Abstract

Glycosylation is considered as a critical quality attribute for the production of recombinant biopharmaceuticals such as hormones, blood clotting factors, or monoclonal antibodies. In contrast, glycan patterns of immunogenic viral proteins, which differ significantly between the various expression systems, are hardly analyzed yet. The influenza A virus (IAV) proteins hemagglutinin (HA) and neuraminidase (NA) have multiple N-glycosylation sites, and alteration of N-glycan micro- and macroheterogeneity can have strong effects on virulence and immunogenicity. Here, we present a versatile and powerful glycoanalytical workflow that enables a comprehensive N-glycosylation analysis of IAV glycoproteins. We challenged our workflow with IAV (A/PR/8/34 H1N1) propagated in two closely related Madin-Darby canine kidney (MDCK) cell lines, namely an adherent MDCK cell line and its corresponding suspension cell line. As expected, N-glycan patterns of HA and NA from virus particles produced in both MDCK cell lines were similar. Detailed analysis of the HA N-glycan microheterogeneity showed an increasing variability and a higher complexity for N-glycosylation sites located closer to the head region of the molecule. In contrast, NA was found to be exclusively N-glycosylated at site N73. Almost all N-glycan structures were fucosylated. Furthermore, HA and NA N-glycan structures were exclusively hybrid- and complex-type structures, to some extent terminated with alpha-linked galactose(s) but also with blood group H type 2 and blood group A epitopes. In contrast to the similarity of the overall glycan pattern, differences in the relative abundance of individual structures were identified. This concerned, in particular, oligomannose-type, alpha-linked galactose, and multiantennary complex-type N-glycans.

Highlights

  • In this paper, we discuss an optimal control problem for the unsteady Navier–Stokes equations influenced by noise terms

  • We studied a control problem constrained by the stochastic Navier–Stokes equations driven by linear multiplicative noise in multi-dimensional domains

  • Due to a local existence and uniqueness result of the solution to the stochastic Navier–Stokes equations, the control problem is formulated as a nonconvex optimization problem

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Summary

Introduction

We discuss an optimal control problem for the unsteady Navier–Stokes equations influenced by noise terms. In [26, 27], optimal control problems for the stochastic Navier–Stokes equations in bounded three-dimensional domains are considered, where the state equation is defined as a martingale solution. Recall that the martingale solution for bounded three-dimensional domains is not unique and only existence results can be obtained To overcome these issues, we consider a generalization of the control problems mentioned above. To derive a formula for the optimal control based on this variational inequality, we apply a duality principle providing a relation between the linearized stochastic Navier–Stokes equations and the corresponding adjoint equation. An existence and uniqueness result as well as some properties of the local mild solution to the stochastic Navier–Stokes equations are stated in Sect.

Preliminaries
Functional Background
Stochastic Processes and the Stochastic Integral
Stochastic Navier–Stokes Equations
The Control Problem and a Necessary Optimality Condition
Linearized Stochastic Navier–Stokes Equations
The Derivatives of the Cost Functional
The Optimal Control
The Adjoint Equation
Approximation by a Strong Formulation
The Duality Principle and the Derivation of an Explicit Formula
A Sufficient Optimality Condition
Conclusion
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