In animals and plants, a specific class of extracellular diffusible molecules called morphogens are secreted from cells to coordinate spatial patterning of cell differentiation, gene expression, and proliferation to regulate organ size, shape, and function. In one example, a specific morphogen, sonic hedgehog, is secreted by spatially localized cells and local morphogen concentration defines differentiation events that are encoded by intracellular gene regulatory networks (GRN). This multicellular interaction is an example of sender-receiver type signaling, where morphogen secretion from one cell type induces a response from another cell type. Often deviations in the strength or positioning of morphogen concentrations and gradients regulate this intercellular interaction and underpin developmental diseases and congenital birth defects. Since these interactions function at the multicellular level (tissue scale) with spatial heterogeneity, many traditional methods of inferring the gene regulatory networks that comprise these interactions are insufficient. Studies inferring GRNs between cell types, assume availability of stock solution with known concentration of the diffusible factor mediating intercellular gene interactions. This may not be available in general as identification and purification of the factor is technically challenging in tissue and organ systems. In this work we develop a combined experimental and computational methodology, to infer intercellular GRN parameters agnostic of the concentration measurement of the diffusible factor.

In the first objective, we develop a deterministic computational framework together with proposed experiments to infer intercellular GRN parameters. In place of quantification of the diffusible factor concentration, our methodology uses fluorescence measurements from reporter proteins for inference. These proteins are expressed from reporter genes, which are placed under the regulation of the same promoter as the gene of interest. To generate the spatiotemporal fluorescence data required for the inference, we propose simple plate reader experiments and 2D spatial coculture experiments in a petri dish. We develop a 2D reaction-diffusion framework based on the finite-volume method capable of simulating these experiments. The spatiotemporal data is then fit using a custom genetic algorithm built for inference of type of gene interactions (edges) in the intercellular GRN. Given the GRN edges, a framework for structural identifiability gives uniquely identifiable parameters/combinations. Likelihood functions are formulated for inference of identifiable parameters and Markov Chain Monte Carlo sampling estimates uncertainty given measurement noise. To validate the methodology, we consider three case studies inspired from developmental and synthetic biology:​ sender-receiver activation, reciprocal signaling, and sender-receiver band-pass expression. Using experimental data generated in silico, the methodology successfully infers intercellular GRNs in these cases, barring practical identifiability issues.

In the second objective we show that given fixed deterministic mean levels of a target protein, single-cell noise in copy numbers in an intracellular GRN varies significantly with unidentifiable parameters. We use stochastic modeling to investigate the suppression of single-cell noise in a target protein. We take examples of classical controller GRNs namely proportional, integral and derivative feedback controllers to investigate the performance of each component for suppression of fluctuations originating from two noise sources:​ bursty expression of the protein, and external disturbance in protein synthesis. Our results show that proportional controllers are effective in buffering protein copy number fluctuations from both noise sources. In contrast, integral feedback has no effect on the protein noise level from stochastic expression, but significantly minimizes the impact of external disturbances. Meanwhile, the derivative controller effectively buffers output fluctuations from bursty stochastic expression. This study paves the way for synthetic design of biochemical controllers and their implementation to minimize deleterious fluctuations in gene product levels around a fixed target mean. In this pursuit, we also observe that noise metrics hold signatures of underlying parameters, making the inverse problem of inference possible.

In the last objective, we show that noise characteristics of reporter protein levels can be used to obtain deterministically unidentifiable parameters of the underlying intercellular GRN. With the advent of microfluidics and high-resolution microscopy, single-cell data can be obtained in the form of time trajectory of reporter fluorescence. Deriving single-cell noise metrics from these trajectories and fitting them to a model gives the deterministically unidentifiable parameters. To do this, first we formulate a stochastic model of intercellular GRN and use the linear noise approximation to derive moment dynamics equations. These equations are solved numerically and allow us to efficiently fit the noise metrics (involving moments) to bootstrapped data. We validate the method using data generated in silico in two case studies:​ the sender-receiver and reciprocal signaling and show that the confidence intervals of the inferred parameters include the true values.

In summary, we develop a combined computational and experimental methodology for the inference of intercellular GRNs agnostic of the knowledge of the diffusible factors. This will help remove roadblocks for inference, which are inherent to traditional methods and will lead to better understanding of diseases and the development of therapeutics.