No abstract

Background Mutations in the leucine-rich repeat kinase 2 (LRRK2) gene have been recognized as genetic risk factors for Parkinson’s disease (PD). However, compared to cancer, fewer genetic mutations contribute to the cause of PD, propelling the search for protein biomarkers for early detection of the disease. Methods Utilizing 138 urine samples from four groups, healthy individuals (control), healthy individuals with G2019S mutation in the LRRK2 gene (non-manifesting carrier/NMC), PD individuals without G2019S mutation (idiopathic PD/iPD), and PD individuals with G2019S mutation (LRRK2 PD), we applied a proteomics strategy to determine potential diagnostic biomarkers for PD from urinary extracellular vesicles (EVs). Results After efficient isolation of urinary EVs through chemical affinity followed by mass spectrometric analyses of EV peptides and enriched phosphopeptides, we identify and quantify 4476 unique proteins and 2680 unique phosphoproteins. We detect multiple proteins and phosphoproteins elevated in PD EVs that are known to be involved in important PD pathways, in particular the autophagy pathway, as well as neuronal cell death, neuroinflammation, and formation of amyloid fibrils. We establish a panel of proteins and phosphoproteins as novel candidates for disease biomarkers and substantiate the biomarkers using machine learning, ROC, clinical correlation, and in-depth network analysis. Several putative disease biomarkers are further partially validated in patients with PD using parallel reaction monitoring (PRM) and immunoassay for targeted quantitation. Conclusions These findings demonstrate a general strategy of utilizing biofluid EV proteome/phosphoproteome as an outstanding and non-invasive source for a wide range of disease exploration.

Mutations in the leucine-rich repeat kinase 2 (LRRK2) gene have been recognized as genetic risk factors for both familial and sporadic forms of Parkinson's disease (PD). However, compared to cancer, overall lower genetic mutations contribute to the cause of PD, propelling the search for protein biomarkers for early detection of the disease. Utilizing 141 urine samples from four groups, healthy individuals (control), healthy individuals with G2019S mutation in the LRRK2 gene (non-manifesting carrier/NMC), PD individuals without G2019S mutation (idiopathic PD/iPD), and PD individuals with G2019S mutation (LRRK2 PD), we applied a proteomics strategy to determine potential diagnostic and prognostic biomarkers for PD from urinary extracellular vesicles (EVs). After efficient isolation of urinary EVs through chemical affinity followed by mass spectrometric analyses of EV peptides and enriched phosphopeptides, we identified and quantified 4,480 unique proteins and 2,682 unique phosphoproteins. We detected multiple proteins and phosphoproteins elevated in PD EVs that are known to be involved in important PD pathways such as neuronal cell death, neuroinflammation, autophagy, and formation of amyloid fibrils. We established two panels of proteins and phosphoproteins as novel candidates for disease and risk biomarkers, and substantiated using ROC, machine learning, and in-depth network analysis. Several disease biomarkers were further validated in patients with PD using parallel reaction monitoring (PRM) and immunoassay for targeted quantitation. These findings demonstrate a general strategy of utilizing biofluid EV proteome/phosphoproteome as an outstanding and non-invasive source for a wide range of disease exploration.

The problem of finding the minimizer of a sum of convex functions is central to the field of distributed optimization. Thus, it is of interest to understand how that minimizer is related to the properties of the individual functions in the sum. In this paper, we provide an upper bound on the region containing the minimizer of the sum of two strongly convex functions. We consider two scenarios with different constraints on the upper bound of the gradients of the functions. In the first scenario, the gradient constraint is imposed on the location of the potential minimizer, while in the second scenario, the gradient constraint is imposed on a given convex set in which the minimizers of two original functions are embedded. We characterize the boundaries of the regions containing the minimizer in both scenarios.

The problem of distributed optimization requires a group of agents to reach agreement on a parameter that minimizes the average of their local cost functions using information received from their neighbors. While there are a variety of distributed optimization algorithms that can solve this problem, they are typically vulnerable to malicious (or "Byzantine") agents that do not follow the algorithm. Recent attempts to address this issue focus on single dimensional functions, or provide analysis under certain assumptions on the statistical properties of the functions at the agents. In this paper, we propose a resilient distributed optimization algorithm for multidimensional convex functions. Our scheme involves two filtering steps at each iteration of the algorithm: (1) distance-based and (2) component-wise removal of extreme states. We show that this algorithm can mitigate the impact of up to F Byzantine agents in the neighborhood of each regular node, without knowing the identities of the Byzantine agents in advance. In particular, we show that if the network topology satisfies certain conditions, all of the regular states are guaranteed to asymptotically converge to a bounded region that contains the global minimizer.