Parameter estimation and identifiability analysis for a bivalent analyte model of monoclonal antibody-antigen binding.

Surface plasmon resonance (SPR) is an extensively used technique to characterize antigen-antibody interactions. Affinity measurements by SPR typically involve testing the binding of antigen in solution to monoclonal antibodies (mAbs) immobilized on a chip and fitting the kinetics data using 1:1 Langmuir binding model to derive rate constants. However, when it is necessary to immobilize antigens instead of the mAbs, a bivalent analyte (1:2) binding model is required for kinetics analysis. This model is lacking in data analysis packages associated with high throughput SPR instruments and the packages containing this model do not explore multiple local minima and parameter identifiability issues that are common in non-linear optimization. Therefore, we developed a method to use a system of ordinary differential equations for analyzing 1:2 binding kinetics data. Salient features of this method include a grid search on parameter initialization and a profile likelihood approach to determine parameter identifiability. Using this method we found a non-identifiable parameter in data set collected under the standard experimental design. A simulation-guided improved experimental design led to reliable estimation of all rate constants. The method and approach developed here for analyzing 1:2 binding kinetics data will be valuable for expeditious therapeutic antibody discovery research.

Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate Spatiotemporal Data.

Reaction-diffusion equations have been used to model a wide range of biological phenomenon related to population spread and proliferation from ecology to cancer. It is commonly assumed that individuals in a population have homogeneous diffusion and growth rates; however, this assumption can be inaccurate when the population is intrinsically divided into many distinct subpopulations that compete with each other. In previous work, the task of inferring the degree of phenotypic heterogeneity between subpopulations from total population density has been performed within a framework that combines parameter distribution estimation with reaction-diffusion models. Here, we extend this approach so that it is compatible with reaction-diffusion models that include competition between subpopulations. We use a reaction-diffusion model of glioblastoma multiforme, an aggressive type of brain cancer, to test our approach on simulated data that are similar to measurements that could be collected in practice. We use Prokhorov metric framework and convert the reaction-diffusion model to a random differential equation model to estimate joint distributions of diffusion and growth rates among heterogeneous subpopulations. We then compare the new random differential equation model performance against other partial differential equation models' performance. We find that the random differential equation is more capable at predicting the cell density compared to other models while being more time efficient. Finally, we use k-means clustering to predict the number of subpopulations based on the recovered distributions.

Negotiating mutualism: A locus for exploitation by rhizobia has a broad effect size distribution and context-dependent effects on legume hosts.

In mutualisms, variation at genes determining partner fitness provides the raw material upon which coevolutionary selection acts, setting the dynamics and pace of coevolution. However, we know little about variation in the effects of genes that underlie symbiotic fitness in natural mutualist populations. In some species of legumes that form root nodule symbioses with nitrogen-fixing rhizobial bacteria, hosts secrete nodule-specific cysteine-rich (NCR) peptides that cause rhizobia to differentiate in the nodule environment. However, rhizobia can cleave NCR peptides through the expression of genes like the plasmid-borne Host range restriction peptidase (hrrP), whose product degrades specific NCR peptides. Although hrrP activity can confer host exploitation by depressing host fitness and enhancing symbiont fitness, the effects of hrrP on symbiosis phenotypes depend strongly on the genotypes of the interacting partners. However, the effects of hrrP have yet to be characterised in a natural population context, so its contribution to variation in wild mutualist populations is unknown. To understand the distribution of effects of hrrP in wild rhizobia, we measured mutualism phenotypes conferred by hrrP in 12 wild Ensifer medicae strains. To evaluate context dependency of hrrP effects, we compared hrrP effects across two Medicago polymorpha host genotypes and across two experimental years for five E. medicae strains. We show for the first time in a natural population context that hrrP has a wide distribution of effect sizes for many mutualism traits, ranging from strongly positive to strongly negative. Furthermore, we show that hrrP effect size varies across host genotypes and experiment years, suggesting that researchers should be cautious about extrapolating the role of genes in natural populations from controlled laboratory studies of single genetic variants.

Modeling the synergistic properties of drugs in hormonal treatment for prostate cancer.

Prostate cancer is one of the most prevalent cancers in men, with increasing incidence worldwide. This public health concern has inspired considerable effort to study various aspects of prostate cancer treatment using dynamical models, especially in clinical settings. The standard of care for metastatic prostate cancer is hormonal therapy, which reduces the production of androgen that fuels the growth of prostate tumor cells prior to treatment resistance. Existing population models often use patients' prostate-specific antigen levels as a biomarker for model validation and for finding optimal treatment schedules; however, the synergistic effects of drugs used in hormonal therapy have not been well-examined. This paper describes the first mathematical model that explicitly incorporates the synergistic effects of two drugs used to inhibit androgen production in hormonal therapy. The drugs are cyproterone acetate, representing the drug family of anti-androgens that affect luteinizing hormones, and leuprolide acetate, representing the drug family of gonadotropin-releasing hormone analogs. By fitting the model to clinical data, we show that the proposed model can capture the dynamics of serum androgen levels during intermittent hormonal therapy better than previously published models. Our results highlight the importance of considering the synergistic effects of drugs in cancer treatment, thus suggesting that the dynamics of the drugs should be taken into account in optimal treatment studies, particularly for adaptive therapy. Otherwise, an unrealistic treatment schedule may be prescribed and render the treatment less effective. Furthermore, the drug dynamics allow our model to explain the delay in the relapse of androgen the moment a patient is taken off treatment, which supports that this delay is due to the residual effects of the drugs.

Aggregate Elasticity, Crystal Structure, and Tableting Performance for p-Aminobenzoic Acid and a Series of Its Benzoate Esters.

The tableting performance for p-aminobenzoic acid (PABA) and a series of its benzoate esters with increasing alkyl chain length (methyl-, ethyl-, and n-butyl) was determined over a broad range of compaction pressures. The crystalline structure of methyl benzoate (Me-PABA) exhibits no slip systems and does not form viable compacts under any compaction pressure. The ethyl (Et-PABA) and n-butyl (Bu-PABA) esters each have a similar, corrugated-layer structure that displays a prominent slip plane and improves material plasticity at low compaction pressure. The compact tensile strength for Et-PABA is superior to that for Bu-PABA; however, neither material achieved a tensile strength greater than 2 MPa over the compression range studied. Complementary studies with powder Brillouin light scattering (BLS) show the maxima of the shear wave, acoustic frequency distribution red shift in an order consistent with both the observed tabletability and attachment energy calculations. Moreover, zero-porosity aggregate elastic moduli are determined for each material using the average acoustic frequency obtained from specific characteristics of the powder BLS spectra. The Young's moduli for Et- and Bu-PABA is significantly reduced relative to PABA and Me-PABA, and this reduction is further evident in tablet compressibility plots. PABA, however, is distinct with high elastic isotropy as interpreted from the narrow and well-defined powder BLS frequency distributions for both the shear and compressional acoustic modes. The acoustic isotropy is consistent with the quasi-isotropic distribution of hydrogen bonding for PABA. At low compaction pressure, PABA tablets display the lowest tensile strength of the series; however, above a compaction pressure of ca. 70 MPa PABA tablet tensile strength continues to increase while that for Et- and Bu-PABA plateaus. PABA displays lower plasticity relative to either ester, and this is consistent with its crystalline structure and high yield pressure determined from in-die Heckel analysis. Overall the complementary approach of using both structural and the acoustic inputs uniquely provided from powder BLS is anticipated to expand our comprehension of the structure-mechanics relationship and its role in tableting performance.

Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling.

Fibroblasts in a confluent monolayer are known to adopt elongated morphologies in which cells are oriented parallel to their neighbors. We collected and analyzed new microscopy movies to show that confluent fibroblasts are motile and that neighboring cells often move in anti-parallel directions in a collective motion phenomenon we refer to as "fluidization" of the cell population. We used machine learning to perform cell tracking for each movie and then leveraged topological data analysis (TDA) to show that time-varying point-clouds generated by the tracks contain significant topological information content that is driven by fluidization, i.e., the anti-parallel movement of individual neighboring cells and neighboring groups of cells over long distances. We then utilized the TDA summaries extracted from each movie to perform Bayesian parameter estimation for the D'Orsgona model, an agent-based model (ABM) known to produce a wide array of different patterns, including patterns that are qualitatively similar to fluidization. Although the D'Orsgona ABM is a phenomenological model that only describes inter-cellular attraction and repulsion, the estimated region of D'Orsogna model parameter space was consistent across all movies, suggesting that a specific level of inter-cellular repulsion force at close range may be a mechanism that helps drive fluidization patterns in confluent mesenchymal cell populations.

Selective nitration of Hsp90 acts as a metabolic switch promoting tumor cell proliferation.

Tumors develop in an oxidative environment characterized by peroxynitrite production and downstream protein tyrosine (Y) nitration. We showed that tyrosine nitration supports schwannoma cell proliferation and regulates cell metabolism in the inheritable tumor disorder NF2-related Schwannomatosis (NF2-SWN). Here, we identified the chaperone Heat shock protein 90 (Hsp90) as the first nitrated protein that acts as a metabolic switch to promote schwannoma cell proliferation. Doubling the endogenous levels of nitrated Hsp90 in schwannoma cells or supplementing nitrated Hsp90 into normal Schwann cells increased their proliferation. Metabolically, nitration on either Y33 or Y56 conferred Hsp90 distinct functions; nitration at Y33 (Hsp90NY33) down-regulated mitochondrial oxidative phosphorylation, while nitration at Y56 (Hsp90NY56) increased glycolysis by activating the purinergic receptor P2X7 in both schwannoma and normal Schwann cells. Hsp90NY33 and Hsp90NY56 showed differential subcellular and spatial distribution corresponding with their metabolic and proliferative functions in schwannoma three-dimensional cell culture models. Collectively, these results underscore the role of tyrosine nitration as a post-translational modification regulating critical cellular processes. Nitrated proteins, particularly nitrated Hsp90, emerge as a novel category of tumor-directed therapeutic targets.

Genetic encoding of 3-nitro-tyrosine reveals the impacts of 14-3-3 nitration on client binding and dephosphorylation.

14-3-3 proteins are central hub regulators of hundreds of phosphorylated "client" proteins. They are subject to over 60 post-translational modifications (PTMs), yet little is known how these PTMs alter 14-3-3 function and its ability to regulate downstream signaling pathways. An often neglected, but well-documented 14-3-3 PTM found under physiological and immune-stimulatory conditions is the conversion of tyrosine to 3-nitro-tyrosine at several Tyr sites, two of which are located at sites considered important for 14-3-3 function: Y130 (ß-isoform numbering) is located in the primary phospho-client peptide-binding groove, while Y213 is found on a secondary binding site that engages with clients for full 14-3-3/client complex formation and client regulation. By genetically encoding 3-nitro-tyrosine, we sought to understand if nitration at Y130 and Y213 effectively modulated 14-3-3 structure, function, and client complexation. The 1.5 Å resolution crystal structure of 14-3-3 nitrated at Y130 showed the nitro group altered the conformation of key residues in the primary binding site, while functional studies confirmed client proteins failed to bind this variant of 14-3-3. But, in contrast to other client-binding deficient variants, it did not localize to the nucleus. The 1.9 Å resolution structure of 14-3-3 nitrated at Y213 revealed unusual flexibility of its C-terminal α-helix resulting in domain swapping, suggesting additional structural plasticity though its relevance is not clear as this nitrated form retained its ability to bind clients. Collectively, our data suggest that nitration of 14-3-3 will alter downstream signaling systems, and if uncontrolled could result in global dysregulation of the 14-3-3 interactome.

Decreased coevolutionary potential and increased symbiont fecundity during the biological invasion of a legume-rhizobium mutualism.

Although most invasive species engage in mutualism, we know little about how mutualism evolves as partners colonize novel environments. Selection on cooperation and standing genetic variation for mutualism traits may differ between a mutualism's invaded and native ranges, which could alter cooperation and coevolutionary dynamics. To test for such differences, we compare mutualism traits between invaded- and native-range host-symbiont genotype combinations of the weedy legume, Medicago polymorpha, and its nitrogen-fixing rhizobium symbiont, Ensifer medicae, which have coinvaded North America. We find that mutualism benefits for plants are indistinguishable between invaded- and native-range symbioses. However, rhizobia gain greater fitness from invaded-range mutualisms than from native-range mutualisms, and this enhancement of symbiont fecundity could increase the mutualism's spread by increasing symbiont availability during plant colonization. Furthermore, mutualism traits in invaded-range symbioses show lower genetic variance and a simpler partitioning of genetic variance between host and symbiont sources, compared to native-range symbioses. This suggests that biological invasion has reduced mutualists' potential to respond to coevolutionary selection. Additionally, rhizobia bearing a locus (hrrP) that can enhance symbiotic fitness have more exploitative phenotypes in invaded-range than in native-range symbioses. These findings highlight the impacts of biological invasion on the evolution of mutualistic interactions.