BubR1 recruitment to the kinetochore via Bub1 enhances spindle assembly checkpoint signaling.

During mitosis, unattached kinetochores in a dividing cell activate the spindle assembly checkpoint (SAC) and delay anaphase onset by generating the anaphase-inhibitory mitotic checkpoint complex (MCC). These kinetochores generate the MCC by recruiting its constituent proteins, including BubR1. In principle, BubR1 recruitment to signaling kinetochores should increase its local concentration and promote MCC formation. However, in human cells BubR1 is mainly thought to sensitize the SAC to silencing. Whether BubR1 localization to signaling kinetochores by itself enhances SAC signaling remains unknown. Therefore, we used ectopic SAC activation (eSAC) systems to isolate two molecules that recruit BubR1 to the kinetochore, the checkpoint protein Bub1 and the KI and MELT motifs in the kinetochore protein KNL1, and observed their contribution to eSAC signaling. Our quantitative analyses and mathematical modeling show that Bub1-mediated BubR1 recruitment to the human kinetochore promotes SAC signaling and highlight BubR1's dual role of strengthening the SAC directly and silencing it indirectly.

A stochastic model for error correction of kinetochore-microtubule attachments in budding yeast.

To divide replicated chromosomes equally between daughter cells, kinetochores must attach to microtubules emanating from opposite poles of the mitotic spindle (biorientation). An error correction mechanism facilitates this process by destabilizing erroneous kinetochore-microtubule attachments. Here we present a stochastic model of kinetochore-microtubule attachments, via an essential protein Ndc80 in budding yeast, Saccharomyces cerevisiae. Using the model, we calculate the stochastic dynamics of a pair of sister kinetochores as they transition among different attachment states. First of all, we determine the kinase-to-phosphatase balance point that maximizes the probability of biorientation, while starting from an erroneous attachment state. We find that the balance point is sensitive to the rates of microtubule-Ndc80 dissociation and derive an approximate analytical formula that defines the balance point. Secondly, we determine the probability of transition from low-tension amphitelic to monotelic attachment and find that, despite this probability being approximately 33%, biorientation can be achieved with high probability. Thirdly, we calculate the contribution of the geometrical orientation of sister kinetochores to the probability of biorientation and show that, in the absence of geometrical orientation, the biorientation error rate is much larger than that observed in experiments. Finally, we study the coupling of the error correction mechanism to the spindle assembly checkpoint by calculating the average binding of checkpoint-related proteins to the kinetochore during the error correction process.

Ectopic Activation of the Spindle Assembly Checkpoint Signaling Cascade Reveals Its Biochemical Design.

Switch-like activation of the spindle assembly checkpoint (SAC) is critical for accurate chromosome segregation and for cell division in a timely manner. To determine the mechanisms that achieve this, we engineered an ectopic, kinetochore-independent SAC activator: the "eSAC." The eSAC stimulates SAC signaling by artificially dimerizing Mps1 kinase domain and a cytosolic KNL1 phosphodomain, the kinetochore signaling scaffold. By exploiting variable eSAC expression in a cell population, we defined the dependence of the eSAC-induced mitotic delay on eSAC concentration in a cell to reveal the dose-response behavior of the core signaling cascade of the SAC. These quantitative analyses and subsequent mathematical modeling of the dose-response data uncover two crucial properties of the core SAC signaling cascade: (1) a cellular limit on the maximum anaphase-inhibitory signal that the cascade can generate due to the limited supply of SAC proteins and (2) the ability of the KNL1 phosphodomain to produce the anaphase-inhibitory signal synergistically, when it recruits multiple SAC proteins simultaneously. We propose that these properties together achieve inverse, non-linear scaling between the signal output per kinetochore and the number of signaling kinetochores. When the number of kinetochores is low, synergistic signaling by KNL1 enables each kinetochore to produce a disproportionately strong signal output. However, when many kinetochores signal concurrently, they compete for a limited supply of SAC proteins. This frustrates synergistic signaling and lowers their signal output. Thus, the signaling activity of unattached kinetochores will adapt to the changing number of signaling kinetochores to enable the SAC to approximate switch-like behavior.

Kinetics of cellular uptake of viruses and nanoparticles via clathrin-mediated endocytosis.

Several viruses exploit clathrin-mediated endocytosis to gain entry into host cells. This process is also used extensively in biomedical applications to deliver nanoparticles (NPs) to diseased cells. The internalization of these nano-objects is controlled by the assembly of a clathrin-containing protein coat on the cytoplasmic side of the plasma membrane, which drives the invagination of the membrane and the formation of a cargo-containing endocytic vesicle. Current theoretical models of receptor-mediated endocytosis of viruses and NPs do not explicitly take coat assembly into consideration. In this paper we study cellular uptake of viruses and NPs with a focus on coat assembly. We characterize the internalization process by the mean time between the binding of a particle to the membrane and its entry into the cell. Using a coarse-grained model which maps the stochastic dynamics of coat formation onto a one-dimensional random walk, we derive an analytical formula for this quantity. A study of the dependence of the mean internalization time on NP size shows that there is an upper bound above which this time becomes extremely large, and an optimal size at which it attains a minimum. Our estimates of these sizes compare well with experimental data. We also study the sensitivity of the obtained results on coat parameters to identify factors which significantly affect the internalization kinetics.

Distributions of lifetime and maximum size of abortive clathrin-coated pits.

Clathrin-mediated endocytosis is a complex process through which eukaryotic cells internalize nutrients, antigens, growth factors, pathogens, etc. The process occurs via the formation of invaginations on the cell membrane, called clathrin-coated pits (CCPs). Over the years, much has been learned about the mechanism of CCP assembly, but a complete understanding of the assembly process still remains elusive. In recent years, using fluorescence microscopy, studies have been done to determine the statistical properties of CCP formation. In this paper, using a recently proposed coarse-grained, stochastic model of CCP assembly [Banerjee, Berezhkovskii, and Nossal, Biophys. J. 102, 2725 (2012)], we suggest new ways of analyzing such experimental data. To be more specific, we derive analytical expressions for the distribution of maximum size of abortive CCPs, and the probability density of their lifetimes. Our results show how these functions depend on the kinetic and energetic parameters characterizing the assembly process, and therefore could be useful in extracting information about the mechanism of CCP assembly from experimental data. We find excellent agreement between our analytical results and those obtained from kinetic Monte Carlo simulations of the assembly process.

Stochastic model of clathrin-coated pit assembly.

In recent years, fluorescence microscopy has enabled researchers to observe the dynamics of clathrin-coated pit (CCP) assembly in real time. The assembly dynamics of CCPs shows striking heterogeneity. Some CCPs are long-lived (productive CCPs); they bind cargo and grow in size to form clathrin-coated vesicles. In contrast, other CCPs (abortive CCPs) are relatively short-lived and disassemble well before reaching vesicle size. Within both populations there is significant variance in CCP lifetime. We propose a stochastic biophysical model that links these observations with the energetics of CCPs and kinetics of their assembly. We show that without cargo, CCP assembly faces a high energy barrier that is difficult to overcome. As a consequence, CCPs without cargo are almost always abortive. We suggest a mechanism by which cargo binding stabilizes CCPs and facilitates their growth. The lifetime distribution of abortive pits calculated from our model agrees well with published experimental data. We also estimate the lifetimes of productive CCPs and show that the stochastic nature of CCP assembly plays a crucial role in causing their observed wide distribution.