Danh-Tai Hoang

Morphogenesis, spontaneous formation of organism structure, is essential for life. In the pancreas, endocrine α, β, and δ cells are clustered to form islets of Langerhans, the critical micro-organ for glucose homeostasis. The spatial organization of endocrine cells in islets looks different between species. Based on the three-dimensional positions of individual cells in islets, we computationally inferred the relative attractions between cell types, and found that the attractions between homotypic cells were slightly, but significantly, stronger than the attractions between heterotypic cells commonly in mouse, pig, and human islets. The difference between α-β cell attraction and β-β cell attraction was minimal in human islets, maximizing the plasticity of islet structures. Our result suggests that although the cellular composition and attractions of pancreatic endocrine cells are quantitatively different between species, the physical mechanism of islet morphogenesis may be evolutionarily conserved.

Pancreatic islets are functional units involved in glucose homeostasis. The multicellular system comprises three main cell types; β and α cells reciprocally decrease and increase blood glucose by producing insulin and glucagon pulses, while the role of δ cells is less clear. Although their spatial organization and the paracrine/autocrine interactions between them have been extensively studied, the functional implications of the design principles are still lacking. In this study, we formulated a mathematical model that integrates the pulsatility of hormone secretion and the interactions and organization of islet cells and examined the effects of different cellular compositions and organizations in mouse and human islets. A common feature of both species was that islet cells produced synchronous hormone pulses under low- and high-glucose conditions, while they produced asynchronous hormone pulses under normal glucose conditions. However, the synchronous coordination of insulin and glucagon pulses at low glucose was more pronounced in human islets that had more α cells. When β cells were selectively removed to mimic diabetic conditions, the anti-synchronicity of insulin and glucagon pulses was deteriorated at high glucose, but it could be partially recovered when the re-aggregation of remaining cells was considered. Finally, the third cell type, δ cells, which introduced additional complexity in the multicellular system, prevented the excessive synchronization of hormone pulses. Our computational study suggests that controllable synchronization is a design principle of pancreatic islets.

The fundamental problem in modeling complex phenomena such as human perception using probabilistic methods is that of deducing a stochastic model of interactions between the constituents of a system from observed configurations. Even in this era of big data, the complexity of the systems being modeled implies that inference methods must be effective in the difficult regimes of small sample sizes and large coupling variability. Thus, model inference by means of minimization of a cost function requires additional assumptions such as sparsity of interactions to avoid overfitting. In this paper, we completely divorce iterative model updates from the value of a cost function quantifying goodness of fit. This separation enables the use of goodness of fit as a natural rationale for terminating model updates, thereby avoiding overfitting. We do this within the mathematical formalism of statistical physics by defining a formal free energy of observations from a partition function with an energy function chosen precisely to enable an iterative model update. Minimizing this free energy, we demonstrate coupling strength inference in nonequilibrium kinetic Ising models, and show that our method outperforms other existing methods in the regimes of interest. Our method has no tunable learning rate, scales to large system sizes, and has a systematic expansion to obtain higher-order interactions. As applications, we infer a functional connectivity network in the salamander retina and a currency exchange rate network from time-series data of neuronal spiking and currency exchange rates, respectively. Accurate small sample size inference is critical for devising a profitable currency hedging strategy.