A Characterization of Scale Invariant Responses in Enzymatic Networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of enzymatic networks. Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions

Scale-invariance.

<p>Plots overlap, for responses to steps and . Network is the one described by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002748#pcbi.1002748.e076" target="_blank">Eq.2</a>. Random parameter set: , , , , , , , .</p

QSS quadratic approximation.

<p>Network is the one described by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002748#pcbi.1002748.e076" target="_blank">Eq.2</a>. Random parameter set is as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002748#pcbi-1002748-g002" target="_blank">Fig. 2</a>.</p

Constant A/B ratio in responses to <b> and </b>.

<p>Network is the one described by <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002748#pcbi.1002748.e076" target="_blank">Eq.2</a>. Random parameter set is as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002748#pcbi-1002748-g002" target="_blank">Fig. 2</a>. Similar results are available for all ASI circuits (see <i><a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002748#pcbi.1002748.s001" target="_blank">Text S1</a></i>).</p

Scale-invariance computed when using the model in [<b>34</b>]:

<p>Responses to steps and coincide.</p

An Approach Based on Hierarchical Bayesian Graphical Models for Measurement Interpretation under Uncertainty

It is not uncommon in the field of non-destructive evaluation that multiple measurements encompassing a variety of modalities are available for analysis and interpretation for determining the underlying states of nature of the materials or parts being tested. Despite and sometimes due to the richness of data, significant challenges arise in the interpretation manifested as ambiguities and inconsistencies due to various uncertain factors in the physical properties (inputs), environment, measurement device properties, human errors, and the measurement data (outputs). Most of these uncertainties cannot be described by any rigorous mathematical means, and modeling of all possibilities is usually infeasible for many real time applications.In this work, we will discuss an approach based on Hierarchical Bayesian Graphical Models (HBGM) for the improved interpretation of complex (multi-dimensional) problems with parametric uncertainties that lack usable physical models. In this setting, the input space of the physical properties is specified through prior distributions based on domain knowledge and expertise, which are represented as Gaussian mixtures to model the various possible scenarios of interest for non-destructive testing applications. Forward models are then used offline to generate the expected distribution of the proposed measurements which are used to train a hierarchical Bayesian network. In Bayesian analysis, all model parameters are treated as random variables, and inference of the parameters is made on the basis of posterior distribution given the observed data. Learned parameters of the posterior distribution obtained after the training can therefore be used to build an efficient classifier for differentiating new observed data in real time on the basis of pre-trained models. We will illustrate the implementation of the HBGM approach to ultrasonic measurements used for cement evaluation of cased wells in the oil industry.</p

Topology 2293.

<p>An example of a topology.</p