Potential energy landscape and robustness of a gene regulatory network: Toggle switch

Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers.

Quantifying robustness and dissipation cost of yeast cell cycle network: The funneled energy landscape perspectives

We study the origin of robustness of yeast cell cycle cellular network through uncovering its underlying energy landscape. This is realized from the information of the steady-state probabilities by solving a discrete set of kinetic master equations for the network. We discovered that the potential landscape of yeast cell cycle network is funneled toward the global minimum, G1 state. The ratio of the energy gap between G1 and average versus roughness of the landscape termed as robustness ratio ( RR) becomes a quantitative measure of the robustness and stability for the network. The funneled landscape is quite robust against random perturbations from the inherent wiring or connections of the network. There exists a global phase transition between the more sensitive response or less self-degradation phase leading to underlying funneled global landscape with large RR, and insensitive response or more self-degradation phase leading to shallower underlying landscape of the network with small RR. Furthermore, we show that the more robust landscape also leads to less dissipation cost of the network. Least dissipation and robust landscape might be a realization of Darwinian principle of natural selection at cellular network level. It may provide an optimal criterion for network wiring connections and design.

Transformation from ordered islands to holes in phase-separating P2VP/PS blend films by adding triton X-100

Our previous investigation showed that the ordered hexagonal island pattern in the phase-separating polymeric blend films of polystyrene and poly(2-vinylpyridine) (PS/P2VP) formed due to the convection effect by proper control of PS molecular weight, solvent evaporation rate, and the weight ratio of PS to P2VP. In this paper, we further illustrate that, by adding a proper amount of the surfactant Triton X-100 to the PS/P2VP toluene solution, the ordered hexagonal island pattern can be transformed to the ordered honeycomb pattern. The effects of the amount of Triton X-100 on the surface morphology evolution and the pattern transformation are discussed in terms of the collapse of Triton X-100, phase separation between Triton X-100/P2VP and PS, the interfacial interaction between Triton X-100/P2VP and the mica substrate, and the Benard-Marangoni convection.

The combined catalytic action of solid acids with nickel for the transformation of polypropylene into carbon nanotubes by pyrolysis

The effects of both organically modified montmorillonite (OMMT) and Ni2O3 on the carbonization of polypropylene (PP) during pyrolysis were investigated. The results from TEM and Raman spectroscopy showed that the carbonized products of PP were mainly multiwalled carbon nanotubes (MWNTs). Surprisingly, a combination of OMMT and Ni2O3 led to high-yield formation of MWNTs. X-ray powder diffraction (XRD) and GC-MS were used to investigate the mechanism of this combination for the high-yield formation of MWNTs from PP. Bronsted acid sites were created in degraded OMMT layers by thermal decomposition of the modifiers. The resultant carbenium ions play an important role in the carbonization of PP and the formation of MWNTs. The degradation of PP was induced by the presence of carbenium ions to form predominantly products with lower carbon numbers that could be easily catalyzed by the nickel catalyst for the growth of MWNTs. Furthermore, carbenium ions are active intermediates that promote the growth of MWNTs from the degradation products with higher carbon numbers through hydride-transfer reactions. The XRD measurements showed that Ni2O3 was reduced into metallic nickel (Ni) in situ to afford the active sites for the growth of MWNTs.

Dominant kinetic paths on biomolecular binding-folding energy landscape

The identification of kinetic pathways is a central issue in understanding the nature of flexible binding. A new approach is proposed here to study the dynamics of this binding-folding process through the establishment of a path integral framework on the underlying energy landscape. The dominant kinetic paths of binding and folding can be determined and quantified. In this case, the corresponding kinetic paths of binding are shown to be intimately correlated with those of folding and the dynamics becomes quite cooperative. The kinetic time can be obtained through the contributions from the dominant paths and has a U-shape dependence on temperature.

Funneled landscape leads to robustness of cellular networks: MAPK signal transduction

We uncover the underlying potential energy landscape for a cellular network. We find that the potential energy landscape of the mitogen-activated protein-kinase signal transduction network is funneled toward the global minimum. The funneled landscape is quite robust against random perturbations. This naturally explains robustness from a physical point of view. The ratio of slope versus roughness of the landscape becomes a quantitative measure of robustness of the network. Funneled landscape is a realization of the Darwinian principle of natural selection at the cellular network level. It provides an optimal criterion for network connections and design. Our approach is general and can be applied to other cellular networks.

Multiple morphologies and their transformation of a polystyrene-block-poly(4-vinylpyridine) block copolymer

We report the multiple morphologies and their transformation of polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) in low-alkanol solvents. In order to improve the solubility of polystyrene block in alcohol solvents, the solution of block copolymer sample was treated at a higher temperature, and then the influence of rate of decreasing temperature on multiple morphologies (including spheres, rods, vesicles, porous vesicles, large compound vesicles, and large compound micelles) was observed. The transformation of spheres to rods, to tyre-shaped large compound micelles, and to sphere-shaped large compound micelles was also realized. The formation mechanisms of the multiple morphologies and their transformation are discussed briefly.

Diffusion and single molecule dynamics on biomolecular interface binding energy landscape

We propose a new approach to study the diffusion dynamics on biomolecular interface binding energy landscape. The resulting mean first passage time (MFPT) has 'U'curve dependence on the temperature. It is shown that the large specificity ratio of gap to roughness of the underlying binding energy landscape not only guarantees the thermodynamic stability and the specificity [P.A. Rejto, G.M. Verkhivker, in: Proc. Natl. Acad. Sci. 93 (1996) 8945; C.J. Tsai, S. Kumar, B. Ma, R. Nussinov, Protein Sci. 8 (1999) 1181; G.A. Papoian, P.G. Wolynes, Biopolymers 68 (2003) 333; J. Wang, G.M. Verkhivker, Phys. Rev. Lett. 90 (2003) 198101] but also the kinetic accessibility. The complex kinetics and the associated fluctuations reflecting the structures of the binding energy landscape emerge upon temperature changes. The theory suggests a way of connecting the models/simulations with single molecule experiments by analysing the kinetic trajectories.

Mechanism of phase transformation and formation of barium hexaferrite doped with rare-earths in sol-gel process

The phase-transformation in sol-gel preparation of barium hexaferrite and the formation of barium hexaferrite doped with La3+ Were studied by chemical phase analysis, X-ray diffraction and infrared spectrometry analysis. The experimental results show that phase transformation reactions of FeCO3, Fe2O3 and BaFe2O4, barium hexaferrite and gamma-Fe2O3 take place in the heat treatment of gel. While the doping lanthanide ion replace barium ion, an equivalent quantity of Fe3+ are reduced to Fe2+ to maintain the charge equilibrium.

Energy landscape theory, funnels, specificity, and optimal criterion of biomolecular binding

We study the nature of biomolecular binding. We found that in general there exists several thermodynamic phases: a native binding phase, a non-native phase, and a glass or local trapping phase. The quantitative optimal criterion for the binding specificity is found to be the maximization of the ratio of the binding transition temperature versus the trapping transition temperature, or equivalently the ratio of the energy gap of binding between the native state and the average non-native states versus the dispersion or variance of the non-native states. This leads to a funneled binding energy landscape.

Diffusion dynamics, moments, and distribution of first-passage time on the protein-folding energy landscape, with applications to single molecules

We study the dynamics of protein folding via statistical energy-landscape theory. In particular, we concentrate on the local-connectivity case with the folding progress described by the fraction of native conformations. We found that the first passage-time (FPT) distribution undergoes a dynamic transition at a temperature below which the FPT distribution develops a power-law tail, a signature of the intermittent nonexponential kinetic phenomena for the folding dynamics. Possible applications to single-molecule dynamics experiments are discussed.