On the equilibria of the MAPK cascade: Cooperativity, modularity and bistability

In this paper we present a discussion of a phenomenological model of the MAPK cascade which was originally proposed by Angeli et al. [D. Angeli, J.E. Ferrell, Jr., E.D. Sontag, PNAS 101 (2004), 1822]. The model and its solution are extended in several respects: (a) an analytical solution is given for the cascade equilibria, exploiting a parameter-based symmetry of the rate equations; (b) we discuss the cooperativity (Hill coefficients) of the cascade and show that a feedforward loop within the cascade increases its cooperativity. The relevance of this result for the notion of modularity is discussed; (c) the feedback model for cascade bistability by Angeli et al. is reconsidered. We argue that care must be taken in modeling the interactions and a biologically realistic phenomenological model cannot be too reductionist. The inclusion of a time-dependent degradation rate is needed to account for a switching of the cascade.     

Towards molecular computers that operate in a biological environment

Even though electronic computers are the only computer species we are accustomed to, the mathematical notion of a programmable computer has nothing to do with electronics. In fact, Alan Turing’s notional computer [L.M. Turing, On computable numbers, with an application to the entcheidungsproblem, Proc. Lond. Math. Soc. 42 (1936) 230-265], which marked in 1936 the birth of modern computer science and still stands at its heart, has greater similarity to natural biomolecular machines such as the ribosome and polymerases than to electronic computers. This similarity led to the investigation of DNA-based computers [C.H. Bennett, The thermodynamics of computation — Review, Int. J. Theoret. Phys. 21 (1982) 905-940; A.M. Adleman, Molecular computation of solutions to combinatorial problems, Science 266 (1994) 1021-1024]. Although parallelism, sequence specific hybridization and storage capacity, inherent to DNA and RNA molecules, can be exploited in molecular computers to solve complex mathematical problems [Q. Ouyang, et al., DNA solution of the maximal clique problem, Science 278 (1997) 446-449; R.J. Lipton, DNA solution of hard computational problems, Science 268 (1995) 542-545; R.S. Braich, et al., Solution of a 20-variable 3-SAT problem on a DNA computer, Science 296 (2002) 499-502; Liu Q., et al., DNA computing on surfaces, Nature 403 (2000) 175-179; D. Faulhammer, et al., Molecular computation: RNA solutions to chess problems, Proc. Natl. Acad. Sci. USA 97 (2000) 1385-1389; C. Mao, et al., Logical computation using algorithmic self-assembly of DNA triple-crossover molecules, Nature 407 (2000) 493-496; A.J. Ruben, et al., The past, present and future of molecular computing, Nat. Rev. Mol. Cell. Biol. 1 (2000) 69-72], we believe that the more significant potential of molecular computers lies in their ability to interact directly with a biochemical environment such as the bloodstream and living cells. From this perspective, even simple molecular computations may have important consequences when performed in a proper context. We envision that molecular computers that operate in a biological environment can be the basis of “smart drugs”, which are potent drugs that activate only if certain environmental conditions hold. These conditions could include abnormalities in the molecular composition of the biological environment that are indicative of a particular disease. Here we review the research direction that set this vision and attempts to realize it.     

Green functions and Langevin equations for nonlinear diffusion equations: A comment on ‘Markov processes, Hurst exponents, and nonlinear diffusion equations’ by Bassler et al.

We discuss two central claims made in the study by Bassler et al. [K.E. Bassler, G.H. Gunaratne, J.L. McCauley, Physica A 369 (2006) 343]. Bassler et al. claimed that Green functions and Langevin equations cannot be defined for nonlinear diffusion equations. In addition, they claimed that nonlinear diffusion equations are linear partial differential equations disguised as nonlinear ones. We review bottom-up and top-down approaches that have been used in the literature to derive Green functions for nonlinear diffusion equations and, in doing so, show that the first claim needs to be revised. We show that the second claim as well needs to be revised. To this end, we point out similarities and differences between non-autonomous linear Fokker-Planck equations and autonomous nonlinear Fokker-Planck equations. In this context, we raise the question whether Bassler et al.’s approach to financial markets is physically plausible because it necessitates the introduction of external traders and causes. Such external entities can easily be eliminated when taking self-organization principles and concepts of nonextensive thermostatistics into account and modeling financial processes by means of nonlinear Fokker-Planck equations.     

The discrimination algorithms for overlapped MPSK and MQAM modulations using higher-order cumulants

Automatic Modulation Classification (AMC) is responsible for detecting the correct modulation types in the intelligent receivers. AMC performance degrades when the signal-to-noise ratio (SNR) decreases because of the overlapping among the digital modulation types’ features, and this performance worsens under fading channel conditions. This paper proposes two new algorithms that improve the AMC performance accuracy of the overlapped digital modulations in feature space by improving their discrimination. These algorithms are named temporal Fisher discriminant analysis (TFDA) and supervised Fisher discriminant analysis (SFDA). The simulation results show that TFDA improves AMC performance accuracy up to 19.01% compared with the reference paper (Ge et al., 2021) and up to 38.15% compared with the reference paper (Teng et al., 2018). In contrast, SFDA improves AMC performance accuracy up to 23.12 % compared with the reference paper (Ge et al., 2021) and up to 49.025% compared with the reference paper (Teng et al., 2018).     

Radial distribution of dose within heavy charged particle tracks – Models and experimental verification using LiF:Mg,Cu,P TL detectors

A new method of experimental verification of radial dose distribution models using solid state thermoluminescent (TL) detectors LiF:Mg,Cu,P has been recently proposed. In this work the method was applied to verify the spatial distribution of energy deposition within a single ¹³¹Xe ion track. Detectors were irradiated at the Department of Physics of the University of Jyväskylä, Finland. The obtained results have been compared with theoretical data, calculated according to the Zhang et al., Cucinotta et al. and Geiss et al. radial dose distribution (RDD) models. At the lowest dose range the Zhang et al. RDD model exhibited the best agreement as compared to experimental data. In the intermediate dose range, up to 10⁴ Gy, the best agreement was found for the RDD model of Cucinotta et al. The probability of occurrence of doses higher than 10⁴ Gy within a single ¹³¹Xe ion track was found to be lower than predicted by all the studied RDD models. This may be a result of diffusion of the charge, which is then captured by TL-related trapping sites, at the distances up to dozens of nanometers from the ionization site.     

Rare Event Simulation for T-cell Activation

The problem of statistical recognition is considered, as it arises in immunobiology, namely, the discrimination of foreign antigens against a background of the body’s own molecules. The precise mechanism of this foreign-self-distinction, though one of the major tasks of the immune system, continues to be a fundamental puzzle. Recent progress has been made by van den Berg, Rand, and Burroughs (J. Theor. Biol. 209:465–486, 2001), who modelled the probabilistic nature of the interaction between the relevant cell types, namely, T-cells and antigen-presenting cells (APCs). Here, the stochasticity is due to the random sample of antigens present on the surface of every APC, and to the random receptor type that characterises individual T-cells. It has been shown previously (van den Berg et al. in J. Theor. Biol. 209:465–486, 2001; Zint et al. in J. Math. Biol. 57:841–861, 2008) that this model, though highly idealised, is capable of reproducing important aspects of the recognition phenomenon, and of explaining them on the basis of stochastic rare events. These results were obtained with the help of a refined large deviation theorem and were thus asymptotic in nature. Simulations have, so far, been restricted to the straightforward simple sampling approach, which does not allow for sample sizes large enough to address more detailed questions. Building on the available large deviation results, we develop an importance sampling technique that allows for a convenient exploration of the relevant tail events by means of simulation. With its help, we investigate the mechanism of statistical recognition in some depth. In particular, we illustrate how a foreign antigen can stand out against the self background if it is present in sufficiently many copies, although no a priori difference between self and nonself is built into the model.     

The effects of nutrient chemotaxis on bacterial aggregation patterns with non-linear degenerate cross diffusion

This paper studies a reaction–diffusion–chemotaxis model for bacterial aggregation patterns on the surface of thin agar plates. It is based on the non-linear degenerate cross diffusion model proposed by Kawasaki et al. (1997) [5] and it includes a suitable nutrient chemotactic term compatible with such type of diffusion, as suggested by Ben-Jacob et al. (2000) [20]. An asymptotic estimation predicts the growth velocity of the colony envelope as a function of both the nutrient concentration and the chemotactic sensitivity. It is shown that the growth velocity is an increasing function of the chemotactic sensitivity. High resolution numerical simulations using Graphic Processing Units (GPUs), which include noise in the diffusion coefficient for the bacteria, are presented. The numerical results verify that the chemotactic term enhances the velocity of propagation of the colony envelope. In addition, the chemotaxis seems to stabilize the formation of branches in the soft-agar, low-nutrient regime.     

Reply to comment on “Negative refraction in 1D photonic crystals”

I refute the criticisms of Srivastava et al. (2008) [13] raised in Bénédicto et al. [14].     

The Ho thickness dependence of spin-triplet supercurrents in Nb/Ho/Co/Ho/Nb films

Robinson et al. [J.W.A. Robinson, et al., Science 329 (2010) 59] reported control of spin-triplet supercurrents into ferromagnets by varying the thicknesses of the Ho injector and attributed the voltage peaks to non-integer spiral wavelengths of λ/2 and 5λ/2 in Ho. Here we demonstrate that these peaks correspond to λ/2 and 3λ/2.     

Parameter identification of chaos system based on unknown parameter observer

Parameter identification of chaos system based on unknown parameter observer is discussed generally. Based on the work of Guan et al. [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26], the design of unknown parameter observer is improved. The application of the improved approach is extended greatly. The works in some literatures [X.P. Guan, H.P. Peng, L.X. Li, et al., Acta Phys. Sinica 50 (2001) 26; J.H. Lü, S.C. Zhang, Phys. Lett. A 286 (2001) 148; X.Q. Wu, J.A. Lu, Chaos Solitons Fractals 18 (2003) 721; J. Liu, S.H. Chen, J. Xie, Chaos Solitons Fractals 19 (2004) 533] are only the special cases of our Corollaries 1 and 2. Some observers for Lü system and a new chaos system are designed to test our improved method, and simulations results demonstrate the effectiveness and feasibility of the improved approach.     

Adsorption of water monomer and clusters on platinum(111) terrace and related steps and kinks II. Surface diffusion

Surface diffusion of water monomer, dimer, and trimer on the (111) terrace, (221) and (322) stepped, and (763) and (854) kinked surfaces of platinum was studied by density functional theory using the PW91 approximation to the energy functional. Monomer diffusion on the terrace is facile, with an activation barrier of 0.20 eV, while dimer and trimer diffusions are restricted due to their high activation barriers of 0.43 and 0.48 eV, respectively. During monomer diffusion on the terrace the O–Pt distance increases by 0.54 Å, about 23% of the initial distance of 2.34 Å. The calculated rate of monomer diffusion hops is in good agreement with the onset temperature of diffusion measurements of Daschbach et al., J. Chem. Phys., 120 (2004) 1516. Alternative monomer diffusion pathways, in which the molecule rolls or flips, were also found. These pathways have diffusion barriers of 0.22 eV. During dimer diffusion on the terrace, the donor molecule rises 0.4 Å at the saddle point, while the acceptor rises by only 0.03 Å. Monomer diffusion up to steps and kinks, with activation barriers of 0.11–0.13 eV, facilitate chain formation on top of step edges. The energy landscape of monomer diffusion from terrace to step to kink sites is downhill with a maximum activation barrier of 0.26 eV. A model for water adsorption is presented in which monomer diffusion leads to concurrent formation of terrace clusters and population of steps/kinks, the latter consistent with the STM measurements of Morgenstern et al., Phys. Rev. Lett., 77 (1996) 703.     

Biquantization of symmetric pairs and the quantum shift

The biquantization of symmetric pairs was studied by Cattaneo et al. (2008)  [1] in terms of Kontsevich-like graphs. This note, also in view of recent results by Calaque et al. (2009)  [3], amends a minor mistake that did not spoil the main results of the paper. The mistake consisted in ignoring a regular term in the boundary contribution of some propagators. On the other hand, its correction brings back the quantum shift, present in the approaches by the orbit method, that was otherwise puzzlingly missing. In addition a detailed comparison of the two, equivalent, ways of defining biquantization working on the upper half plane or on one quadrant is presented, as well as a more conceptual approach to biquantization and the due corrections of some results of Cattaneo et al. (2008)  [1] in view of the aforementioned correction by the quantum shift.     

On the motif distribution in random block-hierarchical networks

The distribution of motifs in random hierarchical topological networks defined by nonsymmetric random block-hierarchical adjacency matrices, is constructed for the first time. According to the classification of U. Alon et al. of network superfamilies (Milo et al., 2004 [11]) by their motifs distributions, our artificial directed random hierarchical networks fall into the superfamily of natural networks to which the neuron networks belong. This is the first example of a class of “handmade” topological networks with the motifs distribution as in a special class of natural networks of essential biological importance.     

Analysis of stock prices of mining business

Stock exchanges have a diversity of so-called business groups and much evidence has been presented by covariance matrix analysis (Laloux et al. (1999) [6], Plerou et al. (2002) [7], Plerou et al. (1999) [8], Mantegna (1999) [9], Utsugi et al. (2004) [21] and Lim et al. (2009) [26]). A market-wide effect plays a crucial role in shifting the correlation structure from random to non-random. In this work, we study the structural properties of stocks related to the mining industry, especially rare earth minerals, listed on two exchanges, namely the TSX (Toronto stock exchange) and the TSX-V (Toronto stock exchange-ventures). In general, raw-material businesses are sensitively affected by the global economy while each firm has its own cycle. We prove that the global crisis during 2006–2009 affected the mineral market considerably. These two aspects compete to control price fluctuations. We show that the internal cycle overwhelms the global economic environment in terms of random matrix theory and overlapping matrices. However, during the period of 2006–2009, the effect of the global economic environment emerges. This result is well explained by the recent global financial/economic crisis. For comparison, we analyze the time stability of business clusters of the KOSPI, that is, the electric/electronic business, using an overlapping matrix. A clear difference in behavior is confirmed. Consequently, rare earth minerals in the raw-material business should be classified not by standard business classifications but by the internal cycle of business.     

Are per capita incomes of MENA countries converging or diverging?

This study considers the issue of income convergence among the MENA (Middle East and North African) countries by using real per capita incomes over the period 1950-2006. We employed (Kapetanios et al. 2003) [21] unit root test by incorporating an additive constant and a trend component as Chong et al. (2008) [20] did in their study and found most of the MENA countries diverging during the sample period.     

Chemical structure of atmospheric pressure premixed laminar formic acid/hydrogen flames

The work presents an experimental and kinetic modeling study of laminar premixed formic acid [HC(O)OH]/H₂/O₂/Ar flames at different equivalence ratios (φ=0.85, 1.1 and 1.3) stabilized on a flat burner at atmospheric pressure, as well as laminar flame speed of HC(O)OH/O₂/Ar flames (φ=0.5–1.5) at 1 atm. Flame structure as well as laminar flame speed were simulated using three different detailed chemical kinetic mechanisms proposed for formic acid oxidation. The components in the fuel blends show different consumption profiles, namely, hydrogen is consumed slower than formic acid. According to kinetic analysis, the reason of the observed phenomenon is that the studied flames have hydrogen as a fuel but also as an intermediate product formed from HC(O)OH decomposition. Comparison of the measured and simulated flame structure shows that all the mechanisms satisfactorily predict the mole fraction profiles of the reactants, main products, and intermediates. It is noteworthy that the mechanisms proposed by Glarborg et al., Konnov et al. and the updated AramcoMech2.0 adequately predict the spatial variations in the mole fractions of free radicals, such as H, OH O and HO₂. However, some drawbacks of the mechanisms used were identified; in particular, they predict different concentrations of CH₂O. As for laminar flame speed simulations, the Konnov et al. mechanism predicts around two times higher values than in experiment, while the Glarborg et al. and updated AramcoMech2.0 show good agreement with the experimental data.     

The phase dynamics of spiral turbulence in the Couette-Taylorsystem

Spiral turbulence observed in Couette-Taylor system has been characterized using the phase diffusion equation suggested by Hegseth et al. [Phys. Rev. Lett. 62, 257 (1989)]. From space-time diagrams, we have measured the diffusion coefficient, the diffusion velocity, and the turbulent spiral pitch.     

Can spontaneous cell movements be modelled as Lévy walks?

Spontaneous cell movement is a random motion that takes place in the absence of external guiding stimuli. The spontaneous movements of HaCaT and NHDF cells (cells of the epidermis) are well represented as continuous Markovian processes driven by multiplicative noise [D. Selmeczi, S. Mosler, P.H. Hagedorn, N.B. Larsen, H. Flyvbjerg, Biophysical Journal 89 (2005) 912]. Model components are, however, ad hoc as they are inspired by fits to experimental data. As a consequence, model agreement with experimental data does not add much to our understanding of spontaneous movements of these cells beyond demonstrating that they can be modelled phenomenologically. Here it is noted that a slight re-parameterization and re-interpretation of the driving noise leads to the model of Lubashevsky et al. (2009) [I. Lubashevsky, R. Friedrich, A. Heuer, Physical Review E 79 (2009) 011110] that realises Lévy walks as Markovian stochastic processes. This brings forth new biological insight as Lévy walks are advantageous when searching in the absence of external stimuli and without knowledge of the target distribution, as may be the case with cells of the epidermis that form new tissue by locating and then attaching on to one another. The Hänggi-Klimontovich interpretation of the driving noise in the model of Lubashevsky et al. (2009) and Cauchy distributions of predicted velocities do, however, appear problematic, even unphysical. Here it is shown that these are perceived rather than actual difficulties. Intermittent stop-start motions of the kind displayed by some cells and protozoan are found to underlie the formulation of the model of Lubashevsky et al. (2009) and the velocities of starved Dictyostelium discoideum (a unicellular organism) are found to be Cauchy distributed to a good approximation. It is therefore suggested that the model of Lubashevsky et al. (2009) can describe the spontaneous movements of some cells, and that some cells have spontaneous movement patterns that can be approximated by Lévy walks, as first proposed by Schuster and Levandowsky (1996) [F.L. Schuster, M. Levandowsky, Journal of Eukaryotic Microbiology 43 (1996) 150].