Parameter inference for an individual based model of chytridiomycosis in frogs

Individual based models (IBMs) and Agent based models (ABMs) have become widely used tools to understand complex biological systems. However, general methods of parameter inference for IBMs are not available. In this paper we show that it is possible to address this problem with a traditional likelihood-based approach, using an example of an IBM developed to describe the spread of chytridiomycosis in a population of frogs as a case study. We show that if the IBM satisfies certain criteria we can find the likelihood (or posterior) analytically, and use standard computational techniques, such as MCMC, for parameter inference.     

Pareto front analysis of flight time and energy use in long-distance bird migration

Optimality models are frequently used in studies of long distance bird migration to help understand and predict migration routes, stopover strategies and fuelling behaviour in a spatially varying environment. These models typically evaluate bird behaviour by focusing on a single optimization currency, such as total migration time or energy-use, without explicitly considering trade-offs between the involved objectives. In this paper, we demonstrate that this classic single-objective approach downplays the importance of variability in bird behaviour. In the light of these considerations, we therefore propose to use a full multi-criteria optimization method to isolate the set of non-dominated, efficient or Pareto optimal solutions. Unlike single-objective optimization where there is only one combination of bird behaviour maximizing fitness, the Pareto solution set represents a range of optimal solutions to conflicting objectives. Our results demonstrate that this multi-objective approach provides important new ways of analyzing how environmental factors and behavioural constraints have driven the evolution of migratory behaviour.     

Switching neuronal state: optimal stimuli revealed using a stochastically-seeded gradient algorithm

Inducing a switch in neuronal state using energy optimal stimuli is relevant to a variety of problems in neuroscience. Analytical techniques from optimal control theory can identify such stimuli; however, solutions to the optimization problem using indirect variational approaches can be elusive in models that describe neuronal behavior. Here we develop and apply a direct gradient-based optimization algorithm to find stimulus waveforms that elicit a change in neuronal state while minimizing energy usage. We analyze standard models of neuronal behavior, the Hodgkin-Huxley and FitzHugh-Nagumo models, to show that the gradient-based algorithm: 1) enables automated exploration of a wide solution space, using stochastically generated initial waveforms that converge to multiple locally optimal solutions; and 2) finds optimal stimulus waveforms that achieve a physiological outcome condition, without a priori knowledge of the optimal terminal condition of all state variables. Analysis of biological systems using stochastically-seeded gradient methods can reveal salient dynamical mechanisms underlying the optimal control of system behavior. The gradient algorithm may also have practical applications in future work, for example, finding energy optimal waveforms for therapeutic neural stimulation that minimizes power usage and diminishes off-target effects and damage to neighboring tissue.     

一类生物种群投资的最优采收控制

在原有的Gauss白噪声刻画环境噪声项的基础上,考虑环境不可预知的跳跃性变化,运用Lévy白噪声建立了有界环境中的随机生物种群模型.并且,引入随机奇异控制来描述投资者的最优采收策略.进一步地,构造一族有着不同起点的控制问题,利用动态规划的思想,给出了最优采收控制问题解的充分条件,进而,将随机控制问题的求解转化为确定型偏微分方程的求解.     

Managing the environmental problem of seawater intrusion in coastal aquifers through simulation–optimization modeling

The seawater intrusion is a widespread environmental problem of coastal aquifers where more than two third of the world’s population lives. The indiscriminate and unplanned groundwater withdrawal for fulfilling the growing freshwater needs of coastal regions causes this problem. Computer-based models are useful tools for achieving the optimal solution of seawater intrusion management problems. Various simulation and optimization modeling approaches have been used to solve the problems. Optimization approaches have been shown to be of great importance when combined with simulation models. A review on the combined applications of simulation and optimization modeling for the seawater intrusion management of the coastal aquifers are done and is presented in this paper. The reviews revealed that the simulation–optimization modeling approach is very suitable for achieving an optimal solution of seawater intrusion management problems even with a large number of variables. It is recommended that the future research should be directed toward improving the long-term hydraulic assessment by collecting and analyzing widespread spatial data, which can be done by increasing the observation and monitoring networks. The coupling of socioeconomic aspects in the seawater intrusion modeling would be another aspect which could be included in the future studies.     

Heuristic and optimal solutions for set-covering problems in conservation biology

Area-selection methods have recently gained prominence in conservation biology. A typical problem is to identify the minimum number of areas required to represent all species over some geographic region. Iterative heuristic methods have been developed by conservation scientists to solve these problems, although the solutions cannot be guaranteed to be optimal. Although optimal solutions can often be found, heuristics continue to be popular as they are perceived to be faster and more transparent as they are intuitively easy to understand. We used distributional data for 1921 bird species, 939 mammal species, 405 snake species, and 617 amphibian species compiled at the Zoological Museum, Univ. of Copenhagen for all 1° cells of mainland sub-Saharan Africa to compare the quality of the solutions found using two heuristic methods (simple-greedy algorithm and a progressive-rarity algorithm) with optimal solutions. We found that the heuristic methods considered here often provide solutions as good as optimal solutions. Even in those cases where the optimal solutions were better the difference was relatively small, with the heuristics providing solutions requiring a 2–10% increase in area selected compared with the optimal solution, which importantly, represented an increase of <1% of the total area. Our study also suggests that the heuristic algorithms performed least well for datasets with few single cell endemics and taxa that tend to have larger range sizes. Despite the good quality of solutions using heuristics there was no time penalty associated with finding optimal solutions for the problems considered here, suggesting that the major obstacle to their use is making optimal methods accessible to conservation biologists. We encourage conservation biologists to work with operations researchers and so gain the benefit of their expertise and experience in solving these kinds of problems.     

The role of vocal individuality in conservation

Identifying the individuals within a population can generate information on life history parameters, generate input data for conservation models, and highlight behavioural traits that may affect management decisions and error or bias within census methods. Individual animals can be discriminated by features of their vocalisations. This vocal individuality can be utilised as an alternative marking technique in situations where the marks are difficult to detect or animals are sensitive to disturbance. Vocal individuality can also be used in cases were the capture and handling of an animal is either logistically or ethically problematic. Many studies have suggested that vocal individuality can be used to count and monitor populations over time; however, few have explicitly tested the method in this role. In this review we discuss methods for extracting individuality information from vocalisations and techniques for using this to count and monitor populations over time. We present case studies in birds where vocal individuality has been applied to conservation and we discuss its role in mammals.     

Interrogating the effect of enzyme kinetics on metabolism using differentiable constraint-based models

Metabolic models are typically characterized by a large number of parameters. Traditionally, metabolic control analysis is applied to differential equation-based models to investigate the sensitivity of predictions to parameters. A corresponding theory for constraint-based models is lacking, due to their formulation as optimization problems. Here, we show that optimal solutions of optimization problems can be efficiently differentiated using constrained optimization duality and implicit differentiation. We use this to calculate the sensitivities of predicted reaction fluxes and enzyme concentrations to turnover numbers in an enzyme-constrained metabolic model of Escherichia coli. The sensitivities quantitatively identify rate limiting enzymes and are mathematically precise, unlike current finite difference based approaches used for sensitivity analysis. Further, efficient differentiation of constraint-based models unlocks the ability to use gradient information for parameter estimation. We demonstrate this by improving, genome-wide, the state-of-the-art turnover number estimates for E. coli. Finally, we show that this technique can be generalized to arbitrarily complex models. By differentiating the optimal solution of a model incorporating both thermodynamic and kinetic rate equations, the effect of metabolite concentrations on biomass growth can be elucidated. We benchmark these metabolite sensitivities against a large experimental gene knockdown study, and find good alignment between the predicted sensitivities and in vivo metabolome changes. In sum, we demonstrate several applications of differentiating optimal solutions of constraint-based metabolic models, and show how it connects to classic metabolic control analysis.     

Parameter Estimation Methods for Single Neuron Models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.     

Behavioural ecology in traditional societies

Can models from behavioural ecology explain cultural diversity in human populations? Studies of variation in reproductive and productive behaviour, both within and between traditional societies, are beginning to show that specific predictions from sexual selection and optimal foraging theory can be developed and tested with human data. Greatest success has been in the study of foraging; whereas attempts to understand patterns of marriage and parental investment have been most convincing in those cases where behaviour is related to specific ecological and social conditions. The aim of human behavioural ecologists in the future will be to determine the constraints that the dual goals of reproduction and production place on individuals.     

Multi-objective behavioural mechanisms are adopted by foraging animals to achieve several optimality goals simultaneously

1. Animals foraging for resources are under a variety of selective pressures, and separate optimality models have been developed predicting the optimal reproductive strategies they should adopt. 2. In most cases, the proximate behavioural mechanisms adopted to achieve such optimality goals have been identified. This is the case, for example, for optimal patch time and sex allocation in insect parasitoids. However, behaviours modelled within this framework have mainly been studied separately, even though real animals have to optimize some behaviours simultaneously. 3. For this reason, it would be better if proximate behavioural rules were designed to attain several goals simultaneously. Despite their importance, such multi-objective proximate rules remain to be discovered. 4. Based on experiments on insect parasitoids that simultaneously examine their optimal patch time and sex allocation strategies, it is shown here that animals can adopt multi-objective behavioural mechanisms that appear consistent with the two optimal goals simultaneously. 5. Results of computer simulations demonstrate that these behavioural mechanisms are indeed consistent with optimal reproductive strategies and have thus been most likely selected over the course of the evolutionary time.     

ING1 inhibits Twist1 expression to block EMT and is antagonized by the HDAC inhibitor vorinostat

ING1 is a chromatin targeting subunit of the Sin3a histone deacetylase (HDAC) complex that alters chromatin structure to subsequently regulate gene expression. We find that ING1 knockdown increases expression of Twist1, Zeb 1&2, Snai1, Bmi1 and TSHZ1 drivers of EMT, promoting EMT and cell motility. ING1 expression had the opposite effect, promoting epithelial cell morphology and inhibiting basal and TGF-β-induced motility in 3D organoid cultures. ING1 binds the Twist1 promoter and Twist1 was largely responsible for the ability of ING1 to reduce cell migration. Consistent with ING1 inhibiting Twist1 expression in vivo, an inverse relationship between ING1 and Twist1 levels was seen in breast cancer samples from The Cancer Genome Atlas (TCGA). The HDAC inhibitor vorinostat is approved for treatment of multiple myeloma and cutaneous T cell lymphoma and is in clinical trials for solid tumours as adjuvant therapy. One molecular target of vorinostat is INhibitor of Growth 2 (ING2), that together with ING1 serve as targeting subunits of the Sin3a HDAC complex. Treatment with sublethal (LD25-LD50) levels of vorinostat promoted breast cancer cell migration several-fold, which increased further upon ING1 knockout. These observations indicate that correct targeting of the Sin3a HDAC complex, and HDAC activity in general decreases luminal and basal breast cancer cell motility, suggesting that use of HDAC inhibitors as adjuvant therapies in breast cancers that are prone to metastasize may not be optimal and requires further investigation.     

A Mixture of Delta-Rules Approximation to Bayesian Inference in Change-Point Problems

Error-driven learning rules have received considerable attention because of their close relationships to both optimal theory and neurobiological mechanisms. However, basic forms of these rules are effective under only a restricted set of conditions in which the environment is stable. Recent studies have defined optimal solutions to learning problems in more general, potentially unstable, environments, but the relevance of these complex mathematical solutions to how the brain solves these problems remains unclear. Here, we show that one such Bayesian solution can be approximated by a computationally straightforward mixture of simple error-driven ‘Delta’ rules. This simpler model can make effective inferences in a dynamic environment and matches human performance on a predictive-inference task using a mixture of a small number of Delta rules. This model represents an important conceptual advance in our understanding of how the brain can use relatively simple computations to make nearly optimal inferences in a dynamic world.     

Resonance scattering detection of trace microalbumin using immunonanogold probe as the catalyst of Fehling reagent-glucose reaction

A novel and sensitive resonance scattering (RS) spectral immunoassay for the determination of microalbumin (Malb) was developed, based on the catalytic effect of immunonanogold (ING) probe on Fehling reagent-glucose reaction, and resonance scattering effect of Cu(2)O particles. Nanogold particles in size of 10nm were used to label goat anti-human microalbumin (GMalb) to obtain an ING probe (AuGMalb) for Malb. The probe produced unspecific aggregation in pH 5.0 citric acid-Na(2)HPO(4) buffer solutions. Upon addition of Malb, the dispersed ING complex formed. The ING complex in supernatant was obtained by centrifuging and was used as catalyst for the reaction between Fehling reagent and glucose to form the Cu(2)O particles to amplify the resonance scattering signal at 610 nm. With addition of Malb, the ING complex in the supernatant increased and the RS intensity at 610 nm (I(610 nm)) enhanced linearly. The enhanced intensity DeltaI(610 nm) was proportional to the Malb concentration in the range of 0.014-0.43 ng ml(-1), with a detection limit of 7.2 pg ml(-1). The proposed method was applied to detect Malb in human urine sample with satisfactory results.     

Dynamics of a physiologically structured population in a time-varying environment

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.     

Integrating Biosystem Models Using Waveform Relaxation

Modelling in systems biology often involves the integration of component models into larger composite models. How to do this systematically and efficiently is a significant challenge: coupling of components can be unidirectional or bidirectional, and of variable strengths. We adapt the waveform relaxation (WR) method for parallel computation of ODEs as a general methodology for computing systems of linked submodels. Four test cases are presented: (i) a cascade of unidirectionally and bidirectionally coupled harmonic oscillators, (ii) deterministic and stochastic simulations of calcium oscillations, (iii) single cell calcium oscillations showing complex behaviour such as periodic and chaotic bursting, and (iv) a multicellular calcium model for a cell plate of hepatocytes. We conclude that WR provides a flexible means to deal with multitime-scale computation and model heterogeneity. Global solutions over time can be captured independently of the solution techniques for the individual components, which may be distributed in different computing environments.