Gene expression time delays & Turing pattern formation systems

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning

Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays

Turing’s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing’s model has received limited attention. Here, we novelly focus on the Gierer–Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing’s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99–130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing’s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing’s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing’s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning

Phase behavior of ganglioside-lecithin mixtures. Relation to dispersion of gangliosides in membranes.

Ganglioside GM1 and mixed brain gangliosides were mixed with 1-stearoyl-2-oleoyl lecithin (SOPC) and examined by differential scanning calorimetry as a function of ganglioside content and temperature. Low mole fractions of ganglioside GM1 and of mixed brain gangliosides are shown to be miscible with SOPC in the gel phase up to X = 0.3, with the possible exception of a small region of immiscibility for the mixed brain gangliosides system centered around X = 0.05. Above X = 0.3, the low-temperature phases demix into a (gel) phase of composition X = 0.3 and a (micellar) phase of composition X = 1.0. Above the endothermic phase transition temperature, no phase boundaries are discerned. It is pointed out that phase structures need to be determined in each domain delineated in the phase diagrams, and that cylindrical phases may exist at higher temperatures and intermediate compositions. The effects of addition of wheat germ agglutinin, which binds to ganglioside GM1, on a ganglioside GM1-SOPC mixture (X = 0.5), are described and interpreted in terms of partial demixing of ganglioside and lecithin. Behavior of the ganglioside-SOPC system is discussed with respect to the kinetics of cholera toxin action in lymphocytes, as well as to other physiological roles of gangliosides in membranes

Signal Corps Schottische

186? Publisher: Blackmar Brothers, Augusta, Ga.https://mds.marshall.edu/sc_cwmusic/1094/thumbnail.jp

Molecular conformations of cerebrosides in bilayers determined by Raman spectroscopy.

Vibrational Raman spectra of the solid and gel phases of bovine brain cerebrosides and the component fractions, kerasin and phrenosin, provide conformational information for these glycosphingolipids in bilayer systems. The carbon-carbon stretching mode profiles (1,150-1,000 cm-1) indicate that at 22 degrees C the alkyl chains assume an almost all-trans arrangement. These spectral data, combined with those from the C-H stretching region (3,050-2,800 cm-1), show that phrenosin forms the most highly ordered polycrystalline solid and kerasin the most ordered gel phase. The conformation of the unsaturated, 24-carbon acyl chains is monitored independently by a skeletal stretching mode at 1,112 cm-1. The alkyl chains in the kerasin and phrenosin gels are sufficiently extended to allow interdigitation of the 24-carbon acyl chains across the midplane of the bilayer. The amide I vibrational mode occurs at a lower frequency in solid phrenosin than kerasin, a shift consistent with stronger hydrogen bounding. This band is broadened and shifted to higher frequencies, however, in the phrenosin gel phase. In both the solid and gel phases natural cerebroside exhibits a composite amide I mode. The disruptive effects on cerebroside chain packing and headgroup orientation arising from mixing with dimyristoyl phosphatidylcholine are examined. Vibrational data for cerebroside are also compared to those for ceramide, sphingosine, and distearoyl phosphatidylcholine structures. Spectral interpretations are discussed in terms of calorimetric and X-ray structural data

MORPHOGENÈSE DANS UN SYSTÈME DE DIFFUSION-RÉACTION

Une enzyme immobilisée est représentée par : st – sxx = γf(s,a), at – βaxx = γg(s,a) où : f(s,a) = s0 – s – ρaF(s), g(s,a) = g(s,a) = α(a0 – a) – ρaF(s), F(s) = s/(1 + s + ks2). Les conditions aux limites sont : sx(0,t) = sx(1,t) = ax(1, t) = ax(0,t) = ax(1,t) = 0. s(x, t) et a(x, t) représentent les concentrations d'un substrat et d'un cosubstrat. γc est un paramètre positif, le paramètre de bifurcation. Pour γ inférieur à une valeur critique γc, le système possède un état stationnaire uniforme stable, les valeurs de s et a étant solutions de f(s,a) = 0, g(s,a) = 0. Pour γ > γc, cet état trivial perd sa stabilité et il apparaît d'autres états stationnaires stables, mais structurés en espace, proportionnels en première approximation à cos npx. L'analogie avec la morphogénèse est soulignée.An immobilized enzyme is represented by : st – sxx = γf(s,a), at – βaxx = γg(s,a) where : f(s,a) = s0 – s – ρaF(s), g(s,a) = g(s,a) = α(a0 – a) – ρaF(s), F(s) = s/(1 + s + ks2). The boundary conditions are : sx(0,t) = sx(1,t) = ax(1, t) = ax(0,t) = ax(1,t) = 0. s(x, t) and a(x, t) represent the concentration of a substrate and cosubstrate. γ is a positive parameter, the bifurcation parameter. For γ less than a critical value γc, the system possesses a uniform, stationary, stable state, the values of s and a being solutions for f(x,a) = 0 and g(s,a) = 0. For γ > γc this trivial state loses its stability and other stationary, stable states appear, these being structured in space and by first approximations, proportional to cos npx. The analogy with morphogenesis is thus pointed out