Plant–pollinator population dynamics

We formulate and analyze a multi-generation population dynamics model for pollinators’ mutualism with plants. The centerpiece of our model is an analytical expression for population-level plant–pollinator interactions extrapolated from a model of individual-level flowers and bees interactions. We also show that this analytical expression can be productively approximated by the Beddington–DeAngelis formula—a function used to model trophic interactions in mathematical ecology.     

Stochastic Modeling of Gene Regulation by Noncoding Small RNAs in the Strong Interaction Limit

Noncoding small RNAs (sRNAs) are known to play a key role in regulating diverse cellular processes, and their dysregulation is linked to various diseases such as cancer. Such diseases are also marked by phenotypic heterogeneity, which is often driven by the intrinsic stochasticity of gene expression. Correspondingly, there is significant interest in developing quantitative models focusing on the interplay between stochastic gene expression and regulation by sRNAs. We consider the canonical model of regulation of stochastic gene expression by sRNAs, wherein interaction between constitutively expressed sRNAs and mRNAs leads to stoichiometric mutual degradation. The exact solution of this model is analytically intractable given the nonlinear interaction term between sRNAs and mRNAs, and theoretical approaches typically invoke the mean-field approximation. However, mean-field results are inaccurate in the limit of strong interactions and low abundances; thus, alternative theoretical approaches are needed. In this work, we obtain analytical results for the canonical model of regulation of stochastic gene expression by sRNAs in the strong interaction limit. We derive analytical results for the steady-state generating function of the joint distribution of mRNAs and sRNAs in the limit of strong interactions and use the results derived to obtain analytical expressions characterizing the corresponding protein steady-state distribution. The results obtained can serve as building blocks for the analysis of genetic circuits involving sRNAs and provide new insights into the role of sRNAs in regulating stochastic gene expression in the limit of strong interactions.     

From within-host interactions to epidemiological competition: a general model for multiple infections

Many hosts are infected by several parasite genotypes at a time. In these co-infected hosts, parasites can interact in various ways thus creating diverse within-host dynamics, making it difficult to predict the expression and the evolution of virulence. Moreover, multiple infections generate a combinatorial diversity of cotransmission routes at the host population level, which complicates the epidemiology and may lead to non-trivial outcomes. We introduce a new model for multiple infections, which allows any number of parasite genotypes to infect hosts and potentially coexist in the population. In our model, parasites affect one another''s within-host growth through density-dependent interactions and by means of public goods and spite. These within-host interactions determine virulence, recovery and transmission rates, which are then integrated in a transmission network. We use analytical solutions and numerical simulations to investigate epidemiological feedbacks in host populations infected by several parasite genotypes. Finally, we discuss general perspectives on multiple infections.     

Analyzing protein lists with large networks: edge-count probabilities in random graphs with given expected degrees.

We present an analytical framework to analyze lists of proteins with large undirected graphs representing their known functional relationships. We consider edge-count variables such as the number of interactions between a protein and a list, the size of a subgraph induced by a list, and the number of interactions bridging two lists. We derive approximate analytical expressions for the probability distributions of these variables in a model of a random graph with given expected degrees. Probabilities obtained with the analytical expressions are used to mine a protein interaction network for functional modules, characterize the connectedness of protein functional categories, and measure the strength of relations between modules.     

Minimal biophysical model of combined antibiotic action

Phenomenological relations such as Ohm’s or Fourier’s law have a venerable history in physics but are still scarce in biology. This situation restrains predictive theory. Here, we build on bacterial “growth laws,” which capture physiological feedback between translation and cell growth, to construct a minimal biophysical model for the combined action of ribosome-targeting antibiotics. Our model predicts drug interactions like antagonism or synergy solely from responses to individual drugs. We provide analytical results for limiting cases, which agree well with numerical results. We systematically refine the model by including direct physical interactions of different antibiotics on the ribosome. In a limiting case, our model provides a mechanistic underpinning for recent predictions of higher-order interactions that were derived using entropy maximization. We further refine the model to include the effects of antibiotics that mimic starvation and the presence of resistance genes. We describe the impact of a starvation-mimicking antibiotic on drug interactions analytically and verify it experimentally. Our extended model suggests a change in the type of drug interaction that depends on the strength of resistance, which challenges established rescaling paradigms. We experimentally show that the presence of unregulated resistance genes can lead to altered drug interaction, which agrees with the prediction of the model. While minimal, the model is readily adaptable and opens the door to predicting interactions of second and higher-order in a broad range of biological systems.     

Energy patterns in twist-opening models of DNA with solvent interactions

Energy localization, via modulation instability, is addressed in a modified twist-opening model of DNA with solvent interactions. The Fourier expansion method is used to reduce the complex roto-torsional equations of the system to a set of discrete coupled nonlinear Schrödinger equations, which are used to perform the analytical investigation of modulation instability. We find that the instability criterion is highly influenced by the solvent parameters. Direct numerical simulations, performed on the generic model, further confirm our analytical predictions, as solvent interactions bring about highly localized energy patterns. These patterns are also shown to be robust under thermal fluctuations.     

Social structure modulates the evolutionary consequences of social plasticity: A social network perspective on interacting phenotypes

Organisms express phenotypic plasticity during social interactions. Interacting phenotype theory has explored the consequences of social plasticity for evolution, but it is unclear how this theory applies to complex social structures. We adapt interacting phenotype models to general social structures to explore how the number of social connections between individuals and preference for phenotypically similar social partners affect phenotypic variation and evolution. We derive an analytical model that ignores phenotypic feedback and use simulations to test the predictions of this model. We find that adapting previous models to more general social structures does not alter their general conclusions but generates insights into the effect of social plasticity and social structure on the maintenance of phenotypic variation and evolution. Contribution of indirect genetic effects to phenotypic variance is highest when interactions occur at intermediate densities and decrease at higher densities, when individuals approach interacting with all group members, homogenizing the social environment across individuals. However, evolutionary response to selection tends to increase at greater network densities as the effects of an individual's genes are amplified through increasing effects on other group members. Preferential associations among similar individuals (homophily) increase both phenotypic variance within groups and evolutionary response to selection. Our results represent a first step in relating social network structure to the expression of social plasticity and evolutionary responses to selection.     

Inferring network interactions within a cell

The continuing growth in high-throughput data acquisition has led to a proliferation of network models to represent and analyse biological systems. These networks involve distinct interaction types detected by a combination of methods, ranging from directly observed physical interactions based in biochemistry to interactions inferred from phenotype measurements, genomic expression and comparative genomics. The discovery of interactions increasingly requires a blend of experimental and computational methods. Considering yeast as a model system, recent analytical methods are reviewed here and specific aims are proposed to improve network interaction inference and facilitate predictive biological modelling.     

A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development

The cerebral cortex is divided into many functionally distinct areas. The emergence of these areas during neural development is dependent on the expression patterns of several genes. Along the anterior-posterior axis, gradients of Fgf8, Emx2, Pax6, Coup-tfi, and Sp8 play a particularly strong role in specifying areal identity. However, our understanding of the regulatory interactions between these genes that lead to their confinement to particular spatial patterns is currently qualitative and incomplete. We therefore used a computational model of the interactions between these five genes to determine which interactions, and combinations of interactions, occur in networks that reproduce the anterior-posterior expression patterns observed experimentally. The model treats expression levels as Boolean, reflecting the qualitative nature of the expression data currently available. We simulated gene expression patterns created by all possible networks containing the five genes of interest. We found that only of these networks were able to reproduce the experimentally observed expression patterns. These networks all lacked certain interactions and combinations of interactions including auto-regulation and inductive loops. Many higher order combinations of interactions also never appeared in networks that satisfied our criteria for good performance. While there was remarkable diversity in the structure of the networks that perform well, an analysis of the probability of each interaction gave an indication of which interactions are most likely to be present in the gene network regulating cortical area development. We found that in general, repressive interactions are much more likely than inductive ones, but that mutually repressive loops are not critical for correct network functioning. Overall, our model illuminates the design principles of the gene network regulating cortical area development, and makes novel predictions that can be tested experimentally.     

Stabilizing patterning in the Drosophila segment polarity network by selecting models in silico

The segmentation of Drosophila is a prime model to study spatial patterning during embryogenesis. The spatial expression of segment polarity genes results from a complex network of interacting proteins whose expression products are maintained after successful segmentation. This prompted us to investigate the stability and robustness of this process using a dynamical model for the segmentation network based on Boolean states. The model consists of intra-cellular as well as inter-cellular interactions between adjacent cells in one spatial dimension. We quantify the robustness of the dynamical segmentation process by a systematic analysis of mutations. Our starting point consists in a previous Boolean model for Drosophila segmentation. We define mathematically the notion of dynamical robustness and show that the proposed model exhibits limited robustness in gene expression under perturbations. We applied in silico evolution (mutation and selection) and discover two classes of modified gene networks that have a more robust spatial expression pattern. We verified that the enhanced robustness of the two new models is maintained in differential equations models. By comparing the predicted model with experiments on mutated flies, we then discuss the two types of enhanced models. Drosophila patterning can be explained by modelling the underlying network of interacting genes. Here we demonstrate that simple dynamical considerations and in silico evolution can enhance the model to robustly express the expected pattern, helping to elucidate the role of further interactions.     

Strategies to mitigate transgene–promoter interactions

The expression pattern of tissue-specific promoters in transgenes can be influenced by promoter/enhancer elements employed for the expression of selectable marker genes or elements found in DNA flanking the insertion site. We have developed an analytical system in Arabidopsis thaliana to investigate strategies useful in blocking or reducing nonspecific interactions. These experiments confirm that the DNA configuration and the insertion of spacer DNA aid in the appropriate expression of tissue-specific promoters. It is also demonstrated that the novel tobacco cryptic promoter (tCUP), when used to replace the cauliflower mosaic virus (CaMV) 35S promoter/enhancer, does not show nonspecific interactions. Furthermore, it is shown that insulators isolated from yeast and animals may have potential application in plants. Our results may allow the design of strategies that, individually or in combination, can be used to minimize nonspecific interactions and to design vectors for individual tissue-specific promoters.     

A closed‐form solution for steady‐state coupled phloem/xylem flow using the Lambert‐W function

A closed‐form solution for steady‐state coupled phloem/xylem flow is presented. This incorporates the basic Münch flow model of phloem transport, the cohesion model of xylem flow, and local variation in the xylem water potential and lateral water flow along the transport pathway. Use of the Lambert‐W function allows this solution to be obtained under much more general and realistic conditions than has previously been possible. Variation in phloem resistance (i.e. viscosity) with solute concentration, and deviations from the Van't Hoff expression for osmotic potential are included. It is shown that the model predictions match those of the equilibrium solution of a numerical time‐dependent model based upon the same mechanistic assumptions. The effect of xylem flow upon phloem flow can readily be calculated, which has not been possible in any previous analytical model. It is also shown how this new analytical solution can handle multiple sources and sinks within a complex architecture, and can describe competition between sinks. The model provides new insights into Münch flow by explicitly including interactions with xylem flow and water potential in the closed‐form solution, and is expected to be useful as a component part of larger numerical models of entire plants.     

Asymptotic distribution for epistatic tests in case-control studies

We propose a statistical model for dissecting a multilocus genotypic value into its main (additive and dominant) effects and epistatic effects between different loci in a case-control association study. The model can discern four different kinds of epistasis, additive × additive, additive × dominant, dominant × additive, and dominant × dominant interactions. To test each kind of epistasis, a χ² test statistic was computed for a two by two contingency table derived from combined genotypes in both case and control groups. We derived an analytical approach for estimating the asymptotic distribution of the χ² test statistic for epistatic tests under the null hypothesis, with the result being consistent with that from Monte Carlo simulations. The new model was used to analyze a case-control data set for candidate gene studies of stroke, leading to the identification of several significant interactions between causal SNPs on this disease.     

Assessment and significance of protein–protein interactions during development of protein biopharmaceuticals

Early development of protein biotherapeutics using recombinant DNA technology involved progress in the areas of cloning, screening, expression and recovery/purification. As the biotechnology industry matured, resulting in marketed products, a greater emphasis was placed on development of formulations and delivery systems requiring a better understanding of the chemical and physical properties of newly developed protein drugs. Biophysical techniques such as analytical ultracentrifugation, dynamic and static light scattering, and circular dichroism were used to study protein–protein interactions during various stages of development of protein therapeutics. These studies included investigation of protein self-association in many of the early development projects including analysis of highly glycosylated proteins expressed in mammalian CHO cell cultures. Assessment of protein–protein interactions during development of an IgG1 monoclonal antibody that binds to IgE were important in understanding the pharmacokinetics and dosing for this important biotherapeutic used to treat severe allergic IgE-mediated asthma. These studies were extended to the investigation of monoclonal antibody–antigen interactions in human serum using the fluorescent detection system of the analytical ultracentrifuge. Analysis by sedimentation velocity analytical ultracentrifugation was also used to investigate competitive binding to monoclonal antibody targets. Recent development of high concentration protein formulations for subcutaneous administration of therapeutics posed challenges, which resulted in the use of dynamic and static light scattering, and preparative analytical ultracentrifugation to understand the self-association and rheological properties of concentrated monoclonal antibody solutions.     

An investigation of a nonlocal hyperbolic model for self-organization of biological groups

In this article, we introduce and study a new nonlocal hyperbolic model for the formation and movement of animal aggregations. We assume that the nonlocal attractive, repulsive, and alignment interactions between individuals can influence both the speed and the turning rates of group members. We use analytical and numerical techniques to investigate the effect of these nonlocal interactions on the long-time behavior of the patterns exhibited by the model. We establish the local existence and uniqueness and show that the nonlinear hyperbolic system does not develop shock solutions (gradient blow-up). Depending on the relative magnitudes of attraction and repulsion, we show that the solutions of the model either exist globally in time or may exhibit finite-time amplitude blow-up. We illustrate numerically the various patterns displayed by the model: dispersive aggregations, finite-size groups and blow-up patterns, the latter corresponding to aggregations which may collapse to a point. The transition from finite-size to blow-up patterns is governed by the magnitude of the social interactions and the random turning rates. The presence of these types of patterns and the absence of shocks are consequences of the biologically relevant assumptions regarding the form of the speed and the turning rate functions, as well as of the kernels describing the social interactions.