Our main focus is to develop coarse-grained models (using mathematical tools to understand stochastic processes and non-linear dynamics) for collective dynamics of large populations of cells based on controlled laboratory experiments with simplified biological systems. The projects although diverse in their biological context are fundamentally related via the governing principles that shape the structure of these populations, and more practically by the empirical and experimental techniques we use to study these systems. Below, we provide details of projects that remain active and are completed. 

Current projects 


P1. Cellular dynamics that shape 3D structures during development

Project description: 

Multiple organ primordia are composed of a volume of confluent cells. Although mechanisms that shape tissue sheets are increasingly understood, those which shape a volume of cells remain obscure. We show here that the spatial distributions of cell cycle time, tissue elasticity and viscosity are important for growth of the mandibular arch in the mouse embryo, but do not adequately explain tissue shape. Rather, mesenchymal cells intercalate in 3D to narrow and elongate the middle region of the arch. Using a knock-in vinculin tension sensor, we show that cortical force oscillations promote mesenchymal cell intercalations. Wnt5a functions as a spatial cue to orient cortical actomyosin and promotes high amplitude oscillations, in part by regulating cytosolic calcium fluctuations in a Piezo1-dependent manner. Our data support cell neighbour exchange as a conserved mechanism that drives morphogenesis of a volume of tissue and is spatially coordinated by pathways, which tune cytoskeletal oscillation.

Experimental collaboration with: Sevan Hopyan

P2. Eco-evolutionary consequences of acquired immunity in bacteria

Project description:

(A) The dependence of bacterial population size at steady-state on spacer effectiveness e and flow rate f is plotted for three values of f (solid blue lines). Fixed points are indicated with solid circles (stable) and open circles (unstable). We model upregulation from quorum sensing by introducing a density-spacer effectiveness (dashed black line) so that spacer effectiveness is no longer a constant parameter. 
(B) A strong density dependence can induce bistability as a function of the flow rate, a parameter that is easy to tune experimentally. The bacterial population size exhibits hysteresis between a low-expression, low-density state and a high-expression, high-density state.

Interactions between bacteria and phages have large impacts on bacterial populations and their surrounding ecosystems. We have modeled a population of bacteria with a CRISPR adaptive immune system interacting with viruses to study the impact of CRISPR on the population.

Our model shows that bacteria can exist in one of two stable ecological states determined by the strength of cas gene expression. Population-level differences also correspond to differences in the underlying distribution of CRISPR spacers, suggesting spacer distributions as an observable with ecological information.


Members involved: Madeleine Bonsma-Fisher, Dominique Soutiere (alumni)

P3. Building turbidostats for eco-evolutionary experiments

 Project description:

Host-parasite interactions form the backbone of many natural ecosystems and are important to pathogenesis. Human micro-biomes are no exception and recent works have brought attention to the role of bacteria-phage interactions in maintaining a healthy bacterial composition. Recent discovery of a rudimentary adaptive immune system, called CRISPR-cas system, in bacteria has challenged our understanding of the co-evolutionary dynamics between bacteria and their parasitic phages in natural settings, however there are only a handful of laboratory studies to understand the evolutionary dynamics of the CRISPR-phage interactions. Crucially, questions about the role of the CRISPR system in maintaining stable bacterial and phage diversity in natural ecosystems, such as human gut, remain open.

The design of previous experiments fails to capture the statistical properties of bacteria-phage system, which are essential for developing a quantitative model for such systems. To distill a statistical theory an ensemble of at least a few tens (if not hundreds) of parallel experiments need to be performed. To this end we are building a mini-chemostat-array system inspired by Toprak et al. with additional features required to track bacteria-phage dynamics. Crucially, we have incorporated florescence measurement in real time. To facilitate effective control and flexibility in experimental design, we have integrated temperature and stirring control to each chemostat.

Our immediate experimental goals are: i) Characterize an antagonistically interacting two-species bacterial system on short ecological time scales (tens of generations). ii) Co-evolutionary dynamics of the two-species bacterial system over long evolutionary time scales (hundreds to thousands of generations). iii) Quantify the role of phage in stabilizing bacterial composition.

Members involved:  Ue Yu Penn  and Chris Nunn

Experimental collaboration with: Alan Davidson & Karen Maxwell

P4. Quantifying tumor heterogeneity

Project description:  

Cellular heterogeneity among cancer initiating cells (CIC’s) remains an open question. To address this we analyzed cellular dynamics in human colorectal cancer (CRC) samples by following the fate of distinct tumor cells in vivo using lentiviral barcoding and high throughput sequencing in immunocompromised murine xenograft models. In vivo limiting dilution assay (LDA) gave a frequency of cancer initiating cells (CIC’s) to be roughly 1 in 455 cells (~0.22%). In addition high throughput sequencing was used to determine clonal composition of tumors at high dosage. A deterministic growth model (DGM) would suggest equal size of successful clones as they descend from equipotent CIC’s. In contrast, we find a broad distribution of clonal contribution (100-fold difference) across the successful lineages. Does this suggest cellular heterogeneity among cancer initiating cells, i.e. are some cells are better than others at forming tumors? Surprisingly, outcomes of mixing experiments between dominant monoclonal tumors and polyclonal tumors showed a pattern where fractional contribution from monoclonal tumor was below its injected fraction. We show that a stochastic-equipotent-growth-model (SEGM) constrained only by LDA frequency, explains differences in clonal composition among different lineages and the surprising pattern in mixing experiments. Finally, we did observe a small (but statistically significant) increase in number of unique clones that form the tumor in mixing experiments that we interpret as evidence for extra-cellular signaling. Taken together, our model suggest stochastic cellular fate for tumor cells, which can be modulated.

Members involved: Chris Farfan (alumni)

Experimental collaboration with: Catherine O’Brien 

P5. Competition in a population of reprogramming somatic cells 

Project description:  

Induced pluripotent stem cells have opened the door to cell programming, enabling scientists to engineer the cell state. However, the process of reprogramming to pluripotency remains incompletely understood. While comprehensive molecular analyses have mapped global state transitions during population reprogramming, these data do not account for cell state heterogeneity. In contrast, clonal studies, though useful for documenting cell potential, provide little insight into the impact of cell interactions on reprogramming outcomes. To understand how reprogramming potential and cellular heterogeneity influence population dynamics, we use a combined cellular barcoding and mathematical modeling approach. Strikingly, our data demonstrate that population dynamics are not representative of single cell reprogramming trajectories but are driven by a few dominant clones. These findings indicate that an a priori population of poised cells gives rise to “elite” clones that dominate the reprogramming pool in a reproducible manner, providing the first analysis of clonal competition dynamics in reprogramming.

Members involved: Sophie McGibbon-Gardner

Experimental collaboration with:  Peter Zandstra

P6. Finding rule for mitochondrial maintenance in yeast 

Project description:

Mitochondria, unlike most other organelles in the cell, have their own organellular DNA. This mitochondrial DNA (mtDNA) mutates at higher rate than nuclear DNA and mostly encodes for enzymes that are critical for cellular respiration. Because most eukaryotes heavily rely on respiration for cell function, mitochondria and their mtDNA are often considered to be targets of, or instigators of aging and mitochondrial related diseases. Can we directly observe deleterious or beneficial changes in mtDNA in eukaryotes over time? What can these changes due to mutation and selection teach us about maintenance or transmission of this mtDNA within a population and at the single cell level? This project aims to address these questions.

Members involved:  Chris Nunn

Experimental collaboration with: Boris Shraiman

P7. Building developmental lineages using single cell sequencing data

Project description: 


Our challenge is to combine different types of high throughput data into one comprehensive computational framework, which allows identification of potential control points to guide and bias cellular differentiation. Although Waddington’s epigenetic landscape picture to visualize embryonic development is now widely accepted, computational approaches to understand this landscape and the underlying regulatory networks are only now beginning to attract attention. We will use the classical spin glass framework from physics to quantitatively understand cellular differentiation and cellular reprogramming. Spin glasses come with a wide variety of tools that enable rapid progress and have successfully been applied to diverse biological systems where multiple stable states emerge from interactions among its constituents, including recently to understanding cellular reprogramming. We will attempt to design a control algorithm for guided cell fate differentiation based on lineage experiments and numerical studies.

Members involved: Sabyasachi Dasgupta

Collaboration with: Gary Bader and others

Past projects 

Blood regeneration in macaques: 

Background: How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 1011 mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages.


Results: While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs.

Conclusions: Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation.

Relevant publication