Danh-Tai Hoang

A Conserved Rule for Pancreatic Islet Organization

Morphogenesis, spontaneous formation of organism structure, is essential for life. In the pancreas, endocrine , , and 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 cell attraction and 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.

Design Principles of Pancreatic Islets: Glucose-Dependent Coordination of Hormone Pulses.

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.

Effect of dipolar interaction in molecular crystals.

In this paper we investigate the ground state and the nature of the transition from an orientational ordered phase at low temperature to the disordered state at high temperature in a molecular crystal. Our model is a Potts model which takes into account the exchange interaction J between nearest-neighbor molecules and a dipolar interaction between molecular axes in three dimensions. The dipolar interaction is characterized by two parameters: its amplitude D and the cutoff distance r(c). If the molecular axis at a lattice site has three orientations, say the x, y or z axes, then when D = 0, the system is equivalent to the 3-state Potts model: the transition to the disordered phase is known to be of first order. When D ≠ 0, the ground-state configuration is shown to be composed of two independent interpenetrating layered subsystems which form a sandwich whose periodicity depends on D and r(c). We show by extensive Monte Carlo simulation with a histogram method that the phase transition remains of first order at relatively large values of r(c).

Phase transition in dimer liquids.

We study the phase transition in a system composed of dimers interacting with each other via a nearest-neighbor (NN) exchange J and competing interactions taken from a truncated dipolar coupling. Each dimer occupies a link between two nearest sites of a simple cubic lattice. We suppose that dimers are self-avoiding and can have only three orientations, which coincide with the x, y or z direction. The interaction J is attractive if the two dimers are parallel to each other at the NN distance, zero otherwise. The truncated dipolar interaction is characterized by two parameters: its amplitude D and the cutoff distance rc. Using the steepest descent method, we determine the ground-state (GS) configuration as functions of D and rc. We then use Monte Carlo simulations to investigate the nature of the low-temperature phase and to determine characteristics of the phase transition from the ordered phase to the disordered phase at high temperatures at a given dimer concentration. We show that as the temperature increases, dimers remain in the compact state and the transition from the low-T compact phase to the disordered phase where dimers occupy the whole space is of second order when D is small, but becomes of first order for large enough D, for both polarized and nonpolarized dimers. This transition has a resemblance to the unfolding polymer transition. The effect of rc is discussed.

Minimal perceptrons for memorizing complex patterns

Feedforward neural networks have been investigated to understand learning and memory, as well as applied to numerous practical problems in pattern classification. It is a rule of thumb that more complex tasks require larger networks. However, the design of optimal network architectures for specific tasks is still an unsolved fundamental problem. In this study, we consider three-layered neural networks for memorizing binary patterns. We developed a new complexity measure of binary patterns, and estimated the minimal network size for memorizing them as a function of their complexity. We formulated the minimal network size for regular, random, and complex patterns. In particular, the minimal size for complex patterns, which are neither ordered nor disordered, was predicted by measuring their Hamming distances from known ordered patterns. Our predictions agree with simulations based on the back-propagation algorithm.

Theory and Simulation of Magnetic Materials: Physics at Phase Frontiers

The combination of theory and simulation is necessary in the investigation of properties of complex systems where each method alone cannot do the task properly. Theory needs simulation to test ideas and to check approximations. Simulation needs theory for modeling and for understanding results coming out from computers. In this review, we give recent examples to illustrate this necessary combination in a few domains of interest such as frustrated spin systems, surface magnetism, spin transport and melting. Frustrated spin systems have been intensively studied for more than 30 years. Surface effects in magnetic materials have been widely investigated also in the last three decades. These fields are closely related to each other and their spectacular development is due to numerous applications. We confine ourselves to theoretical developments and numerical simulations on these subjects with emphasis on spectacular effects occurring at frontiers of different phases.