Protective effect of Peucedanum praeruptorum Dunn extract on oxidative damage of LLC­PK1 cells induced by H2O2.

Peucedanum praeruptorum Dunn extract (PPDE) is a well-known treatment used in traditional Chinese medicines, where it is most commonly used to treat coughs and symptoms such as headaches and fever. In the present study, the antioxidant capacity of PPDE in vitro was determined by scavenging experiments using DPPH, ABTS+·, ·OH, and ·O2-. The cell survival rate was determined by MTT assay. The MDA, SOD, CAT, GSH, and GSH-Px content were determined by colorimetry assays. The expression levels of antioxidant genes SOD, CAT, GSH, and GSH-Px were assessed by reverse transcription-quantitative PCR. HPLC was used to identify the PPDE components. The results suggested that PPDE had scavenging effects on DPPH, ABTS, hydroxyl, and superoxide anion radicals in a concentration-dependent manner; H2O2 treatment resulted in oxidative stress in LLC-PK1 cells, and the degree of injury of LLC-PK1 cells following PPDE treatment was improved, which was positively correlated with its concentration. Peucedanum praeruptorum Dunn extract treatment reduced the content of MDA and increased the content of CAT, SOD1, GSH, and GSH-Px. The mRNA expression levels of antioxidant genes detected by quantitative PCR were consistent with changes in CAT, SOD, GSS, and GSH-Px. Additionally, the trend in CAT, SOD1, GSH, and GSS protein expression levels was also consistent at the mRNA level. PPDE was found to consist of isochlorogenic acid C, myricetin, baicalin, luteolin, and kaempferol. Therefore, PPDE, which was formed of products derived from natural substances, functioned in the inhibition of oxidative damage. The present study aimed to obtain a better understanding of the traditional Chinese medicine Peucedanum praeruptorum Dunn and preliminarily elucidate its antioxidant mechanism at the cellular level. Further animal or human experiments are required to verify the antioxidant effects of PPDE for further development and utilization.

Competition between the catalyzed birth and death in the exchange-driven growth.

We propose a three-species ( A , B , and C ) exchange-driven aggregate growth model with competition between catalyzed birth and catalyzed death. In the system, exchange-driven aggregation occurs between any two aggregates of the same species with the size-dependent rate kernel Kn(k,j)=Knkj (n=1,2,3) , and, meanwhile, monomer birth and death of species A occur under the catalysis of species B and C with the catalyzed birth and catalyzed death rate kernels I(k,j)=Ikjv and J(k,j)=Jkjv , respectively. The kinetic behavior is investigated by means of the mean-field rate equation approach. The form of the aggregate size distribution ak(t) of species A is found to depend crucially on the competition between species- B -catalyzed birth of species A and species- C -catalyzed death of species A , as well as the exchange-driven growth. The results show that (i) when exchange-driven aggregation dominates the process, ak(t) satisfies the conventional scaling form; (ii) when catalyzed birth dominates the process, ak(t) takes the conventional or generalized scaling form; and (iii) when catalyzed death dominates the process, the aggregate size distribution of species A evolves only according to some modified scaling forms.

Mutually catalyzed birth of population and assets in exchange-driven growth.

We propose an exchange-driven aggregation growth model of population and assets with mutually catalyzed birth to study the interaction between the population and assets in their exchange-driven processes. In this model, monomer (or equivalently, individual) exchange occurs between any pair of aggregates of the same species (population or assets). The rate kernels of the exchanges of population and assets are K(k,l) = Kkl and L(k,l) = Lkl , respectively, at which one monomer migrates from an aggregate of size k to another of size l. Meanwhile, an aggregate of one species can yield a new monomer by the catalysis of an arbitrary aggregate of the other species. The rate kernel of asset-catalyzed population birth is I(k,l) = Iklmu [and that of population-catalyzed asset birth is J(k,l) = Jklnu], at which an aggregate of size k gains a monomer birth when it meets a catalyst aggregate of size l . The kinetic behaviors of the population and asset aggregates are solved based on the rate equations. The evolution of the aggregate size distributions of population and assets is found to fall into one of three categories for different parameters mu and nu: (i) population (asset) aggregates evolve according to the conventional scaling form in the case of mu < or = 0 (nu < or = 0), (ii) population (asset) aggregates evolve according to a modified scaling form in the case of nu = 0 and mu > 0 (mu = 0 and nu > 0 ), and (iii) both population and asset aggregates undergo gelation transitions at a finite time in the case of mu = nu > 0.

Kinetics of migration-driven aggregation processes on scale-free networks.

We propose a solvable model for the migration-driven aggregate growth on completely connected scale-free networks. A reversible migration system is considered with the produce rate kernel K(k;l|i;j) approximately k(u)i(upsilon)(lj)(nu) or the generalized kernel K(k;l|i;j) approximately (k(upsilon)i(omega)+k(omega)i(upsilon)(lj)(nu), at which an i-mer aggregate locating on the node with j links gains one monomer from a k-mer aggregate locating on the node with l links. It is found that the evolution behavior of the system depends crucially on the details of the rate kernel. In some cases, the aggregate size distribution approaches a scaling form and the typical size S(t,l) of the aggregates locating on the nodes with l links grows infinitely with time; while in other cases, a gelation transition may emerge in the system at a finite critical time. We also introduce a simplified model, in which the aggregates independently gain or lose one monomer at the rate I(1)(k;l)=I(2)(k;l) proportional to k(omega)l(nu), and find the similar results. Most intriguingly, these models exhibit that the evolution behavior of the total distribution of the aggregates with the same size is drastically different from that for the corresponding system in normal space. We test our analytical results with the population data of all counties in the U.S. during the past century and find good agreement between the theoretical predictions and the realistic data.

Scale-free multicomponent growing networks.

We propose a multicomponent growing network model which consists of many types of nodes as well as links only between the nodes of different types. Such a multicomponent network is constructed by (i) introducing a new node of one type and immediately linking it to a preexisting node of the other type, and (ii) creating a new link between two nodes of different types. We then investigate the connectivity of the multicomponent growing networks by means of the rate equations. For a network system with shifted or asymptotically linear connection rate kernels, the degree distributions take scale-free power-law forms, while a random growing network has exponential degree distributions.

Solvable n-species aggregation processes with joint annihilation.

We study the kinetic behavior of the aggregation-annihilation processes of an n-species (n> or =3) system, in which an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible complete annihilation reaction occurs only between one certain A(n) species and each of the other A(m) species (m=1,2,...n-1). Based on the mean-field theory, we investigate the rate equations of the processes to obtain the asymptotic solutions of the cluster-mass distributions in several different cases. The results show that the evolution behavior of the system depends crucially on the ratios of the equivalent aggregation rate of A(m) species and the aggregation rate of A(n) species to the annihilation rate. The cluster-mass distribution of each species always obeys a conventional scaling law or a modified one, and the scaling exponents depend only on the reaction rates for most cases. However, when both the equivalent aggregation rate of A(m) species and the aggregation rate of A(n) species are twice as large as the annihilation rate, the scaling exponents depend on the reaction rates as well as the initial concentrations.

Kinetics of the catalysis-driven aggregation processes.

We study a catalysis-driven aggregation model in which irreversible growth of A aggregates occurs only with the help of the catalyst. The results show that kinetics of the system depends strongly on whether the catalyst coagulates by itself or not. The mass distribution of A clusters obeys a conventional scaling law in the case without self-coagulation of the catalyst, while for the reverse case the evolution of the system falls in a peculiar scaling regime. Our theory applies to diverse phenomena such as the cluster-size distribution in a chemical system.

Kinetics of migration-driven aggregation processes.

We study the kinetic behavior of the growth of aggregates driven by reversible migration between any two aggregates. For the simple system with the migration rate kernel K(k;j)=K(')(k;j) proportional, variant kj(upsilon) at which the monomers migrate between the aggregates of size k and those of size j, we find that for the upsilon< or =2 case the evolution of the system always obeys a scaling law. Moreover, the typical aggregate size grows as exp(2IA(0)t) in the case of upsilon=2 and as t(1/(2-upsilon)) in the case of -1

Kinetic behavior of aggregation processes with complete annihilation.

The kinetic behavior of an aggregation-annihilation process of an n-species (n> or =2) system is studied. In this model, an irreversible aggregation reaction occurs between any two clusters of the same species and an irreversible complete annihilation reaction occurs between any two different species. Based on the mean-field theory, we investigate the rate equations of the process with constant reaction rates to obtain the asymptotic solutions for the cluster-mass distributions. We find that the cluster-mass distribution of each species satisfies a modified scaling law, which reduces to the standard scaling law in some special cases. The scaling exponents of the system may strongly depend on the reaction rates for most cases; however, for the case with all the aggregation rates twice the annihilation rate, these exponents depend only on the initial concentrations. All the species annihilate each other completely except in the case in which at least one aggregation rate is less than twice the annihilation rate.

Kinetics of a migration-driven aggregation process with birth and death.

We propose an irreversible aggregation model driven by migration and birth-death processes with the symmetric migration rate kernel K(k;j)=K'(k;j)=Ikj(upsilon), and the birth rate J(1)k and death rate J(2)k proportional to the aggregate's size k. Based on the mean-field theory, we investigate the evolution behavior of the system through developing the scaling theory. The total mass M1 is reserved in the J(1)=J(2) case and increases exponentially with time in the J1>J2 case. In these cases, the long-time asymptotic behavior of the aggregate size distribution a(k)(t) always obeys the scaling law for the upsilon

Solvable aggregation model with monomer annihilation.

We propose a simple model in which irreversible aggregations occur between any two clusters of the same species and monomer annihilations occur between any two clusters of different species. We investigate the mean-field rate equation to analyze kinetics of the system under symmetrical initial conditions. In the constant-reaction-rate case, the cluster-mass distribution of either species approaches a conventional scaling form and both species survive finally; while for the system with a fast rate kernel, both species scale according to a modified form and no species can survive at the end.

Study on properties of residue-residue contacts in protein.

Residue-residue contacts are very important in forming protein structure. In this work, we calculated the average probability of residue-residue contacts in 470 globular proteins and analyzed the distribution of contacts in the different interval of residues using Contacts of Structural Units (CSU) and Structural Classification (SCOP) software. It was found that the relationship between the average probability PL and the residue distance L for four structural classes of proteins could be expressed as lgPL=a+b x L, where a and b are coefficients. We also discussed the connection between two aspects of proteins which have equal array residue number and found that the distribution probability was stable (or un-stable) if the proteins had the same (or different) compact (for example synthase) in the same structural class.

Instability in evolutionary games.

BACKGROUND: Phenomena of instability are widely observed in many dissimilar systems, with punctuated equilibrium in biological evolution and economic crises being noticeable examples. Recent studies suggested that such instabilities, quantified by the abrupt changes of the composition of individuals, could result within the framework of a collection of individuals interacting through the prisoner's dilemma and incorporating three mechanisms: (i) imitation and mutation, (ii) preferred selection on successful individuals, and (iii) networking effects. METHODOLOGY/PRINCIPAL FINDINGS: We study the importance of each mechanism using simplified models. The models are studied numerically and analytically via rate equations and mean-field approximation. It is shown that imitation and mutation alone can lead to the instability on the number of cooperators, and preferred selection modifies the instability in an asymmetric way. The co-evolution of network topology and game dynamics is not necessary to the occurrence of instability and the network topology is found to have almost no impact on instability if new links are added in a global manner. The results are valid in both the contexts of the snowdrift game and prisoner's dilemma. CONCLUSIONS/SIGNIFICANCE: The imitation and mutation mechanism, which gives a heterogeneous rate of change in the system's composition, is the dominating reason of the instability on the number of cooperators. The effects of payoffs and network topology are relatively insignificant. Our work refines the understanding on the driving forces of system instability.

Cooperative behavior in evolutionary snowdrift games with the unconditional imitation rule on regular lattices.

We study an evolutionary snowdrift game with the unconditional imitation updating rule on regular lattices. Detailed numerical simulations establish the structure of plateaus and discontinuous jumps of the equilibrium cooperation frequency f(c) as a function of the cost-to-benefit ratio r. By analyzing the stability of local configurations, it is found that the transitions occur at values of r at which there are changes in the ranking of the payoffs to the different local configurations of agents using different strategies. Nonmonotonic behavior of f(c)(r) at the intermediate range of r is analyzed in terms of the formation of blocks of agents using the cooperative strategy that are stabilized by agents inside the block due to the updating rule. For random initial condition with 50%-50% agents of different strategies randomly dispersed, cooperation persists in the whole range of r and the level of cooperation is higher than that in the well-mixed case in a wide range of r. These results are in sharp contrast to those based on the replicator updating rule. The sensitivity to initial states with different fractions of cooperative agents is also discussed. The results serve to illustrate that both the spatial structure and the updating rule are important in determining the level of cooperation in a competing population. When extreme initial states are used where there are very few agents of a strategy in a background of the opposite strategy, the result would depend on the stability of the clusters formed by the initially minority agents.

Polymer growth through radical polymerization and termination.

We propose a polymer growth model, in which propagating radicals can grow through propagation processes or annihilate through termination (disproportionation or combination) processes. Considering a simple case in which the propagation and termination rates of each polymer chain are both independent of its length, we then investigate analytically the kinetics of the model by means of the rate-equation approach. The propagating radicals will be exhausted eventually and only the inert polymers (the termination products of propagating radicals) can survive in the end. Moreover, the size distribution of propagating radicals can always take the form of the Poisson distribution at a given time, while that of inert polymers is dependent strongly on the details of the reaction-rate kernels. For the case in which the propagation rate constant J1 is less than the termination rate constant J2 , the size distribution of inert polymers can always take a power-law form ck(t) approximately k-2-J/1/(J2-J1), in the region of t>>1 and k>>1 . For the J1>J2 case, the kinetic evolution of inert polymers is very complex and ck(t) can take one of the three forms: monotone decreasing, single peak (Poisson-like distribution), and double peak. For the special J1=J2 case, ck(t) exhibits an exponential decay in size.

Migration-driven aggregate growth on scale-free networks.

We study the kinetics of migration-driven aggregate growth on completely connected scale-free networks. A reversible migration system is considered with the size-dependent rate kernel K(k; l/i;j) approximately k(u)i(v)(lj)(v), at which an i-mer aggregate located on the node with j links gains one monomer from a k-mer aggregate on the node with l links. The results show that the evolution behavior of the aggregate size distribution is drastically different from that for the corresponding same system in normal space. This model can be used to mimic some phenomena such as the distribution of city populations. Moreover, we verify our analytic results in good agreement with the data of the population distributions of all U.S. counties.