Mapping parameter spaces of biological switches

Lattice structures that parameterize regulatory network dynamics

We consider two types of models of regulatory network dynamics: Boolean maps and systems of switching ordinary differential equations. Our goal is to construct all models in each category that are compatible with the directed signed graph that describe the network interactions. This leads to consideration of lattice of monotone Boolean functions (MBF), poset of non-degenerate MBFs, and a lattice of chains in these sets. We describe explicit inductive construction of these posets where the induction is on the number of inputs in MBF. Our results allow enumeration of potential dynamic behavior of the network for both model types, subject to practical limitation imposed by the size of the lattice of MBFs described by the Dedekind number.

DyMMM-LEAPS: An ML-based framework for modulating evenness and stability in synthetic microbial communities

There have been a growing number of computational strategies to aid in the design of synthetic microbial consortia. A framework to identify regions in parametric space to maximize two essential properties, evenness and stability, is critical. In this study, we introduce DyMMM-LEAPS (dynamic multispecies metabolic modeling-locating evenness and stability in large parametric space), an extension of the DyMMM framework. Our method explores the large parametric space of genetic circuits in synthetic microbial communities to identify regions of evenness and stability. Due to the high computational costs of exhaustive sampling, we utilize adaptive sampling and surrogate modeling to reduce the number of simulations required to map the vast space. Our framework predicts engineering targets and computes their operating ranges to maximize the probability of the engineered community to have high evenness and stability. We demonstrate our approach by simulating five cocultures and one three-strain culture with different social interactions (cooperation, competition, and predation) employing quorum-sensing-based genetic circuits. In addition to guiding circuit tuning, our pipeline gives an opportunity for a detailed analysis of pockets of evenness and stability for the circuit under investigation, which can further help dissect the relationship between the two properties. DyMMM-LEAPS is easily customizable and can be expanded to a larger community with more complex interactions.

To be or not to be: orb, the fusome and oocyte specification in Drosophila

In the fruit fly Drosophila melanogaster, two cells in a cyst of 16 interconnected cells have the potential to become the oocyte, but only one of these will assume an oocyte fate as the cysts transition through regions 2a and 2b of the germarium. The mechanism of specification depends on a polarized microtubule network, a dynein dependent Egl:BicD mRNA cargo complex, a special membranous structure called the fusome and its associated proteins, and the translational regulator orb. In this work, we have investigated the role of orb and the fusome in oocyte specification. We show here that specification is a stepwise process. Initially, orb mRNAs accumulate in the two pro-oocytes in close association with the fusome. This association is accompanied by the activation of the orb autoregulatory loop, generating high levels of Orb. Subsequently, orb mRNAs become enriched in only one of the pro-oocytes, the presumptive oocyte, and this is followed, with a delay, by Orb localization to the oocyte. We find that fusome association of orb mRNAs is essential for oocyte specification in the germarium, is mediated by the orb 3' UTR, and requires Orb protein. We also show that the microtubule minus end binding protein Patronin functions downstream of orb in oocyte specification. Finally, in contrast to a previously proposed model for oocyte selection, we find that the choice of which pro-oocyte becomes the oocyte does not seem to be predetermined by the amount of fusome material in these two cells, but instead depends upon a competition for orb gene products.

Fusome topology and inheritance during insect gametogenesis

From insects to mammals, oocytes and sperm develop within germline cysts comprising cells connected by intercellular bridges (ICBs). In numerous insects, formation of the cyst is accompanied by growth of the fusome-a membranous organelle that permeates the cyst. Fusome composition and function are best understood in Drosophila melanogaster: during oogenesis, the fusome dictates cyst topology and size and facilitates oocyte selection, while during spermatogenesis, the fusome synchronizes the cyst's response to DNA damage. Despite its distinct and sex-specific roles during insect gametogenesis, elucidating fusome growth and inheritance in females and its structure and connectivity in males has remained challenging. Here, we take advantage of advances in three-dimensional (3D) confocal microscopy and computational image processing tools to reconstruct the topology, growth, and distribution of the fusome in both sexes. In females, our experimental findings inform a theoretical model for fusome assembly and inheritance and suggest that oocyte selection proceeds through an 'equivalency with a bias' mechanism. In males, we find that cell divisions can deviate from the maximally branched pattern observed in females, leading to greater topological variability. Our work consolidates existing disjointed experimental observations and contributes a readily generalizable computational approach for quantitative studies of gametogenesis within and across species.

Mechanics of stabilized intercellular bridges

Numerous engineered and natural systems form through reinforcement and stabilization of a deformed configuration that was generated by a transient force. An important class of such structures arises during gametogenesis, when a dividing cell undergoes incomplete cytokinesis, giving rise to daughter cells that remain connected through a stabilized intercellular bridge (ICB). ICBs can form through arrest of the contractile cytokinetic furrow and its subsequent stabilization. Despite knowledge of the molecular components, the mechanics underlying robust ICB assembly and the interplay between ring contractility and stiffening are poorly understood. Here, we report joint experimental and theoretical work that explores the physics underlying robust ICB assembly. We develop a continuum mechanics model that reveals the minimal requirements for the formation of stable ICBs, and validate the model's equilibrium predictions through a tabletop experimental analog. With insight into the equilibrium states, we turn to the dynamics: we demonstrate that contractility and stiffening are in dynamic competition and that the time intervals of their action must overlap to ensure assembly of ICBs of biologically observed proportions. Our results highlight a mechanism in which deformation and remodeling are tightly coordinated-one that is applicable to several mechanics-based applications and is a common theme in biological systems spanning several length scales.

Quantitative models for building and growing fated small cell networks

Small cell clusters exhibit numerous phenomena typically associated with complex systems, such as division of labour and programmed cell death. A conserved class of such clusters occurs during oogenesis in the form of germline cysts that give rise to oocytes. Germline cysts form through cell divisions with incomplete cytokinesis, leaving cells intimately connected through intercellular bridges that facilitate cyst generation, cell fate determination and collective growth dynamics. Using the well-characterized Drosophila melanogaster female germline cyst as a foundation, we present mathematical models rooted in the dynamics of cell cycle proteins and their interactions to explain the generation of germline cell lineage trees (CLTs) and highlight the diversity of observed CLT sizes and topologies across species. We analyse competing models of symmetry breaking in CLTs to rationalize the observed dynamics and robustness of oocyte fate specification, and highlight remaining gaps in knowledge. We also explore how CLT topology affects cell cycle dynamics and synchronization and highlight mechanisms of intercellular coupling that underlie the observed collective growth patterns during oogenesis. Throughout, we point to similarities across organisms that warrant further investigation and comment on the extent to which experimental and theoretical findings made in model systems extend to other species.

Size scaling in collective cell growth

Size is a fundamental feature of living entities and is intimately tied to their function. Scaling laws, which can be traced to D'Arcy Thompson and Julian Huxley, have emerged as a powerful tool for studying regulation of the growth dynamics of organisms and their constituent parts. Yet, throughout the 20th century, as scaling laws were established for single cells, quantitative studies of the coordinated growth of multicellular structures have lagged, largely owing to technical challenges associated with imaging and image processing. Here, we present a supervised learning approach for quantifying the growth dynamics of germline cysts during oogenesis. Our analysis uncovers growth patterns induced by the groupwise developmental dynamics among connected cells, and differential growth rates of their organelles. We also identify inter-organelle volumetric scaling laws, finding that nurse cell growth is linear over several orders of magnitude. Our approach leverages the ever-increasing quantity and quality of imaging data, and is readily amenable for studies of collective cell growth in other developmental contexts, including early mammalian embryogenesis and germline development.