Summary Skeletal stem cells regulate bone growth and homeostasis by generating diverse cell types including chondrocytes, osteoblasts and marrow stromal cells. The emerging model postulates a distinct type of skeletal stem cells closely associated with the growth plate 1 - 4 , a special cartilaginous tissue playing critical roles in bone elongation 5 . The resting zone maintains the growth plate by expressing parathyroid hormone-related protein (PTHrP) that interacts with Indian hedgehog (Ihh) released from the hypertrophic zone 6 - 10 , while providing a source of other chondrocytes 11 . However, the identity of skeletal stem cells and how they are maintained in the growth plate are unknown. Here we show that skeletal stem cells are formed among PTHrP + chondrocytes within the resting zone of the postnatal growth plate. PTHrP + chondrocytes expressed a panel of markers for skeletal stem/progenitor cells and uniquely possessed the properties as skeletal stem cells in cultured conditions. Cell lineage analysis revealed that PTHrP + resting chondrocytes continued to form columnar chondrocytes long term, which underwent hypertrophy and became osteoblasts and marrow stromal cells beneath the growth plate. Transit-amplifying chondrocytes in the proliferating zone, which was concertedly maintained by a forward signal from undifferentiated cells (PTHrP) and a reverse signal from hypertrophic cells (Ihh), provided instructive cues to maintain cell fates of PTHrP + resting chondrocytes. Our findings unravel a unique somatic stem cell type that is initially unipotent and acquires multipotency at the post-mitotic stage, underscoring the malleable nature of the skeletal cell lineage. This system provides a model in which functionally dedicated stem cells and their niche are specified postnatally and maintained throughout tissue growth by a tight feedback regulation system.

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The representations of a compound, called "descriptors" or "features", play an essential role in constructing a machine-learning model of its physical properties. In this study, we adopt a procedure for generating a systematic set of descriptors from simple elemental and structural representations. First it is applied to a large dataset composed of the cohesive energy for about 18000 compounds computed by density functional theory (DFT) calculation. As a result, we obtain a kernel ridge prediction model with a prediction error of 0.041 eV/atom, which is close to the "chemical accuracy" of 1 kcal/mol (0.043 eV/atom). The procedure is also applied to two smaller datasets, i.e., a dataset of the lattice thermal conductivity (LTC) for 110 compounds computed by DFT calculation and a dataset of the experimental melting temperature for 248 compounds. We examine the performance of the descriptor sets on the efficiency of Bayesian optimization in addition to the accuracy of the kernel ridge regression models. They exhibit good predictive performances.

We propose a simple scheme to estimate the potential energy surface (PES) for which the accuracy can be easily controlled and improved. It is based on model selection within the framework of linear regression using the least absolute shrinkage and selection operator (LASSO) technique. Basis functions are selected from a systematic large set of candidate functions. The sparsity of the PES significantly reduces the computational cost of evaluating the energy and force in molecular dynamics simulations without losing accuracy. The usefulness of the scheme for describing the elemental metals Na and Mg is clearly demonstrated.PACS numbers: 31.50. Bc,71.15.Pd

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