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.

Dynamics and intrinsic statistical fluctuations of a gene switch

We studied a simple gene regulatory network, the toggle switch. Specifically, we examined the means and statistical fluctuations in numbers of proteins. We found that when omega, the ratio of rates of protein-gene unbinding to protein degradation, was between similar to 10(-3) and similar to 10, the fluctuations were much larger than those we would have expected from Poisson statistics. In addition, we examined characteristic time values for system relaxation and found both that they increased with omega and that they have significant phase transition effects, with a secondary time scale appearing near the boundary between bistable and other phases. Last, we discuss the bistability of the toggle switch.

Comparing the morphology and phase diagram of H-shaped ABC block copolymers and linear ABC block copolymers

By using a combinatorial screening method based on the self-consistent field theory (SCFT) for polymers, we have investigated the morphology of H-shaped ABC block copolymers (A(2)BC(2)) and compared them with those of the linear ABC block copolymers. By changing the ratios of the volume fractions of two A arms and two C arms, one can obtain block copolymers with different architectures ranging from linear block copolymer to H-shaped block copolymer. By systematically varying the volume fractions of block A, B, and C, the triangle phase diagrams of the H-shaped ABC block copolymer with equal interactions among the three species are constructed. In this study, we find four different morphologies ( lamellar phase ( LAM), hexagonal lattice phase ( HEX), core-shell hexagonal lattice phase (CSH), and two interpenetrating tetragonal lattice (TET2)). Furthermore, the order-order transitions driven by architectural change are discussed.

Miscibility and phase behavior in blends containing random copolymers of poly(ether ether ketone) and phenolphthalein poly(ether ether ketone)

The miscibility and phase behavior of polysulfone (PSF) and poly(hydroxyether of bisphenol A) (phenoxy) with a series of copoly(ether ether ketone) (COPEEK), a random copolymer of poly(ether ether ketone) (PEEK), and phenolphthalein poly(ether ether ketone) (PEK-C) was studied using differential scanning calorimetry. A COPEEK copolymer containing 6 mol % ether ether ketone (EEK) repeat units is miscible with PSF, whereas copolymers containing 12 mol % EEK and more are not. COPEEK copolymers containing 6 and 12 mol % EEK are completely miscible with phenoxy, but those containing 24 mol % EEK and more are immiscible with phenoxy. Moreover, a copolymer containing 17 mol % EEK is partially miscible with phenoxy; the blends show two transitions in the midcomposition region and single transitions at either extreme. Two T(g)s were observed for the 50/50 blend of phenoxy with the copolymer containing 17 mol % EEK, whereas a single composition-dependent T-g appeared for all the other compositions. An FTIR study revealed that there exist hydrogen-bonding interactions between phenoxy and the copolymers. The strengths of the hydrogen-bonding interactions in the blends of the COPEEK copolymers containing 6 and 12 mol % EEK are the same as that in the phenoxy/PEK-C blend. However, for the blends of copolymers containing 17, 24, and 28 mol % EEK, the hydrogen-bonding interactions become increasingly unfavorable and the self-association of the hydroxyl groups of phenoxy is preferable as the content of EEK units in the copolymer increases. The observed miscibility was interpreted qualitatively in terms of the mean-field approach. (C) 1996 John Wiley & Sons, Inc.

MISCIBILITY AND PHASE-BEHAVIOR IN BLENDS OF POLY(HYDROXYETHER OF BISPHENOL-A) WITH POLY(ETHYLENE OXIDE-CO-PROPYLENE OXIDE)

The miscibility of poly(hydroxyether of bisphenol A) (phenoxy) with a series of poly(ethylene oxide-co-propylene oxide) (EPO) has been studied. It was found that the critical copolymer composition for achieving miscibility with phenoxy around 60-degrees-C is about 22 mol % ethylene oxide (EO). Some blends undergo phase separation at elevated temperatures, but there is no maximum in the miscibility window. The mean-field approach has been used to describe this homopolymer/copolymer system. From the miscibility maps and the melting-point depression of the crystallizable component in the blends, the binary interaction energy densities, B(ij), have been calculated for all three pairs. The miscibility of phenoxy with EPO is considered to be caused mainly by the intermolecular hydrogen-bonding interactions between the hydroxyl groups of phenoxy and the ether oxygens of the EO units in the copolymers, while the intramolecular repulsion between EO and propylene oxide units in the copolymers contributes relatively little to the miscibility.

Dielectric responses of graded cylindrical composites

The effective dielectric responses of linear composites with graded cylindrical particles are investigated under an external uniform electric field. As an example, with the Kummer function, we have obtained the analytical solutions of electric potentials of graded composites with a cylindrical inclusion particle of dielectric function profile epsilon(i) = cr(k)e(betar), where r is the inside distance of a point in cylindrical particle from the original point of cylindrical coordinates. In the dilute limit, the effective dielectric response is derived by means of the mean field method. For larger volume fraction, we have estimated the dielectric response of the graded composites with an effective medium approximation. Furthermore, from our results, we have discussed the effective responses of graded composites for power-law and exponential dielectric function profiles, respectively. (C) 2004 Elsevier B.V. All rights reserved.

Dielectric responses of anisotropic graded granular composites having arbitrary inclusion shapes

The transformation field method (TFM) originated from Eshelby's transformation field theory is developed to estimate the effective permittivity of an anisotropic graded granular composite having inclusions of arbitrary shape and arbitrary anisotropic grading profile. The complicated boundary-value problem of the anisotropic graded composite is solved by introducing an appropriate transformation field within the whole composite region. As an example, the effective dielectric response for an anisotropic graded composite with inclusions having arbitrary geometrical shape and arbitrary grading profile is formulated. The validity of TFM is tested by comparing our results with the exact solution of an isotropic graded composite having inclusions with a power-law dielectric grading profile and good agreement is achieved in the dilute limit. Furthermore, it is found that the inclusion shape and the parameters of the grading profile can have profound effect on the effective permittivity at high concentrations of the inclusions. It is pointed out that TFM used in this paper can be further extended to investigate the effective elastic, thermal, and electroelastic properties of anisotropic graded granular composite materials.