First Passage and Cooperativity of Queuing Kinetics

We model the kinetics of ligand-receptor systems, where multiple ligands may bind and unbind to the receptor, either randomly or in a specific order. Equilibrium occupation and first occurrence of complete filling of the receptor are determined and compared. At equilibrium, receptors that bind ligands sequentially are more likely to be saturated than those that bind in random order. Surprisingly however, for low cooperativity, the random process first reaches full occupancy faster than the sequential one. This is true {\it except} near a critical binding energy where a 'kinetic trap' arises and the random process dramatically slows down when the number of binding sites $N\geq 8$. These results demonstrate the subtle interplay between cooperativity and sequentiality for a wide class of kinetic phenomena, including chemical binding, nucleation, and assembly line strategies.Comment: 5pp, 5 figure

Information flow during gene activation by signaling molecules: ethylene transduction in Arabidopsis cells as a study system

<p>Abstract</p> <p>Background</p> <p>We study root cells from the model plant <it>Arabidopsis thaliana </it>and the communication channel conformed by the ethylene signal transduction pathway. A basic equation taken from our previous work relates the probability of expression of the gene <it>ERF</it>1 to the concentration of ethylene.</p> <p>Results</p> <p>The above equation is used to compute the Shannon entropy (<it>H</it>) or degree of uncertainty that the genetic machinery has during the decoding of the message encoded by the ethylene specific receptors embedded in the endoplasmic reticulum membrane and transmitted into the nucleus by the ethylene signaling pathway. We show that the amount of information associated with the expression of the master gene <it>ERF</it>1 (Ethylene Response Factor 1) can be computed. Then we examine the system response to sinusoidal input signals with varying frequencies to determine if the cell can distinguish between different regimes of information flow from the environment. Our results demonstrate that the amount of information managed by the root cell can be correlated with the frequency of the input signal.</p> <p>Conclusion</p> <p>The ethylene signaling pathway cuts off very low and very high frequencies, allowing a window of frequency response in which the nucleus reads the incoming message as a sinusoidal input. Out of this window the nucleus reads the input message as an approximately non-varying one. From this frequency response analysis we estimate: a) the gain of the system during the synthesis of the protein ERF1 (~-5.6 dB); b) the rate of information transfer (0.003 bits) during the transport of each new ERF1 molecule into the nucleus and c) the time of synthesis of each new ERF1 molecule (~21.3 s). Finally, we demonstrate that in the case of the system of a single master gene (<it>ERF</it>1) and a single slave gene (<it>HLS</it>1), the total Shannon entropy is completely determined by the uncertainty associated with the expression of the master gene. A second proposition shows that the Shannon entropy associated with the expression of the <it>HLS</it>1 gene determines the information content of the system that is related to the interaction of the antagonistic genes <it>ARF</it>1, 2 and <it>HLS</it>1.</p

The mEPN scheme: an intuitive and flexible graphical system for rendering biological pathways

<p>Abstract</p> <p>Background</p> <p>There is general agreement amongst biologists about the need for good pathway diagrams and a need to formalize the way biological pathways are depicted. However, implementing and agreeing how best to do this is currently the subject of some debate.</p> <p>Results</p> <p>The modified Edinburgh Pathway Notation (mEPN) scheme is founded on a notation system originally devised a number of years ago and through use has now been refined extensively. This process has been primarily driven by the author's attempts to produce process diagrams for a diverse range of biological pathways, particularly with respect to immune signaling in mammals. Here we provide a specification of the mEPN notation, its symbols, rules for its use and a comparison to the proposed Systems Biology Graphical Notation (SBGN) scheme.</p> <p>Conclusions</p> <p>We hope this work will contribute to the on-going community effort to develop a standard for depicting pathways and will provide a coherent guide to those planning to construct pathway diagrams of their biological systems of interest.</p

Construction of a large scale integrated map of macrophage pathogen recognition and effector systems

<p>Abstract</p> <p>Background</p> <p>In an effort to better understand the molecular networks that underpin macrophage activation we have been assembling a map of relevant pathways. Manual curation of the published literature was carried out in order to define the components of these pathways and the interactions between them. This information has been assembled into a large integrated directional network and represented graphically using the modified Edinburgh Pathway Notation (mEPN) scheme.</p> <p>Results</p> <p>The diagram includes detailed views of the toll-like receptor (TLR) pathways, other pathogen recognition systems, NF-kappa-B, apoptosis, interferon signalling, MAP-kinase cascades, MHC antigen presentation and proteasome assembly, as well as selected views of the transcriptional networks they regulate. The integrated pathway includes a total of 496 unique proteins, the complexes formed between them and the processes in which they are involved. This produces a network of 2,170 nodes connected by 2,553 edges.</p> <p>Conclusions</p> <p>The pathway diagram is a navigable visual aid for displaying a consensus view of the pathway information available for these systems. It is also a valuable resource for computational modelling and aid in the interpretation of functional genomics data. We envisage that this work will be of value to those interested in macrophage biology and also contribute to the ongoing Systems Biology community effort to develop a standard notation scheme for the graphical representation of biological pathways.</p

Understanding the Sub-Cellular Dynamics of Silicon Transportation and Synthesis in Diatoms Using Population-Level Data and Computational Optimization

Controlled synthesis of silicon is a major challenge in nanotechnology and material science. Diatoms, the unicellular algae, are an inspiring example of silica biosynthesis, producing complex and delicate nano-structures. This happens in several cell compartments, including cytoplasm and silica deposition vesicle (SDV). Considering the low concentration of silicic acid in oceans, cells have developed silicon transporter proteins (SIT). Moreover, cells change the level of active SITs during one cell cycle, likely as a response to the level of external nutrients and internal deposition rates. Despite this topic being of fundamental interest, the intracellular dynamics of nutrients and cell regulation strategies remain poorly understood. One reason is the difficulties in measurements and manipulation of these mechanisms at such small scales, and even when possible, data often contain large errors. Therefore, using computational techniques seems inevitable. We have constructed a mathematical model for silicon dynamics in the diatom Thalassiosira pseudonana in four compartments: external environment, cytoplasm, SDV and deposited silica. The model builds on mass conservation and Michaelis-Menten kinetics as mass transport equations. In order to find the free parameters of the model from sparse, noisy experimental data, an optimization technique (global and local search), together with enzyme related penalty terms, has been applied. We have connected population-level data to individual-cell-level quantities including the effect of early division of non-synchronized cells. Our model is robust, proven by sensitivity and perturbation analysis, and predicts dynamics of intracellular nutrients and enzymes in different compartments. The model produces different uptake regimes, previously recognized as surge, externally-controlled and internally-controlled uptakes. Finally, we imposed a flux of SITs to the model and compared it with previous classical kinetics. The model introduced can be generalized in order to analyze different biomineralizing organisms and to test different chemical pathways only by switching the system of mass transport equations