Quantifying dynamic stability of genetic memory circuits

Bistability/Multistability has been found in many biological systems including genetic memory circuits. Proper characterization of system stability helps to understand biological functions and has potential applications in fields such as synthetic biology. Existing methods of analyzing bistability are either qualitative or in a static way. Assuming the circuit is in a steady state, the latter can only reveal the susceptibility of the stability to injected DC noises. However, this can be inappropriate and inadequate as dynamics are crucial for many biological networks. In this paper, we quantitatively characterize the dynamic stability of a genetic conditional memory circuit by developing new dynamic noise margin (DNM) concepts and associated algorithms based on system theory. Taking into account the duration of the noisy perturbation, the DNMs are more general cases of their static counterparts. Using our techniques, we analyze the noise immunity of the memory circuit and derive insights on dynamic hold and write operations. Considering cell-to-cell variations, our parametric analysis reveals that the dynamic stability of the memory circuit has significantly varying sensitivities to underlying biochemical reactions attributable to differences in structure, time scales, and nonlinear interactions between reactions. With proper extensions, our techniques are broadly applicable to other multistable biological systems.     

Motivation and Benefits of Complex Systems Approaches in Ecology

Studies of complex systems in other disciplines provide models and analytical strategies for understanding ecosystems and landscapes. The emphasis is on invariant properties, particularly processes that create scaling relations over wide ranges of scale, both in time and space. Translations between levels of ecological organization may be accomplished by succinct characterizations of processes that operate at fine scales, followed by renormalization group analysis to reveal patterns at broad scales. The self-organized patterns found in simple ecosystem, landscape, and forest-fire models may be explained as feedback between the system state and control parameters. Critical phenomena and phase transitions are expected in open, dissipative systems where long-range correlations defy predictions based on average population densities, a concept that becomes irrelevant as nonstationary conditions prevail. Thus, complexity theory for open systems relates to the ecology of self-entailing ecosystems that function as their own environments and thereby create constraints through emergence. Received: 14 April 1998; accepted 26 May 1998     

On the interpretation of optical illusions

If excited by stimuli adjacent in space and time, the optical system frequently perceives illusions in the form of apparent movements. These effects may be attributed to the dynamic properties of the retinal nerve nets. On the basis of a specific psychophysical experiment the mechanism underlying the generation of optical illusions is interpreted by the methods of systems theory and its use in systems analysis is discussed. It is shown that for the perception of apparent movements the transit times of the signals in the dendrites are particularly important.     

Controllability of non-linear biochemical systems

Mathematical methods of biochemical pathway analysis are rapidly maturing to a point where it is possible to provide objective rationale for the natural design of metabolic systems and where it is becoming feasible to manipulate these systems based on model predictions, for instance, with the goal of optimizing the yield of a desired microbial product. So far, theory-based metabolic optimization techniques have mostly been applied to steady-state conditions or the minimization of transition time, using either linear stoichiometric models or fully kinetic models within biochemical systems theory (BST). This article addresses the related problem of controllability, where the task is to steer a non-linear biochemical system, within a given time period, from an initial state to some target state, which may or may not be a steady state. For this purpose, BST models in S-system form are transformed into affine non-linear control systems, which are subjected to an exact feedback linearization that permits controllability through independent variables. The method is exemplified with a small glycolytic-glycogenolytic pathway that had been analyzed previously by several other authors in different contexts.     

Decoy selection for protein structure prediction via extreme gradient boosting and ranking

Numerical solutions of the chemical master equation (CME) are important for understanding the stochasticity of biochemical systems. However, solving CMEs is a formidable task. This task is complicated due to the nonlinear nature of the reactions and the size of the networks which result in different realizations. Most importantly, the exponential growth of the size of the state-space, with respect to the number of different species in the system makes this a challenging assignment. When the biochemical system has a large number of variables, the CME solution becomes intractable. We introduce the intelligent state projection (ISP) method to use in the stochastic analysis of these systems. For any biochemical reaction network, it is important to capture more than one moment: this allows one to describe the system’s dynamic behaviour. ISP is based on a state-space search and the data structure standards of artificial intelligence (AI). It can be used to explore and update the states of a biochemical system. To support the expansion in ISP, we also develop a Bayesian likelihood node projection (BLNP) function to predict the likelihood of the states. To demonstrate the acceptability and effectiveness of our method, we apply the ISP method to several biological models discussed in prior literature. The results of our computational experiments reveal that the ISP method is effective both in terms of the speed and accuracy of the expansion, and the accuracy of the solution. This method also provides a better understanding of the state-space of the system in terms of blueprint patterns. The ISP is the de-novo method which addresses both accuracy and performance problems for CME solutions. It systematically expands the projection space based on predefined inputs. This ensures accuracy in the approximation and an exact analytical solution for the time of interest. The ISP was more effective both in predicting the behavior of the state-space of the system and in performance management, which is a vital step towards modeling large biochemical systems.     

RankAggreg, an R package for weighted rank aggregation

Background

Determining the parameters of a mathematical model from quantitative measurements is the main bottleneck of modelling biological systems. Parameter values can be estimated from steady-state data or from dynamic data. The nature of suitable data for these two types of estimation is rather different. For instance, estimations of parameter values in pathway models, such as kinetic orders, rate constants, flux control coefficients or elasticities, from steady-state data are generally based on experiments that measure how a biochemical system responds to small perturbations around the steady state. In contrast, parameter estimation from dynamic data requires time series measurements for all dependent variables. Almost no literature has so far discussed the combined use of both steady-state and transient data for estimating parameter values of biochemical systems.

Results

In this study we introduce a constrained optimization method for estimating parameter values of biochemical pathway models using steady-state information and transient measurements. The constraints are derived from the flux connectivity relationships of the system at the steady state. Two case studies demonstrate the estimation results with and without flux connectivity constraints. The unconstrained optimal estimates from dynamic data may fit the experiments well, but they do not necessarily maintain the connectivity relationships. As a consequence, individual fluxes may be misrepresented, which may cause problems in later extrapolations. By contrast, the constrained estimation accounting for flux connectivity information reduces this misrepresentation and thereby yields improved model parameters.

Conclusion

The method combines transient metabolic profiles and steady-state information and leads to the formulation of an inverse parameter estimation task as a constrained optimization problem. Parameter estimation and model selection are simultaneously carried out on the constrained optimization problem and yield realistic model parameters that are more likely to hold up in extrapolations with the model.     

DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis

Background

Dynamic Flux Balance Analysis (DFBA) is a dynamic simulation framework for biochemical processes. DFBA can be performed using different approaches such as static optimization (SOA), dynamic optimization (DOA), and direct approaches (DA). Few existing simulators address the theoretical and practical challenges of nonunique exchange fluxes or infeasible linear programs (LPs). Both are common sources of failure and inefficiencies for these simulators.

Results

DFBAlab, a MATLAB-based simulator that uses the LP feasibility problem to obtain an extended system and lexicographic optimization to yield unique exchange fluxes, is presented. DFBAlab is able to simulate complex dynamic cultures with multiple species rapidly and reliably, including differential-algebraic equation (DAE) systems. In addition, DFBAlab’s running time scales linearly with the number of species models. Three examples are presented where the performance of COBRA, DyMMM and DFBAlab are compared.

Conclusions

Lexicographic optimization is used to determine unique exchange fluxes which are necessary for a well-defined dynamic system. DFBAlab does not fail during numerical integration due to infeasible LPs. The extended system obtained through the LP feasibility problem in DFBAlab provides a penalty function that can be used in optimization algorithms.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0409-8) contains supplementary material, which is available to authorized users.     

Attractor analysis of asynchronous Boolean models of signal transduction networks

Prior work on the dynamics of Boolean networks, including analysis of the state space attractors and the basin of attraction of each attractor, has mainly focused on synchronous update of the nodes’ states. Although the simplicity of synchronous updating makes it very attractive, it fails to take into account the variety of time scales associated with different types of biological processes. Several different asynchronous update methods have been proposed to overcome this limitation, but there have not been any systematic comparisons of the dynamic behaviors displayed by the same system under different update methods. Here we fill this gap by combining theoretical analysis such as solution of scalar equations and Markov chain techniques, as well as numerical simulations to carry out a thorough comparative study on the dynamic behavior of a previously proposed Boolean model of a signal transduction network in plants. Prior evidence suggests that this network admits oscillations, but it is not known whether these oscillations are sustained. We perform an attractor analysis of this system using synchronous and three different asynchronous updating schemes both in the case of the unperturbed (wild-type) and perturbed (node-disrupted) systems. This analysis reveals that while the wild-type system possesses an update-independent fixed point, any oscillations eventually disappear unless strict constraints regarding the timing of certain processes and the initial state of the system are satisfied. Interestingly, in the case of disruption of a particular node all models lead to an extended attractor. Overall, our work provides a roadmap on how Boolean network modeling can be used as a predictive tool to uncover the dynamic patterns of a biological system under various internal and environmental perturbations.     

A review of the evidence from in vitro and in vivo studies for a role for phorbol ester tumour promoters from the Euphorbiales in the selection and clonal expansion of specific cell populations

Review of the evidence from in vitro and in vivo studies for a role for phorbol ester tumour promoters from the Euphorbiales in the selection and clonal expansion of specific cell populations. The identification of the active principle of croton oil as 12-0-tetradecanoylphorbol-13-acetate (TPA) and the advent of in vitro studies, facilitated the identification of a plethora of biochemical effects, certain of which could be correlated with biological and differentiation end points. Evidence is presented for the ability of TPA to select and expand specific cell populations in two different cell culture systems. The roles of differentiation state and second messenger systems will be discussed in relation to models of multi-step carcinogenesis.     

The effect of slow allosteric transitions in a coupled biochemical oscillator model.

The effect of slowed allosteric transitions in a coupled biochemical oscillator model showing complex dynamic behavior is investigated. When the allosteric transitions are sufficiently fast one can obtain a low-dimensional asymptotic approximation for the dynamics of the species that evolve on a slow time-scale. Such low-dimensional models are common in studies of biological control systems and little attention has, so far, been given to the dynamic effect of the large number of species usually eliminated from more biochemically detailed models. Here we investigate the dynamic effect of explicit inclusion of allosteric transitions having finite time-scales of equilibration. It is found that slowed allosteric transitions suppress complex dynamic modes such a bursting, quasi-periodicity and chaos. The effect arises as the enzyme of consideration becomes trapped in an active state where it is unable to respond to changes in effector concentration on the time-scale necessary to support the modes of complex dynamics. Slow allosteric transitions may be favourable in biological systems in which complex oscillations are not desirable but which, at the same time, may benefit from the presence of positive feedbacks. Our findings suggest that slow allosteric transitions and finite internal rates in general may contribute significantly to the dynamics of biological control mechanisms.     

Dynamics of non-linear biochemical systems and the evolutionary significance of time hierarchy

Several non-linear reaction networks are analyzed in order to study the influence of time hierarchy on the dynamics of biochemical systems. The analysis is based on the assumption that the separation of the time constants within metabolic systems is a direct consequence of strong differences of enzyme concentrations. Therefore, as variable system parameters, only the enzyme concentrations are considered. By investigation of the stationary states of various three-component models with feedback-activation bifurcation diagrams within a two-dimensional parameter space, the enzyme simplex, are constructed. The diagrams contain the information about the number of stationary states, their stability properties as well as the type of motion expected at different parameter combinations. The results support the hypothesis that systems with separated time constants generally show a simple dynamic behaviour. Complex motions can be expected mainly for systems without time hierarchy, which are characterized by parameters located within the centre of the enzyme simplex. Quantitative measures for the time hierarchy and the complexity of the dynamics are derived. It is supposed that the separation of time constants is a main feature of the evolution of biochemical systems. The hypothesis is further supported by the consideration of the time hierarchy of the glycolytic pathway.     

Multiplicity and stability analysis of microorganisms in continuous culture: effects of metabolic overflow and growth inhibition

Metabolic overflow (enhanced uptake of substrate and secretion of intermediates) is a phenomenon often observed for cells grown under substrate excess. Growth inhibition by substrate and/or product is also normally found for this kind of culture. An effort is made in this work to analyze the dynamic behavior of a continuous culture subject to metabolic overflow and growth inhibition by substrate and/or product. Analysis of a model system shows that in a certain range of operating conditions three nonwashout steady state solutions are possible. Local stability analysis indicates that only two of them are stable thus leading to multiplicity and hysteresis. Further analysis of the intrinsic effects of different terms describing the metabolic overflow and growth inhibitions reveals that for the model system and the parameters considered, the combined effects of product inhibition and an enhanced formation rate of product under substrate excess cause the multiplicity and hysteresis. Growth inhibition by substrate and/or an enhanced substrate uptake appear not to be necessary conditions. The combined effects of enhanced product formation and product inhibition can also lead to unusual dynamic behavior such as a prolonged time period to reach a steady state, oscillatory transition from one steady state to another, and sustained oscillations. Using the occurrence of multiplicity and oscillation as criteria, the operating regime of a continuous culture can be divided into four domains: one with multiplicity and oscillation, one with unique steady state but possible oscillatory behavior, the other two with unique and stable steady state. The model predictions are in accordance with recent experimental results. The results presented in this work may be used as guidelines for choosing proper operating conditions of similar culture systems to avoid undesired instability and multiplicity. Copyright 1998 John Wiley & Sons, Inc.     

Mixed‐Effects State‐Space Models for Analysis of Longitudinal Dynamic Systems

Summary The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject‐specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed‐effects state‐space models based on the longitudinal feature of dynamic systems. State‐space models with mixed‐effects components are very flexible in modeling the serial correlation of within‐subject observations and between‐subject variations. The Bayesian approach and the maximum likelihood method for standard mixed‐effects models and state‐space models are modified and investigated for estimating unknown parameters in the proposed models. In the Bayesian approach, full conditional distributions are derived and the Gibbs sampler is constructed to explore the posterior distributions. For the maximum likelihood method, we develop a Monte Carlo EM algorithm with a Gibbs sampler step to approximate the conditional expectations in the E‐step. Simulation studies are conducted to compare the two proposed methods. We apply the mixed‐effects state‐space model to a data set from an AIDS clinical trial to illustrate the proposed methodologies. The proposed models and methods may also have potential applications in other biomedical system analyses such as tumor dynamics in cancer research and genetic regulatory network modeling.     

A dynamical system analysis of the development of spontaneous lower extremity movements in newborn and young infants

This study's aim was to evaluate the characteristics of newborn and young infants' spontaneous lower extremity movements by using dynamical systems analysis. Participants were 8 healthy full-term newborn infants (3 boys, 5 girls, mean birth weight and gestational age were 3070.6 g and 39 weeks). A tri-axial accelerometer measured limb movement acceleration in 3-dimensional space. Movement acceleration signals were recorded during 200 s from just below the ankle when the infant was in an active alert state and lying supine (sampling rate 200 Hz). Data were analyzed linearly and nonlinearly. As a result, the optimal embedding dimension showed more than 5 at all times. Time dependent changes started at 6 or 7, and over the next four months decreased to 5 and from 6 months old, increased. The maximal Lyapnov exponent was positive for all segments. The mutual information is at its greatest range at 0 months. Between 3 and 4 months the range in results is narrowest and lowest in value. The mean coefficient of correlation for the x-axis component was negative and y-axis component changed to a positive value between 1 month old and 4 months old. Nonlinear time series analysis suggested that newborn and young infants' spontaneous lower extremity movements are characterized by a nonlinear chaotic dynamics with 5 to 7 embedding dimensions. Developmental changes of an optimal embedding dimension showed a U-shaped phenomenon. In addition, the maximal Lyapnov exponents were positive for all segments (0.79-2.99). Infants' spontaneous movement involves chaotic dynamic systems that are capable of generating voluntary skill movements.     

Transitions and new dynamical states induced by noise in a multiply regulated biochemical system

Noise-induced transitions between coexisting states, and the emergence of a new oscillatory state, are examined in a model for a multiply regulated biochemical system. For the undisturbed system, three oscillatory states, I, II, and III, coexist. It is found that noise above a critical amplitude can cause a transition between states III and II and between states III or II and state I, whereas a transition from state I to either states II or III is never observed. This indicates that the relative stability under noise perturbations is greatest for state I, and progressively less for states II and III. In addition to this transition behaviour, a purely noise-induced state is found. Under noise perturbations, the average concentration of metabolites may depend on both the time duration and amplitude of the superimposed noise. The implications of these results for understanding the in vivo behaviour of complex biochemical systems are discussed.     

Significance of Variability in Archaic Point Assemblages

Abstract

The analysis of a sample of Archaic points from , private collections led the author to question the effectiveness of traditional tool typologies to explain morphological variability. Causes of variations are discussed; time, space and functional specialization are estimated to contribute only part of the total variation. A systems model relating point manufacture and use to hunting strategies is presented. Chipping and retouching techniques are defined as elements of the system variety. Technical choices constitute the mechanisms maintaining the system in a state of equilibrium; technological change results from the introduction of new sets of techniques. The nature of the choices and the range of variations tolerated within the system are deduced from the analysis of the sample. The analysis relies on a recently developed method of recording morphological characteristics. More extensive methods of testing the model are briefly described.     

Natural selection governs local, but not global, evolutionary gene coexpression networks in Caenorhabditis elegans

Background

Signal duration (e.g. the time over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments. Accompanying differences in signal duration are numerous downstream biological processes that require multiple steps of biochemical regulation.

Results

Here we present an analysis that investigates how simple biochemical motifs that involve multiple stages of regulation can be constructed to differentially process signals that persist at different time scales. We compute the dynamic, frequency dependent gain within these networks and resulting power spectra to better understand how biochemical networks can integrate signals at different time scales. We identify topological features of these networks that allow for different frequency dependent signal processing properties.

Conclusion

We show that multi-staged cascades are effective in integrating signals of long duration whereas multi-staged cascades that operate in the presence of negative feedback are effective in integrating signals of short duration. Our studies suggest principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous motif in biochemical systems.     

Measuring collective behaviour of multicellular ensembles: role of space-time scales

Living systems are spectacular examples of spatiotemporally organized structures. During the development of complex organization there is dynamic equilibrium between the local and global processes acting at the intra-and intercellular levels in multiple space and time scales. Although in modelling studies such spatiotemporal systems can be described by different space-time scales and at many organizational levels, the experimental quantities measured and predictions useful for practical applications are at a macroscopic (coarser or averaged) level/scale; these are limited by the resolution of the measuring method and experimental protocol. In this work, we address whether the spatiotemporal collective dynamics exhibited by a multiscale system can discriminate between, or be borne out by, the coarse-grained and averaged measurements done at different spatial and temporal scales. Using a simple model of a ring of cells, we show that measurements of both spatial and spatiotemporal average behaviour in this multicellular ensemble can mask the variety of collective dynamics observed at other space-time scales, and exhibit completely different behaviours. Such outcomes of measurements can lead to incomplete and incorrect understanding of physiological functions and pathogenesis in multicell ensembles.     

Sustainable agriculture and plant diseases: an epidemiological perspective

The potential for modern biology to identify new sources for genetical, chemical and biological control of plant disease is remarkably high. Successful implementation of these methods within globally and locally changing agricultural environments demands new approaches to durable control. This, in turn, requires fusion of population genetics and epidemiology at a range of scales from the field to the landscape and even to continental deployment of control measures. It also requires an understanding of economic and social constraints that influence the deployment of control. Here I propose an epidemiological framework to model invasion, persistence and variability of epidemics that encompasses a wide range of scales and topologies through which disease spreads. By considering how to map control methods onto epidemiological parameters and variables, some new approaches towards optimizing the efficiency of control at the landscape scale are introduced. Epidemiological strategies to minimize the risks of failure of chemical and genetical control are presented and some consequences of heterogeneous selection pressures in time and space on the persistence and evolutionary changes of the pathogen population are discussed. Finally, some approaches towards embedding epidemiological models for the deployment of control in an economically plausible framework are presented.