First passage in a stochastic process may be influenced by the presence of an external confining potential, as well as "stochastic resetting" in which the process is repeatedly reset back to its initial position. Here we study the interplay between these two strategies, for a diffusing particle in an onedimensional trapping potential V (x), being randomly reset at a constant rate r. Stochastic resetting has been of great interest as it is known to provide an 'optimal rate' (r * ) at which the mean first passage time is a minimum. On the other hand an attractive potential also assists in first capture process. Interestingly, we find that for a sufficiently strong external potential, the advantageous optimal resetting rate vanishes (i.e. r * → 0). We derive a condition for this optimal resetting rate vanishing transition, which is continuous. We study this problem for various functional forms of V (x), some analytically, and the rest numerically. We find that the optimal rate r * vanishes with the deviation from critical strength of the potential as a power law with an exponent β which appears to be universal. PACS number(s): 05.40.-a,02.50.-r,02.50.Ey

The biophysical mechanisms of kinetochore capture by spindle microtubules within cells are stochastic processes with a moving target searched by multiple walkers inside a confined volume. We study and compare two such mechanisms: dynamic instability-driven search and capture, common in many eukaryotes, and angular diffusion of pivoted microtubules reported in fission yeast. Characteristic times associated with the rare events of capture scale as a power law with the microtubule number, and their comparison provides a physical basis for the selection of one mechanism over another.

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The mechanism by which microtubules find kinetochores during spindle formation is a key question in cell biology. Previous experimental studies have shown that although search-and-capture of kinetochores by dynamic microtubules is a dominant mechanism in many organisms, several other capture mechanisms are also possible. One such mechanism reported in Schizosaccharomyces pombe shows that microtubules can exhibit a prolonged pause between growth and shrinkage. During the pause, the microtubules pivoted at the spindle pole body search for the kinetochores by performing an angular di↵usion. Is the latter mechanism purely accidental, or could there be any physical advantage underlying its selection? To compare the e ciency of these two mechanisms, we numerically study distinct models and compute the timescales of kinetochore capture as a function of microtubule number N . We find that the capture timescales have non-trivial dependences on microtubule number, and one mechanism may be preferred over the other depending on this number. While for small N (as in fission yeast), the typical capture times due to rotational di↵usion are lesser than those for search-and-capture, the situation is reversed beyond a certain N . The capture times for rotational di↵usion tend to saturate due to geometrical constraints, while those for search-and-capture reduce monotonically with increasing N making it physically more e cient. The results provide a rationale for the common occurrence of classic search-and-capture process in many eukaryotes which have few hundreds of dynamic microtubules, as well as justify exceptions in cells with fewer microtubules.

An assortment of robust intracellular defence mechanisms are critical for restricting proliferation of pathogens and maintaining sanctity of the cytosol. Defect in these mechanisms could be exploited by the pathogens for creation of a safe sanctuary which can act as a transient reservoir for periodic dissemination into the host. While residing inside the host cell, pore forming toxins secreted by the pathogens compromises the integrity of the vacuole and exposes the microbe to diverse intracellular defence mechanisms. However, the correlation between toxin expression levels and consequent pore dynamics, fostering pathogens intracellular life, remains largely unexplored. In this study, using Streptococcus pneumoniae (SPN) and its secreted pore forming toxin pneumolysin (Ply), as model systems, we explored various facets of host-pathogen interactions in host cytosol, governed by the toxin expression and the resultant pore formation. The extent of damage on the endosomal membrane was found to dictate subsequent interaction with different host endosomal damage sensors. This in turn governed the routes of SPN clearance, revealing multiple layers of defence mechanisms at hosts disposal for counteracting invaded pathogens. A subset of SPN population producing extremely low amount of Ply inflicted minimal damage to the endomembrane, precluding decoration by endomembrane damage sensors and significantly prolonging its intracellular persistence. Such long persisting bacterial population could be key for pathogenic transmission or ensuing invasive disease. Using time-lapse fluorescence imaging, we monitored lifespans of different pneumococcal population subsets inside host cells. After quantitative analysis of various timescales such as pore formation time, vacuolar or cytosolic residence time and total degradation time, we developed a mathematical model that could correlate these to intravacuolar accumulation of Ply monomers. By proposing events like pore formation and vacuolar degradation of SPN as first passage processes, our theoretical modelling yields estimates of Ply production rate, burst size, and threshold Ply quantities which triggers these outcomes. Collectively, we present a general method by which intracellular lifespans of pathogens could be correlated to differential levels of toxins that they produce.