Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations

High-dimensional partial differential equations (PDEs) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model. Such high-dimensional fully nonlinear PDEs are exceedingly difficult to solve as the computational effort for standard approximation methods grows exponentially with the dimension. In this work, we propose a new method for solving high-dimensional fully nonlinear second-order PDEs. Our method can in particular be used to sample from high-dimensional nonlinear expectations. The method is based on (1) a connection between fully nonlinear second-order PDEs and second-order backward stochastic differential equations (2BSDEs), (2) a merged formulation of the PDE and the 2BSDE problem, (3) a temporal forward discretization of the 2BSDE and a spatial approximation via deep neural nets, and (4) a stochastic gradient descent-type optimization procedure. Numerical results obtained using TensorFlow in Python illustrate the efficiency and the accuracy of the method in the cases of a 100-dimensional Black–Scholes–Barenblatt equation, a 100-dimensional Hamilton–Jacobi–Bellman equation, and a nonlinear expectation of a 100-dimensional G-Brownian motion.

     

Desorption of plasmid DNA from anion exchangers: Salt concentration at elution is independent of plasmid size and load

Detailed studies on the sorption behavior of plasmids on anion exchangers are rare compared to proteins. In this study, we systematically compare the elution behavior of plasmid DNA on three common anion exchange resins using linear gradient and isocratic elution experiments. Two plasmids of different lengths, 8 and 20 kbp, were studied and their elution characteristics were compared to a green fluorescent protein. Using established methods for determining retention characteristics of biomolecules in ion exchange chromatography lead to remarkable results. In contrast to the green fluorescent protein, plasmid DNA consistently elutes at one characteristic salt concentration in linear gradient elution. This salt concentration was the same independent of plasmid size but differed slightly for different resins. The behavior is consistent also at preparative loadings of plasmid DNA. Thus, only a single linear gradient elution experiment is sufficient to design elution in a process scale capture step. At isocratic elution conditions, plasmid DNA elutes only above this characteristic concentration. Even at slightly lower concentrations most plasmids remain tightly bound. We hypothesize, that the desorption is accompanied by a conformational change leading to a reduced number of available negative charges for binding. This explanation is supported by structural analysis before and after elution.     

Beyond p-Hexaphenylenes: Synthesis of Unsubstituted p-Nonaphenylene by a Precursor Protocol

The synthesis of unsubstituted oligo-para-phenylenes ( OPP ) exceeding para-hexaphenylene—in the literature often referred to as p-sexiphenyl—has long remained elusive due to their insolubility. We report the first preparation of unsubstituted para-nonaphenylenes ( 9PP s) by extending our precursor route to poly-para-phenylenes ( PPP ) to a discrete oligomer. Two geometric isomers of methoxylated syn- and anti-cyclohexadienylenes were synthesized, from which 9PP was obtained via thermal aromatization in thin films. 9PP was characterized via optical, infrared and solid-state ¹³C NMR spectroscopy as well as atomic force microscopy and mass spectrometry, and compared to polymeric analogues. Due to the lack of substitution, para-nonaphenylene, irrespective of the precursor isomer employed, displays pronounced aggregation in the solid state. Intermolecular excitonic coupling leads to formation of H-type aggregates, red-shifting emission of the films to greenish. 9PP allows to study the structure–property relationship of para-phenylene oligomers and polymers, especially since the optical properties of PPP depend on the molecular shape of the precursor.     

Combined Subcutaneous Fat Aspirate and Skin Tru-Cut Biopsy for Amyloid Screening in Patients with Suspected Systemic Amyloidosis

Screening for systemic amyloidosis is typically carried out with abdominal fat aspirates with varying reported sensitivities. Fat aspirates are preferred for use in primary screening instead of organ biopsies as they are less invasive and thereby minimize the potential risk of complications. At Odense Amyloidosis Center, we performed a prospective study on whether the combined use of fat aspirate and tru-cut skin biopsy could increase the diagnostic sensitivity. Both fat aspirates and skin biopsies were screened with Congo Red staining, and positive biopsies were subsequently subtyped using immunoelectron microscopy and mass spectrometry. Seventy-six patients were included. In total, 24 patients had systemic amyloidosis (11 AL, 12 wtATTR, 1 AA), and 6 patients had localized amyloidosis. Combined fat aspirate and skin biopsy were Congo Red-positive in 15 patients (overall sensitivity (OS) 62.5%). Fat aspirates were positive in 14 patients (OS 58.3%), and the skin biopsy was positive in 5 patients (OS 20.8%). In only one patient did the skin biopsy add extra diagnostic information. The sensitivity differed between AL and ATTR amyloidosis—81.8% and 41.7%, respectively. Using skin biopsy as the only screening method is not recommended.     

Selective Aptamer‐Based Control of Intraneuronal Signaling

Cellular behavior is orchestrated by the complex interactions of a myriad of intracellular signal transduction pathways. To understand and investigate the role of individual components in such signaling networks, the availability of specific inhibitors is of paramount importance. We report the generation and validation of a novel variant of an RNA aptamer that selectively inhibits the mitogen‐activated kinase pathway in neurons. We demonstrate that the aptamer retains function under intracellular conditions and that application of the aptamer through the patch‐clamp pipette efficiently inhibits mitogen‐activated kinase‐dependent synaptic plasticity. This approach introduces synthetic aptamers as generic tools, readily applicable to inhibit different components of intraneuronal signaling networks with utmost specificity.     

Identification of a β1/β2‐Specific Sulfonamide Proteasome Ligand by Crystallographic Screening

The proteasome represents a validated drug target for the treatment of cancer, however, new types of inhibitors are required to tackle the development of resistant tumors. Current fluorescence‐based screening methods suffer from low sensitivity and are limited to the detection of ligands with conventional binding profiles. In response to these drawbacks, a crystallographic screening procedure for the discovery of agents with a novel mode of action was utilized. The optimized workflow was applied to the screening of a focused set of compounds, resulting in the discovery of a β1/β2‐specific sulfonamide derivative that noncovalently binds between subunits β1 and β2. The binding pocket displays significant differences in size and polarity between the immuno‐ and constitutive proteasome. The identified ligand thus provides valuable insights for the future structure‐based design of subtype‐specific proteasome inhibitors.     

Locked by Design: A Conformationally Constrained Transglutaminase Tag Enables Efficient Site‐Specific Conjugation

Based on the crystal structure of a natural protein substrate for microbial transglutaminase, an enzyme that catalyzes protein crosslinking, a recognition motif for site‐specific conjugation was rationally designed. Conformationally locked by an intramolecular disulfide bond, this structural mimic of a native conjugation site ensured efficient conjugation of a reporter cargo to the therapeutic monoclonal antibody cetuximab without erosion of its binding properties.