Estimating Koopman operators for nonlinear dynamical systems: a nonparametric approach

The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most popular finite dimensional approximation. In this paper we capture their core essence as a dual version of the same framework, incorporating them into the Kernel framework. To do so, we leverage the RKHS as a suitable space for learning the Koopman dynamics, thanks to its intrinsic finite-dimensional nature, shaped by data. We finally establish a strong link between kernel methods and Koopman operators, leading to the estimation of the latter through Kernel functions. We provide also simulations for comparison with standard procedures.Comment: Pre-print submitted for 19th IFAC Symposium, System Identification: learning models for decision and contro

Regulation of PTP1B stability and signaling by the PKA scaffold protein praja2

Protein tyrosine phosphatase 1B (PTP1B) is a non-transmembrane protein implicated as negative regulator in the insulin and leptin pathways. PTP1B is also implicated in the development of breast cancer due to its dephosphorylating role on the proto-oncogene Src. During these years, PTP1B has emerged as a promising potential therapeutic target for the treatment of the type 2 diabetes. PTP1B control mechanisms are still controversial and not well understood. Here, I've contributed to identify a novel mechanism of regulation of PTP1B mediated by the ubiquitin-proteasome pathway. We identify the E3 ligase praja2 as novel interactor and regulator of PTP1B. Thus, praja2 ubiquitinates PTP1B and sustains the insulin pathway, interfering with praja2 expression or activity negatively impacts on the insulin pathway. This different control mechanism of the insulin pathway through PTP1B ubiquitination adds a new dowel to the comprehension of the molecular basis of metabolic disorders

Control of Mitochondrial Activity by the Ubiquitin Code in Health and Cancer

Cellular homeostasis is tightly connected to the broad variety of mitochondrial functions. To stay healthy, cells need a constant supply of nutrients, energy production and antioxidants defenses, undergoing programmed death when a serious, irreversible damage occurs. The key element of a functional integration of all these processes is the correct crosstalk between cell signaling and mitochondrial activities. Once this crosstalk is interrupted, the cell is not able to communicate its needs to mitochondria, resulting in oxidative stress and development of pathological conditions. Conversely, dysfunctional mitochondria may affect cell viability, even in the presence of nutrients supply and energy production, indicating the existence of feed-back control mechanisms between mitochondria and other cellular compartments. The ubiquitin proteasome system (UPS) is a multi-step biochemical pathway that, through the conjugation of ubiquitin moieties to specific protein substrates, controls cellular proteostasis and signaling, removing damaged or aged proteins that might otherwise accumulate and affect cell viability. In response to specific needs or changed extracellular microenvironment, the UPS modulates the turnover of mitochondrial proteins, thus influencing the organelle shape, dynamics and function. Alterations of the dynamic and reciprocal regulation between mitochondria and UPS underpin genetic and proliferative disorders. This review focuses on the mitochondrial metabolism and activities supervised by UPS and examines how deregulation of this control mechanism results in proliferative disorders and cancer

Pathophysiology of Primary Cilia: Signaling and Proteostasis Regulation

: Primary cilia are microtubule-based, non-motile sensory organelles present in most types of growth-arrested eukaryotic cells. They are transduction hubs that receive and transmit external signals to the cells in order to control growth, differentiation and development. Mutations of genes involved in the formation, maintenance or disassembly of ciliary structures cause a wide array of developmental genetic disorders, also known as ciliopathies. The primary cilium is formed during G1 in the cell cycle and disassembles at the G2/M transition. Following the completion of the cell division, the cilium reassembles in G1. This cycle is finely regulated at multiple levels. The ubiquitin-proteasome system (UPS) and the autophagy machinery, two main protein degradative systems in cells, play a fundamental role in cilium dynamics. Evidence indicate that UPS, autophagy and signaling pathways may act in synergy to control the ciliary homeostasis. However, the mechanisms involved and the links between these regulatory systems and cilium biogenesis, dynamics and signaling are not well defined yet. Here, we discuss the reciprocal regulation of signaling pathways and proteolytic machineries in the control of the assembly and disassembly of the primary cilium, and the impact of the derangement of these regulatory networks in human ciliopathies

BDNF and NGF Expression in Preneoplastic Cervical Disease According to HIV Status

Background: Neurotrophins, such as BDNF and NGF, are overexpressed in tumor cells in cervical cancer, and HIV infection is associated with the upregulation of neurotrophin expression. Therefore, we aimed to investigate whether BDNF and NGF are overexpressed in preneoplastic cervical disease from HIV-infected women. Methods: Women with preneoplastic cervical lesions (cervical intraepithelial neoplasia grade 2 or 3) were prospectively enrolled and grouped according to their HIV status. Samples from Loop Electrosurgical Excision Procedure (LEEP) for suspected cervical cancer were obtained, and immunohistochemistry was performed to evaluate BDNF and NGF expression. Results: We included in our analysis 12 HIV-infected patients who were matched with 23 HIV-negative patients as a control group. Immunohistochemistry analysis showed that BDNF expression was significantly higher in cervical preneoplastic lesions from HIV-positive women than in the lesions from the control group. In particular, BDNF was expressed in 8/12 HIV-positive patients and 7/23 HIV-negative patients (66.7% vs. 30.4%, χ2 = 4.227; p = 0.040). NGF expression was not significantly higher in cervical preneoplastic lesions from HIV-positive women compared with that in the lesions from the control group. In particular, NGF was expressed in 8/12 HIV-positive patients and in 12/23 HIV-negative patients (66.7% vs. 52.2% χ2 = 0.676; p = 0.411). Logistic regression analysis showed that the HIV status is an independent predictor of BDNF expression in pre-invasive preneoplastic cervical disease when considered alone (crude OR 4.6, 95% CI 0.027-20.347; p = 0.046) and when analyzed with other co-factors (adjusted OR 6.786, 95% CI 1.084-42.476; p = 0.041). Conclusions: In preneoplastic cervical disease, BDNF expression is higher in HIV-infected women than in non-infected controls, and this is independent of the clinical features of the patients and from the presence of the HPV-HR genotype. BDNF can play a key role as a link between the pathways by which HIV and HPV interact to accelerate cervical cancer progression and invasion. These data can be useful to better understand the role of neurotrophins in the cancerogenesis of cervical cancer and the possible therapeutic strategies to improve disease outcomes

Ubiquitylation of BBSome is required for ciliary assembly and signaling

Bardet-Biedl syndrome (BBS) is a ciliopathy characterized by retinal degeneration, obesity, renal abnormalities, postaxial polydactyly, and developmental defects. Genes mutated in BBS encode for components and regulators of the BBSome, an octameric complex that controls the trafficking of cargos and receptors within the primary cilium. Although both structure and function of the BBSome have been extensively studied, the impact of ubiquitin signaling on BBSome is largely unknown. We identify the E3 ubiquitin ligase PJA2 as a novel resident of the ciliary compartment and regulator of the BBSome. Upon GPCR-cAMP stimulation, PJA2 ubiquitylates BBSome subunits. We demonstrate that ubiquitylation of BBS1 at lysine 143 increases the stability of the BBSome and promotes its binding to BBS3, an Arf-like GTPase protein controlling the targeting of the BBSome to the ciliary membrane. Downregulation of PJA2 or expression of a ubiquitylation-defective BBS1 mutant (BBS1 K143R) affects the trafficking of G-proteincoupled receptors (GPCRs) and Shh-dependent gene transcription. Expression of BBS1 K143R in vivo impairs cilium formation, embryonic development, and photoreceptors' morphogenesis, thus recapitulating the BBS phenotype in the medaka fish model

Feedback inhibition of cAMP effector signaling by a chaperone-assisted ubiquitin system

Activation of G-protein coupled receptors elevates cAMP levels promoting dissociation of protein kinase A (PKA) holoenzymes and release of catalytic subunits (PKAc). This results in PKAc-mediated phosphorylation of compartmentalized substrates that control central aspects of cell physiology. The mechanism of PKAc activation and signaling have been largely characterized. However, the modes of PKAc inactivation by regulated proteolysis were unknown. Here, we identify a regulatory mechanism that precisely tunes PKAc stability and downstream signaling. Following agonist stimulation, the recruitment of the chaperonebound E3 ligase CHIP promotes ubiquitylation and proteolysis of PKAc, thus attenuating cAMP signaling. Genetic inactivation of CHIP or pharmacological inhibition of HSP70 enhances PKAc signaling and sustains hippocampal long-term potentiation. Interestingly, primary fibroblasts from autosomal recessive spinocerebellar ataxia 16 (SCAR16) patients carrying germline inactivating mutations of CHIP show a dramatic dysregulation of PKA signaling. This suggests the existence of a negative feedback mechanism for restricting hormonally controlled PKA activities

Targeted inhibition of ubiquitin signaling reverses metabolic reprogramming and suppresses glioblastoma growth

Glioblastoma multiforme (GBM) is the most frequent and aggressive form of primary brain tumor in the adult population; its high recurrence rate and resistance to current therapeutics urgently demand a better therapy. Regulation of protein stability by the ubiquitin proteasome system (UPS) represents an important control mechanism of cell growth. UPS deregulation is mechanistically linked to the development and progression of a variety of human cancers, including GBM. Thus, the UPS represents a potentially valuable target for GBM treatment. Using an integrated approach that includes proteomics, transcriptomics and metabolic profiling, we identify praja2, a RING E3 ubiquitin ligase, as the key component of a signaling network that regulates GBM cell growth and metabolism. Praja2 is preferentially expressed in primary GBM lesions expressing the wild-type isocitrate dehydrogenase 1 gene (IDH1). Mechanistically, we found that praja2 ubiquitylates and degrades the kinase suppressor of Ras 2 (KSR2). As a consequence, praja2 restrains the activity of downstream AMP-dependent protein kinase in GBM cells and attenuates the oxidative metabolism. Delivery in the brain of siRNA targeting praja2 by transferrin-targeted self-assembling nanoparticles (SANPs) prevented KSR2 degradation and inhibited GBM growth, reducing the size of the tumor and prolonging the survival rate of treated mice. These data identify praja2 as an essential regulator of cancer cell metabolism, and as a potential therapeutic target to suppress GBM growth

Downregulation of praja2 restrains endocytosis and boosts tyrosine kinase receptors in kidney cancer

Abstract Clear cell renal cell carcinoma (ccRCC) is the most common kidney cancer in the adult population. Late diagnosis, resistance to therapeutics and recurrence of metastatic lesions account for the highest mortality rate among kidney cancer patients. Identifying novel biomarkers for early cancer detection and elucidating the mechanisms underlying ccRCC will provide clues to treat this aggressive malignant tumor. Here, we report that the ubiquitin ligase praja2 forms a complex with-and ubiquitylates the AP2 adapter complex, contributing to receptor endocytosis and clearance. In human RCC tissues and cells, downregulation of praja2 by oncogenic miRNAs (oncomiRs) and the proteasome markedly impairs endocytosis and clearance of the epidermal growth factor receptor (EGFR), and amplifies downstream mitogenic and proliferative signaling. Restoring praja2 levels in RCC cells downregulates EGFR, rewires cancer cell metabolism and ultimately inhibits tumor cell growth and metastasis. Accordingly, genetic ablation of praja2 in mice upregulates RTKs (i.e. EGFR and VEGFR) and induces epithelial and vascular alterations in the kidney tissue. In summary, our findings identify a regulatory loop between oncomiRs and the ubiquitin proteasome system that finely controls RTKs endocytosis and clearance, positively impacting mitogenic signaling and kidney cancer growth