Search

Both mathematical models and biological model systems stand as tractable representations of complex biological systems or behaviors. They facilitate research and provide insights, and they can describe general rules. Models that represent biological processes or formalize general hypotheses are essential to any broad understanding. Mathematical or biological models necessarily omit details of the natural systems and thus may ultimately be "incorrect" representations. A key challenge is that tractability requires relatively simple models but simplification can result in models that are incorrect in their qualitative, broad implications if the abstracted details matter. Our paper discusses this tension, and how we can improve our inferences from models. We advocate for further efforts dedicated to model development, improvement, and acceptance by the scientific community, all of which may necessitate a more explicit discussion of the purpose and power of models. We argue that models should play a central role in reintegrating biology as a way to test our integrated understanding of how molecules, cells, organs, organisms, populations, and ecosystems function. [ABSTRACT FROM AUTHOR]

A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify heterogeneous mixtures of dynamic processes within single phylogenies. I developed a method that can identify arbitrary numbers of time-varying diversification processes on phylogenies without specifying their locations in advance. The method uses reversible-jump Markov Chain Monte Carlo to move between model subspaces that vary in the number of distinct diversification regimes. The model assumes that changes in evolutionary regimes occur across the branches of phylogenetic trees under a compound Poisson process and explicitly accounts for rate variation through time and among lineages. Using simulated datasets, I demonstrate that the method can be used to quantify complex mixtures of time-dependent, diversity-dependent, and constant-rate diversification processes. I compared the performance of the method to the MEDUSA model of rate variation among lineages. As an empirical example, I analyzed the history of speciation and extinction during the radiation of modern whales. The method described here will greatly facilitate the exploration of macroevolutionary dynamics across large phylogenetic trees, which may have been shaped by heterogeneous mixtures of distinct evolutionary processes. [ABSTRACT FROM AUTHOR]

The convergence of corticostriatal glutamate and dopamine from the midbrain in the striatal medium spiny neurons (MSN) triggers synaptic plasticity that underlies reinforcement learning and pathological conditions such as psychostimulant addiction. The increase in striatal dopamine produced by the acute administration of psychostimulants has been found to activate not only effectors of the AC5/cAMP/PKA signaling cascade such as GluR1, but also effectors of the NMDAR/Ca2+/RAS cascade such as ERK. The dopamine-triggered effects on both these cascades are mediated by D1R coupled to Golf but while the phosphorylation of GluR1 is affected by reductions in the available amount of Golf but not of D1R, the activation of ERK follows the opposite pattern. This segregation is puzzling considering that D1R-induced Golf activation monotonically increases with DA and that there is crosstalk from the AC5/cAMP/PKA cascade to the NMDAR/Ca2+/RAS cascade via a STEP (a tyrosine phosphatase). In this work, we developed a signaling model which accounts for this segregation based on the assumption that a common pool of D1R and Golf is distributed in two D1R/Golf signaling compartments. This model integrates a relatively large amount of experimental data for neurons in vivo and in vitro. We used it to explore the crosstalk topologies under which the sensitivities of the AC5/cAMP/PKA signaling cascade to reductions in D1R or Golf are transferred or not to the activation of ERK. We found that the sequestration of STEP by its substrate ERK together with the insensitivity of STEP activity on targets upstream of ERK (i.e. Fyn and NR2B) to PKA phosphorylation are able to explain the experimentally observed segregation. This model provides a quantitative framework for simulation based experiments to study signaling required for long term potentiation in MSNs. [ABSTRACT FROM AUTHOR]

The splicing regulator Polypyrimidine Tract Binding Protein (PTBP1) has four RNA binding domains that each binds a short pyrimidine element, allowing recognition of diverse pyrimidine-rich sequences. This variation makes it difficult to evaluate PTBP1 binding to particular sites based on sequence alone and thus to identify target RNAs. Conversely, transcriptome-wide binding assays such as CLIP identify many in vivo targets, but do not provide a quantitative assessment of binding and are informative only for the cells where the analysis is performed. A general method of predicting PTBP1 binding and possible targets in any cell type is needed. We developed computational models that predict the binding and splicing targets of PTBP1. A Hidden Markov Model (HMM), trained on CLIP-seq data, was used to score probable PTBP1 binding sites. Scores from this model are highly correlated (ρ = −0.9) with experimentally determined dissociation constants. Notably, we find that the protein is not strictly pyrimidine specific, as interspersed Guanosine residues are well tolerated within PTBP1 binding sites. This model identifies many previously unrecognized PTBP1 binding sites, and can score PTBP1 binding across the transcriptome in the absence of CLIP data. Using this model to examine the placement of PTBP1 binding sites in controlling splicing, we trained a multinomial logistic model on sets of PTBP1 regulated and unregulated exons. Applying this model to rank exons across the mouse transcriptome identifies known PTBP1 targets and many new exons that were confirmed as PTBP1-repressed by RT-PCR and RNA-seq after PTBP1 depletion. We find that PTBP1 dependent exons are diverse in structure and do not all fit previous descriptions of the placement of PTBP1 binding sites. Our study uncovers new features of RNA recognition and splicing regulation by PTBP1. This approach can be applied to other multi-RRM domain proteins to assess binding site degeneracy and multifactorial splicing regulation. [ABSTRACT FROM AUTHOR]

A few broadly neutralizing antibodies, isolated from HIV-1 infected individuals, recognize epitopes in the membrane proximal external region (MPER) of gp41 that are transiently exposed during viral entry. The best characterized, 4E10 and 2F5, are polyreactive, binding to the viral membrane and their epitopes in the MPER. We present a model to calculate, for any antibody concentration, the probability that during the pre-hairpin intermediate, the transient period when the epitopes are first exposed, a bound antibody will disable a trivalent gp41 before fusion is complete. When 4E10 or 2F5 bind to the MPER, a conformational change is induced that results in a stably bound complex. The model predicts that for these antibodies to be effective at neutralization, the time to disable an epitope must be shorter than the time the antibody remains bound in this conformation, about five minutes or less for 4E10 and 2F5. We investigate the role of avidity in neutralization and show that 2F5 IgG, but not 4E10, is much more effective at neutralization than its Fab fragment. We attribute this to 2F5 interacting more stably than 4E10 with the viral membrane. We use the model to elucidate the parameters that determine the ability of these antibodies to disable epitopes and propose an extension of the model to analyze neutralization data. The extended model predicts the dependencies of for neutralization on the rate constants that characterize antibody binding, the rate of fusion of gp41, and the number of gp41 bridging the virus and target cell at the start of the pre-hairpin intermediate. Analysis of neutralization experiments indicate that only a small number of gp41 bridges must be disabled to prevent fusion. However, the model cannot determine the exact number from neutralization experiments alone. [ABSTRACT FROM AUTHOR]

In metazoans, each cell type follows a characteristic, spatio-temporally regulated DNA replication program. Histone modifications (HMs) and chromatin binding proteins (CBPs) are fundamental for a faithful progression and completion of this process. However, no individual HM is strictly indispensable for origin function, suggesting that HMs may act combinatorially in analogy to the histone code hypothesis for transcriptional regulation. In contrast to gene expression however, the relationship between combinations of chromatin features and DNA replication timing has not yet been demonstrated. Here, by exploiting a comprehensive data collection consisting of 95 CBPs and HMs we investigated their combinatorial potential for the prediction of DNA replication timing in Drosophila using quantitative statistical models. We found that while combinations of CBPs exhibit moderate predictive power for replication timing, pairwise interactions between HMs lead to accurate predictions genome-wide that can be locally further improved by CBPs. Independent feature importance and model analyses led us to derive a simplified, biologically interpretable model of the relationship between chromatin landscape and replication timing reaching 80% of the full model accuracy using six model terms. Finally, we show that pairwise combinations of HMs are able to predict differential DNA replication timing across different cell types. All in all, our work provides support to the existence of combinatorial HM patterns for DNA replication and reveal cell-type independent key elements thereof, whose experimental investigation might contribute to elucidate the regulatory mode of this fundamental cellular process. [ABSTRACT FROM AUTHOR]

Mathematical modeling of biochemical processes significantly contributes to a better understanding of biological functionality and underlying dynamic mechanisms. To support time consuming and costly lab experiments, kinetic reaction equations can be formulated as a set of ordinary differential equations, which in turn allows to simulate and compare hypothetical models in silico. To identify new experimental designs that are able to discriminate between investigated models, the approach used in this work solves a semi-infinite constrained nonlinear optimization problem using derivative based numerical algorithms. The method takes into account parameter variabilities such that new experimental designs are robust against parameter changes while maintaining the optimal potential to discriminate between hypothetical models. In this contribution we present a newly developed software tool that offers a convenient graphical user interface for model discrimination. We demonstrate the beneficial operation of the discrimination approach and the usefulness of the software tool by analyzing a realistic benchmark experiment from literature. New robust optimal designs that allow to discriminate between the investigated model hypotheses of the benchmark experiment are successfully calculated and yield promising results. The involved robustification approach provides maximally discriminating experiments for the worst parameter configurations, which can be used to estimate the meaningfulness of upcoming experiments. A major benefit of the graphical user interface is the ability to interactively investigate the model behavior and the clear arrangement of numerous variables. In addition to a brief theoretical overview of the discrimination method and the functionality of the software tool, the importance of robustness of experimental designs against parameter variability is demonstrated on a biochemical benchmark problem. The software is licensed under the GNU General Public License and freely available at http://sourceforge.net/projects/mdtgui/. [ABSTRACT FROM AUTHOR]