Mitochondrial and Nuclear Genes of Mitochondrial Components in Cancer

Although the observation of aerobic glycolysis of tumor cells by Otto v. Warburg had demonstrated abnormalities of mitochondrial energy metabolism in cancer decades ago, there was no clear evidence for a functional role of mutant mitochondrial proteins in cancer development until the early years of the 21st century. In the year 2000, a major breakthrough was achieved by the observation, that several genes coding for subunits of the respiratory chain (ETC) complex II, succinate dehydrogenase (SDH) are tumor suppressor genes in heritable paragangliomas, fulfilling Knudson’s classical two-hit hypothesis. A functional inactivation of both alleles by germline mutations and chromosomal losses in the tumor tissue was found in the patients. Later, SDH mutations were also identified in sporadic paragangliomas and pheochromocytomas. Genes of the mitochondrial ATP-synthase and of mitochondrial iron homeostasis have been implicated in cancer development at the level of cell culture and mouse experiments. In contrast to the well established role of some nuclear SDH genes, a functional impact of the mitochondrial genome itself (mtDNA) in cancer development remains unclear. Nevertheless, the extremely high frequency of mtDNA mutations in solid tumors raises the question, whether this small circular genome might be applicable to early cancer detection. This is a meaningful approach, especially in cancers, which tend to spread tumor cells early into bodily fluids or faeces, which can be screened by non-invasive methods

Do mtDNA Mutations Participate in the Pathogenesis of Sporadic Parkinson’s Disease?

The pathogenesis of sporadic Parkinson’s disease (PD) remains enigmatic. Mitochondrial complex-I defects are known to occur in the substantia nigra (SN) of PD patients and are also debated in some extracerebral tissues. Early sequencing efforts of the mitochondrial DNA (mtDNA) did not reveal specific mutations, but a long lasting discussion was devoted to the issue of randomly distributed low level point mutations, caused by oxidative stress. However, a potential functional impact remained a matter of speculation, since heteroplasmy (mutational load) at any base position analyzed, remained far below the relevant functional threshold. A clearly age-dependent increase of the ‘common mtDNA deletion’ had been demonstrated in most brain regions by several authors since 1992. However, heteroplasmy did hardly exceed 1% of total mtDNA. It became necessary to exploit PCR techniques, which were able to detect any deletion in a few microdissected dopaminergic neurons of the SN. In 2006, two groups published biochemically relevant loads of somatic mtDNA deletions in these neurons. They seem to accumulate to relevant levels in the SN dopaminergic neurons of aged individuals in general, but faster in those developing PD. It is reasonable to assume that this accumulation causes mitochondrial dysfunction of the SN, although it cannot be taken as a final proof for an early pathogenetic role of this dysfunction. Recent studies demonstrate a distribution of deletion breakpoints, which does not differ between PD, aging and classical mitochondrial disorders, suggesting a common, but yet unknown mechanism

Convergence of Successive Linear Programming Algorithms for Noisy Functions

Gradient-based methods have been highly successful for solving a variety of both unconstrained and constrained nonlinear optimization problems. In real-world applications, such as optimal control or machine learning, the necessary function and derivative information may be corrupted by noise, however. Sun and Nocedal have recently proposed a remedy for smooth unconstrained problems by means of a stabilization of the acceptance criterion for computed iterates, which leads to convergence of the iterates of a trust-region method to a region of criticality, Sun and Nocedal (2022). We extend their analysis to the successive linear programming algorithm, Byrd et al. (2023a,2023b), for unconstrained optimization problems with objectives that can be characterized as the composition of a polyhedral function with a smooth function, where the latter and its gradient may be corrupted by noise. This gives the flexibility to cover, for example, (sub)problems arising image reconstruction or constrained optimization algorithms. We provide computational examples that illustrate the findings and point to possible strategies for practical determination of the stabilization parameter that balances the size of the critical region with a relaxation of the acceptance criterion (or descent property) of the algorithm

Fast numerical methods for mixed--integer nonlinear model--predictive control

This thesis aims at the investigation and development of fast numerical methods for nonlinear mixed--integer optimal control and model- predictive control problems. A new algorithm is developed based on the direct multiple shooting method for optimal control and on the idea of real--time iterations, and using a convex reformulation and relaxation of dynamics and constraints of the original predictive control problem. This algorithm relies on theoretical results and is based on a nonconvex SQP method and a new active set method for nonconvex parametric quadratic programming. It achieves real--time capable control feedback though block structured linear algebra for which we develop new matrix updates techniques. The applicability of the developed methods is demonstrated on several applications. This thesis presents novel results and advances over previously established techniques in a number of areas as follows: We develop a new algorithm for mixed--integer nonlinear model- predictive control by combining Bock's direct multiple shooting method, a reformulation based on outer convexification and relaxation of the integer controls, on rounding schemes, and on a real--time iteration scheme. For this new algorithm we establish an interpretation in the framework of inexact Newton-type methods and give a proof of local contractivity assuming an upper bound on the sampling time, implying nominal stability of this new algorithm. We propose a convexification of path constraints directly depending on integer controls that guarantees feasibility after rounding, and investigate the properties of the obtained nonlinear programs. We show that these programs can be treated favorably as MPVCs, a young and challenging class of nonconvex problems. We describe a SQP method and develop a new parametric active set method for the arising nonconvex quadratic subproblems. This method is based on strong stationarity conditions for MPVCs under certain regularity assumptions. We further present a heuristic for improving stationary points of the nonconvex quadratic subproblems to global optimality. The mixed--integer control feedback delay is determined by the computational demand of our active set method. We describe a block structured factorization that is tailored to Bock's direct multiple shooting method. It has favorable run time complexity for problems with long horizons or many controls unknowns, as is the case for mixed- integer optimal control problems after outer convexification. We develop new matrix update techniques for this factorization that reduce the run time complexity of all but the first active set iteration by one order. All developed algorithms are implemented in a software package that allows for the generic, efficient solution of nonlinear mixed-integer optimal control and model-predictive control problems using the developed methods