UCLA

Biological assays typically employ large numbers of constituent agents (virus particles, fluorescing antibodies, oligonucleotides, etc) to quantitatively measure the effects of various natural processes such as virus infectivity, cell membrane receptor concentrations, and the binding affinity of biomarkers. For the simplicity of analysis, these assays often intentionally eliminate most random variability by factoring only expected values of experimental quantities. However, ignoring the prevalent stochastic effects on the individual agent level may risk depriving this analysis of important and even confounding results. In this work, we model the kinetics, combinatorics, and statistical effects of various biological assays involving virology, cell identification, and molecular evolution in order to argue the importance of stochasticity in experimental results. First, concerning the variability in viral entry pathways, specifically for human immunodeficiency virus (HIV), we model the kinetics of receptor/coreceptor binding and membrane fusion, presenting a more accurate functional expression for infection in the presence of inhibiting drugs. Second, we create probabilistic models of virological assays including the plaque, endpoint dilution, and luciferase reporter assays, showing how parameters relating the statistical multiplicity of infection (SMOI) and particle to PFU ratios directly effect the distribution of infected cells. We use these stochastic models to formulate updated analytic techniques to estimate unknown and desired quantities such as the initial viral particle count in solution or the infectivity of a strain. Third, we investigate the effects of non-specific binding of fluorescing antibodies in flow cytometry and how a modified Langmuir adsorption model can inform optimal protocol design. Furthermore, we create a full probabilistic model of equilibrium binding dynamics in order to develop an automatic-gating procedure for improved cell identification and sorting. Finally, an attractive alternative to the use of antibodies in many biological assays and medical procedures is the use of short, genetic sequences called aptamers with strong binding affinity to mark specific target epitopes. The enrichment of target aptamers employs the SELEX (Systematic Evolution of Ligands by EXponential enrichment) protocol, a method that employs molecular evolution to filter out unwanted gene sequences. We create a probabilistic model of the enrichment procedure using concepts of statistical mechanics in order to present optimal improvements to the protocol.