Biological problemThe fate map of C.elegans as illustrated in Figure 1, is an incomplete model of its embryonic development. If lineage causally determined cellular differentiation, then all intracellular interactions would be irrelevant and growth would occur properly even in disconnected topologies. In other words, autonomous development of the worm would be observed. Putatively, C. elegans represents the classical paradigm of said determinate mode lauded for their highly invariant cellular lineage. However, fully autonomous development has been experimentally repudiated; the AB cell and its children, responsible for 389 of 558 cells of the hatched larva, produces only a fraction of its descendant lineage if left in isolation from its would be neighbors.
Figure 1 C. elegans development: A) Adult worm with developing embryos B) Early stage of development with cell fate labelings C) Celllineage map
Furthermore, it seems empirically true that AB relatives distant on the lineage tree produce the same form of differentiated cell. This necessitates the following question: Can one confidently infer deterministic differentiation solely from an invariant cellular lineage? An alternative hypothesis is that the invariance of the C.elegans cellular lineage is a result of “invariant cleavage patterns [that] set up reproducible patterns of cellcell interactions.” As such, we will explore a new framework that tracks the dynamics of such intracellular interactions in the early development of the worm.
Physical Model A generic property of the important, experimentally characterized, interactions to developmental fidelity is that they are mediated through direct cellcell contact. This stands in juxtaposition to morphogen models (e.g. Bicoid in early fly development). As such, we will characterize interaction topologies based upon who is touching who via an adjacency matrix. This is illustrated in Figure 2. The adjacency matrix is a simple object for a system of N cells: it is an NxN symmetric binary matrix with a 1 in position (i,j) if cells i and j are nearest neighbors or a 0 otherwise. A priori it would seem that the space of all adjacency matrices is astronomically large growing exponentially with N and thus the number of interaction topologies accessible to the embryo is very large. If so, could the wildtype worm really exhibit reproducible patterns of celltocell interactions? Fortunately, this is not the case; theoretically we find that given a topology at the current stage, the number of nearest neighbor topologies that can be explored with the next cleavage is tightly constrained.
Figure 2 Analysis : A) 4D data of labeled nuclei and membrane B) 3D image segmentation C) Correspodning adjacency matrix (note the exterior cell is labeled cell 7)
This supports the picture of reproducible intracellular interactions  past cleavage patterns constrain potential cleavage patterns in the future. The benefit of such a reformulation is that new questions immediately arise. The first question we will probe is to quantify the variance in adjacency space of the development of the wildtype embryo. If it is largely invariant as C.elegans lore states, then what perturbations can we impose that disturb growth from its welldefined trajectory? Do some perturbations lead to recoverable change or are all completely lethal? Can we find a metric in adjacency space that correlates distance from wildtype to lethality of the embryo? These questions within the adjacency matrix formalism will shift the discussion away from the categorical nature of autonomous versus conditional growth and move it towards quantifying how and which cellular interactions are important to early worm development.
ExperimentsTo produce and explore the abovementioned variance we will impose environmental stresses and disrupt wildtype miRNA activity (we shall use RNA interference against dcr1 to globally disrupt miRNA activity). Alteration in temperature effect the rate and fidelity of embryonic development, and we will quantify these dynamics at 22°C and 25°C. Exploring thermal and miRNA dependent stresses are particularly interesting since it has been claimed that the role of microRNAs is in buffering variation in response to environmental stress. Our new framework will allow us to quantify and systematize deviations away from wildtype development. In order to do so we shall use a strain expressing a membrane targeted GFP in addition to a nuclear histone::mCherry marker to allow the construction of adjacency matrices in time.
Microscopy Zeiss LSM 700 Laser lines 488 nm and 561 nm and filter sets optimized for mCherry and GFP. pinhole 2.5AU, xy 512 X512, step size 1µm. Adjust laser power using Autoz correct Temp control stage at 22°C and 25°C  Data Analysis Following acquisition of the movies, the data analysis will involve executing an image analysis pipeline. The first stage will be in ilastik wherein students will have to “train” the machine learning algorithm into partitioning images/stacks into membrane and nonmembrane pixels. Next, a simple 3D watershed algorithm will segment the data into cells, which will allow the construction of adjacency matrices at each time point. This pipeline is illustrated in Figure 2. The dynamics of these adjacency matrices will then be tracked in time. This pipeline will be repeated for several embryos in wildtype and the perturbed conditions mentioned above.
Skills that students will acquire Learn about early worm development Learn how to handle and image worms Experience of how constructing biologically relevant quantitative frameworks alters the nature of the questions that can be asked Biological data is statistical in nature and quantifying this variance is essential Back and forth between model and experiments
Cellular organization in C.elegans embryo
Biological problemThe fate map of C.elegans as illustrated in Figure 1, is an incomplete model of its embryonic development. If lineage causally determined cellular differentiation, then all intracellular interactions would be irrelevant and growth would occur properly even in disconnected topologies. In other words, autonomous development of the worm would be observed. Putatively, C. elegans represents the classical paradigm of said determinate mode lauded for their highly invariant cellular lineage. However, fully autonomous development has been experimentally repudiated; the AB cell and its children, responsible for 389 of 558 cells of the hatched larva, produces only a fraction of its descendant lineage if left in isolation from its would be neighbors.
Furthermore, it seems empirically true that AB relatives distant on the lineage tree produce the same form of differentiated cell. This necessitates the following question: Can one confidently infer deterministic differentiation solely from an invariant cellular lineage? An alternative hypothesis is that the invariance of the C.elegans cellular lineage is a result of “invariant cleavage patterns [that] set up reproducible patterns of cellcell interactions.” As such, we will explore a new framework that tracks the dynamics of such intracellular interactions in the early development of the worm.
Physical Model
A generic property of the important, experimentally characterized, interactions to developmental fidelity is that they are mediated through direct cellcell contact. This stands in juxtaposition to morphogen models (e.g. Bicoid in early fly development). As such, we will characterize interaction topologies based upon who is touching who via an adjacency matrix. This is illustrated in Figure 2. The adjacency matrix is a simple object for a system of N cells: it is an NxN symmetric binary matrix with a 1 in position (i,j) if cells i and j are nearest neighbors or a 0 otherwise. A priori it would seem that the space of all adjacency matrices is astronomically large growing exponentially with N and thus the number of interaction topologies accessible to the embryo is very large. If so, could the wildtype worm really exhibit reproducible patterns of celltocell interactions? Fortunately, this is not the case; theoretically we find that given a topology at the current stage, the number of nearest neighbor topologies that can be explored with the next cleavage is tightly constrained.
This supports the picture of reproducible intracellular interactions  past cleavage patterns constrain potential cleavage patterns in the future. The benefit of such a reformulation is that new questions immediately arise.
The first question we will probe is to quantify the variance in adjacency space of the development of the wildtype embryo. If it is largely invariant as C.elegans lore states, then what perturbations can we impose that disturb growth from its welldefined trajectory? Do some perturbations lead to recoverable change or are all completely lethal? Can we find a metric in adjacency space that correlates distance from wildtype to lethality of the embryo? These questions within the adjacency matrix formalism will shift the discussion away from the categorical nature of autonomous versus conditional growth and move it towards quantifying how and which cellular interactions are important to early worm development.
ExperimentsTo produce and explore the abovementioned variance we will impose environmental stresses and disrupt wildtype miRNA activity (we shall use RNA interference against dcr1 to globally disrupt miRNA activity). Alteration in temperature effect the rate and fidelity of embryonic development, and we will quantify these dynamics at 22°C and 25°C. Exploring thermal and miRNA dependent stresses are particularly interesting since it has been claimed that the role of microRNAs is in buffering variation in response to environmental stress. Our new framework will allow us to quantify and systematize deviations away from wildtype development. In order to do so we shall use a strain expressing a membrane targeted GFP in addition to a nuclear histone::mCherry marker to allow the construction of adjacency matrices in time.
Microscopy
 Zeiss LSM 700 Laser lines 488 nm and 561 nm and filter sets optimized for mCherry and GFP. pinhole 2.5AU, xy 512 X512, step size 1µm. Adjust laser power using Autoz correct
 Temp control stage at 22°C and 25°C

Data Analysis
Following acquisition of the movies, the data analysis will involve executing an image analysis pipeline. The first stage will be in ilastik wherein students will have to “train” the machine learning algorithm into partitioning images/stacks into membrane and nonmembrane pixels. Next, a simple 3D watershed algorithm will segment the data into cells, which will allow the construction of adjacency matrices at each time point. This pipeline is illustrated in Figure 2. The dynamics of these adjacency matrices will then be tracked in time. This pipeline will be repeated for several embryos in wildtype and the perturbed conditions mentioned above.
Skills that students will acquire
 Learn about early worm development
 Learn how to handle and image worms
 Experience of how constructing biologically relevant quantitative frameworks alters the nature of the questions that can be asked
 Biological data is statistical in nature and quantifying this variance is essential
 Back and forth between model and experiments