A new fast algorithm for solving the minimum spanning tree problem based on DNA molecules computation

The minimum spanning tree (MST) problem is to find minimum edge connected subsets containing all the vertex of a given undirected graph. It is a vitally important NP-complete problem in graph theory and applied mathematics, having numerous real life applications. Moreover in previous studies, DNA molecular operations usually were used to solve NP-complete head-to-tail path search problems, rarely for NP-hard problems with multi-lateral path solutions result, such as the minimum spanning tree problem. In this paper, we present a new fast DNA algorithm for solving the MST problem using DNA molecular operations. For an undirected graph with n vertex and m edges, we reasonably design flexible length DNA strands representing the vertex and edges, take appropriate steps and get the solutions of the MST problem in proper length range and O(3m + n) time complexity. We extend the application of DNA molecular operations and simultaneity simplify the complexity of the computation. Results of computer simulative experiments show that the proposed method updates some of the best known values with very short time and that the proposed method provides a better performance with solution accuracy over existing algorithms.     

On the Adjacent Eccentric Distance Sum Index of Graphs

For a given graph G, ε(v) and deg(v) denote the eccentricity and the degree of the vertex v in G, respectively. The adjacent eccentric distance sum index of a graph G is defined as ξsv(G)=∑v∈V(G)ε(v)D(v)deg(v), where D(v)=∑u∈V(G)d(u,v) is the sum of all distances from the vertex v. In this paper we derive some bounds for the adjacent eccentric distance sum index in terms of some graph parameters, such as independence number, covering number, vertex connectivity, chromatic number, diameter and some other graph topological indices.     

地表臭氧浓度增加和UV-B辐射增强及其复合处理对大豆光合特性的影响

基于开顶式气室(OTC),系统开展了地表O3增加和UV-B增强及其复合处理下(自然空气,CK;10%UV-B增强,T1;100nmol/mol O3,T2;100 nmol/mol O3+10%UV-B增强,T3)大豆光合气体交换、光响应、光合色素和类黄酮含量等参数的观测与分析研究。结果表明,与对照相比,T1和T2单因子处理组的如下指标有相似变化:气孔导度、气孔限制值下降,胞间二氧化碳浓度上升,净光合速率、最大净光合速率、半饱和光强显著降低,表观量子效率和暗呼吸速率先升后降。T1的叶绿素含量降低不显著,类胡萝卜素含量先降后升,类黄酮含量上升,而T2的叶绿素和类胡萝卜素含量显著降低,类黄酮含量先降后升。复合处理下,与CK相比各指标的变化和单因子相似,影响程度均强于两单因子组。因此,100 nmol/mol O3浓度增加和10%UV-B辐射增强复合处理对大豆叶绿素含量的影响存在协同作用,且O3胁迫起了主导作用。光合作用下降的主要原因均是非气孔因素,复合处理对大豆光合作用的影响比两因子单独胁迫有所加深,是O3和UV-B共同作用的结果。     

Single-channel analysis of the anion channel-forming protein from the plant pathogenic bacterium Clavibacter michiganense ssp. nebraskense

The anion channel protein from Clavibacter michiganense ssp. nebraskense (Schürholz, Th. et al. 1991, J. Membrane Biol. 123: 1-8) was analyzed at different concentrations of KCl and KF. At 0.8 M KCl the conductance G(V_m) increases exponentially from 21 pS at 50 mV up to 53 pS at V_m = 200 mV, 20°C. The concentration dependence of G(V_m) corresponds to a Michaelis-Menten type saturation function at all membrane voltage values applied (0-200 mV). The anion concentration K_0.5, where G(V_m) has its half-maximum value, increases from 0.12 M at 50 mV to 0.24 M at 175 mV for channels in a soybean phospholipid bilayer. The voltage dependence of the single channel conductance, which is different for charged and neutral lipid bilayers, can be described either by a two-state flicker (2SF) model and the Nernst-Planck continuum theory, or by a two barrier, one-site (2B1S) model with asymmetric barriers. The increase in the number of open channels after a voltage jump from 50 mV to 150 mV has a time constant of 0.8 s. The changes of the single-channel conductance are much faster (<1 ms). The electric part of the gating process is characterized by the (reversible) molar electrical work ΔG^θ_el = ρZ_gFV_m ≈ -1.3 RT, which corresponds to the movement of one charge of the gating charge number |Z_g| = 1 across the fraction ρ = ΔV_m/V_m = 0.15 of the membrane voltage V_m = 200 mV. Unlike with chloride, the single channel conductance of fluoride has a maximum at about 150 mV in the presence of the buffer PIPES (≥5 mM, pH 6.8) with K_0.5 ≈ 1 M. It is shown that the decrease in conductance is due to a blocking of the channel by the PIPES anion. In summary, the results indicate that the anion transport by the Clavibacter anion channel (CAC) does not require a voltage dependent conformation change of the CAC.     

Deviations from Hardy-Weinberg Proportions: Sampling Variances and Use in Estimation of Inbreeding Coefficients

An analysis is made of the distribution of deviations from Hardy-Weinberg proportions with k alleles and of estimates of inbreeding coefficients (f) obtained from these deviations.—If f is small, the best estimate of f in large samples is shown to be 2Σ _i(T_ii/N_i)/(k - 1), where T_ii is an unbiased measure of the excess of the ith homozygote and N_i the number of the ith allele in the sample [frequency = N_i/(2N)]. No extra information is obtained from the T_ij, where these are departures of numbers of heterozygotes from expectation. Alternatively, the best estimator can be computed from the T_ij, ignoring the T_ii. Also (1) the variance of the estimate of f equals 1/(N(k - 1)) when all individuals in the sample are unrelated, and the test for f = 0 with 1 d.f. is given by the ratio of the estimate to its standard error; (2) the variance is reduced if some alleles are rare; and (3) if the sample consists of full-sib families of size n, the variance is increased by a proportion (n - 1)/4 but is not increased by a half-sib relationship.—If f is not small, the structure of the population is of critical importance. (1) If the inbreeding is due to a proportion of inbred matings in an otherwise random-breeding population, f as determined from homozygote excess is the same for all genes and expressions are given for its sampling variance. (2) If the homozygote excess is due to population admixture, f is not the same for all genes. The above estimator is probably close to the best for all f values.     

A Model for the Action of Vinblastine in Vivo

A model for the action of vinblastine (VLB) on cells multiplying exponentially in vivo with a generation time, T_G, has been derived. It is based on the assumption that cells attempting to pass through mitosis in the presence of VLB lose their proliferative capacity and that this lethal effect occurs only when the cells are exposed to a concentration of VLB which is above a critical value, C_k. The model leads to two predictions. First, that the percentage of cells surviving at any time after exposure to a dose, D, of VLB is 100% if D < D_k and decreases to 0% after a time, T_G, following a dose D ≥ D_k·2^{T G/T1/2}, where D_k represents the dose of VLB required to produce the concentration C_k, and T_1/2 is the half-life of the VLB in vivo. Second, that the time, T_G, at which the percentage of cells surviving an exposure to VLB, at doses greater than D_k·2^{U G/T1/2}, decreases to zero should be equal to the generation time of the cells. Both of these predictions were confirmed experimentally which indicates that the model adequately explains the action of VLB in vivo.     

Effect of adherence,cell morphology,and lipopolysaccharide on potassium conductance and passive membrane properties of murine macrophage J774.1 cells

Summary The effects of adherence, cell morphology, and lipopolysaccharide on electrical membrane properties and on the expression of the inwardly rectifying K conductance in J774.1 cells were investigated. Whole-cell inwardly rectifying K currents (K _i), membrane capacitance (C _m), and membrane potential (V _m) were measured using the patch-clamp technique. SpecificK _i conductance (G _K i, whole-cell Ki conductance corrected for leak and normalized to membrane capacitance) was measured as a function of time after adherence, and was found to increase almost twofold one day after plating. Membrane potential (V _m) also increased from –42±4 mV (n=32) to –58±2 mV (n=47) over the same time period.G _K i andV _m were correlated with each other;G _L (leak conductance normalized to membrane capacitance) andV _m were not. The magnitudes ofG _K i andV _m 15 min to 2 hr after adherence were unaffected by the presence of 100 m cycloheximide, but the increase inG _K iandV _m that normally occurred between 2 and 8 hr after adherence was abolished by cycloheximide treatment. Membrane properties were analyzed as a function of cell morphology, by dividing cells into three categories ranging from small round cells to large, extremely spread cells. The capacitance of spread cells increased more than twofold within one day after adherence, which indicates that spread cells inserted new membrane. Spread cells had more negative resting membrane potentials than round cells, butG _K i andG _L were not significantly different. Lipopolysaccharide-(LPS; 1 or 10 g/ml) treated cells showed increasedC _m compared to control cells plated for comparable times. In contrast to the effect of adherence, LPS-treated cells exhibited a significantly lowerG _K i than control cells, indicating that the additional membrane did not have as high a density of functionalG _K i channels. We conclude that both adherence and LPS treatment increase the total surface membrane area of J774 cells and change the density of Ki channels. In addition, this study demonstrates that membrane area and density of Ki channels can vary independently of one another.     

Demiarcs,creaons and genons

Useful insights into the representation of natural systems can be gained by decomposing directed graphs (digraphs) into elementary components. Arcs of digraphs can be split into male demiarcs (outarcs) which leave vertices and female demiarcs (inarcs) which enter demiarcs. Likewise, a vertex can be split into an input perceiving side called the creaon and an output generating side called the genon. Digraphs can be regarded as being hierarchically organized because each vertex in a level-1 digraph can be expanded into a level-2 digraph. In general, each vertex of a level-i digraph can be expanded into a level-(i+1) digraph. Arcs of a level-i digraph can be regarded as bundles of level-(i + 1) arcs which are split at the vertex boundary. These elementary graphical components are shown to be useful for depicting input-output systems such as organisms, ecosystems and societies.     

The gating charge should not be estimated by fitting a two-state model to a Q-V curve

The voltage dependence of charges in voltage-sensitive proteins, typically displayed as charge versus voltage (Q-V) curves, is often quantified by fitting it to a simple two-state Boltzmann function. This procedure overlooks the fact that the fitted parameters, including the total charge, may be incorrect if the charge is moving in multiple steps. We present here the derivation of a general formulation for Q-V curves from multistate sequential models, including the case of infinite number of states. We demonstrate that the commonly used method to estimate the charge per molecule using a simple Boltzmann fit is not only inadequate, but in most cases, it underestimates the moving charge times the fraction of the field.Many ion channels, transporters, enzymes, receptors, and pumps are voltage dependent. This voltage dependence is the result of voltage-induced translocation of intrinsic charges that, in some way, affects the conformation of the molecule. The movement of such charges is manifested as a current that can be recorded under voltage clamp. The best-known examples of these currents are “gating” currents in voltage-gated channels and “sensing” currents in voltage-sensitive phosphatases. The time integral of the gating or sensing current as a function of voltage (V) is the displaced charge Q(V), normally called the Q-V curve.It is important to estimate how much is the total amount of net charge per molecule (Q_max) that relocates within the electric field because it determines whether a small or a large change in voltage is necessary to affect the function of the protein. Most importantly, knowing Q_max is critical if one wishes to correlate charge movement with structural changes in the protein. The charge is the time integral of the current, and it corresponds to the product of the actual moving charge times the fraction of the field it traverses. Therefore, correlating charge movement with structure requires knowledge of where the charged groups are located and the electric field profile. In recent papers by Chowdhury and Chanda (2012) and Sigg (2013), it was demonstrated that the total energy of activating the voltage sensor is equal to Q_max V_M, where V_M is the median voltage of charge transfer, a value that is only equal to the half-point of activation V_1/2 for symmetrical Q-V curves. V_M is easily estimated from the Q-V curve, but Q_max must be obtained with other methods because, as we will show here, it is not directly derived from the Q-V curve in the general case.The typical methods used to estimate charge per molecule Q_max include measurements of limiting slope (Almers, 1978) and the ratio of total charge divided by the number of molecules (Schoppa et al., 1992). The discussion on implementation, accuracy, and reliability of these methodologies has been addressed many times in the literature, and it will not be discussed here (see Sigg and Bezanilla, 1997). However, it is worth mentioning that these approaches tend to be technically demanding, thus driving researchers to seek alternative avenues toward estimating the total charge per molecule. Particularly, we will discuss here the use of a two-state Boltzmann distribution for this purpose. Our intention is to demonstrate that this commonly used method to estimate the charge per molecule is generally incorrect and likely to give a lower bound of the moving charge times the fraction of the field.The two-state Boltzmann distribution describes a charged particle that can only be in one of two positions or states that we could call S₁ and S₂. When the particle with charge Q_max (in units of electronic charge) moves from S₁ to S₂, or vice versa, it does it in a single step. The average charge found in position S₂, Q(V), will depend on the energy difference between S₁ and S₂, and the charge of the particle. The equation that describes Q(V) is:Q(V)=Qmax1+exp[−Qmax(V−V1/2)kT],(1)where V_1/2 is the potential at which the charge is equally distributed between S₁ and S₂, and k and T are the Boltzmann constant and absolute temperature, respectively. The Q(V) is typically normalized by dividing Eq. 1 by the total charge Q_max. The resulting function is frequently called a “single Boltzmann” in the literature and is used to fit normalized, experimentally obtained Q-V curves. The fit yields an apparent V_1/2 (V∼1/2) and an apparent Q_MAX (Q−max), and this last value is then attributed to be the total charge moving Q_max. Indeed, this is correct but only for the case of a charge moving between two positions in a single step. However, the value of Q−max thus obtained does not represent the charge per molecule for the more general (and frequent) case when the charge moves in more than one step.To demonstrate the above statement and also estimate the possible error in using the fitted Q−max from Eq. 1, let us consider the case when the gating charge moves in a series of n steps between n + 1 states, each step with a fractional charge z_i (in units of electronic charge e₀) that will add up to the total charge Q_max.S1↔μ1S2↔μ2…Si↔μiSi+1…Sn↔μnSn+1The probability of being in each of the states S_i is labeled as P_i, and the equilibrium constant of each step is given byμi=exp[zi(V−Vi)kT], i=1…n,where z_i is the charge (in units of e₀) of step i, and V_i is the membrane potential that makes the equilibrium constant equal 1. In steady state, the solution of P_i can be obtained by combiningPi+1Pi=μi, i=1…n and ∑i=1i=n+1Pi=1,givingPi+1=∏m=1iμm1+∑j=1n∏k=1jμk, i=1…n and P1=11+∑j=1n∏k=1jμk.We define the reaction coordinate along the moved charged q asqi=∑j=1izj, i=1…n.The Q-V curve is defined asQ(V)=∑i=1nqiPi+1.Then, replacing P_i yieldsQ(V)=∑i=1n[∑j=1izj][∏m=1iμm]1+∑j=1n∏k=1jμk,or written explicitly as a function of V:Q(V)=∑i=1n[∑j=1izj][∏m=1iexp[zm(V−Vm)kT]]1+∑j=1n∏k=1jexp[zk(V−Vk)kT].(2)Eq. 2 is a general solution of a sequential model with n + 1 states with arbitrary valences and V_i’s for each transition. We can easily see that Eq. 2 has a very different form than Eq. 1, except when there is only a single transition (n = 1). In this latter case, Eq. 2 reduces to Eq. 1 because z₁ and V₁ are equal to Q_max and V_1/2, respectively. For the more general situation where n > 1, if one fits the Q(V) relation obeying Eq. 2 with Eq. 1, the fitted Q−max value will not correspond to the sum of the z_i values (see examples below and Fig. 1). A simple way to visualize the discrepancy between the predicted value of Eqs. 1 and 2 is to compute the maximum slope of the Q-V curve. This can be done analytically assuming that V_i = V_o for all transitions and that the total charge Q_max is evenly divided among those transitions. The limit of the first derivative of the Q(V) with respect to V evaluated at V = V_o is given by this equation:dQ(V)dV|V=V0=Qmax(n+2)12nkT.(3)From Eq. 3, it can be seen that the slope of the Q-V curve decreases with the number of transitions being maximum and equal to Q_max /(4kT) when n = 1 (two states) and a minimum equal to Q_max /(12kT) when n goes to infinity, which is the continuous case (see next paragraph).Open in a separate windowFigure 1.Examples of normalized Q-V curves for a Q_max = 4 computed with Eq. 2 for the cases of one, two, three, four, and six transitions and the continuous case using Eq. 5 (squares). All the Q-V curves were fitted with Eq. 1 (lines). The insets show the fitted valence (Q−max) and half-point (V∼1/2).

Infinite number of steps

Eq. 2 can be generalized to the case where the charge moves continuously, corresponding to an infinite number of steps. If we makez_i = Q_max/n, ?i = 1…n, ??V_i = V_o, ?i = 1…n, then all µ_i = µ, and we can write Eq. 2 as the normalized Q(V) in the limit when n goes to infinity:Qnor(V)=limn→∞∑i=1n[∑j=1iQmaxn]∏m=1iexp[Qmax(V−Vo)nkT]Qmax[1+∑i=1n∏j=1iexp[Qmax(V−Vo)nkT]]=[Qmax(V−Vo)−kT]exp[Qmax(V−Vo)kT]+kTQmax(V−Vo)[exp[Qmax(V−Vo)kT]−1].(4)Eq. 4 can also be written asQnor(V)=12[1+coth[Qmax(V−Vo)2kT]−2kTQmax(V−V0)],(5)which is of the same form of the classical equation of paramagnetism (see Kittel, 2005).

Examples

We will illustrate now that data generated by Eq. 2 can be fitted quite well by Eq. 1, thus leading to an incorrect estimate of the total charge moved. Typically, the experimental value of the charge plotted is normalized to its maximum because there is no knowledge of the absolute amount of charge per molecule and the number of molecules. The normalized Q-V curve, Q_nor, is obtained by dividing Q(V) by the sum of all the partial charges.Fig. 1 shows Q_nor computed using Eq. 2 for one, two, three, four, and six transitions and for the continuous case using Eq. 5 (squares) with superimposed fits to a two-state Boltzmann distribution (Eq. 1, lines). The computations were done with equal charge in each step (for a total charge Q_max = 4e₀) and also the same V_i = −25 mV value for all the steps. It is clear that fits are quite acceptable for cases up to four transitions, but the fit significantly deviates in the continuous case.Considering that experimental data normally have significant scatter, it is then quite likely that the experimenter will accept the single-transition fit even for cases where there are six or more transitions (see Fig. 1). In general, the case up to four transitions will look as a very good fit, and the fitted Q−max value may be inaccurately taken and the total charge transported might be underestimated. To illustrate how bad the estimate can be for these cases, we have included as insets the fitted value of Q−max for the cases presented in Fig. 1. It is clear that the estimated value can be as low as a fourth of the real total charge. The estimated value of V∼1/2 is very close to the correct value for all cases, but we have only considered cases in which all V_i’s are the same.It should be noted that if µ_i of the rightmost transition is heavily biased to the last state (V_i is very negative), then the Q−max estimated by fitting a two-state model is much closer to the total gating charge. In a three-state model, it can be shown that the fitted value is exact when V₁→∞ and V₂→−∞ because in that case, it converts into a two-state model. Although these values of V are unrealistic, the fitted value of Q−max can be very close to the total charge when V₂ is much more negative than V₁ (that is, V₁ >> V₂). On the other hand, If V₁ << V₂, the Q-V curve will exhibit a plateau region and, as the difference between V₁ and V₂ decreases, the plateau becomes less obvious and the curve looks monotonic. These cases have been discussed in detail for the two-transition model in Lacroix et al. (2012).We conclude that it is not possible to estimate unequivocally the gating charge per sensor from a “single-Boltzmann” fit to a Q-V curve of a charge moving in multiple transitions. The estimated Q−max value will be a low estimate of the gating charge Q_max, except in the case of the two-state model or the case of a heavily biased late step, which are rare occurrences. It is then safer to call “apparent gating charge” the fitted Q−max value of the single-Boltzmann fit.

Addendum

The most general case in which transitions between states include loops, branches, and steps can be derived directly from the partition function and follows the general thermodynamic treatment by Sigg and Bezanilla (1997), Chowdhury and Chanda (2012), and Sigg (2013). The reaction coordinate is the charge moving in the general case where it evolves from q = 0 to q = Q_max by means of steps, loops, or branches. In that case, the partition function is given byZ=∑iexp(qi(V−Vi)kT).(6)We can compute the mean gating charge, also called the Q-V curve, asQ(V)=〈q〉=kTZ’Z=kTdlnZdV=∑iqiexp(qi(V−Vi)kT)∑iexp(qi(V−Vi)kT).(7)The slope of the Q-V is obtained by taking the derivative of 〈q〉 with respect to V:dQ(V)dV=(kT)2d2lnZdV2.(8)Let us now consider the gating charge fluctuation. The charge fluctuation will depend on the number of possible conformations of the charge and is expected to be a maximum when there are only two possible charged states to dwell. As the number of intermediate states increases, the charge fluctuation decreases. Now, a measure of the charge fluctuation is given by the variance of the gating charge, which can be computed from the partition function as:〈Δq2〉=〈q2〉−〈q〉2=(kT)2(Z’’Z−(Z’Z)2)=(kT)2d2lnZdV2.(9)But the variance (Eq. 9) is identical to the slope of Q(V) (Eq. 8). This implies that the slope of the Q-V is maximum when there are only two states.     

Nitric-oxide Dioxygenase Function of Human Cytoglobin with Cellular Reductants and in Rat Hepatocytes

Cytoglobin (Cygb) was investigated for its capacity to function as a NO dioxygenase (NOD) in vitro and in hepatocytes. Ascorbate and cytochrome b₅ were found to support a high NOD activity. Cygb-NOD activity shows respective K_m values for ascorbate, cytochrome b₅, NO, and O₂ of 0.25 mm, 0.3 μm, 40 nm, and ∼20 μm and achieves a k_cat of 0.5 s⁻¹. Ascorbate and cytochrome b₅ reduce the oxidized Cygb-NOD intermediate with apparent second order rate constants of 1000 m⁻¹ s⁻¹ and 3 × 10⁶ m⁻¹ s⁻¹, respectively. In rat hepatocytes engineered to express human Cygb, Cygb-NOD activity shows a similar k_cat of 1.2 s⁻¹, a K_m(NO) of 40 nm, and a k_cat/K_m(NO) (k′_NOD) value of 3 × 10⁷ m⁻¹ s⁻¹, demonstrating the efficiency of catalysis. NO inhibits the activity at [NO]/[O₂] ratios >1:500 and limits catalytic turnover. The activity is competitively inhibited by CO, is slowly inactivated by cyanide, and is distinct from the microsomal NOD activity. Cygb-NOD provides protection to the NO-sensitive aconitase. The results define the NOD function of Cygb and demonstrate roles for ascorbate and cytochrome b₅ as reductants.     

The volumes of some compartment systems with sampling and loss from one compartment

If the concentrationc ₁(t)=∑ _i=1 ⁿ A _i exp (−α _i t) for one compartment, one presumes a linear catenaryn-compartment system without sinks and loss only from the same compartment, then the volumesV _i , rate constantsk _ij , and concentrationsc _i (t) in each compartment can be determined in terms of theA _i 's,A _i ′s, α _i ′s, the dose injectedD _o and the partition coefficientsr _ij =k _ij /k _ji . If the concentration would become uniform at equilibrium, then the total volume of distribution may be determined without knowledge ofr _ij or restriction to catenary configuration.     

Modification of yttrium alkoxides: β-Ketoesterate-substituted yttrium alkoxo/hydroxo/oxo clusters

Reaction of Y₅O(OiPr)₁₃ (“yttrium iso-propoxide”) with one molar equivalent of isopropyl acetoacetate (iprac) per Y resulted in the formation of Y₉O(OH)₉(OiPr)₈(iprac)₈, a rare example of an yttrium alkoxo/hydroxo/oxo cluster. Reaction in a 1:3 molar ratio gave Y₄(OH)₂(iprac)₁₀ and Y₆(OH)₆(iprac)₁₂ instead. A fourth cluster, Y₉O(OH)₉(iprac)₁₆, structurally closely related to Y₉O(OH)₉(OiPr)₈(iprac)₈, was obtained upon recrystallization of Y₄(OH)₂(iprac)₁₀ from CDCl₃.     

Control of Seed Germination by Abscisic Acid : III. Effect on Embryo Growth Potential (Minimum Turgor Pressure) and Growth Coefficient (Cell Wall Extensibility) in Brassica napus L

The physical mechanism of seed germination and its inhibition by abscisic acid (ABA) in Brassica napus L. was investigated, using volumetric growth (= water uptake) rate (dV/dt), water conductance (L), cell wall extensibility coefficient (m), osmotic pressure (_i), water potential (Ψ_i), turgor pressure (P), and minimum turgor for cell expansion (Y) of the intact embryo as experimental parameters. dV/dt, _i, and Ψ_i were measured directly, while m, P, and Y were derived by calculation. Based on the general equation of hydraulic cell growth [dV/dt = Lm/(L + m) (Δ - Y), where Δ = _i - of the external medium], the terms (Lm/(L + m) and _i - Y were defined as growth coefficient (k_G) and growth potential (GP), respectively. Both k_G and GP were estimated from curves relating dV/dt (steady state) to of osmotic test solutions (polyethylene glycol 6000).

During the imbibition phase (0-12 hours after sowing), k_G remains very small while GP approaches a stable level of about 10 bar. During the subsequent growth phase of the embryo, k_G increases about 10-fold. ABA, added before the onset of the growth phase, prevents the rise of k_G and lowers GP. These effects are rapidly abolished when germination is induced by removal of ABA. Neither L (as judged from the kinetics of osmotic water efflux) nor the amount of extractable solutes are affected by these changes. _i and Ψ_i remain at a high level in the ABA-treated seed but drop upon induction of germination, and this adds up to a large decrease of P, indicating that water uptake of the germinating embryo is controlled by cell wall loosening rather than by changes of _i or L. ABA inhibits water uptake by preventing cell wall loosening. By calculating Y and m from the growth equation, it is further shown that cell wall loosening during germination comprises both a decrease of Y from about 10 to 0 bar and an at least 10-fold increase of m. ABA-mediated embryo dormancy is caused by a reversible inhibition of both of these changes in cell wall stability.

     

Insights into the nature of Mo(V) species in solution: Modeling catalytic cycles for molybdenum enzymes

The tris(pyrazolyl)borate and related tripodal N-donor ligands originally developed by Trofimenko stabilize mononuclear compounds containing Mo^VIO₂, Mo^VIO, Mo^VO, and Mo^IVO units and effectively inhibit their polynucleation in organic solvents. Dioxo-Mo(VI) complexes of the type LMoO₂(SPh), where L = hydrotris(3,5-dimethylpyrazol-1-yl)borate (Tp^∗), hydrotris(3-isopropylpyrazol-1-yl)borate (Tp^iPr), and hydrotris(3,5-dimethyl-1,2,4-triazol-1-yl)borate (Tz) and related derivatives are the only model systems that mimic the complete reaction sequence of sulfite oxidase, in which oxygen from water is ultimately incorporated into product. The quasi-reversible, one-electron reduction of Tp^∗MoO₂(SPh) in acetonitrile exhibits a positive potential shift upon addition of a hydroxylic proton donor, and the magnitude of the shift correlates with the acidity of the proton donor. These reductions produce two Mo(V) species, [Tp^∗Mo^VO₂(SPh)]⁻ and Tp^∗Mo^VO(OH)(SPh), that are related by protonation. Measurement of the relative amounts of these two Mo(V) species by EPR spectroscopy enabled the pK_a of the Mo^V(OH) unit in acetonitrile to be determined and showed it to be several pK_a units smaller than that for water in acetonitrile. Similar electrochemical-EPR experiments for Tp^iPrMoO₂(SPh) indicated that the pK_a for its Mo^V(OH) unit was ∼1.7 units smaller than that for Tp^∗Mo^VO(OH)(SPh). Density functional theory calculations also predict a smaller pK_a for Tp^iPrMo^VO(OH)(SPh) compared to Tp^∗Mo^VO(OH)(SPh). Analysis of these results indicates that coupled electron-proton transfer (CEPT) is thermodynamically favored over the indirect process of metal reduction followed by protonation. The crystal structure of Tp^iPrMoO₂(SPh) is also presented.     

Inner voltage clamping. A method for studying interactions among hydrophobic ions in a lipid bilayer

Ketterer, et al. (1971) have suggested that a combination of electrostatic and chemical interactions may cause hydrophobic ions absorbed within a bilayer lipid membrane to reside in two potential wells, each close to a membrane surface. The resulting two planes of charges would define three regions of membrane dielectric: two identical outer regions each between a plane of absorbed charges and the plane of closest approach of ions in the aqueous phase; and the inner region between the two planes of adsorbed charges. The theory describing charge translocation across the inner region is based on a simple three-capacitor model. A significant theoretical conclusion is that the difference between the voltage across the inner region, V_i, and the voltage across the entire membrane, V_m, is directly proportional to the amount of charge that has flowed in a voltage clamp experiment. We demonstrate that we can construct an “inner voltage clamp” that can maintain, with positive feedback, a constant inner voltage, V_i. The manifestation of proper feedback is that the clamp current (after a voltage step) will exhibit pure (i.e., single time-constant) exponential decay, because the voltage dependent rate constants governing translocation will be independent of time. The “pureness” of the exponential is maximized when the standard deviation of the least-square fit of the appropriate exponential equation to the experimental data is minimized. The concomitant feedback is directly related to the capacitances of the inner and outer membrane regions, C_i and C_o.

Experimental results with tetraphenylborate ion adsorbed in bacterial phosphatidylethanolamine/n-decane bilayers indicate C_i ~ 5 · 10^-7F/cm² and C_o ≈ 5 · 10^-5F/cm².

     

The Stochastic Theory of Cell Proliferation

A stochastic theory of cell kinetics has been developed based on a realistic model of cell proliferation. A characteristic transit time, _i, has been assigned to each of the four states (G₁, S, G₂, M) of the cell cycle. The actual transit time, t_i, for any cell is represented by a distribution around _i with a variance σ_i². Analytic and computer formulations have been used to describe the time development of such characteristics as age distribution, labeling experiments, and response to perturbations of the system by, for example, irradiation and temperature. The decay of synchrony is analyzed in detail and is shown to proceed as a damped wave. From the first few peaks of the synchrony decay one can obtain the distribution function for the cell cycle time. The later peaks decay exponentially with a characteristic decay constant, λ, which depends only on the average cell-cycle time, , and the associated variance. It is shown that the system, upon any sudden disturbance, approaches new “equilibrium” proliferation characteristics via damped periodic transients, the damping being characterized by λ. Thus, the response time of the system, /λ, is as basic a parameter of the system as the cell-cycle time.     

Central and local limit theorems for RNA structures

A k-noncrossing RNA pseudoknot structure is a graph over {1,…,n} without 1-arcs, i.e. arcs of the form (i,i+1) and in which there exists no k-set of mutually intersecting arcs. In particular, RNA secondary structures are 2-noncrossing RNA structures. In this paper we prove a central and a local limit theorem for the distribution of the number of 3-noncrossing RNA structures over n nucleotides with exactly h bonds. Our analysis employs the generating function of k-noncrossing RNA pseudoknot structures and the asymptotics for the coefficients. The results of this paper explain the findings on the number of arcs of RNA secondary structures obtained by molecular folding algorithms and are of relevance for prediction algorithms of k-noncrossing RNA structures.     

Fast Generation of Sparse Random Kernel Graphs

The development of kernel-based inhomogeneous random graphs has provided models that are flexible enough to capture many observed characteristics of real networks, and that are also mathematically tractable. We specify a class of inhomogeneous random graph models, called random kernel graphs, that produces sparse graphs with tunable graph properties, and we develop an efficient generation algorithm to sample random instances from this model. As real-world networks are usually large, it is essential that the run-time of generation algorithms scales better than quadratically in the number of vertices n. We show that for many practical kernels our algorithm runs in time at most 𝒪(n(logn)²). As a practical example we show how to generate samples of power-law degree distribution graphs with tunable assortativity.     

Acidosis Mediates the Switching of Gs-PKA and Gi-PKCε Dependence in Prolonged Hyperalgesia Induced by Inflammation

Chronic inflammatory pain, when not effectively treated, is a costly health problem and has a harmful effect on all aspects of health-related quality of life. Previous studies suggested that in male Sprague Dawley rats, prostaglandin E₂ (PGE₂)-induced short-term hyperalgesia depends on protein kinase A (PKA) activity, whereas long-lasting hyperalgesia induced by PGE₂ with carrageenan pre-injection, requires protein kinase C_ε (PKC_ε). However, the mechanism underlying the kinase switch with short- to long-term hyperalgesia remains unclear. In this study, we used the inflammatory agents carrageenan or complete Freund’s adjuvant (CFA) to induce long-term hyperalgesia, and examined PKA and PKC_ε dependence and switching time. Hyperalgesia induced by both agents depended on PKA/PKC_ε and G_s/G_i-proteins, and the switching time from PKA to PKC_ε and from G_s to G_i was about 3 to 4 h after inflammation induction. Among the single inflammatory mediators tested, PGE₂ and 5-HT induced transient hyperalgesia, which depended on PKA and PKC_ε, respectively. Only acidic solution-induced hyperalgesia required G_s-PKA and G_i-PKC_ε, and the switch time for kinase dependency matched inflammatory hyperalgesia, in approximately 2 to 4 h. Thus, acidosis in inflamed tissues may be a decisive factor to regulate switching of PKA and PKC_ε dependence via proton-sensing G-protein–coupled receptors.     

Stochastic processes in particle-number fluctuations in an electron-photon shower

The paper is concerned with the existence and asymptotic character of the nonlinear boundary value problemdG/dt=F(t,G,F, ¦α?β¦) (1) ¦α?β¦dF/dt=g(t,G,F, ¦α?β¦)G(o,¦α?β¦)=k ₁,G(∞,¦α?β¦)=k ₂ (2) as ¦α?β¦→ o+ The discussion is related to the problem of particle-number fluctuations in the theory of cosmic radiation andG andF denote respectively the probability generating functions for the electron distribution in an electron-initiated and a photon-initiated shower. A solution of the system (1) satisfying the boundary conditions (2) is constructed so that specified limiting conditions are fulfilled.