David G. Míguez

Intron length increases oscillatory periods of gene expression in animal cells

Introns may affect gene expression by increasing the time required to transcribe the gene. One way for extended transcription times to affect the behavior of a gene expression program is through a negative feedback loop. Here, we show that a logically engineered negative feedback loop in animal cells produces expression pulses, which have a broad time distribution that increases with intron length. These results in combination with mathematical models provide insight into what may produce the intron-dependent pulse distributions. We conclude that the long production time required for large intron-containing genes is significant for the behavior of gene expression programs.

Sonic Hedgehog Signaling Switches the Mode of Division in the Developing Nervous System

The different modes of stem cell division are tightly regulated to balance growth and differentiation during organ development and homeostasis, and these regulatory processes are subverted in tumor formation. Here, we developed markers that provided the single-cell resolution necessary to quantify the three modes of division taking place in the developing nervous system in vivo: self-expanding, PP; self-replacing, PN; and self-consuming, NN. Using these markers and a mathematical model that predicts the dynamics of motor neuron progenitor division, we identify a role for the morphogen Sonic hedgehog in the maintenance of stem cell identity in the developing spinal cord. Moreover, our study provides insight into the process linking lineage commitment to neurogenesis with changes in cell-cycle parameters. As a result, we propose a challenging model in which the external Sonic hedgehog signal dictates stem cell identity, reflected in the consequent readjustment of cell-cycle parameters.

Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase

Waves and patterns in living systems are often driven by biochemical reactions with enzymes as catalysts and regulators. We present a reaction–diffusion system catalyzed by the enzyme glucose oxidase that exhibits traveling wave patterns in a spatially extended medium. Fronts and pulses propagate as a result of the coupling between the enzyme-catalyzed autocatalytic production and diffusion of hydrogen ions. A mathematical model qualitatively explains the experimental observations.

Smad2 and Smad3 cooperate and antagonize simultaneously in vertebrate neurogenesis

Summary The transforming growth factor beta (TGF-&bgr;) pathway plays key roles in development and cancer. TGF-&bgr; signaling converges on the Smad2 and Smad3 effectors, which can either cooperate or antagonize to regulate their transcriptional targets. Here we performed in vivo and in silico experiments to study how such cooperativity and antagonism might function during neurogenesis. In vivo electroporation experiments in the chick embryo neural tube show that Smad2 and Smad3 cooperate to promote neurogenesis, as well as the transcription of Smad3-specific targets. Knockdown of Smad2 enhances neurogenesis and the transcription of Smad3-specific targets. A mathematical model of the TGF-&bgr; pathway fits the experimental results and predicts that the proportions of the three different trimeric complexes formed dictates the transcriptional responses of the R-Smad proteins. As such, Smad2 targets are activated solely by the Smad2–Smad2–Smad4 complex, whereas Smad3 targets are activated both by Smad2–Smad3–Smad4 and Smad3–Smad3–Smad4 trimers. We have modeled the Smad responses onto arbitrary genes and propose that this mechanism might be extended to additional activities of TGF-&bgr; in development and disease.

Novel role for the midbody in primary ciliogenesis by polarized epithelial cells.

Polarized epithelial cells assemble a primary cilium by an unknown mechanism. After cytokinesis, the central part of the intercellular bridge, which is referred to as the midbody, is inherited as a remnant by one of the daughter cells. Here, Bernabé-Rubio et al. show that the midbody remnant meets the centrosome at the cell apex, enabling primary ciliogenesis.

A Tunable Coarse-Grained Model for Ligand-Receptor Interaction

Cell-surface receptors are the most common target for therapeutic drugs. The design and optimization of next generation synthetic drugs require a detailed understanding of the interaction with their corresponding receptors. Mathematical approximations to study ligand-receptor systems based on reaction kinetics strongly simplify the spatial constraints of the interaction, while full atomistic ligand-receptor models do not allow for a statistical many-particle analysis, due to their high computational requirements. Here we present a generic coarse-grained model for ligand-receptor systems that accounts for the essential spatial characteristics of the interaction, while allowing statistical analysis. The model captures the main features of ligand-receptor kinetics, such as diffusion dependence of affinity and dissociation rates. Our model is used to characterize chimeric compounds, designed to take advantage of the receptor over-expression phenotype of certain diseases to selectively target unhealthy cells. Molecular dynamics simulations of chimeric ligands are used to study how selectivity can be optimized based on receptor abundance, ligand-receptor affinity and length of the linker between both ligand subunits. Overall, this coarse-grained model is a useful approximation in the study of systems with complex ligand-receptor interactions or spatial constraints.

A mathematical model for the rational design of chimeric ligands in selective drug therapies

Chimeric drugs with selective potential toward specific cell types constitute one of the most promising forefronts of modern Pharmacology. We present a mathematical model to test and optimize these synthetic constructs, as an alternative to conventional empirical design. We take as a case study a chimeric construct composed of epidermal growth factor (EGF) linked to different mutants of interferon (IFN). Our model quantitatively reproduces all the experimental results, illustrating how chimeras using mutants of IFN with reduced affinity exhibit enhanced selectivity against cell overexpressing EGF receptor. We also investigate how chimeric selectivity can be improved based on the balance between affinity rates, receptor abundance, activity of ligand subunits, and linker length between subunits. The simplicity and generality of the model facilitate a straightforward application to other chimeric constructs, providing a quantitative systematic design and optimization of these selective drugs against certain cell‐based diseases, such as Alzheimers and cancer.

Myosin light-chain phosphatase regulates basal actomyosin oscillations during morphogenesis.

Contractile actomyosin networks generate forces that drive tissue morphogenesis. Actomyosin contractility is controlled primarily by reversible phosphorylation of the myosin-II regulatory light chain through the action of myosin kinases and phosphatases. While the role of myosin light-chain kinase in regulating contractility during morphogenesis has been largely characterized, there is surprisingly little information on myosin light-chain phosphatase (MLCP) function in this context. Here, we use live imaging of Drosophila follicle cells combined with mathematical modelling to demonstrate that the MLCP subunit flapwing (flw) is a key regulator of basal myosin oscillations and cell contractions underlying egg chamber elongation. Flw expression decreases specifically on the basal side of follicle cells at the onset of contraction and flw controls the initiation and periodicity of basal actomyosin oscillations. Contrary to previous reports, basal F-actin pulsates similarly to myosin. Finally, we propose a quantitative model in which periodic basal actomyosin oscillations arise in a cell-autonomous fashion from intrinsic properties of motor assemblies.

A branching process to characterize the dynamics of stem cell differentiation

The understanding of the regulatory processes that orchestrate stem cell maintenance is a cornerstone in developmental biology. Here, we present a mathematical model based on a branching process formalism that predicts average rates of proliferative and differentiative divisions in a given stem cell population. In the context of vertebrate neurogenesis, the model predicts complex non-monotonic variations in the rates of pp, pd and dd modes of division as well as in cell cycle length, in agreement with experimental results. Moreover, the model shows that the differentiation probability follows a binomial distribution, allowing us to develop equations to predict the rates of each mode of division. A phenomenological simulation of the developing spinal cord informed with the average cell cycle length and division rates predicted by the mathematical model reproduces the correct dynamics of proliferation and differentiation in terms of average numbers of progenitors and differentiated cells. Overall, the present mathematical framework represents a powerful tool to unveil the changes in the rate and mode of division of a given stem cell pool by simply quantifying numbers of cells at different times.

Synergistic Interaction between Selective Drugs in Cell Populations Models

The design of selective drugs and combinatorial drug treatments are two of the main focuses in modern pharmacology. In this study we use a mathematical model of chimeric ligand-receptor interaction to show that the combination of selective drugs is synergistic in nature, providing a way to gain optimal selective potential at reduced doses compared to the same drugs when applied individually. We use a cell population model of proliferating cells expressing two different amounts of a target protein to show that both selectivity and synergism are robust against variability and heritability in the cell population. The reduction in the total drug administered due to the synergistic performance of the selective drugs can potentially result in reduced toxicity and off-target interactions, providing a mechanism to improve the treatment of cell-based diseases caused by aberrant gene overexpression, such as cancer and diabetes.