A model about regulation on three division modes of stem cell.

We construct a multi-stage cell lineage model for cell division, apoptosis and movement. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the stem cell divisions (including self-renewal, asymmetrical cell division (ACD) and differentiation). The densities of cells and molecules are described by coupled reaction-diffusion partial differential equations, and the plane wavefront propagation speeds can be obtained analytically and verified numerically. It is found that with ACD the population and propagation of stem cells can be promoted but the negative regulation on self-renewal and differentiation will work slowly. Regulatory inhibition on differentiation will inversely increase stem cells but not affect the population and wave propagation of the cell lineage. While negative regulation on self-renewal and ACD will decrease the population of stem cells and slow down the propagation, and even drive stem cells to extinction. Moreover we find that inhibition on self-renewal has a strength advantage while inhibition on ACD has a range advantage to kill stem cells. Possible relations to model cancer development and therapy are also discussed.

A cell model about symmetric and asymmetric stem cell division.

We construct a multi-stage cell lineage model including self-renewal, apoptosis, cell movement and the symmetrical/asymmetrical division of stem cells. The evolution of cell populations can be described by coupled reaction-diffusion partial differential equations, and the propagating wavefront speeds can be obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effect of symmetric/asymmetric division of stem cells on the population and propagating dynamics of cell lineage. It is found that stem cells' asymmetric cell division (ACD) can move the phase boundary of the homogenous solution of the system. The population of the cell lineage will be promoted in presence of ACD. The concentration of stem cells increases with ACD but that of differentiated daughter cells decreases with ACD. In addition, it is found that the propagating speed of the stem cells can be evaluated with ACD. When the daughter cells move fast to a new space, stem cells can catch them up through increasing ACD. Our results may suggest a mechanism of collective migration of cell lineage through cooperation between ACD of stem cells and fast diffusion of the daughter cells.

The Construction of Ecosystem and Collaboration Platform for Enterprise Open Innovation.

In the era of the knowledge economy that is filled with intense competition, formal closed innovation can no longer meet the market demand. The enterprise needs to implement open innovation involving external resources. The concept of open innovation emphasizes both the use of internal and external resources in the process of enterprise innovation and the use of internal and external markets to promote the commercial application of innovation achievements. With the rapid development of Internet technology, enterprises must build an open innovation ecosystem of benefits-sharing, identify, connect, and utilize external innovation resources, and be committed to creating an open innovation ecosystem without organizational boundaries. Enterprises should pay attention to coordinating the relationships among the innovation ecosystem members, eliminating heterogeneous barriers between enterprises and their partners, and enhancing their cooperative innovation ability with external organizations. It is also necessary to build a collaborative innovation platform convenient for the release and acquisition of innovation information, the collection of customer needs and related ideas, and the full use of external resources for innovation. In particular, it is necessary to guide users and related resources to the innovation platform, realize the maximum effect of resource aggregation, and promote customer demand-oriented new product development. Through building an open innovation ecosystem and a collaboration platform, it is helpful for enterprises to seek all kinds of technical and resource support, enhance their ability of independent innovation, promote the emergence of many innovative achievements, and realize value co-creation and win-win cooperation with partners.

Reorganization of the topological surface mode of topological insulating α-Sn.

α-Sn is a topologically nontrivial semimetal in its natural structure. Upon compressively strained in plane, it transforms into a topological insulator. But, up to now, a clear and systematic understanding of the topological surface mode of topological insulating α-Sn is still lacking. In the present work, first-principle simulations are employed to investigate the electronic structure evolution of Ge1-xSnxalloys aiming at understanding the band reordering, topological phase transition and topological surface mode of α-Sn in detail. Progressing from Ge to Sn with increasing Sn content in Ge1-xSnx, the conduction band inverts with the first valence band (VB) and then with the second VB sequentially, rather than inverting with the latter directly. Correspondingly, a topologically nontrivial surface mode arises in the first inverted band gap. Meanwhile, a fragile Dirac cone appears in the second inverted band gap as a result of the reorganization of the topological surface mode caused by the first VB. The reorganization of the topological surface mode in α-Sn is very similar to the HgTe case. The findings of the present work are helpful for understanding and utilizing of the topological surface mode of α-Sn.

Regulatory feedback effects on tissue growth dynamics in a two-stage cell lineage model.

Identifying the mechanism of intercellular feedback regulation is critical for the basic understanding of tissue growth control in organisms. In this paper, we analyze a tissue growth model consisting of a single lineage of two cell types regulated by negative feedback signaling molecules that undergo spatial diffusion. By deriving the fixed points for the uniform steady states and carrying out linear stability analysis, phase diagrams are obtained analytically for arbitrary parameters of the model. Two different generic growth modes are found: blow-up growth and final-state controlled growth which are governed by the nontrivial fixed point and the trivial fixed point, respectively, and can be sensitively switched by varying the negative feedback regulation on the proliferation of the stem cells. Analytic expressions for the characteristic timescales for these two growth modes are also derived. Remarkably, the trivial and nontrivial uniform steady states can coexist and a sharp transition occurs in the bistable regime as the relevant parameters are varied. Furthermore, the bistable growth properties allows for the external control to switch between these two growth modes. In addition, the condition for an early accelerated growth followed by a retarded growth can be derived. These analytical results are further verified by numerical simulations and provide insights on the growth behavior of the tissue. Our results are also discussed in the light of possible realistic biological experiments and tissue growth control strategy. Furthermore, by external feedback control of the concentration of regulatory molecules, it is possible to achieve a desired growth mode, as demonstrated with an analysis of boosted growth, catch-up growth and the design for the target of a linear growth dynamic.

Keep, break and breakout in food chains with two and three species.

In this paper, through Rosenzweig-MacArthur predator-prey model we study the cyclic coexistence and stationary coexistence and discuss temporal keep and break in the food chain with two species. Then species' diffusion is considered and its effect on oscillation and stability of the ODE system is studied concerning the two different states of coexistence. We find in cyclic coexistence temporal oscillation of population is translated into spatial oscillation although there is fluctuation at the beginning of population waves and finally more stable population evolution is observed. Furthermore, the presence of spatial diffusion of the species can lead to steady wavefront propagation and alter the population distribution in the food chain with two and three species. We show that lower-level species with slow propagation will limit higher-level species and help to keep food chain in space, but through fast propagation lower-level species can survive in a new space without predation and realize a breakout in the linear food chain.

General two-species interacting Lotka-Volterra system: Population dynamics and wave propagation.

The population dynamics of two interacting species modeled by the Lotka-Volterra (LV) model with general parameters that can promote or suppress the other species is studied. It is found that the properties of the two species' isoclines determine the interaction of species, leading to six regimes in the phase diagram of interspecies interaction; i.e., there are six different interspecific relationships described by the LV model. Four regimes allow for nontrivial species coexistence, among which it is found that three of them are stable, namely, weak competition, mutualism, and predator-prey scenarios can lead to win-win coexistence situations. The Lyapunov function for general nontrivial two-species coexistence is also constructed. Furthermore, in the presence of spatial diffusion of the species, the dynamics can lead to steady wavefront propagation and can alter the population map. Propagating wavefront solutions in one dimension are investigated analytically and by numerical solutions. The steady wavefront speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. In addition to the inter- and intraspecific interaction parameters, the intrinsic speed parameters of each species play a decisive role in species populations and wave properties. In some regimes, both species can copropagate with the same wave speeds in a finite range of parameters. Our results are further discussed in the light of possible biological relevance and ecological implications.

Regulatory effects on the population dynamics and wave propagation in a cell lineage model.

We consider the interplay of cell proliferation, cell differentiation (and de-differentiation), cell movement, and the effect of feedback regulations on the population and propagation dynamics of different cell types in a cell lineage model. Cells are assumed to secrete and respond to negative feedback molecules which act as a control on the cell lineage. The cell densities are described by coupled reaction-diffusion partial differential equations, and the propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. In particular, wavefront propagation speeds are obtained analytically and verified by numerical solutions of the equations. The emphasis is on the effects of the feedback regulations on different stages in the cell lineage. It is found that when the progenitor cell is negatively regulated, the populations of the cell lineage are strongly down-regulated with the steady growth rate of the progenitor cell being driven to zero beyond a critical regulatory strength. An analytic expression for the critical regulation strength in terms of the model parameters is derived and verified by numerical solutions. On the other hand, if the inhibition is acting on the differentiated cells, the change in the population dynamics and wave propagation speed is small. In addition, it is found that only the propagating speed of the progenitor cells is affected by the regulation when the diffusion of the differentiated cells is large. In the presence of de-differentiation, the effect on down-regulating the progenitor population is weakened and there is no effect on the propagation speed due to regulation, suggesting that the effect of regulatory control is diminished by de-differentiation pathways.

Model on cell movement, growth, differentiation and de-differentiation: reaction-diffusion equation and wave propagation.

We construct a model for cell proliferation with differentiation into different cell types, allowing backward de-differentiation and cell movement. With different cell types labeled by state variables, the model can be formulated in terms of the associated transition probabilities between various states. The cell population densities can be described by coupled reaction-diffusion partial differential equations, allowing steady wavefront propagation solutions. The wavefront profile is calculated analytically for the simple pure growth case (2-states), and analytic expressions for the steady wavefront propagating speeds and population growth rates are obtained for the simpler cases of 2-, 3- and 4-states systems. These analytic results are verified by direct numerical solutions of the reaction-diffusion PDEs. Furthermore, in the absence of de-differentiation, it is found that, as the mobility and/or self-proliferation rate of the down-lineage descendant cells become sufficiently large, the propagation dynamics can switch from a steady propagating wavefront to the interesting situation of propagation of a faster wavefront with a slower waveback. For the case of a non-vanishing de-differentiation probability, the cell growth rate and wavefront propagation speed are both enhanced, and the wavefront speeds can be obtained analytically and confirmed by numerical solution of the reaction-diffusion equations.

Effect of coil-globule transition on the single-chain crystallization.

The folding process of a single chain including coil-globule transition and crystallization has been investigated through dynamic Monte Carlo simulations. The results based upon ensemble averaging illustrated three distinct states: coil, molten globule, and globule states. Furthermore, the crystallization process from these collapsed states demonstrated various characteristics and it also verified the thermodynamic partitions. The isothermal crystallization in the three states showed the folding rates, and the final crystallite morphologies strongly depended on the collapsed states. Especially, the onset temperature of crystallization in the intermediate molten globule state demonstrated the strongest sensitivity to the solvent qualities in the three different states. Moreover, the crystallization in this intermediate state illustrated a two-step folding mechanism with the prior dense core serving as a precursor to induce the subsequent crystallization. Our observations would help in understanding the thermodynamics and kinetics of phase transition of a single macromolecule. Possible relations to the protein folding were also discussed.

Population dynamics and wave propagation in a Lotka-Volterra system with spatial diffusion.

We consider the competitive population dynamics of two species described by the Lotka-Volterra model in the presence of spatial diffusion. The model is described by the diffusion coefficient (d(α)) and proliferation rate (r(α)) of the species α (α = 1,2 is the species label). Propagating wave front solutions in one dimension are investigated analytically and by numerical solutions. It is found that the wave profiles and wave speeds are determined by the speed parameters, v(α) ≡ 2 sqrt [d(α)r(α)], of the two species, and the phase diagrams for various inter- and intracompetitive scenarios are determined. The steady wave front speeds are obtained analytically via nonlinear dynamics analysis and verified by numerical solutions. The effect of the intermediate stationary state is investigated and propagating wave profiles beyond the simple Fisher wave fronts are revealed. The wave front speed of a species can display abrupt increase as its speed parameter is increased. In particular for the case in which both species are aggressive, our results show that the speed parameter is the deciding factor that determines the ultimate surviving species, in contrast to the case without diffusion in which the final surviving species is decided by its initial population advantage. Possible relations to the biological relevance of modeling cancer development and wound healing are also discussed.

Hierarchical orientational relaxation inducing shish-kebab formations in polymer melt crystallization.

We studied athermal relaxation of bulk extended chains by means of dynamic Monte Carlo simulations, and we got intermediately relaxed melts with a memory of chain orientations but no more crystalline order. The orientational memory in the melts dominated the crystal orientation and nucleation types. The difference in crystallization behaviors induced by orientational relaxation suggested the mechanism of hierarchical crystallization. Thus, we studied the isothermal crystallization of a binary blend of different relaxed chains. We observed the prior crystallization of less relaxed chains could act as a shish to induce epitaxial crystallization of more relaxed chains to form kebabs. This mechanism had demonstrated the structure of precursors and gave insight into the formation of shish-kebab crystals in polymer melts. The results suggested that in flow-induced polymer crystallization the hierarchical orientational relaxation of chains decided the formation of shish-kebabs.

Confined crystallization of cylindrical diblock copolymers studied by dynamic Monte Carlo simulations.

We report dynamic Monte Carlo simulations of polymer crystallization confined in the cylindrical microdomains of diblock copolymers. The microdomains were prepared via spontaneous microphase separation from homogeneous melt, and the major component was then frozen in a vitreous amorphous state to make a hard confinement to the crystallization of the minor component. We found that during the isothermal crystallization at high temperatures, crystal orientations are dominantly perpendicular to the cylinder axis at the early stage of crystal nucleation and remain to the final state; while if the block junctions are broken before crystallization, crystal orientations are dominantly parallel at the early stage of crystal nucleation, and eventually other orientations take the place of parallel preferences. Analysis of bond orientations in the heterogeneous melts demonstrates the microscopic origin of oriented crystal nucleation.