom-built atomic force microscope (AFM). Real-time AFM imaging with a frame rate of 1 frame s⁻¹ is demonstrated.

In silico feedback for in vivo regulation of a gene expression circuit.

We show that difficulties in regulating cellular behavior with synthetic biological circuits may be circumvented using in silico feedback control. By tracking a circuit's output in Saccharomyces cerevisiae in real time, we precisely control its behavior using an in silico feedback algorithm to compute regulatory inputs implemented through a genetically encoded light-responsive module. Moving control functions outside the cell should enable more sophisticated manipulation of cellular processes whenever real-time measurements of cellular variables are possible.

Impulsive control for fast nanopositioning.

In this paper we present a non-linear control scheme for high-speed nanopositioning based on impulsive control. Unlike in the case of a linear feedback controller, the controller states are altered in a discontinuous manner at specific instances in time. Using this technique, it is possible to simultaneously achieve good tracking performance, disturbance rejection and tolerance to measurement noise. Impulsive control is demonstrated experimentally on an atomic force microscope. A significant improvement in tracking performance is demonstrated.

Identification of genetic network dynamics with unate structure.

MOTIVATION: Modern experimental techniques for time course measurement of gene expression enable the identification of dynamical models of genetic regulatory networks. In general, identification involves fitting appropriate network structures and parameters to the data. For a given set of genes, exploring all possible network structures is clearly prohibitive. Modelling and identification methods for the a priori selection of network structures compatible with biological knowledge and experimental data are necessary to make the identification problem tractable. RESULTS: We propose a differential equation modelling framework where the regulatory interactions among genes are expressed in terms of unate functions, a class of gene activation rules commonly encountered in Boolean network modelling. We establish analytical properties of the models in the class and exploit them to devise a two-step procedure for gene network reconstruction from product concentration and synthesis rate time series. The first step isolates a family of model structures compatible with the data from a set of most relevant biological hypotheses. The second step explores this family and returns a pool of best fitting models along with estimates of their parameters. The method is tested on a simulated network and compared with state-of-the-art network inference methods on the benchmark synthetic network IRMA.

Stochastic hybrid delay population dynamics: well-posed models and extinction.

Nonlinear differential equations have been used for decades for studying fluctuations in the populations of species, interactions of species with the environment, and competition and symbiosis between species. Over the years, the original non-linear models have been embellished with delay terms, stochastic terms and more recently discrete dynamics. In this paper, we investigate stochastic hybrid delay population dynamics (SHDPD), a very general class of population dynamics that comprises all of these phenomena. For this class of systems, we provide sufficient conditions to ensure that SHDPD have global positive, ultimately bounded solutions, a minimum requirement for a realistic, well-posed model. We then study the question of extinction and establish conditions under which an ecosystem modelled by SHDPD is doomed.

Stochastic dynamics of genetic networks: modelling and parameter identification.

MOTIVATION: Identification of regulatory networks is typically based on deterministic models of gene expression. Increasing experimental evidence suggests that the gene regulation process is intrinsically random. To ensure accurate and thorough processing of the experimental data, stochasticity must be explicitly accounted for both at the modelling stage and in the design of the identification algorithms. RESULTS: We propose a model of gene expression in prokaryotes where transcription is described as a probabilistic event, whereas protein synthesis and degradation are captured by first-order deterministic kinetics. Based on this model and assuming that the network of interactions is known, a method for estimating unknown parameters, such as synthesis and binding rates, from the outcomes of multiple time-course experiments is introduced. The method accounts naturally for sparse, irregularly sampled and noisy data and is applicable to gene networks of arbitrary size. The performance of the method is evaluated on a model of nutrient stress response in Escherichia coli.

DNA replication in the fission yeast: robustness in the face of uncertainty.

DNA replication, the process of duplication of a cell's genetic content, must be carried out with great precision every time the cell divides, so that genetic information is preserved. Control mechanisms must ensure that every base of the genome is replicated within the allocated time (S-phase) and only once per cell cycle, thereby safeguarding genomic integrity. In eukaryotes, replication starts from many points along the chromosome, termed origins of replication, and then proceeds continuously bidirectionally until an opposing moving fork is encountered. In contrast to bacteria, where a specific site on the genome serves as an origin in every cell division, in most eukaryotes origin selection appears highly stochastic: many potential origins exist, of which only a subset is selected to fire in any given cell, giving rise to an apparently random distribution of initiation events across the genome. Origin states change throughout the cell cycle, through the ordered formation and modification of origin-associated multisubunit protein complexes. State transitions are governed by fluctuations of cyclin-dependent kinase (CDK) activity and guards in these transitions ensure system memory. We present here DNA replication dynamics, emphasizing recent data from the fission yeast Schizosaccharomyces pombe, and discuss how robustness may be ensured in spite of (or even assisted by) system randomness.