Computational approaches for simulating luminogenesis.

Lumens, liquid-filled cavities surrounded by polarized tissue cells, are elementary units involved in the morphogenesis of organs. Theoretical modeling and computations, which can integrate various factors involved in biophysics of morphogenesis of cell assembly and lumens, may play significant roles to elucidate the mechanisms in formation of such complex tissue with lumens. However, up to present, it has not been documented well what computational approaches or frameworks can be applied for this purpose and how we can choose the appropriate approach for each problem. In this review, we report some typical lumen morphologies and basic mechanisms for the development of lumens, focusing on three keywords - mechanics, hydraulics and geometry - while outlining pros and cons of the current main computational strategies. We also describe brief guidance of readouts, i.e., what we should measure in experiments to make the comparison with the model's assumptions and predictions.

Dynamic behavior of elevators under random inflow of passengers.

Elevators can be regarded as oscillators driven by the calls of passengers who arrive randomly. We study the dynamic behavior of elevators during the down peak period numerically and analytically. We assume that new passengers arrive at each floor according to a Poisson process and call the elevators to go down to the ground floor. We numerically examine how the round-trip time of a single elevator depends on the inflow rate of passengers at each floor and reproduce it by a self-consistent equation considering the combination of floors where the call occurs. By setting an order parameter, we show that the synchronization of two elevators occurs irrespective of final destination (whether the elevators did or did not go to the top floor). It indicates that the spontaneous ordering of elevators emerges from the Poisson noise. We also reproduce the round-trip time of two elevators by a self-consistent equation considering the interaction through the existence of passengers and the absence of volume exclusion. Those results suggest that such interaction stabilizes and characterizes the spontaneous ordering of elevators.

Gliding filament system giving both global orientational order and clusters in collective motion.

Emergence and collapse of coherent motions of self-propelled particles are affected more by particle motions and interactions than by their material or biological details. In the reconstructed systems of biofilaments and molecular motors, several types of collective motion including a global-order pattern emerge due to the alignment interaction. Meanwhile, earlier studies show that the alignment interaction of a binary collision of biofilaments is too weak to form the global order. The multiple collision is revealed to be important to achieve global order, but it is still unclear what kind of multifilament collision is actually involved. In this study, we demonstrate that not only alignment but also crossing of two filaments is essential to produce an effective multiple-particle interaction and the global order. We design the reconstructed system of biofilaments and molecular motors to vary a probability of the crossing of biofilaments on a collision and thus control the effect of volume exclusion. In this system, biofilaments glide along their polar strands on the turf of molecular motors and can align themselves nematically when they collide with each other. Our experiments show the counterintuitive result, in which the global order is achieved only when the crossing is allowed. When the crossing is prohibited, the cluster pattern emerges instead. We also investigate the numerical model in which we can change the strength of the volume exclusion effect and find that the global orientational order and clusters emerge with weak and strong volume exclusion effects, respectively. With those results and simple theory, we conclude that not only alignment but also finite crossing probability are necessary for the effective multiple-particles interaction forming the global order. Additionally, we describe the chiral symmetry breaking of a microtubule motion which causes a rotation of global alignment.