Stochastic Models of Gene Expression with Delayed Degradation

In many biochemical reactions occurring in living cells, number of various molecules might be low which results in significant stochastic fluctuations. In addition, most reactions are not instantaneous, there exist natural time delays in the evolution of cell states. It is a challenge to develop a systematic and rigorous treatment of stochastic dynamics with time delays and to investigate combined effects of stochasticity and delays in concrete models.We propose a new methodology to deal with time delays in biological systems and apply it to simple models of gene expression with delayed degradation. We show that time delay of protein degradation does not cause oscillations as it was recently argued. It follows from our rigorous analysis that one should look for different mechanisms responsible for oscillations observed in biological experiments.We develop a systematic analytical treatment of stochastic models of time delays. Specifically we take into account that some reactions, for example degradation, are consuming, that is: once molecules start to degrade they cannot be part in other degradation processes.We introduce an auxiliary stochastic process and calculate analytically the variance and the autocorrelation function of the number of protein molecules in stationary states in basic models of delayed protein degradation.     

Population models with Allee effect: a new model

In this paper, we develop several population models with Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model, which is the focus of our study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.     

Population models with Allee effect: a new model

In this paper, we develop several population models with Allee effects. We start by defining the Allee effect as a phenomenon in which individual fitness increases with increasing density. Based on this biological assumption, we develop several fitness functions that produce corresponding models with Allee effects. In particular, a rational fitness function yields a new mathematical model, which is the focus of our study. Then we study the dynamics of 2-periodic systems with Allee effects and show the existence of an asymptotically stable 2-periodic carrying capacity.     

Stability and parameter dependency analysis of a facilitation tectal column (FTC) model

Mathematical models and computer simulations have been widely used to study the spatio-temporal characteristics of the processing of information carried out by the central nervous system. When trying to show whether or not a neural model accounts for the phenomena under study, if the number of parameters whose values need to be calculated becomes large, then computer simulations alone become very inefficient to define such values. Here, we developed stability and parameter dependency analyses of the mathematical representation of a single facilitation tectal column (FTC) model, to show how by using techniques from non-linear systems theory we can define the ranges of parameter values under which the model would explain the required performance of the neural net model. The benefits of these analyses can be grouped in two parts: first, the advantage of using non-linear systems techniques to analyze, analytically, the dynamics of neural net models; and second, we get a deeper understanding of why the hypotheses embedded in the models yield the appropriate behaviors and what are the critical situations (parametric combinations) under which these behaviors are displayed.     

Remote Neurodegeneration: Multiple Actors for One Play

Remote neurodegeneration significantly influences the clinical outcome in many central nervous system (CNS) pathologies, such as stroke, multiple sclerosis, and traumatic brain and spinal cord injuries. Because these processes develop days or months after injury, they are accompanied by a therapeutic window of opportunity. The complexity and clinical significance of remote damage is prompting many groups to examine the factors of remote degeneration. This research is providing insights into key unanswered questions, opening new avenues for innovative neuroprotective therapies. In this review, we evaluate data from various remote degeneration models to describe the complexity of the systems that are involved and the importance of their interactions in reducing damage and promoting recovery after brain lesions. Specifically, we recapitulate the current data on remote neuronal degeneration, focusing on molecular and cellular events, as studied in stroke and brain and spinal cord injury models. Remote damage is a multifactorial phenomenon in which many components become active in specific time frames. Days, weeks, or months after injury onset, the interplay between key effectors differentially affects neuronal survival and functional outcomes. In particular, we discuss apoptosis, inflammation, oxidative damage, and autophagy—all of which mediate remote degeneration at specific times. We also review current findings on the pharmacological manipulation of remote degeneration mechanisms in reducing damage and sustaining outcomes. These novel treatments differ from those that have been proposed to limit primary lesion site damage, representing new perspectives on neuroprotection.     

Rapid development of indirect effects in ecological networks

Indirect effects are important components of ecological and evolutionary interactions that may maintain biodiversity, enable or inhibit invasive species, and challenge ecosystem assessment and management. A central hypothesis of Network Environ Analysis (NEA), one type of ecological network analysis, is that indirect flows tend to dominate direct flows in ecosystem networks of conservative substance exchanges. However, current NEA methods assume that these ecosystems are stationary (i.e. time invariant exchange rates), which is unlikely to be true for many ecosystems for interesting time and space scales. For the work reported here, we investigated the sensitivity of the dominance of indirect effects hypothesis to the stationary modeling assumption by determining the development rate of indirect effects and flow intensity, as expressed as the number of transfer steps, in thirty‐one ecosystem models. We hypothesized that indirect effects develop rapidly in ecological networks, but that they would develop faster in biogeochemically based models than in trophically based models. In contrast, our results show that indirect effects develop rapidly in all thirty‐one models examined. In 94% of the models, indirect flows exceeded direct flows by a pathway length of 3. This indicates that ecological systems do not need to maintain a particular configuration for long for indirect effects to dominate. Thus, the dominance of indirect effects hypothesis remains plausible. We also found that biogeochemical models tended to require more of the extended path network than the trophic models to account for 50% and 95% of the total system activity, but that both types of models required more of the power series than is typically considered in engineered systems. These results succinctly illustrate the complexity of ecological systems and help explain why they are challenging to assess and manage.     

A Systems Model Approach to Determining Resilience Surrogates for Case Studies

Resilience theory offers a framework for understanding the dynamics of complex systems. However, operationalizing resilience theory to develop and test empirical hypotheses can be difficult. We present a method in which simple systems models are used as a framework to identify resilience surrogates for case studies. The process of constructing a systems model for a particular case offers a path for identifying important variables related to system resilience, including the slowly-changing variables and thresholds that often are keys to understanding the resilience of a system. We develop a four-step process for identifying resilience surrogates through development of systems models. Because systems model development is often a difficult step, we summarize four basic existing systems models and give examples of how each may be used to identify resilience surrogates. The construction and analysis of simple systems models provides a useful basis for guiding and directing the selection of surrogate variables that will offer appropriate empirical measures of resilience.     

Morphing methods to parameterize specimen-specific finite element model geometries

Shape plays an important role in determining the biomechanical response of a structure. Specimen-specific finite element (FE) models have been developed to capture the details of the shape of biological structures and predict their biomechanics. Shape, however, can vary considerably across individuals or change due to aging or disease, and analysis of the sensitivity of specimen-specific models to these variations has proven challenging. An alternative to specimen-specific representation has been to develop generic models with simplified geometries whose shape is relatively easy to parameterize, and can therefore be readily used in sensitivity studies. Despite many successful applications, generic models are limited in that they cannot make predictions for individual specimens.We propose that it is possible to harness the detail available in specimen-specific models while leveraging the power of the parameterization techniques common in generic models. In this work we show that this can be accomplished by using morphing techniques to parameterize the geometry of specimen-specific FE models such that the model shape can be varied in a controlled and systematic way suitable for sensitivity analysis. We demonstrate three morphing techniques by using them on a model of the load-bearing tissues of the posterior pole of the eye. We show that using relatively straightforward procedures these morphing techniques can be combined, which allows the study of factor interactions. Finally, we illustrate that the techniques can be used in other systems by applying them to morph a femur. Morphing techniques provide an exciting new possibility for the analysis of the biomechanical role of shape, independently or in interaction with loading and material properties.     

General quantitative genetic methods for comparative biology: phylogenies,taxonomies and multi‐trait models for continuous and categorical characters

Although many of the statistical techniques used in comparative biology were originally developed in quantitative genetics, subsequent development of comparative techniques has progressed in relative isolation. Consequently, many of the new and planned developments in comparative analysis already have well‐tested solutions in quantitative genetics. In this paper, we take three recent publications that develop phylogenetic meta‐analysis, either implicitly or explicitly, and show how they can be considered as quantitative genetic models. We highlight some of the difficulties with the proposed solutions, and demonstrate that standard quantitative genetic theory and software offer solutions. We also show how results from Bayesian quantitative genetics can be used to create efficient Markov chain Monte Carlo algorithms for phylogenetic mixed models, thereby extending their generality to non‐Gaussian data. Of particular utility is the development of multinomial models for analysing the evolution of discrete traits, and the development of multi‐trait models in which traits can follow different distributions. Meta‐analyses often include a nonrandom collection of species for which the full phylogenetic tree has only been partly resolved. Using missing data theory, we show how the presented models can be used to correct for nonrandom sampling and show how taxonomies and phylogenies can be combined to give a flexible framework with which to model dependence.     

The Mechanisms of Coexistence and Competitive Exclusion in Complex Plankton Ecosystem Models

The biodiversity of plankton ecosystems may no longer be a paradox, but the mechanisms that determine coexistence of explicit competitors in ecosystems remain a mystery. This is particularly so in ecosystem models, where competitive exclusion remains the dominant process. Climate and fisheries models require plankton ecosystem sub-models that maintain competing plankton functional types extant, but coexistence can be reproduced in only a few ‘just so’ theoretical models. This limits our ability to predict the impacts of climate change and fisheries on ocean biota. We consider ecosystems of Kolmogorov form that conserve mass (CK systems). These systems describe a general class of ecosystem models that includes many theoretical and applied models. We develop heuristics that illuminate the key mechanisms that allow the coexistence of explicit competitors in these systems. These heuristics facilitate the identification of a large class of models with the structural property that all species coexist for all time. Our approach unifies many theoretical and applied models in a common biogeochemical framework, providing a powerful tool with the potential to generate new insights into the properties of complex ecosystems.     

Availability Analysis for Multitask Production Systems

A multitask production system is one in which different subsets of the components can be used to perform distinct functions or tasks. For such a system, some of the components are used intermittently and some may be used continuously. This type of operational protocol is often applied to flexible manufacturing systems. In this paper, we develop models of the operational reliability and of the availability of multitask systems. We construct models for both the case in which preventive maintenance is used and the case in which preventive maintenance is not used. The models presented here constitute an extension to existing models to allow the study of the behavior of modern manufacturing equipment.     

Modeling Regulatory Networks to Understand Plant Development: Small Is Beautiful

We now have unprecedented capability to generate large data sets on the myriad genes and molecular players that regulate plant development. Networks of interactions between systems components can be derived from that data in various ways and can be used to develop mathematical models of various degrees of sophistication. Here, we discuss why, in many cases, it is productive to focus on small networks. We provide a brief and accessible introduction to relevant mathematical and computational approaches to model regulatory networks and discuss examples of small network models that have helped generate new insights into plant biology (where small is beautiful), such as in circadian rhythms, hormone signaling, and tissue patterning. We conclude by outlining some of the key technical and modeling challenges for the future.     

Performance Analysis of Flexible Manufacturing Systems with a Single Discrete Material-Handling Device

We present an analytical model for performance prediction of flexible manufacturing systems (FMSs) with a single discrete material-handling device (MHD). This configuration of FMS is significant for many reasons: it is commonly found in industry, it simplifies material-handling control, it is amenable to analytical modeling, and it forms a building block for more complex systems. Standard queueing models are inadequate to analyze this configuration because of the need to take into consideration many nontrivial issues such as state-dependent routing, interference from the MHD, and the analysis of the MHD. To account for state-dependent routing, we develop an iterative method that is built around mean value analysis. To analyze the MHD interference, we use two queueing network models. In the first, we ignore queueing at the MHD but model the interference from the MHD by inflating the station service times. The second network models the queueing for the MHD and estimates the blocking (inflation) times needed for the first model. By iterating between the two networks, we are able to predict the performance of this configuration of FMS. Our analytical estimates are validated against discrete event simulation and shown to be quite accurate for initial system design.     

Phenomenological and molecular-level Petri net modeling and simulation of long-term potentiation

Petri net-based modeling methods have been used in many research projects to represent biological systems. Among these, the hybrid functional Petri net (HFPN) was developed especially for biological modeling in order to provide biologists with a more intuitive Petri net-based method. In the literature, HFPNs are used to represent kinetic models at the molecular level. We present two models of long-term potentiation previously represented by differential equations which we have transformed into HFPN models: a phenomenological synapse model and a molecular-level model of the CaMKII regulation pathway. Through simulation, we obtained results similar to those of previous studies using these models. Our results open the way to a new type of modeling for systems biology where HFPNs are used to combine different levels of abstraction within one model. This approach can be useful in fully modeling a system at the molecular level when kinetic data is missing or when a full study of a system at the molecular level it is not within the scope of the research.     

RNAi and microRNAs: from animal models to disease therapy

The discovery of the phenomenon of RNA interference (RNAi) and its existence in mammals quickly suggested a great potential for use in disease therapy. Rapid advances have been made in the development of RNAi-based technologies and promising results have been obtained from studies on mammalian cell culture systems and animal in vivo models. However, the progress in our understanding of the RNAi pathway and the related function of microRNAs (miRNAs) have also raised concerns regarding various types of side effects that may restrict the use of this technology in human therapy. At the same time, our new knowledge about the functional roles of miRNAs as regulators of many cellular processes, including proliferation, differentiation, development, and neuronal function, is revolutionizing cell biology and will have a major impact on medical research. In this review, we focus on the discoveries that have been made in animal models and how this insight can be translated to human medicine and disease therapy. In this connection, we will particularly discuss the challenges associated with the efforts to develop RNAi-based therapeutics.     

A computational model of limb impedance control based on principles of internal model uncertainty

Efficient human motor control is characterized by an extensive use of joint impedance modulation, which is achieved by co-contracting antagonistic muscles in a way that is beneficial to the specific task. While there is much experimental evidence available that the nervous system employs such strategies, no generally-valid computational model of impedance control derived from first principles has been proposed so far. Here we develop a new impedance control model for antagonistic limb systems which is based on a minimization of uncertainties in the internal model predictions. In contrast to previously proposed models, our framework predicts a wide range of impedance control patterns, during stationary and adaptive tasks. This indicates that many well-known impedance control phenomena naturally emerge from the first principles of a stochastic optimization process that minimizes for internal model prediction uncertainties, along with energy and accuracy demands. The insights from this computational model could be used to interpret existing experimental impedance control data from the viewpoint of optimality or could even govern the design of future experiments based on principles of internal model uncertainty.     

An in vitro approach to the study of target organ toxicity of drugs and chemicals

Summary A major goal of our laboratory has been the development of primary culture systems that retain differentiated fucntions and responses characteristic of intact tissues in vivo. Specifically, we have developed cellular models of primary cultures of rat heart, liver, and kidney cells to explore the mechanisms by which drugs or chemicals may be toxic to key organs of the body and to develop new techniques by which xenobiotics may be evaluated or identified as potential toxicants to living systems. The purpose of this paper is to describe our rationale and approach to the study of target organ toxicology with in vitro cellular systems.     

THE EVOLUTION OF REVERSIBLE SWITCHES IN THE PRESENCE OF IRREVERSIBLE MIMICS

Reversible phenotypic switching can be caused by a number of different mechanisms including epigenetic inheritance systems and DNA-based contingency loci. Previous work has shown that reversible switching systems may be favored by natural selection. Many switches can be characterized as "on/off" where the "off" state constitutes a temporary and reversible loss of function. Loss-of-function phenotypes corresponding to the "off" state can be produced in many different ways, all yielding identical fitness in the short term. In the long term, however, a switch-induced loss of function can be reversed, whereas many loss-of-function mutations, especially deletions, cannot. We refer to these loss-of-function mutations as "irreversible mimics" of the reversible switch. Here, we develop a model in which a reversible switch evolves in the presence of both irreversible mimics and metapopulation structure. We calculate that when the rate of appearance of irreversible mimics exceeds the migration rate, the evolved reversible switching rate will exceed the bet-hedging rate predicted by panmictic models.     

Modeling and Estimation of Kinetic Parameters and Replicative Fitness of HIV-1 from Flow-Cytometry-Based Growth Competition Experiments

Growth competition assays have been developed to quantify the relative fitness of HIV-1 mutants. In this article, we develop mathematical models to describe viral/cellular dynamic interactions in the assay system from which the competitive fitness indices or parameters are defined. In our previous HIV-viral fitness experiments, the concentration of uninfected target cells was assumed to be constant (Wu et al. 2006). But this may not be true in some experiments. In addition, dual infection may frequently occur in viral fitness experiments and may not be ignorable. Here, we relax these two assumptions and extend our earlier viral fitness model (Wu et al. 2006). The resulting models then become nonlinear ODE systems for which closed-form solutions are not achievable. In the new model, the viral relative fitness is a function of time since it depends on the target cell concentration. First, we studied the structure identifiability of the nonlinear ODE models. The identifiability analysis showed that all parameters in the proposed models are identifiable from the flow-cytometry-based experimental data that we collected. We then employed a global optimization approach (the differential evolution algorithm) to directly estimate the kinetic parameters as well as the relative fitness index in the nonlinear ODE models using nonlinear least square regression based on the experimental data. Practical identifiability was investigated via Monte Carlo simulations.