ORCID Profile
0000-0002-8111-1137
Current Organisations
University of Oxford
,
Queensland University of Technology
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Publisher: MDPI AG
Date: 06-12-2022
DOI: 10.3390/NANO12234338
Abstract: History has demonstrated that the uncontrolled fast thriving of potentially pathogenic microorganisms may lead to serious consequences and, thus, the approaches helping to control the microbial numbers in infectional hot-spots are necessary [...]
Publisher: Elsevier BV
Date: 05-1999
Publisher: Elsevier BV
Date: 10-1994
Publisher: ASMEDC
Date: 2011
Abstract: Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et at, J. Magnetic Resonance, 190 (2008) 255–270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.
Publisher: Elsevier BV
Date: 11-1995
Publisher: Elsevier BV
Date: 02-2002
Publisher: Elsevier BV
Date: 08-2007
Publisher: ACTAPRESS
Date: 2014
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2007
DOI: 10.1137/060662629
Publisher: Elsevier BV
Date: 05-2014
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 05-2012
DOI: 10.1109/TCBB.2011.68
Publisher: Oxford University Press (OUP)
Date: 02-12-2013
Publisher: eLife Sciences Publications, Ltd
Date: 29-11-2021
DOI: 10.7554/ELIFE.73020
Abstract: Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, tumour spheroids more closely mimic the avascular tumour microenvironment where spatial differences in nutrient availability strongly influence growth. We show that spheroids initiated using significantly different numbers of cells grow to similar limiting sizes, suggesting that avascular tumours have a limiting structure in agreement with untested predictions of classical mathematical models of tumour spheroids. We develop a novel mathematical and statistical framework to study the structure of tumour spheroids seeded from cells transduced with fluorescent cell cycle indicators, enabling us to discriminate between arrested and cycling cells and identify an arrested region. Our analysis shows that transient spheroid structure is independent of initial spheroid size, and the limiting structure can be independent of seeding density. Standard experimental protocols compare spheroid size as a function of time however, our analysis suggests that comparing spheroid structure as a function of overall size produces results that are relatively insensitive to variability in spheroid size. Our experimental observations are made using two melanoma cell lines, but our modelling framework applies across a wide range of spheroid culture conditions and cell lines.
Publisher: Elsevier BV
Date: 05-2010
Publisher: Elsevier BV
Date: 10-2008
DOI: 10.1016/J.BIOSYSTEMS.2008.05.009
Abstract: We present a general-purpose optimization algorithm inspired by "run-and-tumble", the biased random walk chemotactic swimming strategy used by the bacterium Escherichia coli to locate regions of high nutrient concentration The method uses particles (corresponding to bacteria) that swim through the variable space (corresponding to the attractant concentration profile). By constantly performing temporal comparisons, the particles drift towards the minimum or maximum of the function of interest. We illustrate the use of our method with four ex les. We also present a discrete version of the algorithm. The new algorithm is expected to be useful in combinatorial optimization problems involving many variables, where the functional landscape is apparently stochastic and has local minima, but preserves some derivative structure at intermediate scales.
Publisher: Springer Science and Business Media LLC
Date: 10-11-2006
Publisher: Elsevier BV
Date: 09-2001
Publisher: Elsevier BV
Date: 06-2001
Publisher: IEEE
Date: 08-2011
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2012
DOI: 10.1137/110847007
Publisher: eLife Sciences Publications, Ltd
Date: 19-11-2021
Publisher: SPIE
Date: 21-12-2007
DOI: 10.1117/12.776148
Publisher: Public Library of Science (PLoS)
Date: 28-02-2014
Publisher: Elsevier BV
Date: 05-2010
Publisher: Elsevier BV
Date: 08-2014
Publisher: Elsevier BV
Date: 2016
Publisher: Springer Science and Business Media LLC
Date: 04-03-2010
Publisher: IEEE
Date: 2003
Publisher: American Association for the Advancement of Science (AAAS)
Date: 23-09-2022
Abstract: This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.
Publisher: Elsevier BV
Date: 05-2008
Publisher: Cold Spring Harbor Laboratory
Date: 06-08-2021
DOI: 10.1101/2021.08.05.455334
Abstract: Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, tumour spheroids more closely mimic the avascular tumour microenvironment where spatial differences in nutrient availability strongly influence growth. We show that spheroids initiated using significantly different numbers of cells grow to similar limiting sizes, suggesting that avascular tumours have a limiting structure in agreement with untested predictions of classical mathematical models of tumour spheroids. We develop a novel mathematical and statistical framework to study the structure of tumour spheroids seeded from cells transduced with fluorescent cell cycle indicators, enabling us to discriminate between arrested and cycling cells and identify an arrested region. Our analysis shows that transient spheroid structure is independent of initial spheroid size, and the limiting structure can be independent of seeding density. Standard experimental protocols compare spheroid size as a function of time however, our analysis suggests that comparing spheroid structure as a function of overall size produces results that are relatively insensitive to variability in spheroid size. Our experimental observations are made using two melanoma cell lines, but our modelling framework applies across a wide range of spheroid culture conditions and cell lines.
Publisher: SPIE
Date: 25-05-2004
DOI: 10.1117/12.548672
Publisher: Springer Science and Business Media LLC
Date: 04-01-2008
Publisher: Elsevier BV
Date: 12-2012
Publisher: Elsevier BV
Date: 1993
Publisher: Elsevier BV
Date: 2015
Publisher: AIP Publishing
Date: 15-11-2004
DOI: 10.1063/1.1810475
Abstract: This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the τ-leap and midpoint τ-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of s le values is from zero to infinity, binomial random variables have a finite range of s le values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A s ling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. S les for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches.
Publisher: Elsevier BV
Date: 05-1989
Publisher: Elsevier BV
Date: 12-2014
Publisher: Wiley
Date: 09-06-2006
Publisher: Wiley
Date: 30-12-2023
DOI: 10.1002/NUM.22980
Abstract: Many computational fluid dynamics problems utilize finite volume frameworks for simulation, due to the simplifications provided by conservative formulation of the driving partial differential equations (PDEs). However, fluid dynamics applications can often involve temporal shifts in the domain structure—such as moving boundaries, or pore structure changes—requiring mesh adaptation throughout computation. These mesh adaptations often render classical numerical methods such as the finite volume method infeasible, due to their reliance on a well‐defined static mesh structure. This limitation has led to the development of a wide variety of meshless methods—techniques that can simulate PDEs without requiring a rigid connective structure between nodes. However, most meshless methods are typically based on finite element or finite difference formulations, and the limited number of meshless finite volume methods (MFVMs) either introduce a weak background mesh, or use weak‐form approximations that do not take full advantage of the strong conservative form of the driving equations. Addressing this gap within this study we outline a meshfree numerical scheme for simulation of partial different equations, based on strong‐form finite volume style formulations. Building upon the previously developed MFVM, this technique uses radial basis functions to interpolate the problem domain, and approximate fluxes in a disjoint finite volume scheme, removing reliance on a mesh structure. We present method derivation, including promising new techniques for enforcing boundary conditions in a meshless environment. Following this we discuss method accuracy and computational performance across a variety of problems in two and three dimensions. We then illustrate how this method may prove beneficial for applications in porous media modeling, and computational fluid dynamics. For completeness, we provide a sensitivity analysis of the method hyper‐parameters and investigate the conservative properties of the method. We also illustrate similarities of this approach to the widely used meshless point collocation methods. We close with a discussion of the strengths, limitations, and broader applicability of the technique.
Publisher: Oxford University Press (OUP)
Date: 1985
Publisher: Elsevier BV
Date: 2014
Publisher: Springer Science and Business Media LLC
Date: 02-06-2010
DOI: 10.1038/CLPT.2010.95
Abstract: Side effects account for most of the instances of failure of candidate drugs at late stages of development. These development failures contribute to the exorbitant cost of bringing new compounds to market: a single withdrawal can represent a loss of more than $1 billion. Many unwanted actions of drugs affect the heart, resulting in potentially proarrhythmic alteration of ion channel function. Because these can be fatal, potential electrophysiological cardiotoxicity is among the most stringent exclusion criteria in the licensing process.
Publisher: Springer Science and Business Media LLC
Date: 2002
Publisher: SPIE
Date: 27-12-2007
DOI: 10.1117/12.707691
Publisher: IEEE
Date: 2005
Publisher: Springer Science and Business Media LLC
Date: 18-06-2014
Publisher: Elsevier BV
Date: 08-2015
Publisher: Mary Ann Liebert Inc
Date: 04-2010
Abstract: The modularity that nuclear organization brings has the potential to explain the function of aggregates of proteins and RNA. Promyelocytic leukemia nuclear bodies are implicated in important regulatory processes. To understand the complement of proteins associated with these intra-nuclear bodies, we construct a Bayesian network model that integrates sequence and protein-protein interaction data. The model predicts association with promyelocytic leukemia nuclear bodies accurately when interaction data is available. At a false positive rate of 10%, the true positive rate is almost 50%, indicated by an independent nuclear proteome reference set. The model provides strong support for further expanding the protein complement with several important regulators and a richer functional repertoire. Using special support vector machine (SVM)-nodes (equipped with string kernels), the Bayesian network is also able to produce predictions on the basis of sequence only, with an accuracy superior to that of baseline models. Supplementary Material is available online at www.liebertonline.com.
Publisher: Springer Science and Business Media LLC
Date: 07-02-2012
Publisher: Public Library of Science (PLoS)
Date: 02-04-2014
Publisher: Cold Spring Harbor Laboratory
Date: 11-11-2019
DOI: 10.1101/837849
Abstract: The host-vector shuttle and the bottleneck in dengue transmission is a significant aspect with regard to the study of dengue outbreaks. As mosquitoes require 100-1000 times more virus to become infected than human, the transmission of dengue virus from human to mosquito is a vulnerability that can be targeted to improve disease control. In order to capture the heterogeneity in the infectiousness of an infected patient population towards the mosquito pool, we calibrate a population of host-to-vector virus transmission models based on an experimentally quantified infected fraction of a mosquito population. Once the population of models is well-calibrated, we deploy a population of controls that helps to inhibit the human-to-mosquito transmission of the dengue virus indirectly by reducing the viral load in the patient body fluid. We use an optimal bang-bang control on the administration of the defective virus (transmissible interfering particles, known as TIPs) to symptomatic patients in the course of their febrile period and observe the dynamics in successful reduction of dengue spread into mosquitoes.
Publisher: Cold Spring Harbor Laboratory
Date: 17-03-2021
DOI: 10.1101/2021.03.17.435721
Abstract: Optimal control theory provides insight into complex resource allocation decisions. The forward-backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems (TPBVPs) arising from the application of Pontryagin’s Maximum Principle (PMP) in optimal control. In this review we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualising the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Further, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at github.com/Jesse-Sharp/Sharp2021 .
Publisher: Oxford University Press (OUP)
Date: 26-09-2006
DOI: 10.1093/BIB/BBL033
Abstract: Systems biology is based on computational modelling and simulation of large networks of interacting components. Models may be intended to capture processes, mechanisms, components and interactions at different levels of fidelity. Input data are often large and geographically disperse, and may require the computation to be moved to the data, not vice versa. In addition, complex system-level problems require collaboration across institutions and disciplines. Grid computing can offer robust, scaleable solutions for distributed data, compute and expertise. We illustrate some of the range of computational and data requirements in systems biology with three case studies: one requiring large computation but small data (orthologue mapping in comparative genomics), a second involving complex terabyte data (the Visible Cell project) and a third that is both computationally and data-intensive (simulations at multiple temporal and spatial scales). Authentication, authorisation and audit systems are currently not well scalable and may present bottlenecks for distributed collaboration particularly where outcomes may be commercialised. Challenges remain in providing lightweight standards to facilitate the penetration of robust, scalable grid-type computing into erse user communities to meet the evolving demands of systems biology.
Publisher: Springer Science and Business Media LLC
Date: 11-08-2010
Abstract: With increasing computer power, simulating the dynamics of complex systems in chemistry and biology is becoming increasingly routine. The modelling of in idual reactions in (bio)chemical systems involves a large number of random events that can be simulated by the stochastic simulation algorithm (SSA). The key quantity is the step size, or waiting time, τ , whose value inversely depends on the size of the propensities of the different channel reactions and which needs to be re-evaluated after every firing event. Such a discrete event simulation may be extremely expensive, in particular for stiff systems where τ can be very short due to the fast kinetics of some of the channel reactions. Several alternative methods have been put forward to increase the integration step size. The so-called τ -leap approach takes a larger step size by allowing all the reactions to fire, from a Poisson or Binomial distribution, within that step. Although the expected value for the different species in the reactive system is maintained with respect to more precise methods, the variance at steady state can suffer from large errors as τ grows. In this paper we extend Poisson τ -leap methods to a general class of Runge-Kutta (RK) τ -leap methods. We show that with the proper selection of the coefficients, the variance of the extended τ -leap can be well-behaved, leading to significantly larger step sizes. The benefit of adapting the extended method to the use of RK frameworks is clear in terms of speed of calculation, as the number of evaluations of the Poisson distribution is still one set per time step, as in the original τ -leap method. The approach paves the way to explore new multiscale methods to simulate (bio)chemical systems.
Publisher: Springer Berlin Heidelberg
Date: 2013
Publisher: Public Library of Science (PLoS)
Date: 11-11-2019
Publisher: Elsevier BV
Date: 06-2004
Publisher: Elsevier BV
Date: 09-2004
Publisher: AIP Publishing
Date: 28-05-2008
DOI: 10.1063/1.2919124
Abstract: The delay stochastic simulation algorithm (DSSA) by Barrio et al. [Plos Comput. Biol. 2, 117–E (2006)] was developed to simulate delayed processes in cell biology in the presence of intrinsic noise, that is, when there are small-to-moderate numbers of certain key molecules present in a chemical reaction system. These delayed processes can faithfully represent complex interactions and mechanisms that imply a number of spatiotemporal processes often not explicitly modeled such as transcription and translation, basic in the modeling of cell signaling pathways. However, for systems with widely varying reaction rate constants or large numbers of molecules, the simulation time steps of both the stochastic simulation algorithm (SSA) and the DSSA can become very small causing considerable computational overheads. In order to overcome the limit of small step sizes, various τ-leap strategies have been suggested for improving computational performance of the SSA. In this paper, we present a binomial τ-DSSA method that extends the τ-leap idea to the delay setting and avoids drawing insufficient numbers of reactions, a common shortcoming of existing binomial τ-leap methods that becomes evident when dealing with complex chemical interactions. The resulting inaccuracies are most evident in the delayed case, even when considering reaction products as potential reactants within the same time step in which they are produced. Moreover, we extend the framework to account for multicellular systems with different degrees of intercellular communication. We apply these ideas to two important genetic regulatory models, namely, the hes1 gene, implicated as a molecular clock, and a Her1/Her 7 model for coupled oscillating cells.
Publisher: MDPI AG
Date: 17-04-2023
Abstract: Dynamical properties of numerically approximated discrete systems may become inconsistent with those of the corresponding continuous-time system. We present a qualitative analysis of the dynamical properties of two-species Lotka-Volterra and Ricker-type predator-prey systems under discrete and continuous settings. By creating an arbitrary time discretisation, we obtain stability conditions that preserve the characteristics of continuous-time models and their numerically approximated systems. Here, we show that even small changes to some of the model parameters may alter the system dynamics unless an appropriate time discretisation is chosen to return similar dynamical behaviour to what is observed in the corresponding continuous-time system. We also found similar dynamical properties of the Ricker-type predator-prey systems under certain conditions. Our results demonstrate the need for preliminary analysis to identify which dynamical properties of approximated discretised systems agree or disagree with the corresponding continuous-time systems.
Publisher: Elsevier BV
Date: 09-1999
Publisher: Cold Spring Harbor Laboratory
Date: 19-06-2019
DOI: 10.1101/668848
Abstract: Fibrosis, the pathological excess of fibroblast activity, is a significant health issue that hinders the function of many organs in the body, in some cases fatally. However, the severity of fibrosis-derived conditions depends on both the positioning of fibrotic affliction, and the microscopic patterning of fibroblast-deposited matrix proteins within afflicted regions. Variability in an in idual’s manifestation of a type of fibrosis is an important factor in explaining differences in symptoms, optimum treatment and prognosis, but a need for ex vivo procedures and a lack of experimental control over conflating factors has meant this variability remains poorly understood. In this work, we present a computational methodology for the generation of patterns of fibrosis microstructure, demonstrating the technique using histological images of four types of cardiac fibrosis. Our generator and automated tuning method prove flexible enough to capture each of these very distinct patterns, allowing for rapid generation of new realisations for high-throughput computational studies. We also demonstrate via simulation, using the generated fibrotic patterns, the importance of micro-scale variability by showing significant differences in electrophysiological impact even within a single class of fibrosis.
Publisher: Springer Science and Business Media LLC
Date: 2004
Publisher: Springer Science and Business Media LLC
Date: 14-11-2014
Publisher: Springer Science and Business Media LLC
Date: 09-1980
DOI: 10.1007/BF01932774
Publisher: Springer Science and Business Media LLC
Date: 09-1980
DOI: 10.1007/BF01932773
Publisher: Elsevier BV
Date: 12-2000
Publisher: Proceedings of the National Academy of Sciences
Date: 30-05-2006
Abstract: Bistability arises within a wide range of biological systems from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. Changes in regulatory mechanisms may result in genetic switching in a bistable system. Recently, more and more experimental evidence in the form of bimodal population distributions indicates that noise plays a very important role in the switching of bistable systems. Although deterministic models have been used for studying the existence of bistability properties under various system conditions, these models cannot realize cell-to-cell fluctuations in genetic switching. However, there is a lag in the development of stochastic models for studying the impact of noise in bistable systems because of the lack of detailed knowledge of biochemical reactions, kinetic rates, and molecular numbers. In this work, we develop a previously undescribed general technique for developing quantitative stochastic models for large-scale genetic regulatory networks by introducing Poisson random variables into deterministic models described by ordinary differential equations. Two stochastic models have been proposed for the genetic toggle switch interfaced with either the SOS signaling pathway or a quorum-sensing signaling pathway, and we have successfully realized experimental results showing bimodal population distributions. Because the introduced stochastic models are based on widely used ordinary differential equation models, the success of this work suggests that this approach is a very promising one for studying noise in large-scale genetic regulatory networks.
Publisher: Springer Science and Business Media LLC
Date: 09-2013
Publisher: Public Library of Science (PLoS)
Date: 20-02-2013
Publisher: SPIE
Date: 16-02-2005
DOI: 10.1117/12.585052
Publisher: Springer Science and Business Media LLC
Date: 03-10-2006
Publisher: American Institute of Physics
Date: 2008
DOI: 10.1063/1.2990875
Publisher: Elsevier BV
Date: 05-1996
Publisher: IEEE
Date: 09-2010
Publisher: Global Science Press
Date: 06-2015
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2000
Publisher: Oxford University Press (OUP)
Date: 1987
Publisher: AIP Publishing
Date: 25-02-2011
DOI: 10.1063/1.3554385
Abstract: The stochastic simulation algorithm was introduced by Gillespie and in a different form by Kurtz. There have been many attempts at accelerating the algorithm without deviating from the behavior of the simulated system. The crux of the explicit τ-leaping procedure is the use of Poisson random variables to approximate the number of occurrences of each type of reaction event during a carefully selected time period, τ. This method is acceptable providing the leap condition, that no propensity function changes “significantly” during any time-step, is met. Using this method there is a possibility that species numbers can, artificially, become negative. Several recent papers have demonstrated methods that avoid this situation. One such method classifies, as critical, those reactions in danger of sending species populations negative. At most, one of these critical reactions is allowed to occur in the next time-step. We argue that the criticality of a reactant species and its dependent reaction channels should be related to the probability of the species number becoming negative. This way only reactions that, if fired, produce a high probability of driving a reactant population negative are labeled critical. The number of firings of more reaction channels can be approximated using Poisson random variables thus speeding up the simulation while maintaining the accuracy. In implementing this revised method of criticality selection we make use of the probability distribution from which the random variable describing the change in species number is drawn. We give several numerical ex les to demonstrate the effectiveness of our new method.
Publisher: Elsevier BV
Date: 07-2011
Publisher: Springer Science and Business Media LLC
Date: 04-10-2009
Publisher: Elsevier BV
Date: 12-2013
Publisher: MDPI AG
Date: 31-03-2017
Publisher: IEEE
Date: 11-2007
Publisher: MIT Press - Journals
Date: 02-2011
DOI: 10.1162/NECO_A_00075
Abstract: Chemotaxis plays a crucial role in many biological processes, including nervous system development. However, fundamental physical constraints limit the ability of a small sensing device such as a cell or growth cone to detect an external chemical gradient. One of these is the stochastic nature of receptor binding, leading to a constantly fluctuating binding pattern across the cell's array of receptors. This is analogous to the uncertainty in sensory information often encountered by the brain at the systems level. Here we derive analytically the Bayes-optimal strategy for combining information from a spatial array of receptors in both one and two dimensions to determine gradient direction. We also show how information from more than one receptor species can be optimally integrated, derive the gradient shapes that are optimal for guiding cells or growth cones over the longest possible distances, and illustrate that polarized cell behavior might arise as an adaptation to slowly varying environments. Together our results provide closed-form predictions for variations in chemotactic performance over a wide range of gradient conditions.
Publisher: Elsevier BV
Date: 07-2001
Publisher: Springer Berlin Heidelberg
Date: 2006
DOI: 10.1007/11757344_46
Publisher: Springer Science and Business Media LLC
Date: 15-07-2012
Publisher: Elsevier BV
Date: 09-2004
Publisher: Oxford University Press (OUP)
Date: 29-03-2007
DOI: 10.1093/BIB/BBM033
Abstract: One of the most important aspects of Computational Cell Biology is the understanding of the complicated dynamical processes that take place on plasma membranes. These processes are often so complicated that purely temporal models cannot always adequately capture the dynamics. On the other hand, spatial models can have large computational overheads. In this article, we review some of these issues with respect to chemistry, membrane microdomains and anomalous diffusion and discuss how to select appropriate modelling and simulation paradigms based on some or all the following aspects: discrete, continuous, stochastic, delayed and complex spatial processes.
Publisher: Public Library of Science (PLoS)
Date: 08-09-2006
Publisher: Wiley
Date: 28-04-2014
DOI: 10.1111/VCP.12145
Abstract: Oxalate nephrosis is a highly prevalent disease in the Mount Lofty Ranges koala population in South Australia, but associated clinicopathologic findings remain undescribed. The aims of this study were to determine plasma biochemical and urinalysis variables, particularly for renal function and urinary crystal morphology and composition, in koalas with oxalate nephrosis. Blood and urine s les from Mount Lofty Ranges koalas with oxalate nephrosis were compared with those unaffected by renal oxalate crystal deposition from Mount Lofty and Kangaroo Island, South Australia and Moggill, Queensland. Plasma and urine biochemistry variables were analyzed using a Cobas Bio analyzer, and urinary oxalate by high-performance liquid chromatography. Urinary crystal composition was determined by infrared spectroscopy and energy dispersive X-ray analysis. Azotemia (urea > 6.6 mmol/L, creatinine > 150 μmol/L) was found in 93% of koalas with oxalate nephrosis (n = 15). All azotemic animals had renal insufficiency (urine specific gravity [USG] < 1.035), and in 83%, USG was < 1.030. Koalas with oxalate nephrosis were hyperoxaluric compared with Queensland koalas (P < .01). Urinary crystals from koalas with oxalate nephrosis had atypical morphology and were composed of calcium oxalate. Mount Lofty Ranges koalas unaffected by renal oxalate crystal deposition had renal insufficiency (43%), although only 14% had USG < 1.030 (n = 7). Unaffected Mount Lofty Ranges and Kangaroo Island koalas were hyperoxaluric compared with Queensland koalas (P < .01). Koalas with oxalate nephrosis from the Mount Lofty Ranges had renal insufficiency, hyperoxaluria, and pathognomonic urinary crystals. The findings of this study will aid veterinary diagnosis of this disease.
Publisher: The Royal Society
Date: 08-01-2004
Publisher: Elsevier BV
Date: 02-2003
Publisher: ASMEDC
Date: 2011
Abstract: In this paper, a class of fractional advection-dispersion models (FADM) is investigated. These models include five fractional advection-dispersion models: the immobile, mobile/immobile time FADM with a temporal fractional derivative 0 γ 1, the space FADM with skewness, both the time and space FADM and the time fractional advection-diffusion-wave model with d ing with index 1 γ 2. They describe nonlocal dependence on either time or space, or both, to explain the development of anomalous dispersion. These equations can be used to simulate regional-scale anomalous dispersion with heavy tails, for ex le, the solute transport in watershed catchments and rivers. We propose computationally effective implicit numerical methods for these FADM. The stability and convergence of the implicit numerical methods are analyzed and compared systematically. Finally, some results are given to demonstrate the effectiveness of our theoretical analysis.
Publisher: Cold Spring Harbor Laboratory
Date: 20-12-2019
DOI: 10.1101/2019.12.19.883645
Abstract: Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where ersifying an investment portfolio protects against economic uncertainty. We provide a new theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several novel models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per-capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest at new opportunities for experimental investigation and design. Overall, we provide a new way of conceptualising and modelling cellular decision-making in volatile environments by explicitly unifying theory from mathematical biology and finance.
Publisher: Springer Science and Business Media LLC
Date: 03-1986
DOI: 10.1007/BF02238189
Publisher: Elsevier BV
Date: 2004
Publisher: The Royal Society
Date: 08-2021
Abstract: Optimal control theory provides insight into complex resource allocation decisions. The forward–backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems arising from the application of Pontryagin’s maximum principle (PMP) in optimal control. The FBSM is popular in systems biology as it scales well with system size and is straightforward to implement. In this review, we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualizing the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Furthermore, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at github.com/Jesse-Sharp/Sharp2021 .
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2005
DOI: 10.1137/040612476
Publisher: Elsevier BV
Date: 07-2006
DOI: 10.1016/J.JTBI.2005.12.004
Abstract: High-quality data about protein structures and their gene sequences are essential to the understanding of the relationship between protein folding and protein coding sequences. Firstly we constructed the EcoPDB database, which is a high-quality database of Escherichia coli genes and their corresponding PDB structures. Based on EcoPDB, we presented a novel approach based on information theory to investigate the correlation between cysteine synonymous codon usages and local amino acids flanking cysteines, the correlation between cysteine synonymous codon usages and synonymous codon usages of local amino acids flanking cysteines, as well as the correlation between cysteine synonymous codon usages and the disulfide bonding states of cysteines in the E. coli genome. The results indicate that the nearest neighboring residues and their synonymous codons of the C-terminus have the greatest influence on the usages of the synonymous codons of cysteines and the usage of the synonymous codons has a specific correlation with the disulfide bond formation of cysteines in proteins. The correlations may result from the regulation mechanism of protein structures at gene sequence level and reflect the biological function restriction that cysteines pair to form disulfide bonds. The results may also be helpful in identifying residues that are important for synonymous codon selection of cysteines to introduce disulfide bridges in protein engineering and molecular biology. The approach presented in this paper can also be utilized as a complementary computational method and be applicable to analyse the synonymous codon usages in other model organisms.
Publisher: The Royal Society
Date: 13-05-2013
Abstract: Fractional-order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brownian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As magnetic resonance imaging is applied with increasing temporal and spatial resolution, the spin dynamics is being examined more closely such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here, the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments, where processes are often anisotropic. Anomalous diffusion in the human brain using fractional-order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch–Torrey equation using fractional-order calculus with respect to time and space. However, effective numerical methods and supporting error analyses for the fractional Bloch–Torrey equation are still limited. In this paper, the space and time fractional Bloch–Torrey equation (ST-FBTE) in both fractional Laplacian and Riesz derivative form is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE in fractional Laplacian form with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE based on the Riesz form, and the stability and convergence of the INM are investigated. We prove that the INM for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.
Publisher: Elsevier BV
Date: 05-2012
Publisher: Oxford University Press (OUP)
Date: 20-03-2013
Publisher: Springer Science and Business Media LLC
Date: 14-05-2022
Publisher: American Association for the Advancement of Science (AAAS)
Date: 05-01-2018
Abstract: We describe a statistically informed calibration of in silico populations to explore variability in complex systems.
Publisher: Begell House
Date: 2008
Publisher: AIP Publishing
Date: 09-02-2015
DOI: 10.1063/1.4907008
Abstract: In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the τ-leaping framework to past information. Using the Θ-trapezoidal τ-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k ≥ 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional ex les have been implemented in order to demonstrate the efficacy of this approach.
Publisher: IEEE
Date: 10-2009
DOI: 10.1109/HIBI.2009.18
Publisher: Informa UK Limited
Date: 2006
Publisher: American Physical Society (APS)
Date: 15-05-2012
Publisher: Informa UK Limited
Date: 10-2011
Publisher: Proceedings of the National Academy of Sciences
Date: 23-06-2009
Abstract: Axon guidance by molecular gradients plays a crucial role in wiring up the nervous system. However, the mechanisms axons use to detect gradients are largely unknown. We first develop a Bayesian “ideal observer” analysis of gradient detection by axons, based on the hypothesis that a principal constraint on gradient detection is intrinsic receptor binding noise. Second, from this model, we derive an equation predicting how the degree of response of an axon to a gradient should vary with gradient steepness and absolute concentration. Third, we confirm this prediction quantitatively by performing the first systematic experimental analysis of how axonal response varies with both these quantities. These experiments demonstrate a degree of sensitivity much higher than previously reported for any chemotacting system. Together, these results reveal both the quantitative constraints that must be satisfied for effective axonal guidance and the computational principles that may be used by the underlying signal transduction pathways, and allow predictions for the degree of response of axons to gradients in a wide variety of in vivo and in vitro settings.
Publisher: Wiley
Date: 14-05-2004
DOI: 10.1002/PROT.20160
Abstract: We describe a new method for using neural networks to predict residue contact pairs in a protein. The main inputs to the neural network are a set of 25 measures of correlated mutation between all pairs of residues in two "windows" of size 5 centered on the residues of interest. While the in idual pair-wise correlations are a relatively weak predictor of contact, by training the network on windows of correlation the accuracy of prediction is significantly improved. The neural network is trained on a set of 100 proteins and then tested on a disjoint set of 1033 proteins of known structure. An average predictive accuracy of 21.7% is obtained taking the best L/2 predictions for each protein, where L is the sequence length. Taking the best L/10 predictions gives an average accuracy of 30.7%. The predictor is also tested on a set of 59 proteins from the CASP5 experiment. The accuracy is found to be relatively consistent across different sequence lengths, but to vary widely according to the secondary structure. Predictive accuracy is also found to improve by using multiple sequence alignments containing many sequences to calculate the correlations.
Publisher: Elsevier BV
Date: 08-2011
Publisher: Public Library of Science (PLoS)
Date: 05-01-2011
Publisher: Elsevier BV
Date: 12-2001
Publisher: Elsevier BV
Date: 06-2008
Publisher: Oxford University Press (OUP)
Date: 17-10-2007
DOI: 10.1093/BIOINFORMATICS/BTM505
Abstract: Motivation: Disulfide bonds are primary covalent crosslinks between two cysteine residues in proteins that play critical roles in stabilizing the protein structures and are commonly found in extracy-toplasmatic or secreted proteins. In protein folding prediction, the localization of disulfide bonds can greatly reduce the search in conformational space. Therefore, there is a great need to develop computational methods capable of accurately predicting disulfide connectivity patterns in proteins that could have potentially important applications. Results: We have developed a novel method to predict disulfide connectivity patterns from protein primary sequence, using a support vector regression (SVR) approach based on multiple sequence feature vectors and predicted secondary structure by the PSIPRED program. The results indicate that our method could achieve a prediction accuracy of 74.4% and 77.9%, respectively, when averaged on proteins with two to five disulfide bridges using 4-fold cross-validation, measured on the protein and cysteine pair on a well-defined non-homologous dataset. We assessed the effects of different sequence encoding schemes on the prediction performance of disulfide connectivity. It has been shown that the sequence encoding scheme based on multiple sequence feature vectors coupled with predicted secondary structure can significantly improve the prediction accuracy, thus enabling our method to outperform most of other currently available predictors. Our work provides a complementary approach to the current algorithms that should be useful in computationally assigning disulfide connectivity patterns and helps in the annotation of protein sequences generated by large-scale whole-genome projects. Availability: The prediction web server and Supplementary Material are accessible at foo.maths.uq.edu.au/~huber/disulfide Contact: kb@maths.uq.edu.au Supplementary information: Supplementary data are available at Bioinformatics online.
Publisher: Elsevier BV
Date: 07-2004
Publisher: IGI Global
Date: 2010
DOI: 10.4018/978-1-60566-685-3.CH007
Abstract: This chapter focuses on the interactions and roles between delays and intrinsic noise effects within cellular pathways and regulatory networks. We address these aspects by focusing on genetic regulatory networks that share a common network motif, namely the negative feedback loop, leading to oscillatory gene expression and protein levels. In this context, we discuss computational simulation algorithms for addressing the interplay of delays and noise within the signaling pathways based on biological data. We address implementational issues associated with efficiency and robustness. In a molecular biology setting we present two case studies of temporal models for the Hes1 gene (Monk, 2003 Hirata et al., 2002), known to act as a molecular clock, and the Her1/Her7 regulatory system controlling the periodic somite segmentation in vertebrate embryos (Giudicelli and Lewis, 2004 Horikawa et al., 2006).
Publisher: Elsevier BV
Date: 12-2011
Publisher: AIP
Date: 2012
DOI: 10.1063/1.4756417
Publisher: Elsevier BV
Date: 11-2014
Publisher: Springer Science and Business Media LLC
Date: 04-2014
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2014
DOI: 10.1137/130934192
Publisher: Elsevier BV
Date: 04-1993
Publisher: PeerJ
Date: 11-02-2019
DOI: 10.7717/PEERJ.6315
Abstract: This review was initiated by the COST action CA15114 AMICI “Anti-Microbial Coating Innovations to prevent infectious diseases,” where one important aspect is to analyze ecotoxicological impacts of antimicrobial coatings (AMCs) to ensure their sustainable use. Scopus database was used to collect scientific literature on the types and uses of AMCs, while market reports were used to collect data on production volumes. Special attention was paid on data obtained for the release of the most prevalent ingredients of AMCs into the aqueous phase that was used as the proxy for their possible ecotoxicological effects. Based on the critical analysis of 2,720 papers, it can be concluded that silver-based AMCs are by far the most studied and used coatings followed by those based on titanium, copper, zinc, chitosan and quaternary ammonium compounds. The literature analysis pointed to biomedicine, followed by marine industry, construction industry (paints), food industry and textiles as the main fields of application of AMCs. The published data on ecotoxicological effects of AMCs was scarce, and also only a small number of the papers provided information on release of antimicrobial ingredients from AMCs. The available release data allowed to conclude that silver, copper and zinc are often released in substantial amounts (up to 100%) from the coatings to the aqueous environment. Chitosan and titanium were mostly not used as active released ingredients in AMCs, but rather as carriers for other release-based antimicrobial ingredients (e.g., conventional antibiotics). While minimizing the prevalence of healthcare-associated infections appeared to be the most prosperous field of AMCs application, the release of environmentally hazardous ingredients of AMCs into hospital wastewaters and thus, also the environmental risks associated with AMCs, comprise currently only a fraction of the release and risks of traditional disinfectants. However, being proactive, while the use of antimicrobial/antifouling coatings could currently pose ecotoxicological effects mainly in marine applications, the broad use of AMCs in other applications like medicine, food packaging and textiles should be postponed until reaching evidences on the (i) profound efficiency of these materials in controlling the spread of pathogenic microbes and (ii) safety of AMCs for the human and ecosystems.
Publisher: Springer Science and Business Media LLC
Date: 12-1980
DOI: 10.1007/BF01933639
Publisher: Elsevier BV
Date: 10-2012
Publisher: Public Library of Science (PLoS)
Date: 02-12-2015
Publisher: AIP
Date: 2007
DOI: 10.1063/1.2816628
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2007
DOI: 10.1137/050646032
Publisher: Elsevier BV
Date: 11-2012
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2003
Publisher: Elsevier BV
Date: 07-2000
Publisher: Springer Science and Business Media LLC
Date: 04-2000
DOI: 10.1038/74153
Publisher: Oxford University Press (OUP)
Date: 1988
Publisher: Elsevier BV
Date: 08-2007
Publisher: Springer Science and Business Media LLC
Date: 13-03-2008
DOI: 10.1007/S11538-007-9286-X
Abstract: Epithelial pattern formation is an important phenomenon that, for ex le, has roles in embryogenesis, development and wound-healing. The ligand Epithelial Growth Factor (EGF) and its receptor EGF-R, constitute a system that forms lateral induction patterns by juxtacrine signalling-binding of membrane-bound ligands to receptors on neighbouring cells. Owen et al. developed a generic ordinary differential equation model of juxtacrine lateral induction that exhibits stable patterning under some conditions. The model predicts relatively slow pattern formation. We examine here the effects of both intrinsic and extrinsic cellular noise arising from the stochastic treatment of this model, and show that this noise could have an accelerating effect on the patterning process.
Publisher: Walter de Gruyter GmbH
Date: 2013
DOI: 10.2478/S11534-013-0220-6
Abstract: Recently, the fractional Bloch-Torrey model has been used to study anomalous diffusion in the human brain. In this paper, we consider three types of space and time fractional Bloch-Torrey equations in two dimensions: Model-1 with the Riesz fractional derivative Model-2 with the one-dimensional fractional Laplacian operator and Model-3 with the two-dimensional fractional Laplacian operator. Firstly, we propose a spatially second-order accurate implicit numerical method for Model-1 whereby we discretize the Riesz fractional derivative using a fractional centered difference. We consider a finite domain where the time and space derivatives are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Secondly, we utilize the matrix transfer technique for solving Model-2 and Model-3. Finally, some numerical results are given to show the behaviours of these three models especially on varying domain sizes with zero Dirichlet boundary conditions.
Publisher: Public Library of Science (PLoS)
Date: 26-06-2015
Publisher: Oxford University Press (OUP)
Date: 1990
Publisher: Elsevier BV
Date: 03-2000
Publisher: Wiley
Date: 26-01-2005
DOI: 10.1111/J.1469-8137.2005.01330.X
Abstract: Functional-structural plant models that include detailed mechanistic representation of underlying physiological processes can be expensive to construct and the resulting models can also be extremely complicated. On the other hand, purely empirical models are not able to simulate plant adaptability and response to different conditions. In this paper, we present an intermediate approach to modelling plant function that can simulate plant response without requiring detailed knowledge of underlying physiology. Plant function is modelled using a 'canonical' modelling approach, which uses compartment models with flux functions of a standard mathematical form, while plant structure is modelled using L-systems. Two modelling ex les are used to demonstrate that canonical modelling can be used in conjunction with L-systems to create functional-structural plant models where function is represented either in an accurate and descriptive way, or in a more mechanistic and explanatory way. We conclude that canonical modelling provides a useful, flexible and relatively simple approach to modelling plant function at an intermediate level of abstraction.
Publisher: IEEE
Date: 08-2010
Publisher: IEEE
Date: 08-2010
Publisher: Springer Science and Business Media LLC
Date: 06-1980
DOI: 10.1007/BF01933191
Publisher: Institution of Engineering and Technology (IET)
Date: 02-2015
Publisher: Public Library of Science (PLoS)
Date: 04-09-2014
Publisher: American Physiological Society
Date: 15-07-2012
DOI: 10.1152/AJPHEART.01151.2011
Abstract: Computational models in physiology often integrate functional and structural information from a large range of spatiotemporal scales from the ionic to the whole organ level. Their sophistication raises both expectations and skepticism concerning how computational methods can improve our understanding of living organisms and also how they can reduce, replace, and refine animal experiments. A fundamental requirement to fulfill these expectations and achieve the full potential of computational physiology is a clear understanding of what models represent and how they can be validated. The present study aims at informing strategies for validation by elucidating the complex interrelations among experiments, models, and simulations in cardiac electrophysiology. We describe the processes, data, and knowledge involved in the construction of whole ventricular multiscale models of cardiac electrophysiology. Our analysis reveals that models, simulations, and experiments are intertwined, in an assemblage that is a system itself, namely the model-simulation-experiment (MSE) system. We argue that validation is part of the whole MSE system and is contingent upon 1) understanding and coping with sources of biovariability 2) testing and developing robust techniques and tools as a prerequisite to conducting physiological investigations 3) defining and adopting standards to facilitate the interoperability of experiments, models, and simulations 4) and understanding physiological validation as an iterative process that contributes to defining the specific aspects of cardiac electrophysiology the MSE system targets, rather than being only an external test, and that this is driven by advances in experimental and computational methods and the combination of both.
Publisher: The Royal Society
Date: 28-08-2010
Abstract: Cardiac electrophysiology is a mature discipline, with the first model of a cardiac cell action potential having been developed in 1962. Current models range from single ion channels, through very complex models of in idual cardiac cells, to geometrically and anatomically detailed models of the electrical activity in whole ventricles. A critical issue for model developers is how to choose parameters that allow the model to faithfully reproduce observed physiological effects without over-fitting. In this paper, we discuss the use of a parametric modelling toolkit, called N imrod , that makes it possible both to explore model behaviour as parameters are changed and also to tune parameters by optimizing model output. Importantly, N imrod leverages computers on the Grid, accelerating experiments by using available high-performance platforms. We illustrate the use of N imrod with two case studies, one at the cardiac tissue level and one at the cellular level.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2010
DOI: 10.1137/09077182X
Publisher: Elsevier BV
Date: 03-2007
Publisher: Springer Science and Business Media LLC
Date: 04-2014
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2007
DOI: 10.1137/060678154
Publisher: Oxford University Press (OUP)
Date: 26-10-2006
DOI: 10.1093/BIOINFORMATICS/BTL552
Abstract: Motivation: Kinetic rate in gene expression is a key measurement of the stability of gene products and gives important information for the reconstruction of genetic regulatory networks. Recent developments in experimental technologies have made it possible to measure the numbers of transcripts and protein molecules in single cells. Although estimation methods based on deterministic models have been proposed aimed at evaluating kinetic rates from experimental observations, these methods cannot tackle noise in gene expression that may arise from discrete processes of gene expression, small numbers of mRNA transcript, fluctuations in the activity of transcriptional factors and variability in the experimental environment. Results: In this paper, we develop effective methods for estimating kinetic rates in genetic regulatory networks. The simulated maximum likelihood method is used to evaluate parameters in stochastic models described by either stochastic differential equations or discrete biochemical reactions. Different types of non-parametric density functions are used to measure the transitional probability of experimental observations. For stochastic models described by biochemical reactions, we propose to use the simulated frequency distribution to evaluate the transitional density based on the discrete nature of stochastic simulations. The genetic optimization algorithm is used as an efficient tool to search for optimal reaction rates. Numerical results indicate that the proposed methods can give robust estimations of kinetic rates with good accuracy. Contact: tian@maths.uq.edu.au
Publisher: Elsevier BV
Date: 11-2012
Publisher: Elsevier BV
Date: 09-2020
Publisher: Springer Science and Business Media LLC
Date: 03-1978
DOI: 10.1007/BF01947741
Publisher: Elsevier BV
Date: 05-2012
Publisher: Springer Science and Business Media LLC
Date: 18-07-2013
Publisher: Springer Science and Business Media LLC
Date: 29-01-2014
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Date: 05-2013
DOI: 10.1109/TCBB.2013.40
Publisher: Elsevier BV
Date: 04-2013
Publisher: Springer Science and Business Media LLC
Date: 12-1978
DOI: 10.1007/BF01932017
Publisher: Oxford University Press (OUP)
Date: 1988
Publisher: Elsevier BV
Date: 1996
Publisher: Springer Science and Business Media LLC
Date: 15-09-2012
Publisher: AIP Publishing
Date: 10-07-2023
DOI: 10.1063/5.0146502
Abstract: Stochastic differential equations (SDE) are a powerful tool to model biological regulatory processes with intrinsic and extrinsic noise. However, numerical simulations of SDE models may be problematic if the values of noise terms are negative and large, which is not realistic for biological systems since the molecular copy numbers or protein concentrations should be non-negative. To address this issue, we propose the composite Patankar-Euler methods to obtain positive simulations of SDE models. A SDE model is separated into three parts, namely, the positive-valued drift terms, negative-valued drift terms, and diffusion terms. We first propose the deterministic Patankar-Euler method to avoid negative solutions generated from the negative-valued drift terms. The stochastic Patankar-Euler method is designed to avoid negative solutions generated from both the negative-valued drift terms and diffusion terms. These Patankar-Euler methods have the strong convergence order of a half. The composite Patankar-Euler methods are the combinations of the explicit Euler method, deterministic Patankar-Euler method, and stochastic Patankar-Euler method. Three SDE system models are used to examine the effectiveness, accuracy, and convergence properties of the composite Patankar-Euler methods. Numerical results suggest that the composite Patankar-Euler methods are effective methods to ensure positive simulations when any appropriate stepsize is used.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2002
Publisher: Elsevier BV
Date: 1993
Publisher: Elsevier BV
Date: 08-2014
Publisher: Elsevier BV
Date: 10-1998
Publisher: AIP
Date: 2010
DOI: 10.1063/1.3498353
Publisher: The Royal Society
Date: 07-2023
DOI: 10.1098/RSOS.221177
Abstract: Studying membrane dynamics is important to understand the cellular response to environmental stimuli. A decisive spatial characteristic of the plasma membrane is its compartmental structure created by the actin-based membrane-skeleton (fences) and anchored transmembrane proteins (pickets). Particle-based reaction–diffusion simulation of the membrane offers a suitable temporal and spatial resolution to analyse its spatially heterogeneous and stochastic dynamics. Fences have been modelled via hop probabilities, potentials or explicit picket fences. Our study analyses the different approaches’ constraints and their impact on simulation results and performance. Each of the methods comes with its own constraints the picket fences require small timesteps, potential fences might induce a bias in diffusion in crowded systems, and probabilistic fences, in addition to carefully scaling the probability with the timesteps, induce higher computational costs for each propagation step.
Publisher: Wiley
Date: 25-06-2002
DOI: 10.1002/PROT.10176
Publisher: AIP Publishing
Date: 10-09-2007
DOI: 10.1063/1.2771548
Abstract: In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spatial heterogeneity can all affect the cellular dynamics. However, there are ways in which important effects can be accounted without going to the extent of using highly resolved spatial simulators (such as single-particle software), hence reducing the overall computation time significantly. We present a new coarse grained modified version of the next subvolume method that allows the user to consider both diffusion and reaction events in relatively long simulation time spans as compared with the original method and other commonly used fully stochastic computational methods. Benchmarking of the simulation algorithm was performed through comparison with the next subvolume method and well mixed models (MATLAB), as well as stochastic particle reaction and transport simulations (CHEMCELL, Sandia National Laboratories). Additionally, we construct a model based on a set of chemical reactions in the epidermal growth factor receptor pathway. For this particular application and a bistable chemical system ex le, we analyze and outline the advantages of our presented binomial τ-leap spatial stochastic simulation algorithm, in terms of efficiency and accuracy, in scenarios of both molecular homogeneity and heterogeneity.
Publisher: Walter de Gruyter GmbH
Date: 2013
DOI: 10.2478/S11534-013-0296-Z
Abstract: Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NRT) is considered. A novel alternating direction implicit method for the 2D-RSFDE-NRT with homogeneous Dirichlet boundary conditions is proposed. The stability and convergence of the alternating direction implicit method are discussed. These numerical techniques are used for simulating a two-dimensional Riesz space fractional Fitzhugh-Nagumo model. Finally, a numerical ex le of a two-dimensional Riesz space fractional diffusion equation with an exact solution is given. The numerical results demonstrate the effectiveness of the methods. These methods and techniques can be extended in a straightforward method to three spatial dimensions, which will be the topic of our future research.
Publisher: Elsevier BV
Date: 2009
Publisher: Elsevier BV
Date: 12-1990
Publisher: Elsevier BV
Date: 09-2009
Publisher: American Physical Society (APS)
Date: 22-12-2006
Publisher: Elsevier BV
Date: 08-2011
Publisher: Ovid Technologies (Wolters Kluwer Health)
Date: 22-01-2016
DOI: 10.1161/CIRCRESAHA.115.307836
Abstract: Repolarization alternans (RA) are associated with arrhythmogenesis. Animal studies have revealed potential mechanisms, but human-focused studies are needed. RA generation and frequency dependence may be determined by cell-to-cell variability in protein expression, which is regulated by genetic and external factors. To characterize in vivo RA in human and to investigate in silico using human models, the ionic mechanisms underlying the frequency-dependent differences in RA behavior identified in vivo. In vivo electrograms were acquired at 240 sites covering the epicardium of 41 patients at 6 cycle lengths (600–350 ms). In silico investigations were conducted using a population of biophysically detailed human models incorporating variability in protein expression and calibrated using in vivo recordings. Both in silico and in vivo, 2 types of RA were identified, with Fork- and Eye-type restitution curves, based on RA persistence or disappearance, respectively, at fast pacing rates. In silico simulations show that RA are strongly correlated with fluctuations in sarcoplasmic reticulum calcium, because of strong release and weak reuptake. Large L-type calcium current conductance is responsible for RA disappearance at fast frequencies in Eye-type (30% larger in Eye-type versus Fork-type P .01), because of sarcoplasmic reticulum Ca 2+ ATPase pump potentiation caused by frequency-induced increase in intracellular calcium. Large Na + /Ca 2+ exchanger current is the main driver in translating Ca 2+ fluctuations into RA. In human in vivo and in silico, 2 types of RA are identified, with RA persistence/disappearance as frequency increases. In silico, L-type calcium current and Na + /Ca 2+ exchanger current determine RA human cell-to-cell differences through intracellular and sarcoplasmic reticulum calcium regulation.
Publisher: MDPI AG
Date: 18-05-2020
DOI: 10.3390/V12050558
Abstract: The host-vector shuttle and the bottleneck in dengue transmission is a significant aspect with regard to the study of dengue outbreaks. As mosquitoes require 100–1000 times more virus to become infected than human, the transmission of dengue virus from human to mosquito is a vulnerability that can be targeted to improve disease control. In order to capture the heterogeneity in the infectiousness of an infected patient population towards the mosquito population, we calibrate a population of host-to-vector virus transmission models based on an experimentally quantified infected fraction of a mosquito population. Once the population of models is well-calibrated, we deploy a population of controls that helps to inhibit the human-to-mosquito transmission of the dengue virus indirectly by reducing the viral load in the patient body fluid. We use an optimal bang-bang control on the administration of the defective virus (transmissible interfering particles (TIPs)) to symptomatic patients in the course of their febrile period and observe the dynamics in successful reduction of dengue spread into mosquitoes.
Publisher: Elsevier BV
Date: 04-1993
Publisher: Springer Berlin Heidelberg
Date: 2013
Publisher: Elsevier BV
Date: 08-2007
Publisher: Elsevier BV
Date: 11-1994
Publisher: Elsevier BV
Date: 2015
Publisher: Elsevier BV
Date: 02-1989
Publisher: Elsevier BV
Date: 10-1991
Publisher: Institution of Engineering and Technology (IET)
Date: 08-2012
DOI: 10.1049/IET-SYB.2011.0049
Abstract: There have been many recent studies from both experimental and simulation perspectives in order to understand the effects of spatial crowding in molecular biology. These effects manifest themselves in protein organisation on the plasma membrane, on chemical signalling within the cell and in gene regulation. Simulations are usually done with lattice- or meshless-based random walks but insights can also be gained through the computation of the underlying probability density functions of these stochastic processes. Until recently much of the focus had been on continuous time random walks, but some very recent work has suggested that fractional Brownian motion may be a good descriptor of spatial crowding effects in some cases. The study compares both fractional Brownian motion and continuous time random walks and highlights how well they can represent different types of spatial crowding and physical obstacles. Simulated spatial data, mimicking experimental data, was first generated by using the package Smoldyn. We then attempted to characterise this data through continuous time anomalously diffusing random walks and multifractional Brownian motion (MFBM) by obtaining MFBM paths that match the statistical properties of our s le data. Although diffusion around immovable obstacles can be reasonably characterised by a single Hurst exponent, we find that diffusion in a crowded environment seems to exhibit multifractional properties in the form of a different short- and long-time behaviour.
Publisher: Springer Science and Business Media LLC
Date: 08-04-2014
DOI: 10.1007/S00285-014-0782-Y
Abstract: Messenger RNAs (mRNAs) can be repressed and degraded by small non-coding RNA molecules. In this paper, we formulate a coarsegrained Markov-chain description of the post-transcriptional regulation of mRNAs by either small interfering RNAs (siRNAs) or microRNAs (miRNAs). We calculate the probability of an mRNA escaping from its domain before it is repressed by siRNAs/miRNAs via calculation of the mean time to threshold: when the number of bound siRNAs/miRNAs exceeds a certain threshold value, the mRNA is irreversibly repressed. In some cases, the analysis can be reduced to counting certain paths in a reduced Markov model. We obtain explicit expressions when the small RNA bind irreversibly to the mRNA and we also discuss the reversible binding case. We apply our models to the study of RNA interference in the nucleus, examining the probability of mRNAs escaping via small nuclear pores before being degraded by siRNAs. Using the same modelling framework, we further investigate the effect of small, decoy RNAs (decoys) on the process of post-transcriptional regulation, by studying regulation of the tumor suppressor gene, PTEN: decoys are able to block binding sites on PTEN mRNAs, thereby reducing the number of sites available to siRNAs/miRNAs and helping to protect it from repression. We calculate the probability of a cytoplasmic PTEN mRNA translocating to the endoplasmic reticulum before being repressed by miRNAs. We support our results with stochastic simulations.
Publisher: Springer Science and Business Media LLC
Date: 09-03-2006
Abstract: The majority of peptide bonds in proteins are found to occur in the trans conformation. However, for proline residues, a considerable fraction of Prolyl peptide bonds adopt the cis form. Proline cis / trans isomerization is known to play a critical role in protein folding, splicing, cell signaling and transmembrane active transport. Accurate prediction of proline cis / trans isomerization in proteins would have many important applications towards the understanding of protein structure and function. In this paper, we propose a new approach to predict the proline cis / trans isomerization in proteins using support vector machine (SVM). The preliminary results indicated that using Radial Basis Function (RBF) kernels could lead to better prediction performance than that of polynomial and linear kernel functions. We used single sequence information of different local window sizes, amino acid compositions of different local sequences, multiple sequence alignment obtained from PSI-BLAST and the secondary structure information predicted by PSIPRED. We explored these different sequence encoding schemes in order to investigate their effects on the prediction performance. The training and testing of this approach was performed on a newly enlarged dataset of 2424 non-homologous proteins determined by X-Ray diffraction method using 5-fold cross-validation. Selecting the window size 11 provided the best performance for determining the proline cis / trans isomerization based on the single amino acid sequence. It was found that using multiple sequence alignments in the form of PSI-BLAST profiles could significantly improve the prediction performance, the prediction accuracy increased from 62.8% with single sequence to 69.8% and Matthews Correlation Coefficient (MCC) improved from 0.26 with single local sequence to 0.40. Furthermore, if coupled with the predicted secondary structure information by PSIPRED, our method yielded a prediction accuracy of 71.5% and MCC of 0.43, 9% and 0.17 higher than the accuracy achieved based on the singe sequence information, respectively. A new method has been developed to predict the proline cis / trans isomerization in proteins based on support vector machine, which used the single amino acid sequence with different local window sizes, the amino acid compositions of local sequence flanking centered proline residues, the position-specific scoring matrices (PSSMs) extracted by PSI-BLAST and the predicted secondary structures generated by PSIPRED. The successful application of SVM approach in this study reinforced that SVM is a powerful tool in predicting proline cis / trans isomerization in proteins and biological sequence analysis.
Publisher: AIP Publishing
Date: 03-09-2008
DOI: 10.1063/1.2971036
Abstract: Recently the application of the quasi-steady-state approximation (QSSA) to the stochastic simulation algorithm (SSA) was suggested for the purpose of speeding up stochastic simulations of chemical systems that involve both relatively fast and slow chemical reactions [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)] and further work has led to the nested and slow-scale SSA. Improved numerical efficiency is obtained by respecting the vastly different time scales characterizing the system and then by advancing only the slow reactions exactly, based on a suitable approximation to the fast reactions. We considerably extend these works by applying the QSSA to numerical methods for the direct solution of the chemical master equation (CME) and, in particular, to the finite state projection algorithm [Munsky and Khammash, J. Chem. Phys. 124, 044104 (2006)], in conjunction with Krylov methods. In addition, we point out some important connections to the literature on the (deterministic) total QSSA (tQSSA) and place the stochastic analogue of the QSSA within the more general framework of aggregation of Markov processes. We demonstrate the new methods on four ex les: Michaelis–Menten enzyme kinetics, double phosphorylation, the Goldbeter–Koshland switch, and the mitogen activated protein kinase cascade. Overall, we report dramatic improvements by applying the tQSSA to the CME solver.
Publisher: Elsevier BV
Date: 03-2008
Publisher: No publisher found
Date: 1985
Publisher: Springer Science and Business Media LLC
Date: 03-1987
DOI: 10.1007/BF01937355
Publisher: Cold Spring Harbor Laboratory
Date: 21-11-2019
DOI: 10.1101/850693
Abstract: Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2009
DOI: 10.1137/060677148
Publisher: IEEE
Date: 12-2010
DOI: 10.1109/ACT.2010.10
Publisher: IEEE
Date: 06-2014
Publisher: Elsevier BV
Date: 03-2004
Publisher: Springer Berlin Heidelberg
Date: 2006
DOI: 10.1007/11729976_26
Location: United Kingdom of Great Britain and Northern Ireland
Start Date: 2014
End Date: 2014
Funder: Australian Research Council
View Funded ActivityStart Date: 2012
End Date: 2014
Funder: Australian Research Council
View Funded Activity