Míriam R. García

Towards predictive food process models: A protocol for parameter estimation

ABSTRACT Mathematical models, in particular, physics-based models, are essential tools to food product and process design, optimization and control. The success of mathematical models relies on their predictive capabilities. However, describing physical, chemical and biological changes in food processing requires the values of some, typically unknown, parameters. Therefore, parameter estimation from experimental data is critical to achieving desired model predictive properties. This work takes a new look into the parameter estimation (or identification) problem in food process modeling. First, we examine common pitfalls such as lack of identifiability and multimodality. Second, we present the theoretical background of a parameter identification protocol intended to deal with those challenges. And, to finish, we illustrate the performance of the proposed protocol with an example related to the thermal processing of packaged foods.

Quality and shelf-life prediction for retail fresh hake (Merluccius merluccius)

Fish quality has a direct impact on market price and its accurate assessment and prediction are of main importance to set prices, increase competitiveness, resolve conflicts of interest and prevent food wastage due to conservative product shelf-life estimations. In this work we present a general methodology to derive predictive models of fish freshness under different storage conditions. The approach makes use of the theory of optimal experimental design, to maximize data information and in this way reduce the number of experiments. The resulting growth model for specific spoilage microorganisms in hake (Merluccius merluccius) is sufficiently informative to estimate quality sensory indexes under time-varying temperature profiles. In addition it incorporates quantitative information of the uncertainty induced by fish variability. The model has been employed to test the effect of factors such as fishing gear or evisceration, on fish spoilage and therefore fish quality. Results show no significant differences in terms of microbial growth between hake fished by long-line or bottom-set nets, within the implicit uncertainty of the model. Similar conclusions can be drawn for gutted and un-gutted hake along the experiment horizon. In addition, whenever there is the possibility to carry out the necessary experiments, this approach is sufficiently general to be used in other fish species and under different stress variables.

A Slow Axon Antidromic Blockade Hypothesis for Tremor Reduction via Deep Brain Stimulation

Parkinsonian and essential tremor can often be effectively treated by deep brain stimulation. We propose a novel explanation for the mechanism by which this technique ameliorates tremor: a reduction of the delay in the relevant motor control loops via preferential antidromic blockade of slow axons. The antidromic blockade is preferential because the pulses more rapidly clear fast axons, and the distribution of axonal diameters, and therefore velocities, in the involved tracts, is sufficiently long-tailed to make this effect quite significant. The preferential blockade of slow axons, combined with gain adaptation, results in a reduction of the mean delay in the motor control loop, which serves to stabilize the feedback system, thus ameliorating tremor. This theory, without any tuning, accounts for several previously perplexing phenomena, and makes a variety of novel predictions.

A single compartment model of pacemaking in dissasociated Substantia nigra neurons

Spontaneous oscillations in the mid-brain dopaminergic neurons are an important feature of motor control. The degeneration of these neurons is involved in movement disorders, particularly Parkinson’s Disease. Modelling of this activity is an important part of developing an understanding of the pathogenic process. We develop a mathematical paradigm to describe this activity with a single compartment approach and a CellML version is made publicly available. The model explicitly describes the dynamics of the transmembrane potential with changes in the levels of important cations and is consistent with two major observations in the literature regarding its behaviour in the presence of channel blockers. Stability of the model behaviour is determined from the properties of its Monodromy matrix. We also discuss from the perspective of energy, a pharmacological intervention suggested in the treatment of Parkinson’s Disease.

Spatial quantification of cytosolic Ca 2+ accumulation in nonexcitable cells: an analytical study

Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca2+ accumulation is independent of every intracellular calcium flux and depends on the Ca2+ exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca2+ perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.

Positive feedback in the Akt/mTOR pathway and its implications for growth signal progression in skeletal muscle cells: An analytical study

The IGF-1 mediated Akt/mTOR pathway has been recently proposed as mediator of skeletal muscle growth and a positive feedback between Akt and mTOR was suggested to induce homogeneous growth signals along the whole spatial extension of such long cells. Here we develop two biologically justified approximations which we study under the presence of four different initial conditions that describe different paradigms of IGF-1 receptor-induced Akt/mTOR activation. In first scenario the activation of the feedback cascade was assumed to be mild or protein turnover considered to be high. In turn, in the second scenario the transcriptional regulation was assumed to maintain defined levels of inactive pro-enzymes. For both scenarios, we were able to obtain closed-form formulas for growth signal progression in time and space and found that a localised initial signal maintains its Gaussian shape, but gets delocalised and exponentially degraded. Importantly, mathematical treatment of the reaction diffusion system revealed that diffusion filtered out high frequencies of spatially periodic initiator signals suggesting that the muscle cell is robust against fluctuations in spatial receptor expression or activation. However, neither scenario was consistent with the presence of stably travelling signal waves. Our study highlights the role of feedback loops in spatiotemporal signal progression and results can be applied to studies in cell proliferation, cell differentiation and cell death in other spatially extended cells.

Deep brain stimulation may reduce tremor by preferential blockade of slower axons via antidromic activation

Deep brain stimulation (DBS) has been used to ameliorate essential and Parkinsonian tremor, however the detailed mechanism by which tremor reduction is achieved remains unclear. We hypothesize that DBS works by reducing time delays in the feedback paths of the motor control loops. In particular, we suggest that antidromic activation of axonal pathways induced by stimulation will preferentially block axons with longer propagation times, reducing time delays in neuronal motor circuits in a stabilising manner. We demonstrate the plausibility of this hypothesis using two simple computational models which account for a variety of experimental results, and allow us to makes a number of testable predictions.

Detection of Peptidic Sequences in the Ancient Acidic Sediments of Río Tinto, Spain

Biomarkers are molecules that are produced by or can be associated with biological activities. They can be used as tracers that give us an idea of the ancient biological communities that produced them, the paleoenvironmental conditions where they lived, or the mechanism involved in their transformation and preservation. As a consequence, the preservation potential of molecules over time depends largely on their nature, but also on the conditions of the environment, which controls the decomposition kinetics. In this context, proteins and nucleic acids, which are biomolecules bearing biological information, are among the most labile molecules. In this research, we report the presence of short-chained peptides obtained from extracts of ferruginous sedimentary deposits that have been produced under the acidic and oxidizing solutions of Río Tinto, Spain. These preliminary results go against the paradigmatic idea that considers the acidic and oxidizing environments inappropriate for the preservation of molecular information.

Cumulative Signal Transmission in Nonlinear Reaction- Diffusion Networks

Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network’s ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand.

Analytic computation of the integrated response in nonlinear reaction-diffusion systems

In this work we analytically derive the time-integral of a class of nonlinear reaction-diffusion systems commonly found in networks of biochemical reactions. This formula is inferred using the Laplacian Spectral Decomposition method, which approximates the solution of the Partial Differential Equations by a finite series capturing the most relevant dynamics. The time-integrals allow us to understand how signal transmission depends on initial and boundary conditions, spatial geometry and the turnover rates of some species.