Hybrid semi-parametric models consist of model structures that combine parametric and nonparametric submodels based on different knowledge sources. The development of a hybrid semi-parametric model can offer several advantages over traditional mechanistic or data-driven modeling, as reviewed in this paper. These advantages, such as broader knowledge base, transparency of the modeling approach and cost-effective model development, have been widely recognized, not only in academia but also in the industry.In this paper, the most common hybrid semi-parametric modeling and parameter identification techniques are revisited. Applications in the areas of (bio)chemical engineering for process monitoring, control, optimization, scaleup and model-reduction are reviewed. It is outlined that the application of hybrid semi-parametric techniques does not automatically lead into better results but that rational knowledge integration has potential to significantly improve model-based process operation and design.

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In the process analytical technology (PAT) initiative, the application of sensors technology and modeling methods is promoted. The emphasis is on Quality by Design, online monitoring, and closed-loop control with the general aim of building in product quality into manufacturing operations. As a result, online high-throughput process analyzers find increasing application and therewith high amounts of highly correlated data become available online. In this study, an hybrid chemometric/mathematical modeling method is adopted for data analysis, which is shown to be advantageous over the commonly used chemometric techniques in PAT applications. This methodology was applied to the analysis of process data of Bordetella pertussis cultivations, namely online data of near-infrared, (NIR), pH, temperature and dissolved oxygen, and off-line data of biomass, glutamate, and lactate concentrations. The hybrid model structure consisted of macroscopic material balance equations in which the specific reactions rates are modeled by nonlinear partial least square (PLS). This methodology revealed a significant higher statistical confidence in comparison to PLSs, translated in a reduction of mean squared prediction errors (e.g., individual root mean squared prediction errors calibration/validation obtained through the hybrid model for the concentrations of lactate: 0.8699/0.7190 mmol/L; glutamate: 0.6057/0.2917 mmol/L; and biomass: 0.0520/0.0283 OD; and obtained through the PLS model for the concentrations of lactate: 1.3549/1.0087 mmol/L; glutamate: 0.7628/0.3504 mmol/L; and biomass: 0.0949/0.0412 OD). Moreover, the analysis of loadings and scores in the hybrid approach revealed that process features can, as for PLS, be extracted by the hybrid method.

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BackgroundThis paper presents a method for modelling dynamical biochemical networks with intrinsic time delays. Since the fundamental mechanisms leading to such delays are many times unknown, non conventional modelling approaches become necessary. Herein, a hybrid semi-parametric identification methodology is proposed in which discrete time series are incorporated into fundamental material balance models. This integration results in hybrid delay differential equations which can be applied to identify unknown cellular dynamics.ResultsThe proposed hybrid modelling methodology was evaluated using two case studies. The first of these deals with dynamic modelling of transcriptional factor A in mammalian cells. The protein transport from the cytosol to the nucleus introduced a delay that was accounted for by discrete time series formulation. The second case study focused on a simple network with distributed time delays that demonstrated that the discrete time delay formalism has broad applicability to both discrete and distributed delay problems.ConclusionsSignificantly better prediction qualities of the novel hybrid model were obtained when compared to dynamical structures without time delays, being the more distinctive the more significant the underlying system delay is. The identification of the system delays by studies of different discrete modelling delays was enabled by the proposed structure. Further, it was shown that the hybrid discrete delay methodology is not limited to discrete delay systems. The proposed method is a powerful tool to identify time delays in ill-defined biochemical networks.

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Poly(ethylene) glycol (PEG) is the most used polymer in drug delivery due to its unique properties, such as reduced toxicity and high solubility. PEGylation is the process of attaching PEG chains to compounds. Its effect on drug delivery has motivated a lot of experimental and computational studies. To explain and complement experimental findings, all-atom, coarsegrained and multi-scale molecular dynamics simulations are being increasingly done. This review summarizes the computational studies using molecular dynamics that have been done regarding PEG and PEGylation of small molecules, proteins, peptides and drug nanocarriers such as micelles, liposomes, dendrimers and carbon nanotubes. Generally, the various studies presented indicate that molecular dynamics simulations can be a powerful tool in explaining and predicting experimental results and are efficient in providing an atomic-level insight into the interactions between PEG molecules and other compounds. In particular, MD simulations are nowadays routinely used to provide direct insight into the dominant conformations formed, range of interactions established, and effect of PEGylation on the structural and dynamic properties of different drugs or therapeutic agents, enabling an atomic level analysis of a variety aspects including ionic concentration, identify of ions present, and specific PEG size and number of molecules. Figure 1. Types of PEG chains. X represents functional groups and n represents the number of individual units in the chain. In multi-arm PEG chains oxygen atoms were omitted for clarity.