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  • 1
    Language: English
    In: Journal of Theoretical Biology, May 21, 2012, Vol.301, p.15(13)
    Description: To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.jtbi.2012.01.026 Byline: Fernando Lopez-Caamal (a), Miriam R. Garcia (a), Richard H. Middleton (a), Heinrich J. Huber (b) Abstract: 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. Author Affiliation: (a) Hamilton Institute, National University of Ireland, Maynooth, Co. Kildare, Ireland (b) Centre for Systems Medicine, Department of Physiology & Medical Physics, Royal College of Surgeons in Ireland, Dublin, Ireland Article History: Received 9 August 2011; Revised 25 November 2011; Accepted 13 January 2012
    Keywords: Skeletal Muscle -- Growth ; Skeletal Muscle -- Physiological Aspects
    ISSN: 0022-5193
    Source: Cengage Learning, Inc.
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  • 2
    Language: English
    In: PLoS ONE, 01 January 2014, Vol.9(8), p.e103521
    Description: We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension might be large even for trivial systems. Here, we derive a reduced ODE set that accurately approximates the probabilities of subspaces of interest with a known error bound. Our methodology is based on model reduction by balanced truncation and can be considerably more computationally efficient than solving the chemical master equation directly. We show the applicability of our method by analysing stochastic chemical reactions. First, we obtain a reduced order model for the infinitesimal generator of a Markov chain that models a reversible, monomolecular reaction. Later, we obtain a reduced order model for a catalytic conversion of substrate to a product (a so-called Michaelis-Menten mechanism), and compare its dynamics with a rapid equilibrium approximation method. For this example, we highlight the savings on the computational load obtained by means of the reduced-order model. Furthermore, we revisit the substrate catalytic conversion by obtaining a lower-order model that approximates the probability of having predefined ranges of product molecules. In such an example, we obtain an approximation of the output of a model with 5151 states by a reduced model with 16 states. Finally, we obtain a reduced-order model of the Brusselator.
    Keywords: Sciences (General)
    E-ISSN: 1932-6203
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  • 3
    Language: English
    In: Journal of Theoretical Biology, 2012-05, Vol.301, pp.15-27
    Description: 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.
    Keywords: Algorithms ; Animals ; Enzyme Activation ; Feedback, Physiological ; Models, Biological ; Muscle Proteins ; Muscle, Skeletal ; Proto-Oncogene Proteins C-Akt ; Receptor, IGF Type 1 ; Signal Transduction ; Tor Serine-Threonine Kinases
    ISSN: 0022-5193
    Source: KU Leuven Association
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  • 4
    Language: English
    In: Journal of Theoretical Biology, 21 May 2012, Vol.301, pp.15-27
    Description: 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. ► Using PDE we study the spatiotemporal dynamics of a protein activation/inhibition. ► We focus on one dimensional spatial domain, such as neurons or skeletal muscle cells. ► We obtained formulas describing the activation profile, in some biological scenarios. ► Auto-catalysis and diffusion were able to filter spatial fluctuations. ► Mild activation assumption is incompatible with active enzymes' stable pulses/waves.
    Keywords: Akt/Mtor ; Skeletal Muscle ; Positive Feedback ; Pde ; Analytical Solutions ; Biology
    ISSN: 0022-5193
    E-ISSN: 1095-8541
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  • 5
    Language: English
    In: Journal of theoretical biology, 2012, Vol.301, pp.15-27
    Description: 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. ; p. 15-27.
    Keywords: Cell Death ; Cell Proliferation ; Space And Time ; Muscles ; Insulin-Like Growth Factor I ; Cell Differentiation ; Transcription (Genetics) ; Skeletal Muscle ; Protein Metabolism ; Myocytes
    ISSN: 0022-5193
    Source: AGRIS (Food and Agriculture Organization of the United Nations)
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  • 6
    Language: English
    In: Bulletin of Mathematical Biology, 2014, Vol.76(9), pp.2334-2361
    Description: Chemical reactions are discrete, stochastic events. As such, the species’ molecular numbers can be described by an associated master equation. However, handling such an equation may become difficult due to the large size of reaction networks. A commonly used approach to forecast the behaviour of reaction networks is to perform computational simulations of such systems and analyse their outcome statistically. This approach, however, might require high computational costs to provide accurate results. In this paper we opt for an analytical approach to obtain the time-dependent solution of the Chemical Master Equation for selected species in a general reaction network. When the reaction networks are composed exclusively of zeroth and first-order reactions, this analytical approach significantly alleviates the computational burden required by simulation-based methods. By building upon these analytical solutions, we analyse a general monomolecular reaction network with an arbitrary number of species to obtain the exact marginal probability distribution for selected species. Additionally, we study two particular topologies of monomolecular reaction networks, namely (i) an unbranched chain of monomolecular reactions with and without synthesis and degradation reactions and (ii) a circular chain of monomolecular reactions. We illustrate our methodology and alternative ways to use it for non-linear systems by analysing a protein autoactivation mechanism. Later, we compare the computational load required for the implementation of our results and a pure computational approach to analyse an unbranched chain of monomolecular reactions. Finally, we study calcium ions gates in the sarco/endoplasmic reticulum mediated by ryanodine receptors.
    Keywords: Chemical master equation ; Analytical solutions ; Model reduction
    ISSN: 0092-8240
    E-ISSN: 1522-9602
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  • 7
    Language: English
    In: PLoS ONE, 01 January 2013, Vol.8(5), p.e62834
    Description: 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.
    Keywords: Sciences (General)
    E-ISSN: 1932-6203
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  • 8
    Language: English
    In: IFAC PapersOnLine, 2016, Vol.49(7), pp.224-229
    Description: In this paper, we focus on continuously stirred tank reactors. For such plants we present a dynamical system capable of estimating i) unmeasured concentrations exponentially fast and ii) completely unknown reaction rates exactly and in finite-time. Towards this end, this observer requires the (partial) knowledge of the mathematical model, along with the inputs and outputs to the system; furthermore, we require that the number of measured concentrations equals the number of unknown reaction rates.
    Keywords: Observers ; Reaction Rate Estimation ; State Estimation ; Uncertain Systems ; Uncertain Bioprocess Models ; Discontinuous Observers ; Biotechnology
    ISSN: 2405-8963
    Source: ScienceDirect Journals (Elsevier)
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  • 9
    Language: English
    In: IEEE/ACM Transactions on Computational Biology and Bioinformatics, May 2014, Vol.11(3), pp.592-603
    Description: 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 Ca〈sup〉2+〈/sup〉 accumulation is independent of every intracellular calcium flux and depends on the Ca〈sup〉2+〈/sup〉 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 Ca〈sup〉2+〈/sup〉 perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.
    Keywords: Computational Biology ; Bioinformatics ; Biomembranes ; Biological System Modeling ; Biology
    ISSN: 1545-5963
    E-ISSN: 1557-9964
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  • 10
    Language: English
    In: Journal of Mathematical Biology, 2014, Vol.68(3), pp.609-645
    Description: Positive feedback loops are common regulatory elements in metabolic and protein signalling pathways. The length of such feedback loops determines stability and sensitivity to network perturbations. Here we provide a mathematical analysis of arbitrary length positive feedback loops with protein production and degradation. These loops serve as an abstraction of typical regulation patterns in protein signalling pathways. We first perform a steady state analysis and, independently of the chain length, identify exactly two steady states that represent either biological activity or inactivity. We thereby provide two formulas for the steady state protein concentrations as a function of feedback length, strength of feedback, as well as protein production and degradation rates. Using a control theory approach, analysing the frequency response of the linearisation of the system and exploiting the Small Gain Theorem, we provide conditions for local stability for both steady states. Our results demonstrate that, under some parameter relationships, once a biological meaningful on steady state arises, it is stable, while the off steady state , where all proteins are inactive, becomes unstable. We apply our results to a three-tier feedback of caspase activation in apoptosis and demonstrate how an intermediary protein in such a loop may be used as a signal amplifier within the cascade. Our results provide a rigorous mathematical analysis of positive feedback chains of arbitrary length, thereby relating pathway structure and stability.
    Keywords: Positive feedback ; Recursive protein activation ; Apoptosis ; ODE ; Equilibrium points ; Local stability
    ISSN: 0303-6812
    E-ISSN: 1432-1416
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