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

Determination of the distribution of catalyst activity across a permeable membrane containing an immobilized enzyme. Indeterminacy of a functional approach to a structural problem.

Porous membranes were fabricated from collodion and impregnated with papain, inhomogeneously through the thickness of the membrane. These membranes were placed between reservoirs containing N-alpha-benzoyl arginineamide, a substrate for the enzyme papain. The progress of the reaction was monitored by sampling the reservoirs on each side for ammonia, a reaction product. From these data the diffusion coefficient, enzyme activity, and distribution of enzyme activity of the membrane were estimated. The limitations of this approach are discussed in the context of the analysis of biological transport systems

Complete analysis of the cytochrome components of beef heart mitochondria in terms of spectra and redox properties. Cytochromes aa3.

Using newer techniques of data collection that accumulate entire spectra at a series of discrete voltages and newer techniques of analysis that utilize the additional data, we have re-examined the redox behavior and corresponding difference spectra of redox centers responsible for the alpha absorbance features of cytochromes aa3 in beef heart mitochondria. Our analysis reveals three Nernstian components with Em values of 200, 260, and 340 mV with n values of 2, 2, and 1, respectively. The maximum alpha absorbance in the difference spectra for each of these species is located at 602, 605, and 607 nm respectively. Titrations in the presence of carbon monoxide led to the identification of the lowest voltage species as cytochrome a3. The Em of the carbon monoxide-liganded species was not raised. This is contrary to the result expected when a ligand has a much stronger affinity for the reduced form of a redox couple than the oxidized form. It is, however, consistent with a proton-pumping model of cytochrome oxidase in which the binding of ligand results in the dissociation of protons