Philippe Bogaerts

Fast and accurate predictions of protein stability changes upon mutations using statistical potentials and neural networks

MOTIVATION The rational design of proteins with modified properties, through amino acid substitutions, is of crucial importance in a large variety of applications. Given the huge number of possible substitutions, every protein engineering project would benefit strongly from the guidance of in silico methods able to predict rapidly, and with reasonable accuracy, the stability changes resulting from all possible mutations in a protein. RESULTS We exploit newly developed statistical potentials, based on a formalism that highlights the coupling between four protein sequence and structure descriptors, and take into account the amino acid volume variation upon mutation. The stability change is expressed as a linear combination of these energy functions, whose proportionality coefficients vary with the solvent accessibility of the mutated residue and are identified with the help of a neural network. A correlation coefficient of R = 0.63 and a root mean square error of sigma(c) = 1.15 kcal/mol between measured and predicted stability changes are obtained upon cross-validation. These scores reach R = 0.79, and sigma(c) = 0.86 kcal/mol after exclusion of 10% outliers. The predictive power of our method is shown to be significantly higher than that of other programs described in the literature. AVAILABILITY http://babylone.ulb.ac.be/popmusic

Software sensors for bioprocesses.

State estimation is a significant problem in biotechnological processes, due to the general lack of hardware sensor measurements of the variables describing the process dynamics. The objective of this paper is to review a number of software sensor design methods, including extended Kalman filters, receding-horizon observers, asymptotic observers, and hybrid observers, which can be efficiently applied to bioprocesses. These several methods are illustrated with simulation and real-life case studies.

On-line state estimation of bioprocesses with full horizon observers

Software sensors (or state observers) are able to provide a continuous estimation of some signals (e.g. concentrations of important culture components, like biomass) which are not measured by hardware sensors. They need a mathematical model of the process and (discrete) hardware measurements of some other signals, like the concentrations of the main substrates. In this contribution, the state observer (called full horizon observer) is based on the identification of the most likely initial conditions of the experiment, e.g. the initial concentrations of the culture, these latter being identified at each time where new measurements are available. The basic principles of this observer are given in the general framework of nonlinear systems. Some properties and extensions of this state estimation method are presented. Some comparisons with the linear and extended Kalman filters are also given. The observer performances are illustrated in the case of the biomass concentration estimation within CHO animal cell cultures, for which only rare and asynchronous measurement samples of the glutamine, glucose and lactate concentrations are available.

Systematic Generation of Identifiable Macroscopic Reaction Schemes

Abstract Mathematical modelling of bioprocesses is very useful for building simulators, software sensors, con trollers, etc. Th ese tools are generally based on simple models consisting of the system of mass balances for the macroscopic species involved in a reaction scheme. Although this reaction scheme plays a key role in bioprocess modelling, its determination usually relyon intuition, process knowledge and trials and errors. This paper focuses on a metho d to genera te and to co mpare, in a syste matic way, all the identifiable schemes given a set of components for which concentration measurements are available. “Identifiable schemes” means that the pseudo-stoichiometric coefficients can be (uniquely) identified, independently of the kinetics which are unknown. The method is illustrated on a case study.

Incorporating batch effects in the estimation of drug stability parameters using an Arrhenius model

The nonlinear estimation of drug stability parameters (energy of activation Ea and shelf-life tY) by conventional approaches employs equations relating drug content determination C at time t and temperature T. The identification procedures lead to the determination of only one initial drug content C0 for several different experiments. However, it is well known that because of experimental concentration variation or of intentional modification of the experimental schedule, there are as many initial drug contents as experiments. For these reasons, a method which takes into account batch effects is proposed to determine stability parameters and also all initial drug contents C0j where j is the index of experiment in one step. This method is more accurate from a statistical viewpoint and is suitable for data treatment in pharmaceutical industries where the initial drug content of each batch entering the stability program can be checked a posteriori. The application of this method is shown on real kinetic data from the hydrolysis of acetylsalicylic acid (ASA).

Macroscopic Modelling of Bioprocesses with a View to Engineering Applications

Several motivations exist to use macroscopic models for engineering applications and to define a general modelling methodology. In this context, the framework of system of mass balances based on macroscopic reaction schemes is recalled and a new general kinetic model structure is presented and analysed. A general methodology for the parameter identification (kinetic and pseudo-stoichiometric coefficients) is summarised. Necessary conditions of validation of the reaction scheme (based on the identified model parameters) are proposed. The flexibility of the general kinetic model structure and a part of the parameter identification methodology are illustrated on simulated bacteria cultures.

Maximum likelihood estimation of pseudo-stoichiometry in macroscopic biological reaction schemes

Identification of pseudo-stoichiometric (or yield) coefficients is of primary importance for building a bioprocess model. In most of the applications, the estimation of these coefficients has to be performed without any knowledge of the kinetics and on the basis of a few experiments for which noisy discrete measurements of component concentrations are available. This paper proposes maximum likelihood estimators which are able to deal with measurement errors on all the signals, at each sampling time (including the initial one) and with intrinsic sign constraints on the parameters. This kind of realistic hypotheses exclude the use of the usual (weighted) least-squares estimators. The maximum likelihood estimators are proved to be unbiased (provided a first-order approximation) and their estimation error covariance matrix can be computed (at the same level of first-order approximation). The solutions are proposed in a very general framework, dealing with cell cultures (of bacteria, yeasts or animal cells) performed in stirred tank (continuous, semi-batch or batch) reactors, and without any a priori knowledge on the kinetics. The use of the estimators and their statistical properties are illustrated in a simulation case study (fed-batch bacterial cultures) and in a real case one (batch animal cell cultures).

Biological reaction modeling using radial basis function networks

The difficulty associated with experimental studies of biochemical systems often makes the development of pure black-box neural network models particularly delicate. Hence, it is appealing to resort to a hybrid physical-neural network approach, which uses all the available a priori knowledge about the process, and combines a first-principles model with a partial neural network (NN) model describing the phenomena, which are (at least partly) unknown. In this work, this strategy is applied to a real-case experimental study, i.e. batch CHO animal cell cultures. Several alternative model formulations are considered, including serial model structures, in which neural networks are used to describe either the reaction kinetics or the complete reaction rates (globalizing pseudo-stoichiometry and kinetics), or parallel model structures, in which a NN compensates for the prediction errors of a first-principles model. Attention is focused on the procedure used to estimate the unknown NN parameters and initial conditions from experimental data, including a maximum likelihood approach to take account of all the measurement errors, and a weight decay technique to alleviate identifiability problems. The good model agreement is demonstrated with cross-validation tests.

Improved kinetic parameter estimation in pH-profile data treatment

Statistical problems in temperature stability parameter estimation have been the subject of many papers whereas statistics in, pH-profile parameter estimation have focused little attention. However, the conventional two step method used in data treatment in both cases leads to identical statistical problems. The aim of this study is then to introduce a method that improves statistics in pH-profile parameter estimation. A one step non-linear method that takes into account the errors in drug content determination is proposed. A mathematical relationship between drug content C, pH and time t is tested. The proposed method allows the estimation of the specific kinetic constants and the dissociation constant (pK(a)) in a single run. The most likely experimental initial drug contents C(0j),. where j is the index of a given experiment, are also determined. This approach that takes into account all relevant experimental information for the estimation of kinetic parameters is more rigorous from a statistical viewpoint than the classical two step methods. Kinetic data from acetylsalicylic acid (ASA) hydrolysis was used for the tests.

Macroscopic modelling of baker's yeast production in fed-batch cultures and its link with trehalose production

Abstract A macroscopic model describing the influence of nitrogen on a fed-batch bakers yeast production process is proposed. First, on the basis of a set of biological reactions, inspired by the model of Sonnleitner and Kappeli (1986) , a model in which the nitrogen and glucose consumption are coordinated is proposed. Second, an attempt of estimating trehalose concentration in yeast cells through an extension of this model is presented. The model parameters are obtained via a non-linear least squares identification. It is validated with experimental data and successfully predicts the dynamics of growth, substrate consumption (nitrogen and carbon sources) and metabolite production (ethanol and trehalose). This model allows, on the one hand, quantitatively describing the link between nitrogen and glucose consumption in yeast cultures and, on the other hand, will be valuable for the determination of culture conditions aiming at maximizing yeast productivity while guaranteeing the accumulation of a required amount of trehalose.