[Abstract unavailable

The scaling law between the radius of gyration and the length of a polymer chain has long been an interesting topic since the Flory theory. In this article, we seek to derive a unified formula for the scaling exponent of proteins under different solvent conditions. The formula is obtained by considering the balance between the excluded volume effect and elastic interactions among monomers. Our results show that the scaling exponent is closely related to the fractal dimension of a protein's structure at the equilibrium state. Applying this formula to natural proteins yields a 2/5 law with fractal dimension 2 at the native state, which is in good agreement with other studies based on Protein Data Bank analysis. We also study the dependence of the scaling exponent on the hydrophobicity of a protein chain through a simple two-letters HP model. The results provides a way to estimate the globular structure of a protein, and could be helpful for the investigation of the mechanisms of protein folding. Figure 2. Log-log plot of the radius of gyration vs. chain length for proteins with different folded types. (a) all-␣ proteins, (b) all-␤ proteins, (c) ␣/␤ proteins, (d) unstructured proteins. There are 3080 all-␣ proteins (single ␣ structures are excluded), 334 all-␤ proteins, and 25804 ␣/␤ proteins, with more than 50% amino acids in secondary structures. And there are 839 intrinsically unstructured proteins with less than 20% amino acids in secondary structures. The data are fitted by lines with slope 0.4026 ± 0.0036 for all-␣ proteins, 0.3838 ± 0.0075 for all-␤ proteins, 0.4166 ± 0.0010 for ␣/␤ proteins, and 0.4037 ± 0.

Chronic inflammation is a serious risk factor for cancer; however, the routes from inflammation to cancer are poorly understood. On the basis of the processes implicated by frequently mutated genes associated with inflammation and cancer in three organs (stomach, colon, and liver) extracted from the Gene Expression Omnibus, The Cancer Genome Atlas, and Gene Ontology databases, we present a multiscale model of the long-term evolutionary dynamics leading from inflammation to tumorigenesis. The model incorporates cross-talk among interactions on several scales, including responses to DNA damage, gene mutation, cell-cycle behavior, population dynamics, inflammation, and metabolism-immune balance. Model simulations revealed two stages of inflammation-induced tumorigenesis: a precancerous state and tumorigenesis. The precancerous state was mainly caused by mutations in the cell proliferation pathway; the transition from the precancerous to tumorigenic states was induced by mutations in pathways associated with apoptosis, differentiation, and metabolism-immune balance. We identified opposing effects of inflammation on tumorigenesis. Mild inflammation removed cells with DNA damage through DNA damage-induced cell death, whereas severe inflammation accelerated accumulation of mutations and hence promoted tumorigenesis. These results provide insight into the evolutionary dynamics of inflammation-induced tumorigenesis and highlight the combinatorial effects of inflammation and metabolism-immune balance. This approach establishes methods for quantifying cancer risk, for the discovery of driver pathways in inflammation-induced tumorigenesis, and has direct relevance for early detection and prevention and development of new treatment regimes. .

In this paper, the transitions of burst synchronization are explored in a neuronal network consisting of subnetworks. The studied network is composed of electrically coupled bursting Hindmarsh-Rose neurons. Numerical results show that two types of burst synchronization transitions can be induced not only by the variations of intra- and intercoupling strengths but also by changing the probability of random links between different subnetworks and the number of subnetworks. Furthermore, we find that the underlying mechanisms for these two bursting synchronization transitions are different: one is due to the change of spike numbers per burst, while the other is caused by the change of the bursting type. Considering that changes in the coupling strengths and neuronal connections are closely interlaced with brain plasticity, the presented results could have important implications for the role of the brain plasticity in some functional behavior that are associated with synchronization.

We study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise. The results established here are applied to examining the local stability of the hematopoietic stem cell (HSC) regulation system in the presence of noise. The stability of the first moment for the solutions of a linear differential delay equation under stochastic perturbation is identical to that of the unperturbed system. However, the stability of the second moment is altered by the perturbation. We obtain, using Laplace transform techniques, necessary and sufficient conditions for the second moment to be bounded. In applying the results to the HSC system, we find that the system stability is sensitive to perturbations in the stem cell differentiation and death rates, but insensitive to perturbations in the proliferation rate.