Xist nucleates local protein gradients to propagate silencing across the X chromosome.

The lncRNA Xist forms ∼50 diffraction-limited foci to transcriptionally silence one X chromosome. How this small number of RNA foci and interacting proteins regulate a much larger number of X-linked genes is unknown. We show that Xist foci are locally confined, contain ∼2 RNA molecules, and nucleate supramolecular complexes (SMACs) that include many copies of the critical silencing protein SPEN. Aggregation and exchange of SMAC proteins generate local protein gradients that regulate broad, proximal chromatin regions. Partitioning of numerous SPEN molecules into SMACs is mediated by their intrinsically disordered regions and essential for transcriptional repression. Polycomb deposition via SMACs induces chromatin compaction and the increase in SMACs density around genes, which propagates silencing across the X chromosome. Our findings introduce a mechanism for functional nuclear compartmentalization whereby crowding of transcriptional and architectural regulators enables the silencing of many target genes by few RNA molecules.

Discrete stochastic models of SELEX: Aptamer capture probabilities and protocol optimization.

Antibodies are important biomolecules that are often designed to recognize target antigens. However, they are expensive to produce and their relatively large size prevents their transport across lipid membranes. An alternative to antibodies is aptamers, short (∼15-60 bp) oligonucleotides (and amino acid sequences) with specific secondary and tertiary structures that govern their affinity to specific target molecules. Aptamers are typically generated via solid phase oligonucleotide synthesis before selection and amplification through Systematic Evolution of Ligands by EXponential enrichment (SELEX), a process based on competitive binding that enriches the population of certain strands while removing unwanted sequences, yielding aptamers with high specificity and affinity to a target molecule. Mathematical analyses of SELEX have been formulated in the mass action limit, which assumes large system sizes and/or high aptamer and target molecule concentrations. In this paper, we develop a fully discrete stochastic model of SELEX. While converging to a mass-action model in the large system-size limit, our stochastic model allows us to study statistical quantities when the system size is small, such as the probability of losing the best-binding aptamer during each round of selection. Specifically, we find that optimal SELEX protocols in the stochastic model differ from those predicted by a deterministic model.

The Effects of Statistical Multiplicity of Infection on Virus Quantification and Infectivity Assays.

Many biological assays are employed in virology to quantify parameters of interest. Two such classes of assays, virus quantification assays (VQAs) and infectivity assays (IAs), aim to estimate the number of viruses present in a solution and the ability of a viral strain to successfully infect a host cell, respectively. VQAs operate at extremely dilute concentrations, and results can be subject to stochastic variability in virus-cell interactions. At the other extreme, high viral-particle concentrations are used in IAs, resulting in large numbers of viruses infecting each cell, enough for measurable change in total transcription activity. Furthermore, host cells can be infected at any concentration regime by multiple particles, resulting in a statistical multiplicity of infection and yielding potentially significant variability in the assay signal and parameter estimates. We develop probabilistic models for statistical multiplicity of infection at low and high viral-particle-concentration limits and apply them to the plaque (VQA), endpoint dilution (VQA), and luciferase reporter (IA) assays. A web-based tool implementing our models and analysis is also developed and presented. We test our proposed new methods for inferring experimental parameters from data using numerical simulations and show improvement on existing procedures in all limits.

Nonspecific probe binding and automatic gating in flow cytometry and fluorescence activated cell sorting (FACS).

Flow cytometry is extensively used in cell biology to differentiate cells of interest (mutants) from control cells (wild-types). For mutant cells characterized by expression of a distinct membrane surface structure, fluorescent marker probes can be designed to bind specifically to these structures while the cells are in suspension, resulting in a sufficiently high fluorescence intensity measurement by the cytometer to identify a mutant cell. However, cell membranes may have relatively weak, nonspecific binding affinity to the probes, resulting in false positive results. Furthermore, the same effect would be present on mutant cells, allowing both specific and nonspecific binding to a single cell. We derive and analyze a kinetic model of fluorescent probe binding dynamics by tracking populations of mutant and wild-type cells with differing numbers of probes bound specifically and nonspecifically. By assuming the suspension is in chemical equilibrium prior to cytometry, we use a two-species Langmuir adsorption model to analyze the confounding effects of non-specific binding on the assay. Furthermore, we analytically derive an expectation maximization method to infer an appropriate estimate of the total number of mutant cells as an alternative to existing, heuristic methods. Lastly, using our model, we propose a new method to infer physical and experimental parameters from existing protocols. Our results provide improved ways to quantitatively analyze flow cytometry data.