Diego A. Oyarzún

Cascaded Multilevel Inverter With Regeneration Capability and Reduced Number of Switches

Multilevel converters are a very interesting alternative for medium and high power drives. One of the more flexible topologies of this type is the cascaded multicell converter. This paper proposes the use of a single-phase reduced cell suitable for cascaded multilevel converters. This cell uses a reduced single-phase active rectifier at the input and an H-bridge inverter at the output side. This topology presents a very good performance, effectively controlling the waveform of the input current and of the output voltage and allowing operation in the motoring and regenerative mode. The results presented in this paper confirm that this medium voltage inverter effectively eliminates low frequency input current harmonics at the primary side of the transformer and operates without problems in regenerative mode.

Mechanistic links between cellular trade-offs, gene expression, and growth.

Significance Cells have finite resources. Committing resources to one task therefore reduces the amount of resources available to others. These trade-offs are often overlooked but potentially modify all cellular processes. Building a mathematical cell model that respects such trade-offs and describes the mechanisms of protein synthesis and how cells extract resources from their environment, we quantitatively recover the typical behavior of an individual growing cell and of a population of cells. As trade-offs are experienced by all cells and because growth largely determines cellular fitness, a predictive understanding of how biochemical processes affect others and affect growth is important for diverse applications, such as the use of microbes for biotechnology, the inhibition of antibiotic resistance, and the growth of cancers. Intracellular processes rarely work in isolation but continually interact with the rest of the cell. In microbes, for example, we now know that gene expression across the whole genome typically changes with growth rate. The mechanisms driving such global regulation, however, are not well understood. Here we consider three trade-offs that, because of limitations in levels of cellular energy, free ribosomes, and proteins, are faced by all living cells and we construct a mechanistic model that comprises these trade-offs. Our model couples gene expression with growth rate and growth rate with a growing population of cells. We show that the model recovers Monod’s law for the growth of microbes and two other empirical relationships connecting growth rate to the mass fraction of ribosomes. Further, we can explain growth-related effects in dosage compensation by paralogs and predict host–circuit interactions in synthetic biology. Simulating competitions between strains, we find that the regulation of metabolic pathways may have evolved not to match expression of enzymes to levels of extracellular substrates in changing environments but rather to balance a trade-off between exploiting one type of nutrient over another. Although coarse-grained, the trade-offs that the model embodies are fundamental, and, as such, our modeling framework has potentially wide application, including in both biotechnology and medicine.

Synthetic gene circuits for metabolic control: design trade-offs and constraints.

A grand challenge in synthetic biology is to push the design of biomolecular circuits from purely genetic constructs towards systems that interface different levels of the cellular machinery, including signalling networks and metabolic pathways. In this paper, we focus on a genetic circuit for feedback regulation of unbranched metabolic pathways. The objective of this feedback system is to dampen the effect of flux perturbations caused by changes in cellular demands or by engineered pathways consuming metabolic intermediates. We consider a mathematical model for a control circuit with an operon architecture, whereby the expression of all pathway enzymes is transcriptionally repressed by the metabolic product. We address the existence and stability of the steady state, the dynamic response of the network under perturbations, and their dependence on common tuneable knobs such as the promoter characteristic and ribosome binding site (RBS) strengths. Our analysis reveals trade-offs between the steady state of the enzymes and the intermediates, together with a separation principle between promoter and RBS design. We show that enzymatic saturation imposes limits on the parameter design space, which must be satisfied to prevent metabolite accumulation and guarantee the stability of the network. The use of promoters with a broad dynamic range and a small leaky expression enlarges the design space. Simulation results with realistic parameter values also suggest that the control circuit can effectively upregulate enzyme production to compensate flux perturbations.

Noise Propagation in Synthetic Gene Circuits for Metabolic Control

Dynamic control of enzyme expression can be an effective strategy to engineer robust metabolic pathways. It allows a synthetic pathway to self-regulate in response to changes in bioreactor conditions or the metabolic state of the host. The implementation of this regulatory strategy requires gene circuits that couple metabolic signals with the genetic machinery, which is known to be noisy and one of the main sources of cell-to-cell variability. One of the unexplored design aspects of these circuits is the propagation of biochemical noise between enzyme expression and pathway activity. In this article, we quantify the impact of a synthetic feedback circuit on the noise in a metabolic product in order to propose design criteria to reduce cell-to-cell variability. We consider a stochastic model of a catalytic reaction under negative feedback from the product to enzyme expression. On the basis of stochastic simulations and analysis, we show that, depending on the repression strength and promoter strength, transcriptional repression of enzyme expression can amplify or attenuate the noise in the number of product molecules. We obtain analytic estimates for the metabolic noise as a function of the model parameters and show that noise amplification/attenuation is a structural property of the model. We derive an analytic condition on the parameters that lead to attenuation of metabolic noise, suggesting that a higher promoter sensitivity enlarges the parameter design space. In the theoretical case of a switch-like promoter, our analysis reveals that the ability of the circuit to attenuate noise is subject to a trade-off between the repression strength and promoter strength.

Sequential Activation of Metabolic Pathways: a Dynamic Optimization Approach

The regulation of cellular metabolism facilitates robust cellular operation in the face of changing external conditions. The cellular response to this varying environment may include the activation or inactivation of appropriate metabolic pathways. Experimental and numerical observations of sequential timing in pathway activation have been reported in the literature. It has been argued that such patterns can be rationalized by means of an underlying optimal metabolic design. In this paper we pose a dynamic optimization problem that accounts for time-resource minimization in pathway activation under constrained total enzyme abundance. The optimized variables are time-dependent enzyme concentrations that drive the pathway to a steady state characterized by a prescribed metabolic flux. The problem formulation addresses unbranched pathways with irreversible kinetics. Neither specific reaction kinetics nor fixed pathway length are assumed.In the optimal solution, each enzyme follows a switching profile between zero and maximum concentration, following a temporal sequence that matches the pathway topology. This result provides an analytic justification of the sequential activation previously described in the literature. In contrast with the existent numerical approaches, the activation sequence is proven to be optimal for a generic class of monomolecular kinetics. This class includes, but is not limited to, Mass Action, Michaelis–Menten, Hill, and some Power-law models. This suggests that sequential enzyme expression may be a common feature of metabolic regulation, as it is a robust property of optimal pathway activation.

Dynamic optimization of metabolic networks coupled with gene expression

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition. An approximation by a timescale separation leads to a coupled model of quasi-steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. Discretization of the optimization problems leads to a linear program that can be efficiently solved. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle.

Multistability and oscillations in genetic control of metabolism

Genetic control of enzyme activity drives metabolic adaptations to environmental changes, and therefore the feedback interaction between gene expression and metabolism is essential to cell fitness. In this paper we develop a new formalism to detect the equilibrium regimes of an unbranched metabolic network under transcriptional feedback from one metabolite. Our results indicate that one-to-all transcriptional feedback can induce a wide range of metabolic phenotypes, including mono-, multistability and oscillatory behavior. The analysis is based on the use of switch-like models for transcriptional control and the exploitation of the time scale separation between metabolic and genetic dynamics. For any combination of activation and repression feedback loops, we derive conditions for the emergence of a specific phenotype in terms of genetic parameters such as enzyme expression rates and regulatory thresholds. We find that metabolic oscillations can emerge under uniform thresholds and, in the case of operon-controlled networks, the analysis reveals how nutrient-induced bistability and oscillations can emerge as a consequence of the transcriptional feedback.

Shaping pulses to control bistable systems

In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback control systems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set of all pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to compute this curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results to models with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitations of the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotone biochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics of bistable systems under external inputs and open up numerous directions for future investigation.

Predicting the F(ab)-mediated effect of monoclonal antibodies in vivo by combining cell-level kinetic and pharmacokinetic modelling

Cell-level kinetic models for therapeutically relevant processes increasingly benefit the early stages of drug development. Later stages of the drug development processes, however, rely on pharmacokinetic compartment models while cell-level dynamics are typically neglected. We here present a systematic approach to integrate cell-level kinetic models and pharmacokinetic compartment models. Incorporating target dynamics into pharmacokinetic models is especially useful for the development of therapeutic antibodies because their effect and pharmacokinetics are inherently interdependent. The approach is illustrated by analysing the F(ab)-mediated inhibitory effect of therapeutic antibodies targeting the epidermal growth factor receptor. We build a multi-level model for anti-EGFR antibodies by combining a systems biology model with in vitro determined parameters and a pharmacokinetic model based on in vivo pharmacokinetic data. Using this model, we investigated in silico the impact of biochemical properties of anti-EGFR antibodies on their F(ab)-mediated inhibitory effect. The multi-level model suggests that the F(ab)-mediated inhibitory effect saturates with increasing drug-receptor affinity, thereby limiting the impact of increasing antibody affinity on improving the effect. This indicates that observed differences in the therapeutic effects of high affinity antibodies in the market and in clinical development may result mainly from Fc-mediated indirect mechanisms such as antibody-dependent cell cytotoxicity.

Fundamental Design Principles for Transcription-Factor-Based Metabolite Biosensors

Metabolite biosensors are central to current efforts toward precision engineering of metabolism. Although most research has focused on building new biosensors, their tunability remains poorly understood and is fundamental for their broad applicability. Here we asked how genetic modifications shape the dose-response curve of biosensors based on metabolite-responsive transcription factors. Using the lac system in Escherichia coli as a model system, we built promoter libraries with variable operator sites that reveal interdependencies between biosensor dynamic range and response threshold. We developed a phenomenological theory to quantify such design constraints in biosensors with various architectures and tunable parameters. Our theory reveals a maximal achievable dynamic range and exposes tunable parameters for orthogonal control of dynamic range and response threshold. Our work sheds light on fundamental limits of synthetic biology designs and provides quantitative guidelines for biosensor design in applications such as dynamic pathway control, strain optimization, and real-time monitoring of metabolism.