Extreme escape from a cusp: When does geometry matter for the fastest Brownian particles moving in crowded cellular environments?

We study here the extreme statistics of Brownian particles escaping from a cusp funnel: the fastest Brownian particles among n follow an ensemble of optimal trajectories located near the shortest path from the source to the target. For the time of such first arrivers, we derive an asymptotic formula that differs from the mean first passage times obtained for classical narrow escape and dire strait. When particles are initially distributed at a given distance from a cusp, the time of the fastest particles depends on the cusp geometry. Therefore, when many particles diffuse around impermeable obstacles, the geometry plays a role in the time it takes to reach a target. In the context of cellular transduction with signaling molecules, having to escape from such cusp-like domains slows down signaling pathways. Consequently, generating multiple copies of the same molecule enables molecular signals to be delivered through crowded environments in sufficient time.

Redundancy principle and the role of extreme statistics in molecular and cellular biology.

The paradigm of chemical activation rates in cellular biology has been shifted from the mean arrival time of a single particle to the mean of the first among many particles to arrive at a small activation site. The activation rate is set by extremely rare events, which have drastically different time scales from the mean times between activations, and depends on different structural parameters. This shift calls for reconsideration of physical processes used in deterministic and stochastic modeling of chemical reactions that are based on the traditional forward rate, especially for fast activation processes in living cells. Consequently, the biological activation time is not necessarily exponentially distributed. We review here the physical models, the mathematical analysis and the new paradigm of setting the scale to be the shortest time for activation that clarifies the role of population redundancy in selecting and accelerating transient cellular search processes. We provide examples in cellular transduction, gene activation, cell senescence activation or spermatozoa selection during fertilization, where the rate depends on numbers. We conclude that the statistics of the minimal time to activation set kinetic laws in biology, which can be very different from the ones associated to average times.

The importance of screening for serum free light chains in suspected cases of multiple myeloma and their impact on the kidney.

Multiple myeloma (MM) is the second most common haematological malignancy in the UK. We present a case series of three patients with light chain only myeloma who had normal serum protein electrophoretic studies at screening and were diagnosed using serum and urine free light chain assessment. This series reiterates the importance of thorough and robust screening for MM in patients presenting with renal disease. We review the up to date literature and we highlight the need to screen patients for MM with a combination of serum electrophoresis/immunofixation and either urinary or serum free light chain measurement and to maintain a high index of suspicion regardless of the presence or absence of proteinuria. We also discuss the emerging role of the serum free light chain assay.