András Hartmann

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.

An extended dynamic model of Lactococcus lactis metabolism for mannitol and 2,3-butanediol production

Biomedical research and biotechnological production are greatly benefiting from the results provided by the development of dynamic models of microbial metabolism. Although several kinetic models of Lactococcus lactis (a Lactic Acid Bacterium (LAB) commonly used in the dairy industry) have been developed so far, most of them are simplified and focus only on specific metabolic pathways. Therefore, the application of mathematical models in the design of an engineering strategy for the production of industrially important products by L. lactis has been very limited. In this work, we extend the existing kinetic model of L. lactis central metabolism to include industrially relevant production pathways such as mannitol and 2,3-butanediol. In this way, we expect to study the dynamics of metabolite production and make predictive simulations in L. lactis. We used a system of ordinary differential equations (ODEs) with approximate Michaelis-Menten-like kinetics for each reaction, where the parameters were estimated from multivariate time-series metabolite concentrations obtained by our team through in vivo Nuclear Magnetic Resonance (NMR). The results show that the model captures observed transient dynamics when validated under a wide range of experimental conditions. Furthermore, we analyzed the model using global perturbations, which corroborate experimental evidence about metabolic responses upon enzymatic changes. These include that mannitol production is very sensitive to lactate dehydrogenase (LDH) in the wild type (W.T.) strain, and to mannitol phosphoenolpyruvate: a phosphotransferase system (PTS(Mtl)) in a LDH mutant strain. LDH reduction has also a positive control on 2,3-butanediol levels. Furthermore, it was found that overproduction of mannitol-1-phosphate dehydrogenase (MPD) in a LDH/PTS(Mtl) deficient strain can increase the mannitol levels. The results show that this model has prediction capability over new experimental conditions and offers promising possibilities to elucidate the effect of alterations in the main metabolism of L. lactis, with application in strain optimization.

BacHBerry: BACterial Hosts for production of Bioactive phenolics from bERRY fruits

BACterial Hosts for production of Bioactive phenolics from bERRY fruits (BacHBerry) was a 3-year project funded by the Seventh Framework Programme (FP7) of the European Union that ran between November 2013 and October 2016. The overall aim of the project was to establish a sustainable and economically-feasible strategy for the production of novel high-value phenolic compounds isolated from berry fruits using bacterial platforms. The project aimed at covering all stages of the discovery and pre-commercialization process, including berry collection, screening and characterization of their bioactive components, identification and functional characterization of the corresponding biosynthetic pathways, and construction of Gram-positive bacterial cell factories producing phenolic compounds. Further activities included optimization of polyphenol extraction methods from bacterial cultures, scale-up of production by fermentation up to pilot scale, as well as societal and economic analyses of the processes. This review article summarizes some of the key findings obtained throughout the duration of the project.

Online Bayesian Time-varying Parameter Estimation of HIV-1 Time-series*

Abstract Nonlinear Bayesian filtering offers various online tools for system identification of (parametric) ordinary differential equation models. Since parameters may change with time, it is a relevant question to assess how well time-varying parameters can be estimated. For this purpose we tested two filtering methods, Extended Kalman Filter and Particle Filter for joint state and time-varying parameter estimation on a dynamic model of HIV-1 virus immune response. After evaluating the methods on simulated time-series we applied them to clinical datasets. Estimated time-varying parameters on clinical data are consistent with previously reported results with offline algorithms.

Modeling multiple experiments using regularized optimization

The aim of inverse modeling is to capture the systems׳ dynamics through a set of parameterized Ordinary Differential Equations (ODEs). Parameters are often required to fit multiple repeated measurements or different experimental conditions. This typically leads to a multi-objective optimization problem that can be formulated as a non-convex optimization problem. Modeling of glucose utilization of Lactococcus lactis bacteria is considered using in vivo Nuclear Magnetic Resonance (NMR) measurements in perturbation experiments. We propose an ODE model based on a modified time-varying exponential decay that is flexible enough to model several different experimental conditions. The starting point is an over-parameterized non-linear model that will be further simplified through an optimization procedure with regularization penalties. For the parameter estimation, a stochastic global optimization method, particle swarm optimization (PSO) is used. A regularization is introduced to the identification, imposing that parameters should be the same across several experiments in order to identify a general model. On the remaining parameter that varies across the experiments a function is fit in order to be able to predict new experiments for any initial condition. The method is cross-validated by fitting the model to two experiments and validating the third one. Finally, the proposed model is integrated with existing models of glycolysis in order to reconstruct the remaining metabolites. The method was found useful as a general procedure to reduce the number of parameters of unidentifiable and over-parameterized models, thus supporting feature selection methods for parametric models.

Hybrid identification of time-varying parameter with particle filtering and expectation maximization

The problem of time-varying parameter identification is considered on a class of nonlinear hybrid systems. It is assumed that inputs and outputs are directly measured, and a subset of system parameters can take different values from a finite set at each time instance. An offline (batch) algorithm that combines particle filtering and the expectation maximization is introduced for the identification of such systems. The efficiency of the proposed method is illustrated through simulated examples.

Identification and automatic segmentation of multiphasic cell growth using a linear hybrid model

This article considers a new mathematical model for the description of multiphasic cell growth. A linear hybrid model is proposed and it is shown that the two-parameter logistic model with switching parameters can be represented by a Switched affine AutoRegressive model with eXogenous inputs (SARX). The growth phases are modeled as continuous processes, while the switches between the phases are considered to be discrete events triggering a change in growth parameters. This framework provides an easily interpretable model, because the intrinsic behavior is the same along all the phases but with a different parameterization. Another advantage of the hybrid model is that it offers a simpler alternative to recent more complex nonlinear models. The growth phases and parameters from datasets of different microorganisms exhibiting multiphasic growth behavior such as Lactococcus lactis, Streptococcus pneumoniae, and Saccharomyces cerevisiae, were inferred. The segments and parameters obtained from the growth data are close to the ones determined by the experts. The fact that the model could explain the data from three different microorganisms and experiments demonstrates the strength of this modeling approach for multiphasic growth, and presumably other processes consisting of multiple phases.

OptPipe - a pipeline for optimizing metabolic engineering targets

BackgroundWe propose OptPipe - a Pipeline for Optimizing Metabolic Engineering Targets, based on a consensus approach. The method generates consensus hypotheses for metabolic engineering applications by combining several optimization solutions obtained from distinct algorithms. The solutions are ranked according to several objectives, such as biomass and target production, by using the rank product tests corrected for multiple comparisons.ResultsOptPipe was applied in a genome-scale model of Corynebacterium glutamicum for maximizing malonyl-CoA, which is a valuable precursor for many phenolic compounds. In vivo experimental validation confirmed increased malonyl-CoA level in case of ΔsdhCAB deletion, as predicted in silico.ConclusionsA method was developed to combine the optimization solutions provided by common knockout prediction procedures and rank the suggested mutants according to the expected growth rate, production and a new adaptability measure. The implementation of the pipeline along with the complete documentation is freely available at https://github.com/AndrasHartmann/OptPipe.

Exploring the Cellular Objective in Flux Balance Constraint-Based Models

Genome-scale reconstructions are usually stoichiometric and analyzed under steady-state assumptions using constraint-based modelling with flux balance analysis (FBA). FBA requires not only the stoichiometry of the network, but also an appropriate cellular objective function and possible additional physico-chemical constraints to predict the set of resulting flux distributions of an organism.