Clustering in cell cycle dynamics with general response/signaling feedback.
ABSTRACT: Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call responsive/signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and emergent behavior of solutions, particularly temporal clustering and stability of clustered solutions. We establish the existence of certain periodic clustered solutions as well as "uniform" solutions and add to the evidence that cell-cycle dependent feedback robustly leads to cell-cycle clustering. We highlight the fundamental differences in dynamics between systems with negative and positive feedback. For positive feedback systems the most important mechanism seems to be the stability of individual isolated clusters. On the other hand we find that in negative feedback systems, clusters must interact with each other to reinforce coherence. We conclude from various details of the mathematical analysis that negative feedback is most consistent with observations in yeast experiments.
Project description:In all eukaryotic cells, DNA is packaged into multiple chromosomes that are linked to microtubules through a large protein complex called a kinetochore. Previous data show that the kinetochores are clustered together during most of the cell cycle, but the mechanism and the biological significance of kinetochore clustering are unknown. As a kinetochore protein in budding yeast, the role of Slk19 in the stability of the anaphase spindle has been well studied, but its function in chromosome segregation has remained elusive. Here we show that Slk19 is required for kinetochore clustering when yeast cells are treated with the microtubule-depolymerizing agent nocodazole. We further find that slk19? mutant cells exhibit delayed kinetochore capture and chromosome bipolar attachment after the disruption of the kinetochore-microtubule interaction by nocodazole, which is likely attributed to defective kinetochore clustering. In addition, we show that Slk19 interacts with itself, suggesting that the dimerization of Slk19 may mediate the interaction between kinetochores for clustering. Therefore Slk19 likely acts as kinetochore glue that clusters kinetochores to facilitate efficient and faithful chromosome segregation.
Project description:Many cells undergo symmetry-breaking polarization toward a randomly oriented "front" in the absence of spatial cues. In budding yeast, such polarization involves a positive feedback loop that enables amplification of stochastically arising clusters of polarity factors. Previous mathematical modeling suggested that, if more than one cluster were amplified, the clusters would compete for limiting resources and the largest would "win," explaining why yeast cells always make one and only one bud. Here, using imaging with improved spatiotemporal resolution, we show the transient coexistence of multiple clusters during polarity establishment, as predicted by the model. Unexpectedly, we also find that initial polarity factor clustering is oscillatory, revealing the presence of a negative feedback loop that disperses the factors. Mathematical modeling predicts that negative feedback would confer robustness to the polarity circuit and make the kinetics of competition between polarity factor clusters relatively insensitive to polarity factor concentration. These predictions are confirmed experimentally.
Project description:Positive feedback plays a key role in the ability of signaling molecules to form highly localized clusters in the membrane or cytosol of cells. Such clustering can occur in the absence of localizing mechanisms such as pre-existing spatial cues, diffusional barriers, or molecular cross-linking. What prevents positive feedback from amplifying inevitable biological noise when an un-clustered "off" state is desired? And, what limits the spread of clusters when an "on" state is desired? Here, we show that a minimal positive feedback circuit provides the general principle for both suppressing and amplifying noise: below a critical density of signaling molecules, clustering switches off; above this threshold, highly localized clusters are recurrently generated. Clustering occurs only in the stochastic regime, suggesting that finite sizes of molecular populations cannot be ignored in signal transduction networks. The emergence of a dominant cluster for finite numbers of molecules is partly a phenomenon of random sampling, analogous to the fixation or loss of neutral mutations in finite populations. We refer to our model as the "neutral drift polarity model." Regulating the density of signaling molecules provides a simple mechanism for a positive feedback circuit to robustly switch between clustered and un-clustered states. The intrinsic ability of positive feedback both to create and suppress clustering is a general mechanism that could operate within diverse biological networks to create dynamic spatial organization.
Project description:BACKGROUND: The landscape of biological and biomedical research is being changed rapidly with the invention of microarrays which enables simultaneous view on the transcription levels of a huge number of genes across different experimental conditions or time points. Using microarray data sets, clustering algorithms have been actively utilized in order to identify groups of co-expressed genes. This article poses the problem of fuzzy clustering in microarray data as a multiobjective optimization problem which simultaneously optimizes two internal fuzzy cluster validity indices to yield a set of Pareto-optimal clustering solutions. Each of these clustering solutions possesses some amount of information regarding the clustering structure of the input data. Motivated by this fact, a novel fuzzy majority voting approach is proposed to combine the clustering information from all the solutions in the resultant Pareto-optimal set. This approach first identifies the genes which are assigned to some particular cluster with high membership degree by most of the Pareto-optimal solutions. Using this set of genes as the training set, the remaining genes are classified by a supervised learning algorithm. In this work, we have used a Support Vector Machine (SVM) classifier for this purpose. RESULTS: The performance of the proposed clustering technique has been demonstrated on five publicly available benchmark microarray data sets, viz., Yeast Sporulation, Yeast Cell Cycle, Arabidopsis Thaliana, Human Fibroblasts Serum and Rat Central Nervous System. Comparative studies of the use of different SVM kernels and several widely used microarray clustering techniques are reported. Moreover, statistical significance tests have been carried out to establish the statistical superiority of the proposed clustering approach. Finally, biological significance tests have been carried out using a web based gene annotation tool to show that the proposed method is able to produce biologically relevant clusters of co-expressed genes. CONCLUSION: The proposed clustering method has been shown to perform better than other well-known clustering algorithms in finding clusters of co-expressed genes efficiently. The clusters of genes produced by the proposed technique are also found to be biologically significant, i.e., consist of genes which belong to the same functional groups. This indicates that the proposed clustering method can be used efficiently to identify co-expressed genes in microarray gene expression data.Supplementary Website The pre-processed and normalized data sets, the matlab code and other related materials are available at http://anirbanmukhopadhyay.50webs.com/mogasvm.html.
Project description:Strongly nonlinear degrade-and-fire (DF) oscillations may emerge in genetic circuits having a delayed negative feedback loop as their core element. Here we study the synchronization of DF oscillators coupled through a common repressor field. For weak coupling, initially distinct oscillators remain desynchronized. For stronger coupling, oscillators can be forced to wait in the repressed state until the global repressor field is sufficiently degraded, and then they fire simultaneously forming a synchronized cluster. Our analytical theory provides necessary and sufficient conditions for clustering and specifies the maximum number of clusters that can be formed in the asymptotic regime. We find that in the thermodynamic limit a phase transition occurs at a certain coupling strength from the weakly clustered regime with only microscopic clusters to a strongly clustered regime where at least one giant cluster has to be present.
Project description:Optimizing spike-sorting algorithms is difficult because sorted clusters can rarely be checked against independently obtained "ground truth" data. In most spike-sorting algorithms in use today, the optimality of a clustering solution is assessed relative to some assumption on the distribution of the spike shapes associated with a particular single unit (e.g., Gaussianity) and by visual inspection of the clustering solution followed by manual validation. When the spatiotemporal waveforms of spikes from different cells overlap, the decision as to whether two spikes should be assigned to the same source can be quite subjective, if it is not based on reliable quantitative measures. We propose a new approach, whereby spike clusters are identified from the most consensual partition across an ensemble of clustering solutions. Using the variability of the clustering solutions across successive iterations of the same clustering algorithm (template matching based on K-means clusters), we estimate the probability of spikes being clustered together and identify groups of spikes that are not statistically distinguishable from one another. Thus, we identify spikes that are most likely to be clustered together and therefore correspond to consistent spike clusters. This method has the potential advantage that it does not rely on any model of the spike shapes. It also provides estimates of the proportion of misclassified spikes for each of the identified clusters. We tested our algorithm on several datasets for which there exists a ground truth (simultaneous intracellular data), and show that it performs close to the optimum reached by a support vector machine trained on the ground truth. We also show that the estimated rate of misclassification matches the proportion of misclassified spikes measured from the ground truth data.
Project description:The mammalian cochlea relies on active electromotility of outer hair cells (OHCs) to resolve sound frequencies. OHCs use ionic channels and somatic electromotility to achieve the process. It is unclear, though, how the kinetics of voltage-gated ionic channels operate to overcome extrinsic viscous drag on OHCs at high frequency. Here, we report ultrafast electromechanical gating of clustered Kv7.4 in OHCs. Increases in kinetics and sensitivity resulting from cooperativity among clustered-Kv7.4 were revealed, using optogenetics strategies. Upon clustering, the half-activation voltage shifted negative, and the speed of activation increased relative to solitary channels. Clustering also rendered Kv7.4 channels mechanically sensitive, confirmed in consolidated Kv7.4 channels at the base of OHCs. Kv7.4 clusters provide OHCs with ultrafast electromechanical channel gating, varying in magnitude and speed along the cochlea axis. Ultrafast Kv7.4 gating provides OHCs with a feedback mechanism that enables the cochlea to overcome viscous drag and resolve sounds at auditory frequencies.
Project description:Peer-grouping is used in many sectors for organisational learning, policy implementation, and benchmarking. Clustering provides a statistical, data-driven method for constructing meaningful peer groups, but peer groups must be compatible with business constraints such as size and stability considerations. Additionally, statistical peer groups are constructed from many different variables, and can be difficult to understand, especially for non-statistical audiences. We developed methodology to apply business constraints to clustering solutions and allow the decision-maker to choose the balance between statistical goodness-of-fit and conformity to business constraints. Several tools were utilised to identify complex distinguishing features in peer groups, and a number of visualisations are developed to explain high-dimensional clusters for non-statistical audiences. In a case study where peer group size was required to be small (≤ 100 members), we applied constrained clustering to a noisy high-dimensional data-set over two subsequent years, ensuring that the clusters were sufficiently stable between years. Our approach not only satisfied clustering constraints on the test data, but maintained an almost monotonic negative relationship between goodness-of-fit and stability between subsequent years. We demonstrated in the context of the case study how distinguishing features between clusters can be communicated clearly to different stakeholders with substantial and limited statistical knowledge.
Project description:Metabolic gene clusters--functionally related and physically clustered genes--are a common feature of some eukaryotic genomes. Two hypotheses have been advanced to explain the origin and maintenance of metabolic gene clusters: coordinated gene expression and genetic linkage. Here we test the hypothesis that selection for coordinated gene expression underlies the clustering of GAL genes in the yeast genome. We find that, although clustering coordinates the expression of GAL1 and GAL10, disrupting the GAL cluster does not impair fitness, suggesting that other mechanisms, such as genetic linkage, drive the origin and maintenance metabolic gene clusters.
Project description:Viable gamete formation requires segregation of homologous chromosomes connected, in most species, by cross-overs. DNA double-strand break (DSB) formation and the resulting cross-overs are regulated at multiple levels to prevent overabundance along chromosomes. Meiotic cells coordinate these events between distant sites, but the physical basis of long-distance chromosomal communication has been unknown. We show that DSB hotspots up to ?200 kb (?35 cM) apart form clusters via hotspot-binding proteins Rec25 and Rec27 in fission yeast. Clustering coincides with hotspot competition and interference over similar distances. Without Tel1 (an ATM tumor-suppressor homolog), DSB and crossover interference become negative, reflecting coordinated action along a chromosome. These results indicate that DSB hotspots within a limited chromosomal region and bound by their protein determinants form a clustered structure that, via Tel1, allows only one DSB per region. Such a "roulette" process within clusters explains the observed pattern of crossover interference in fission yeast. Key structural and regulatory components of clusters are phylogenetically conserved, suggesting conservation of this vital regulation. Based on these observations, we propose a model and discuss variations in which clustering and competition between DSB sites leads to DSB interference and in turn produces crossover interference.