In this paper we develop a computationally efficient, two-population, time-dependent Fokker-Plank approach in the two dimensions of energy and angular momentum to study the rates of tidal disruption events (TDEs), extreme mass ratio inspirals (EMRIs) and direct plunges occurring around massive black holes (MBHs) in galactic nuclei. We test our code by exploring a wide range of the astrophysically relevant parameter space, including MBH masses, galaxy central densities and inner density slopes. We find that mass segregation and, more in general, the time dependency of the distribution function regulate the event rate: TDEs always decline with time, whereas EMRIs and plunges reach a maximum and undergo a subsequent nearly exponential decay. Once suitably normalized, the rates associated to different choices of MBH mass and galaxy density overlap nearly perfectly. Based on this, we provide a simple scaling that allows to reproduce the time-dependent event rates for any MBH mass and underlying galactic nucleus. Although our peak rates are in general agreement with the literature relying on the steady-state (non time-dependent) assumption, those can be sustained on a timescale that strongly depends on the properties of the system. In particular this can be much shorter than a Gyr for relatively light MBHs residing in dense systems. This warns against using steady state models to compute global TDE, EMRI and plunge rates and calls for a more sophisticated, time dependent treatment of the problem.

Proteasome inhibitors (PIs) represent the gold standard in the treatment of multiple myeloma. Among PIs, Bortezomib (BTZ) is frequently used as first line therapy, but peripheral neuropathy (PN), occurring approximately in 50% of patients, impairs their life, representing a dose-limiting toxicity. Carfilzomib (CFZ), a second-generation PI, induces a significantly less severe PN. We investigated possible BTZ and CFZ off-targets able to explain their different neurotoxicity profiles. In order to identify the possible PIs off-targets we used the SPILLO-PBSS software that performs a structure-based in silico screening on a proteome-wide scale. Among the top-ranked off-targets of BTZ identified by SPILLO-PBSS we focused on tubulin which, by contrast, did not turn out to be an off-target of CFZ. We tested the hypothesis that the direct interaction between BTZ and microtubules would inhibit the tubulin alfa GTPase activity, thus reducing the microtubule catastrophe and consequently furthering the microtubules polymerization. This hypothesis was validated in a cell-free model, since BTZ (but not CFZ) reduces the concentration of the free phosphate released during GTP hydrolysis. Moreover, NMR binding studies clearly demonstrated that BTZ, unlike CFZ, is able to interact with both tubulin dimers and polymerized form. Our data suggest that different BTZ and CFZ neurotoxicity profiles are independent from their proteasome inhibition, as demonstrated in adult mice dorsal root ganglia primary sensory neurons, and, first, we demonstrate, in a cell free model, that BTZ is able to directly bind and perturb microtubules.

Tidal disruption events (TDEs) of stars operated by massive black holes (MBHs) will be detected in thousands by upcoming facilities such as the Vera Rubin Observatory. In this work, we assess the rates of standard total TDEs, destroying the entire star, and partial TDEs, in which a stellar remnant survives the interaction, by solving 1-D Fokker-Planck equations. Our rate estimates are based on a novel definition of the loss cone whose size is commensurate to the largest radius at which partial disruptions can occur, as motivated by relativistic hydrodynamical simulations. Our novel approach unveils two important results. First, partial TDEs can be more abundant than total disruptions by a factor of a few to a few tens. Second, the rates of complete stellar disruptions can be overestimated by a factor of a few to a few tens if one neglects partial TDEs, as we find that many of the events classified as total disruptions in the standard framework are in fact partial TDEs. Accounting for partial TDEs is particularly relevant for galaxies harbouring a nuclear stellar cluster featuring many events coming from the empty loss cone. Based on these findings, we stress that partial disruptions should be considered when constraining the luminosity function of TDE flares; accounting for this may reconcile the theoretically estimated TDE rates with the observed ones.