Optimal stopping with signatures

We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process. We consider classic and randomized stopping times represented by linear functionals of the associated rough path signature, and prove that maximizing over the class of signature stopping times, in fact, solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a (deterministic) optimization problem depending only on the (truncated) expected signature. The only assumption on the process is that it is a continuous (geometric) random rough path. Hence, the theory encompasses processes such as fractional Brownian motion which fail to be either semi-martingales or Markov processes

From rough path estimates to multilevel Monte Carlo

Discrete approximations to solutions of stochastic differential equations are well-known to converge with strong rate 1/2. Such rates have played a key-role in Giles' multilevel Monte Carlo method [Giles, Oper. Res. 2008] which gives a substantial reduction of the computational effort necessary for the evaluation of diffusion functionals. In the present article similar results are established for large classes of rough differential equations driven by Gaussian processes (including fractional Brownian motion with H>1/4 as special case)

Optimal stopping with signatures

We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process. We consider classic and randomized stopping times represented by linear functionals of the associated rough path signature, and prove that maximizing over the class of signature stopping times, in fact, solves the original optimal stopping problem. Using the algebraic properties of the signature, we can then recast the problem as a (deterministic) optimization problem depending only on the (truncated) expected signature. The only assumption on the process is that it is a continuous (geometric) random rough path. Hence, the theory encompasses processes such as fractional Brownian motion which fail to be either semi-martingales or Markov processes

The Evolutionarily Conserved Longevity Determinants HCF-1 and SIR-2.1/SIRT1 Collaborate to Regulate DAF-16/FOXO

The conserved DAF-16/FOXO transcription factors and SIR-2.1/SIRT1 deacetylases are critical for diverse biological processes, particularly longevity and stress response; and complex regulation of DAF-16/FOXO by SIR-2.1/SIRT1 is central to appropriate biological outcomes. Caenorhabditis elegans Host Cell Factor 1 (HCF-1) is a longevity determinant previously shown to act as a co-repressor of DAF-16. We report here that HCF-1 represents an integral player in the regulatory loop linking SIR-2.1/SIRT1 and DAF-16/FOXO in both worms and mammals. Genetic analyses showed that hcf-1 acts downstream of sir-2.1 to influence lifespan and oxidative stress response in C. elegans. Gene expression profiling revealed a striking 80% overlap between the DAF-16 target genes responsive to hcf-1 mutation and sir-2.1 overexpression. Subsequent GO-term analyses of HCF-1 and SIR-2.1-coregulated DAF-16 targets suggested that HCF-1 and SIR-2.1 together regulate specific aspects of DAF-16-mediated transcription particularly important for aging and stress responses. Analogous to its role in regulating DAF-16/SIR-2.1 target genes in C. elegans, the mammalian HCF-1 also repressed the expression of several FOXO/SIRT1 target genes. Protein–protein association studies demonstrated that SIR-2.1/SIRT1 and HCF-1 form protein complexes in worms and mammalian cells, highlighting the conservation of their regulatory relationship. Our findings uncover a conserved interaction between the key longevity determinants SIR-2.1/SIRT1 and HCF-1, and they provide new insights into the complex regulation of FOXO proteins

Histone Purification Combined with High-Resolution Mass Spectrometry to Examine Histone Post-Translational Modifications and Histone Variants in Caenorhabditis elegans

Histones are the major proteinaceous component of chromatin in eukaryotic cells and an important part of the epigenome, affecting most DNA-related events, including transcription, DNA replication, and chromosome segregation. The properties of histones are greatly influenced by their post-translational modifications (PTMs), over 200 of which are known today. Given this large number, researchers need sophisticated methods to study histone PTMs comprehensively. In particular, mass spectrometry (MS)-based approaches have gained popularity, allowing for the quantification of dozens of histone PTMs at once. Using these approaches, even the study of co-occurring PTMs and the discovery of novel PTMs become feasible. The success of MS-based approaches relies substantially on obtaining pure and well-preserved histones for analysis, which can be difficult depending on the source material. Caenorhabditis elegans has been a popular model organism to study the epigenome, but isolation of pure histones from these animals has been challenging. Here, we address this issue, presenting a method for efficient isolation of pure histone proteins from C. elegans at good yield. Further, we describe an MS pipeline optimized for accurate relative quantification of histone PTMs from C. elegans. We alkylate and tryptically digest the histones, analyze them by bottom-up MS, and then evaluate the resulting data by a C. elegans-adapted version of the software EpiProfile 2.0. Finally, we show the utility of this pipeline by determining differences in histone PTMs between C. elegans strains that age at different rates and thereby achieve very different lifespans. © 2020 The Authors. Basic Protocol 1: Large-scale growth and harvesting of synchronized C. elegans Basic Protocol 2: Nuclear preparation, histone extraction, and histone purification Basic Protocol 3: Bottom-up mass spectrometry analysis of histone PTMs and histone variants

Quantitative assessment of the asphericity of pretherapeutic FDG uptake as an independent predictor of outcome in NSCLC

Background The aim of the present study was to evaluate the predictive value of a novel quantitative measure for the spatial heterogeneity of FDG uptake, the asphericity (ASP) in patients with non-small cell lung cancer (NSCLC). Methods FDG-PET/CT had been performed in 60 patients (15 women, 45 men; median age, 65.5 years) with newly diagnosed NSCLC prior to therapy. The FDG-PET image of the primary tumor was segmented using the ROVER 3D segmentation tool based on thresholding at the volume-reproducing intensity threshold after subtraction of local background. ASP was defined as the relative deviation of the tumor’s shape from a sphere. Univariate and multivariate Cox regression as well as Kaplan-Meier (KM) analysis and log-rank test with respect to overall (OAS) and progression-free survival (PFS) were performed for clinical variables, SUVmax/mean, metabolically active tumor volume (MTV), total lesion glycolysis (TLG), ASP and “solidity”, another measure of shape irregularity. Results ASP, solidity and “primary surgical treatment” were significant independent predictors of PFS in multivariate Cox regression with binarized parameters (HR, 3.66; p < 0.001, HR, 2.11; p = 0.05 and HR, 2.09; p = 0.05), ASP and “primary surgical treatment” of OAS (HR, 3.19; p = 0.02 and HR, 3.78; p = 0.01, respectively). None of the other semi-quantitative PET parameters showed significant predictive value with respect to OAS or PFS. Kaplan-Meier analysis revealed a probability of 2-year PFS of 52% in patients with low ASP compared to 12% in patients with high ASP (p < 0.001). Furthermore, it showed a higher OAS rate in the case of low versus high ASP (1-year-OAS, 91% vs. 67%: p = 0.02). Conclusions The novel parameter asphericity of pretherapeutic FDG uptake seems to provide better prognostic value for PFS and OAS in NCSLC compared to SUV, metabolic tumor volume, total lesion glycolysis and solidity

The Deubiquitylase MATH-33 Controls DAF-16 Stability and Function in Metabolism and Longevity

SummaryFOXO family transcription factors are downstream effectors of Insulin/IGF-1 signaling (IIS) and major determinants of aging in organisms ranging from worms to man. The molecular mechanisms that actively promote DAF16/FOXO stability and function are unknown. Here we identify the deubiquitylating enzyme MATH-33 as an essential DAF-16 regulator in IIS, which stabilizes active DAF-16 protein levels and, as a consequence, influences DAF-16 functions, such as metabolism, stress response, and longevity in C. elegans. MATH-33 associates with DAF-16 in cellulo and in vitro. MATH-33 functions as a deubiquitylase by actively removing ubiquitin moieties from DAF-16, thus counteracting the action of the RLE-1 E3-ubiquitin ligase. Our findings support a model in which MATH-33 promotes DAF-16 stability in response to decreased IIS by directly modulating its ubiquitylation state, suggesting that regulated oscillations in the stability of DAF-16 protein play an integral role in controlling processes such as metabolism and longevity

DAF-16/FOXO requires Protein Phosphatase 4 to initiate transcription of stress resistance and longevity promoting genes

In C. elegans, the conserved transcription factor DAF-16/FOXO is a powerful aging regulator, relaying dire conditions into expression of stress resistance and longevity promoting genes. For some of these functions, including low insulin/IGF signaling (IIS), DAF-16 depends on the protein SMK-1/SMEK, but how SMK-1 exerts this role has remained unknown. We show that SMK-1 functions as part of a specific Protein Phosphatase 4 complex (PP4(SMK-1)). Loss of PP4(SMK-1) hinders transcriptional initiation at several DAF-16-activated genes, predominantly by impairing RNA polymerase II recruitment to their promoters. Search for the relevant substrate of PP4(SMK-1) by phosphoproteomics identified the conserved transcriptional regulator SPT-5/SUPT5H, whose knockdown phenocopies the loss of PP4(SMK-1). Phosphoregulation of SPT-5 is known to control transcriptional events such as elongation and termination. Here we also show that transcription initiating events are influenced by the phosphorylation status of SPT-5, particularly at DAF-16 target genes where transcriptional initiation appears rate limiting, rendering PP4(SMK-1) crucial for many of DAF-16's physiological roles

DAF-16/FOXO employs the chromatin remodeller SWI/SNF to promote stress resistance and longevity

Organisms are constantly challenged by stresses and privations and require adaptive responses for their survival. The transcription factor DAF-16/FOXO is central nexus in these responses, but despite its importance little is known about how it regulates its target genes. Proteomic identification of DAF-16/FOXO binding partners in Caenorhabditis elegans and their subsequent functional evaluation by RNA interference (RNAi) revealed several candidate DAF-16/FOXO cofactors, most notably the chromatin remodeller SWI/SNF. DAF-16/FOXO and SWI/SNF form a complex and globally colocalize at DAF-16/FOXO target promoters. We show that specifically for gene-activation, DAF-16/FOXO depends on SWI/SNF, facilitating SWI/SNF recruitment to target promoters, in order to activate transcription by presumed remodelling of local chromatin. For the animal, this translates into an essential role of SWI/SNF for DAF-16/FOXO-mediated processes, i.e. dauer formation, stress resistance, and the promotion of longevity. Thus we give insight into the mechanisms of DAF-16/FOXO-mediated transcriptional regulation and establish a critical link between ATP-dependent chromatin remodelling and lifespan regulation