Noise from spatial heterogeneity changes signal amplification magnitude and increases the variability in dose responses

In most molecular level simulations, spatial heterogeneity is neglected by the well-mixed condition assumption. However, the signals of biomolecular networks are affected from both time and space, which are responsible for diverse physiological responses. To account the spatial heterogeneity in the kinetic model, we consider multiple subvolumes of a reaction, introduce parameters representing transfer of ligands between the volumes, and reduce this to an error-term representing the difference between the well-mixed condition and the actual spatial factors. The error-term approach allows modelling of varying spatial heterogeneity without increasing computational burden exponentially. The effect of varying this term, d, between 0 (well-mixed) and 1 (no mixing) and of adding noise to the kinetic constants was then investigated and correlated with knowledge of the behaviour of real systems and situations where network models are inadequate. The spatial distribution effects on the epidermal growth factor receptor (EGFR) in human mammary epithelial tissue, which is involved in proliferation and tumorigenesis, are studied by introducing noisy kinetic constants. The steady-state of the dose response in the EGFR is strongly affected by spatial fluctuations. The ligand-bound receptor is reduced up to 50% from the response without spatial fluctuations and the variance of the steady-state is increased at least 2-fold from the one for no spatial fluctuations. On the other hand, dynamic properties such as the rising time and overshoot are less sensitive to spatial noise

Development, Differentiation, and Yield

The task of reviewing some of the ways development and differentiation may act as determinants of economic yield would be much simpler had knowledge advanced to a point where the basic principles concerned in the control of these processes in eukaryotic organisms were clear. Unfortunately, this stage has not yet been reached. There is no shortage of schemes and hypotheses to set beside a mountain of observational and experimental data, but the unifying thread which might allow us to pick out the significant and reject the irrelevant in any particular context is still lacking. What is incontestable is that development and differentiation are manifestations of gene function, so the fundamental problem can at least be defined: it is to understand how gene action is governed in ontogeny so as to give orderly expression to the potentialities attained during the evolutionary history of a species, producing an organism that is harmoniously coordinated both within itself and with the environment. I will begin by considering some general aspects of this problem as it applies to higher plants

Stochastic noise and synchronisation during Dictyostelium aggregation make cAMP oscillations robust

The molecular network, which underlies the oscillations in the concentration of adenosine 3′, 5′-cyclic monophosphate (cAMP) during the aggregation phase of starvation-induced development in Dictyostelium discoideum, achieves remarkable levels of robust performance in the face of environmental variations and cellular heterogeneity. However, the reasons for this robustness remain poorly understood. Tools and concepts from the field of control engineering provide powerful methods for uncovering the mechanisms underlying the robustness of these types of biological systems. Using such methods, two important factors contributing to the robustness of cAMP oscillations in Dictyostelium are revealed. First, stochastic fluctuations in the molecular interactions of the intracellular network, arising from random or directional noise and biological sources, play an important role in preserving stable oscillations in the face of variations in the kinetics of the network. Second, synchronisation of the aggregating cells through the diffusion of extracellular cAMP appears to be a key factor in ensuring robustness to cell-to-cell variations of the oscillatory waves of cAMP observed in Dictyostelium cell cultures. The conclusions have important general implications for the robustness of oscillating biomolecular networks (whether seen at organism, cell, or intracellular levels and including circadian clocks or Ca2+ oscillations, etc.), and suggest that such analysis can be conducted more reliably by using models including stochastic simulations, even in the case where molecular concentrations are very high

Elucidating the mechanisms of cooperative calcium-calmodulin interactions: a structural systems biology approach

BACKGROUND: Calmodulin is an important multifunctional molecule that regulates the activities of a large number of proteins in the cell. Calcium binding induces conformational transitions in calmodulin that make it specifically active to particular target proteins. The precise mechanisms underlying calcium binding to calmodulin are still, however, quite poorly understood. RESULTS: In this study, we adopt a structural systems biology approach and develop a mathematical model to investigate various types of cooperative calcium-calmodulin interactions. We compare the predictions of our analysis with physiological dose-response curves taken from the literature, in order to provide a quantitative comparison of the effects of different mechanisms of cooperativity on calcium-calmodulin interactions. The results of our analysis reduce the gap between current understanding of intracellular calmodulin function at the structural level and physiological calcium-dependent calmodulin target activation experiments. CONCLUSION: Our model predicts that the specificity and selectivity of CaM target regulation is likely to be due to the following factors: variations in the target-specific Ca2+ dissociation and cooperatively effected dissociation constants, and variations in the number of Ca2+ ions required to bind CaM for target activation

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

<b>Background</b>: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. <b>Results</b>: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and <i>mdm2</i> messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. <b>Conclusion</b>: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks

Crosstalk between G-protein and Ca2+ pathways switches intracellular cAMP levels

Cyclic adenosine monophosphate and cyclic guanosine monophosphate are universal intracellular messengers whose concentrations are regulated by molecular networks comprised of different isoforms of the synthases adenylate cyclase or guanylate cyclase and the phosphodiesterases which degrade these compounds. In this paper, we employ a systems biology approach to develop mathematical models of these networks that, for the first time, take into account the different biochemical properties of the isoforms involved. To investigate the mechanisms underlying the joint regulation of cAMP and cGMP, we apply our models to analyse the regulation of cilia beat frequency in Paramecium by Ca(2+). Based on our analysis of these models, we propose that the diversity of isoform combinations that occurs in living cells provides an explanation for the huge variety of intracellular processes that are dependent on these networks. The inclusion of both G-protein receptor and Ca(2+)-dependent regulation of AC in our models allows us to propose a new explanation for the switching properties of G-protein subunits involved in nucleotide regulation. Analysis of the models suggests that, depending on whether the G-protein subunit is bound to AC, Ca(2+) can either activate or inhibit AC in a concentration-dependent manner. The resulting analysis provides an explanation for previous experimental results that showed that alterations in Ca(2+) concentrations can either increase or decrease cilia beat frequency over particular Ca(2+) concentration ranges

Domestication, Genomics and the Future for Banana

Background Cultivated bananas and plantains are giant herbaceous plants within the genus Musa. They are both sterile and parthenocarpic so the fruit develops without seed. The cultivated hybrids and species are mostly triploid (2n = 3x = 33; a few are diploid or tetraploid), and most have been propagated from mutants found in the wild. With a production of 100 million tons annually, banana is a staple food across the Asian, African and American tropics, with the 15 % that is exported being important to many economies. Scope There are well over a thousand domesticated Musa cultivars and their genetic diversity is high, indicating multiple origins from different wild hybrids between two principle ancestral species. However, the difficulty of genetics and sterility of the crop has meant that the development of new varieties through hybridization, mutation or transformation was not very successful in the 20th century. Knowledge of structural and functional genomics and genes, reproductive physiology, cytogenetics, and comparative genomics with rice, Arabidopsis and other model species has increased our understanding of Musa and its diversity enormously. Conclusions There are major challenges to banana production from virulent diseases, abiotic stresses and new demands for sustainability, quality, transport and yield. Within the genepool of cultivars and wild species there are genetic resistances to many stresses. Genomic approaches are now rapidly advancing in Musa and have the prospect of helping enable banana to maintain and increase its importance as a staple food and cash crop through integration of genetical, evolutionary and structural data, allowing targeted breeding, transformation and efficient use of Musa biodiversity in the future

Validation of a model of regulation in the tryptophan operon against multiple experiment data using global optimisation

This paper is concerned with validating a mathematical model of regulation in the tryptophan operon using global optimization. Although a number of models for this biochemical network are proposed, in many cases only qualitative agreement between the model output and experimental data was demonstrated, since very little information is currently available to guide the selection of parameter values for the models. This paper presents a model validating method using both multiple experimental data and global optimization

Computational modelling suggests dynamic interactions between Ca2+, IP3 and G protein-coupled modules are key to robust Dictyostelium aggregation

Under conditions of starvation, Dictyostelium cells begin a programme of development during which they aggregate to form a multicellular structure by chemotaxis, guided by propagating waves of cyclic AMP that are relayed robustly from cell to cell. In this paper, we develop and analyse a new model for the intracellular and extracellular cAMP dependent processes that regulate Dictyostelium migration. The model allows, for the first time, a quantitative analysis of the dynamic interactions between calcium, IP(3) and G protein-dependent modules that are shown to be key to the generation of robust cAMP oscillations in Dictyostelium cells. The model provides a mechanistic explanation for the transient increase in cytosolic free Ca(2+) concentration seen in recent experiments with the application of the calmodulin inhibitor calmidazolium (R24571) to Dictyostelium cells, and also allows elucidation of the effects of varying both the conductivity of stretch-activated channels and the concentration of external phosphodiesterase on the oscillatory regime of an individual cell. A rigorous analysis of the robustness of the new model shows that interactions between the different modules significantly reduce the sensitivity of the resulting cAMP oscillations to variations in the kinetics of different Dictyostelium cells, an essential requirement for the generation of the spatially and temporally synchronised chemoattractant cAMP waves that guide Dictyostelium aggregation

rRNA gene activity and control of expression mediated by methylation and imprinting during embryo development in wheat x rye hybrids

Ribosomal RNA genes originating from one parent are often suppressed in interspecific hybrids. We show that treatments during germination with the cytosine analogue 5-azacytidine stably reactivate the expression of the suppressed rRNA genes of rye origin in the wheat x rye amphiploid, triticale, by preventing methylation of sites in the rye rDNA. When 5-azacytidine is applied to embryos of triticale and wheat x rye F1 hybrids nine, or more, days after fertilization, rye rRNA gene expression is stably reactivated in the resulting seedling. Earlier treatments have no effect on rye rRNA gene expression, indicating that undermethylation of DNA early in embryo development is reversible. After 9 days, the methylation status of rRNA genes in maintained throughout development. Since the change in expression follows a methylation change at particular restriction-enzyme sites, the data establish a clear correlation between gene activity and methylation in plants