Conventional nanozyme technologies face formidable challenges of intricate size-, composition-, and facet-dependent catalysis and inherently low active site density. We discovered a new class of single-atom nanozymes with atomically dispersed enzyme-like active sites in nanomaterials, which significantly enhanced catalytic performance, and uncovered the underlying mechanism. With oxidase catalysis as a model reaction, experimental studies and theoretical calculations revealed that single-atom nanozymes with carbon nanoframe–confined FeN₅ active centers (FeN₅ SA/CNF) catalytically behaved like the axial ligand–coordinated heme of cytochrome P450. The definite active moieties and crucial synergistic effects endow FeN₅ SA/CNF with a clear electron push-effect mechanism, as well as the highest oxidase-like activity among other nanozymes (the rate constant is 70 times higher than that of commercial Pt/C) and versatile antibacterial applications. These suggest that the single-atom nanozymes have great potential to become the next-generation nanozymes.

We developed a theoretical framework to prove the existence and quantify the Waddington landscape as well as chreode-biological paths for development and differentiation. The cells can have states with the higher probability ones giving the different cell types. Different cell types correspond to different basins of attractions of the probability landscape. We study how the cells develop from undifferentiated cells to differentiated cells from landscape perspectives. We quantified the Waddington landscape through construction of underlying probability landscape for cell development. We show the developmental process proceeds as moving from undifferentiated to the differentiated basins of attractions. The barrier height of the basins of attractions correlates with the escape time that determines the stability of cell types. We show that the developmental process can be quantitatively described and uncovered by the biological paths on the quantified Waddington landscape from undifferentiated to the differentiated cells. We found the dynamics of the developmental process is controlled by a combination of the gradient and curl force on the landscape. The biological paths often do not follow the steepest descent path on the landscape. The landscape framework also quantifies the possibility of reverse differentiation process such as cell reprogramming from differentiated cells back to the original stem cell. We show that the biological path of reverse differentiation is irreversible and different from the one for differentiation process. We found that the developmental process described by the underlying landscape and the associated biological paths is relatively stable and robust against the influences of environmental perturbations.

We established a theoretical framework for studying nonequilibrium networks with two distinct natures essential for characterizing the global probabilistic dynamics: the underlying potential landscape and the corresponding curl flux. We applied the idea to a biochemical oscillation network and found that the underlying potential landscape for the oscillation limit cycle has a distinct closed ring valley (Mexican hat-like) shape when the fluctuations are small. This global landscape structure leads to attractions of the system to the ring valley. On the ring, we found that the nonequilibrium flux is the driving force for oscillations. Therefore, both structured landscape and flux are needed to guarantee a robust oscillating network. The barrier height separating the oscillation ring and other areas derived from the landscape topography is shown to be correlated with the escaping time from the limit cycle attractor and provides a quantitative measure of the robustness for the network. The landscape becomes shallower and the closed ring valley shape structure becomes weaker (lower barrier height) with larger fluctuations. We observe that the period and the amplitude of the oscillations are more dispersed and oscillations become less coherent when the fluctuations increase. We also found that the entropy production of the whole network, characterizing the dissipation costs from the combined effects of both landscapes and fluxes, decreases when the fluctuations decrease. Therefore, less dissipation leads to more robust networks. Our approach is quite general and applicable to other networks, dynamical systems, and biological evolution. It can help in designing robust networks.

Non-alcoholic fatty liver disease (NAFLD) is the most prevalent chronic liver disease, affecting approximately one-quarter of the global population, and has become a world public health issue. NAFLD is a clinicopathological syndrome characterized by hepatic steatosis, excluding ethanol and other definite liver damage factors. Recent studies have shown that the development of NAFLD is associated with lipid accumulation, oxidative stress, endoplasmic reticulum stress, and lipotoxicity. A range of natural products have been reported as regulators of NAFLD in vivo and in vitro. This paper reviews the pathogenesis of NAFLD and some natural products that have been shown to have therapeutic effects on NAFLD. Our work shows that natural products can be a potential therapeutic option for NAFLD.

We present a review of the recently developed landscape and flux theory for non-equilibrium dynamical systems. We point out that the global natures of the associated dynamics for non-equilibrium system are determined by two key factors: the underlying landscape and, importantly, a curl probability flux. The landscape (U) reflects the probability of states (P) ( ) and provides a global characterization and a stability measure of the system. The curl flux term measures how much detailed balance is broken and is one of the two main driving forces for the non-equilibrium dynamics in addition to the landscape gradient. Equilibrium dynamics resembles electron motion in an electric field, while non-equilibrium dynamics resembles electron motion in both electric and magnetic fields. The landscape and flux theory has many interesting consequences including (1) the fact that irreversible kinetic paths do not necessarily pass through the landscape saddles; (2) non-equilibrium transition state theory at the new saddle on the optimal paths for small but finite fluctuations; (3) a generalized fluctuation–dissipation relationship for non-equilibrium dynamical systems where the response function is not just equal to the fluctuations at the steady state alone as in the equilibrium case but there is an additional contribution from the curl flux in maintaining the steady state; (4) non-equilibrium thermodynamics where the free energy change is not just equal to the entropy production alone, as in the equilibrium case, but also there is an additional house-keeping contribution from the non-zero curl flux in maintaining the steady state; (5) gauge theory and a geometrical connection where the flux is found to be the origin of the gauge field curvature and the topological phase in analogy to the Berry phase in quantum mechanics; (6) coupled landscapes where non-adiabaticity of multiple landscapes in non-equilibrium dynamics can be analyzed using the landscape and flux theory and an eddy current emerges from the non-zero curl flux; (7) stochastic spatial dynamics where landscape and flux theory can be generalized for non-equilibrium field theory. We provide concrete examples of biological systems to demonstrate the new insights from the landscape and flux theory. These include models of (1) the cell cycle where the landscape attracts the system down to an oscillation attractor while the flux drives the coherent motion on the oscillation ring, the different phases of the cell cycle are identified as local basins on the cycle path and biological checkpoints are identified as local barriers or transition states between the local basins on the cell-cycle path; (2) stem cell differentiation where the Waddington landscape for development as well as the differentiation and reprogramming paths can be quantified; (3) cancer biology where cancer can be described as a disease of having multiple cellular states and the cancer state as well as the normal state can be quantified as basins of attractions on the underlying landscape while the transitions between normal and cancer states can be quantified as the transitions between the two attractors; (4) evolution where more general evolution dynamics beyond Wright and Fisher can be quantified using the specific example of allele frequency-dependent selection; (5) ecology where the landscape and flux as well as the global stability of predator–prey, cooperation and competition are quantified; (6) neural networks where general asymmetrical connections are considered for learning and memory, gene self-regulators where non-adiabatic dynamics of gene expression can be described with the landscape and flux in expanded dimensions and analytically treated; (7) chaotic strange attractor where the flux is crucial for the chaotic dynamics; (8) development in space where spatial landscape can be used to describe the process and pattern formation. We also give the philosophical implications of the theory and the outlook for future studies.