A Modeling and Analysis Study Reveals That CaMKII in Synaptic Plasticity Is a Dominant Affecter in CaM Systems in a T286 Phosphorylation-Dependent Manner.

NMDAR-dependent synaptic plasticity in the hippocampus consists of two opposing forces: long-term potentiation (LTP), which strengthens synapses and long-term depression (LTD), which weakens synapses. LTP and LTD are associated with memory formation and loss, respectively. Synaptic plasticity is controlled at a molecular level by Ca2+-mediated protein signaling. Here, Ca2+ binds the protein, calmodulin (CaM), which modulates synaptic plasticity in both directions. This is because Ca2+-bound CaM activates both LTD-and LTP-inducing proteins. Understanding how CaM responds to Ca2+ signaling and how this translates into synaptic plasticity is therefore important to understanding synaptic plasticity induction. In this paper, CaM activation by Ca2+ and calmodulin binding to downstream proteins was mathematically modeled using differential equations. Simulations were monitored with and without theoretical knockouts and, global sensitivity analyses were performed to determine how Ca2+/CaM signaling occurred at various Ca2+ signals when CaM levels were limiting. At elevated stimulations, the total CaM pool rapidly bound to its protein binding targets which regulate both LTP and LTD. This was followed by CaM becoming redistributed from low-affinity to high-affinity binding targets. Specifically, CaM was redistributed away from LTD-inducing proteins to bind the high-affinity LTP-inducing protein, calmodulin-dependent kinase II (CaMKII). In this way, CaMKII acted as a dominant affecter and repressed activation of opposing CaM-binding protein targets. The model thereby showed a novel form of CaM signaling by which the two opposing pathways crosstalk indirectly. The model also found that CaMKII can repress cAMP production by repressing CaM-regulated proteins, which catalyze cAMP production. The model also found that at low Ca2+ stimulation levels, typical of LTD induction, CaM signaling was unstable and is therefore unlikely to alone be enough to induce synaptic depression. Overall, this paper demonstrates how limiting levels of CaM may be a fundamental aspect of Ca2+ regulated signaling which allows crosstalk among proteins without requiring directly interaction.

A Comprehensive Conceptual and Computational Dynamics Framework for Autonomous Regeneration Systems.

Many biological organisms regenerate structure and function after damage. Despite the long history of research on molecular mechanisms, many questions remain about algorithms by which cells can cooperate towards the same invariant morphogenetic outcomes. Therefore, conceptual frameworks are needed not only for motivating hypotheses for advancing the understanding of regeneration processes in living organisms, but also for regenerative medicine and synthetic biology. Inspired by planarian regeneration, this study offers a novel generic conceptual framework that hypothesizes mechanisms and algorithms by which cell collectives may internally represent an anatomical target morphology towards which they build after damage. Further, the framework contributes a novel nature-inspired computing method for self-repair in engineering and robotics. Our framework, based on past in vivo and in silico studies on planaria, hypothesizes efficient novel mechanisms and algorithms to achieve complete and accurate regeneration of a simple in silico flatwormlike organism from any damage, much like the body-wide immortality of planaria, with minimal information and algorithmic complexity. This framework that extends our previous circular tissue repair model integrates two levels of organization: tissue and organism. In Level 1, three individual in silico tissues (head, body, and tail-each with a large number of tissue cells and a single stem cell at the centre) repair themselves through efficient local communications. Here, the contribution extends our circular tissue model to other shapes and invests them with tissue-wide immortality through an information field holding the minimum body plan. In Level 2, individual tissues combine to form a simple organism. Specifically, the three stem cells form a network that coordinates organism-wide regeneration with the help of Level 1. Here we contribute novel concepts for collective decision-making by stem cells for stem cell regeneration and large-scale recovery. Both levels (tissue cells and stem cells) represent networks that perform simple neural computations and form a feedback control system. With simple and limited cellular computations, our framework minimises computation and algorithmic complexity to achieve complete recovery. We report results from computer simulations of the framework to demonstrate its robustness in recovering the organism after any injury. This comprehensive hypothetical framework that significantly extends the existing biological regeneration models offers a new way to conceptualise the information-processing aspects of regeneration, which may also help design living and non-living self-repairing agents.

Novel domain expansion methods to improve the computational efficiency of the Chemical Master Equation solution for large biological networks.

BACKGROUND: 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. RESULTS: 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. CONCLUSIONS: 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.

Towards abstraction of computational modelling of mammalian cell cycle: Model reduction pipeline incorporating multi-level hybrid petri nets.

Cell cycle is a large biochemical network and it is crucial to simplify it to gain a clearer understanding and insights into the cell cycle. This is also true for other biochemical networks. In this study, we present a model abstraction scheme/pipeline to create a minimal abstract model of the whole mammalian cell cycle system from a large Ordinary Differential Equation model of cell cycle we published previously (Abroudi et al., 2017). The abstract model is developed in a way that it captures the main characteristics (dynamics of key controllers), responses (G1-S and G2-M transitions and DNA damage) and the signalling subsystems (Growth Factor, G1-S and G2-M checkpoints, and DNA damage) of the original model (benchmark). Further, our model exploits: (i) separation of time scales (slow and fast reactions), (ii) separation of levels of complexity (high-level and low-level interactions), (iii) cell-cycle stages (temporality), (iv) functional subsystems (as mentioned above), and (v) represents the whole cell cycle - within a Multi-Level Hybrid Petri Net (MLHPN) framework. Although hybrid Petri Nets is not new, the abstraction of interactions and timing we introduced here is new to cell cycle and Petri Nets. Importantly, our models builds on the significant elements, representing the core cell cycle system, found through a novel Global Sensitivity Analysis on the benchmark model, using Self Organising Maps and Correlation Analysis that we introduced in (Abroudi et al., 2017). Taken the two aspects together, our study proposes a 2-stage model reduction pipeline for large systems and the main focus of this paper is on stage 2, Petri Net model, put in the context of the pipeline. With the MLHPN model, the benchmark model with 61 continuous variables (ODEs) and 148 parameters were reduced to 14 variables (4 continuous (Cyc_Cdks - the main controllers of cell cycle) and 10 discrete (regulators of Cyc_Cdks)) and 31 parameters. Additional 9 discrete elements represented the temporal progression of cell cycle. Systems dynamics simulation results of the MLHPN model were in close agreement with the benchmark model with respect to the crucial metrics selected for comparison: order and pattern of Cyc_Cdk activation, timing of G1-S and G2-M transitions with or without DNA damage, efficiency of the two cell cycle checkpoints in arresting damaged cells and passing healthy cells, and response to two types of global parameter perturbations. The results show that the MLHPN provides a close approximation to the comprehensive benchmark model in robustly representing systems dynamics and emergent properties while presenting the core cell cycle controller in an intuitive, transparent and subsystems format.

Mathematical modelling of core regulatory mechanism in p53 protein that activates apoptotic switch.

The p53 protein, a tumour suppressor, is a key player in the DNA damage response. The activation of apoptosis by p53 involves the intrinsic apoptotic pathway to eliminate stressed cells that contain DNA lesions. Recent experiments have found that apoptosis happen in an all-or-none switch like manner  (Albeck et al., 2008; Rehm et al., 2002). We focus on modelling the mechanism of p53 activation of apoptosis in response to sustained high DNA double-strand breaks. The aim of the research is to investigate the design principles behind the regulation of p53 activation of apoptotic switch. Building on previous models (Chong et al., 2015; Zhang et al., 2009a), we developed a mathematical model that incorporated the molecular interactions in the core regulation of p53 and the apoptosis initiation module involving Puma, Bcl2 and Bax. Activation of Bax was assumed to be an indicator of apoptosis initiation. Chen et al. (2013) suggested that one of the components in the p53 pathway may control a threshold activation of apoptosis. We hypothesized that ATM auto-activation is the component that controls p53 threshold activation of apoptosis with ATM's multi-site autophosphorylation depending on damage intensity. The constructed model demonstrated how molecular interactions and stress signalling molecule ATM's auto-activation of the p53 network dictate cell fate decisions. Our simulation results are qualitatively consistent with the experimental findings of all-or-none activation of apoptosis and predicted overexpression of Bcl2 as a factor in causing malfunction of the apoptotic switch. We present a simplified yet plausible model of molecular mechanism that controls p53 activation of apoptotic switch.

A comprehensive complex systems approach to the study and analysis of mammalian cell cycle control system in the presence of DNA damage stress.

Not many models of mammalian cell cycle system exist due to its complexity. Some models are too complex and hard to understand, while some others are too simple and not comprehensive enough. Moreover, some essential aspects, such as the response of G1-S and G2-M checkpoints to DNA damage as well as the growth factor signalling, have not been investigated from a systems point of view in current mammalian cell cycle models. To address these issues, we bring a holistic perspective to cell cycle by mathematically modelling it as a complex system consisting of important sub-systems that interact with each other. This retains the functionality of the system and provides a clearer interpretation to the processes within it while reducing the complexity in comprehending these processes. To achieve this, we first update a published ODE mathematical model of cell cycle with current knowledge. Then the part of the mathematical model relevant to each sub-system is shown separately in conjunction with a diagram of the sub-system as part of this representation. The model sub-systems are Growth Factor, DNA damage, G1-S, and G2-M checkpoint signalling. To further simplify the model and better explore the function of sub-systems, they are further divided into modules. Here we also add important new modules of: chk-related rapid cell cycle arrest, p53 modules expanded to seamlessly integrate with the rapid arrest module, Tyrosine phosphatase modules that activate Cyc_Cdk complexes and play a crucial role in rapid and delay arrest at both G1-S and G2-M, Tyrosine Kinase module that is important for inactivating nuclear transport of CycB_cdk1 through Wee1 to resist M phase entry, Plk1-Related module that is crucial in activating Tyrosine phosphatases and inactivating Tyrosine kinase, and APC-Related module to show steps in CycB degradation. This multi-level systems approach incorporating all known aspects of cell cycle allowed us to (i) study, through dynamic simulation of an ODE model, comprehensive details of cell cycle dynamics under normal and DNA damage conditions revealing the role and value of the added new modules and elements, (ii) assess, through a global sensitivity analysis, the most influential sub-systems, modules and parameters on system response, such as G1-S and G2-M transitions, and (iii) probe deeply into the relationship between DNA damage and cell cycle progression and test the biological evidence that G1-S is relatively inefficient in arresting damaged cells compared to G2-M checkpoint. To perform sensitivity analysis, Self-Organizing Map with Correlation Coefficient Analysis (SOMCCA) is developed which shows that Growth Factor and G1-S Checkpoint sub-systems and 13 parameters in the modules within them are crucial for G1-S and G2-M transitions. To study the relative efficiency of DNA damage checkpoints, a Checkpoint Efficiency Evaluator (CEE) is developed based on perturbation studies and statistical Type II error. Accordingly, cell cycle is about 96% efficient in arresting damaged cells with G2-M checkpoint being more efficient than G1-S. Further, both checkpoint systems are near perfect (98.6%) in passing healthy cells. Thus this study has shown the efficacy of the proposed systems approach to gain a better understanding of different aspects of mammalian cell cycle system separately and as an integrated system that will also be useful in investigating targeted therapy in future cancer treatments.

Global sensitivity analysis of a model related to memory formation in synapses: Model reduction based on epistemic parameter uncertainties and related issues.

We investigate the epistemic uncertainties of parameters of a mathematical model that describes the dynamics of CaMKII-NMDAR complex related to memory formation in synapses using global sensitivity analysis (GSA). The model, which was published in this journal, is nonlinear and complex with Ca2+ patterns with different level of frequencies as inputs. We explore the effects of parameter on the key outputs of the model to discover the most sensitive ones using GSA and partial ranking correlation coefficient (PRCC) and to understand why they are sensitive and others are not based on the biology of the problem. We also extend the model to add presynaptic neurotransmitter vesicles release to have action potentials as inputs of different frequencies. We perform GSA on this extended model to show that the parameter sensitivities are different for the extended model as shown by PRCC landscapes. Based on the results of GSA and PRCC, we reduce the original model to a less complex model taking the most important biological processes into account. We validate the reduced model against the outputs of the original model. We show that the parameter sensitivities are dependent on the inputs and GSA would make us understand the sensitivities and the importance of the parameters. A thorough phenomenological understanding of the relationships involved is essential to interpret the results of GSA and hence for the possible model reduction.

Modelling bidirectional modulations in synaptic plasticity: A biochemical pathway model to understand the emergence of long term potentiation (LTP) and long term depression (LTD).

Synaptic plasticity induces bidirectional modulations of the postsynaptic response following a synaptic transmission. The long term forms of synaptic plasticity, named long term potentiation (LTP) and long term depression (LTD), are critical for the antithetic functions of the memory system, memory formation and removal, respectively. A common Ca(2+) signalling upstream triggers both LTP and LTD, and the critical proteins and factors coordinating the LTP/LTD inductions are not well understood. We develop an integrated model based on the sub-models of the indispensable synaptic proteins in the emergence of synaptic plasticity to validate and understand their potential roles in the expression of synaptic plasticity. The model explains Ca(2+)/calmodulin (CaM) complex dependent coordination of LTP/LTD expressions by the interactions among the indispensable proteins using the experimentally estimated kinetic parameters. Analysis of the integrated model provides us with insights into the effective timescales of the key proteins and we conclude that the CaM pool size is critical for the coordination between LTP/LTD expressions.

Collective computational intelligence in biology - Emergence of memory in somatic tissues.

Role of memory in the function of biological tissues, organs and organisms remains unexplored with many unanswered questions. In this study, the emergence of associative memory in somatic (non-neural) tissues and its potential relation to tissue function was explored using a number of biologically plausible network topologies in in silico tissues with computing cells. These topologies were local cooperation; complete system-wide cooperation or inhibition; and local cooperation and short- or long-range inhibition. These were tested with and without self-feedback on two-dimensional (2D) three-dimensional (3D) cell networks, resulting in various forms of fully and partially connected networks. Further, both binary inputs with threshold processing and real-valued inputs with nonlinear processing were considered. Results revealed the emergence of diverse forms of tissue memory. In full cooperation, networks produced one fixed attractor indicating the propensity towards a stable memory pattern which in a real tissue could correspond to an invariable physiological state, such as bioelectric homeostasis. The local neighbourhood cooperation produced both a fixed and a limit cycle attractor that could be beneficial for a tissue to hold few associative memories including circadian rhythms. Most interesting results were found for the local cooperation with short- or long-range inhibition topologies that produced a cluster of fixed and limit cycle attractors offering diverse memories. Fixed attractors could correspond to inactive tissue states and active nonrhythmic functional states and limit cycles could correspond to circadian rhythms such as pumping in heart, kidney or liver in various oscillatory regimes. In all topologies, self-feedback abolished or drastically reduced the limit cycles in favour of fixed stable state. These attractor patterns were found to be largely invariant to scale (2D or 3D) and type of inputs and processing. We also explored the self-optimising ability of the 'local cooperation with global (short- or long-range) inhibition' 2D topologies with Hebbian learning with fixed and flexible topologies. The fixed topology learned to self-model to consolidate memory towards fewer more stable attractors. The flexible topology even formed new connections to bring the system to a single fixed state. Thus local cooperation with global inhibition topology can offer greater freedom to create diverse memory pattens that can be tempered by learning, self-feedback, and to some extent continuous processing to simplify and consolidate memory towards manageable forms.

A Comprehensive conceptual and computational dynamics framework for autonomous regeneration of form and function in biological organisms.

In biology, regeneration is a mysterious phenomenon that has inspired self-repairing systems, robots, and biobots. It is a collective computational process whereby cells communicate to achieve an anatomical set point and restore original function in regenerated tissue or the whole organism. Despite decades of research, the mechanisms involved in this process are still poorly understood. Likewise, the current algorithms are insufficient to overcome this knowledge barrier and enable advances in regenerative medicine, synthetic biology, and living machines/biobots. We propose a comprehensive conceptual framework for the engine of regeneration with hypotheses for the mechanisms and algorithms of stem cell-mediated regeneration that enables a system like the planarian flatworm to fully restore anatomical (form) and bioelectric (function) homeostasis from any small- or large-scale damage. The framework extends the available regeneration knowledge with novel hypotheses to propose collective intelligent self-repair machines with multi-level feedback neural control systems driven by somatic and stem cells. We computationally implemented the framework to demonstrate the robust recovery of both form and function (anatomical and bioelectric homeostasis) in an in silico worm that, in a simple way, resembles the planarian. In the absence of complete regeneration knowledge, the framework contributes to understanding and generating hypotheses for stem cell mediated form and function regeneration, which may help advance regenerative medicine and synthetic biology. Further, as our framework is a bio-inspired and bio-computing self-repair machine, it may be useful for building self-repair robots/biobots and artificial self-repair systems.

Alleviating the unwanted effects of oxidative stress on Aß clearance: a review of related concepts and strategies for the development of computational modelling.

Treatment for Alzheimer's disease (AD) can be more effective in the early stages. Although we do not completely understand the aetiology of the early stages of AD, potential pathological factors (amyloid beta [Aß] and tau) and other co-factors have been identified as causes of AD, which may indicate some of the mechanism at work in the early stages of AD. Today, one of the primary techniques used to help delay or prevent AD in the early stages involves alleviating the unwanted effects of oxidative stress on Aß clearance. 4-Hydroxynonenal (HNE), a product of lipid peroxidation caused by oxidative stress, plays a key role in the adduction of the degrading proteases. This HNE employs a mechanism which decreases catalytic activity. This process ultimately impairs Aß clearance. The degradation of HNE-modified proteins helps to alleviate the unwanted effects of oxidative stress. Having a clear understanding of the mechanisms associated with the degradation of the HNE-modified proteins is essential for the development of strategies and for alleviating the unwanted effects of oxidative stress. The strategies which could be employed to decrease the effects of oxidative stress include enhancing antioxidant activity, as well as the use of nanozymes and/or specific inhibitors. One area which shows promise in reducing oxidative stress is protein design. However, more research is needed to improve the effectiveness and accuracy of this technique. This paper discusses the interplay of potential pathological factors and AD. In particular, it focuses on the effect of oxidative stress on the expression of the Aß-degrading proteases through adduction of the degrading proteases caused by HNE. The paper also elucidates other strategies that can be used to alleviate the unwanted effects of oxidative stress on Aß clearance. To improve the effectiveness and accuracy of protein design, we explain the application of quantum mechanical/molecular mechanical approach.

Detection of Alzheimer's disease onset using MRI and PET neuroimaging: longitudinal data analysis and machine learning.

The scientists are dedicated to studying the detection of Alzheimer's disease onset to find a cure, or at the very least, medication that can slow the progression of the disease. This article explores the effectiveness of longitudinal data analysis, artificial intelligence, and machine learning approaches based on magnetic resonance imaging and positron emission tomography neuroimaging modalities for progression estimation and the detection of Alzheimer's disease onset. The significance of feature extraction in highly complex neuroimaging data, identification of vulnerable brain regions, and the determination of the threshold values for plaques, tangles, and neurodegeneration of these regions will extensively be evaluated. Developing automated methods to improve the aforementioned research areas would enable specialists to determine the progression of the disease and find the link between the biomarkers and more accurate detection of Alzheimer's disease onset.

Proteins as fuzzy controllers: Auto tuning a biological fuzzy inference system to predict protein dynamics in complex biological networks.

Biological systems such as mammalian cell cycle are complex systems consisting of a large number of molecular species interacting in ways that produce complex nonlinear systems dynamics. Discrete models such as Boolean models and continuous models such as Ordinary Differential Equations (ODEs) have been widely used to study these systems. Boolean models are simple and can capture qualitative systems behaviour, but they cannot capture the continuous trends of protein concentrations, while ODE models capture continuous trends but require kinetics parameters that are limited. Further, as systems get larger, complexity of these models becomes an issue for parameterization, analysis and interpretation. Also, molecular systems operate under the conditions of uncertainty and noise and our understanding of molecular processes in general is more at a qualitative level characterised by vagueness, imprecision and ambiguity. Hence, as more data are generated, there is a greater need for simpler data driven methods that can approximate continuous system behaviour while representing vagueness and ambiguity without requiring kinetic parameters. Fuzzy inferencing is one such promising method with the ability to work with qualitative vague/imprecise biological knowledge. In this study, we propose a fuzzy inference system for representing continuous behaviour of proteins and apply to some key proteins in the mammalian cell cycle system. The methods we introduced here is novel to protein interaction systems and cell cycle proteins. Our study proposes a three-stage approach to develop fuzzy protein controllers. In stage one, protein system is studied for interactions. We studied some significant core controllers of mammalian cell cycle and their producers and degraders as presented in a published ODE model. Based on the observations from a dataset generated from it, we developed Fuzzy inference systems (FIS) in the second stage, that involved deriving fuzzy IF-THEN rules and their processing, and manually tuned the FIS to predict the dynamics of individual proteins. In stage three, we employed Particle Swarm Optimisation (PSO) for optimising the FIS to further enhance prediction accuracy. Systems dynamics simulation results of the optimised FIS models were in close agreement with the benchmark ODE model results. The results show that the FIS models provide a close approximation to the comprehensive benchmark model in robustly representing continuous protein dynamics while representing the control of protein behavior in an intuitive and transparent format without requiring kinetic parameters. Therefore, FIS models can be an alternative to ODEs in network modelling. Further, FIS models can be assembled to develop large complex systems without losing information or accuracy.

A Novel Computational Approach for Biomarker Detection for Gene Expression-Based Computer-Aided Diagnostic Systems for Breast Cancer.

Cancer produces complex cellular changes. Microarrays have become crucial to identifying genes involved in causing these changes; however, microarray data analysis is challenged by the high-dimensionality of data compared to the number of samples. This has contributed to inconsistent cancer biomarkers from various gene expression studies. Also, identification of crucial genes in cancer can be expedited through expression profiling of peripheral blood cells. We introduce a novel feature selection method for microarrays involving a two-step filtering process to select a minimum set of genes with greater consistency and relevance, and demonstrate that the selected gene set considerably enhances the diagnostic accuracy of cancer. The preliminary filtering (Bi-biological filter) involves building gene coexpression networks for cancer and healthy conditions using a topological overlap matrix (TOM) and finding cancer specific gene clusters using Spectral Clustering (SC). This is followed by a filtering step to extract a much-reduced set of crucial genes using best first search with support vector machine (BFS-SVM). Finally, artificial neural networks, SVM, and K-nearest neighbor classifiers are used to assess the predictive power of the selected genes as well as to select the most effective diagnostic system. The approach was applied to peripheral blood profiling for breast cancer where Bi-biological filter selected 415 biologically consistent genes, from which BFS-SVM extracted 13 highly cancer specific genes for breast cancer identification. ANN was the superior classifier with 93.2% classification accuracy, a 14% improvement over the study from which data were obtained for this study (Aaroe et al., Breast Cancer Res 12:R7, 2010).

A new hierarchical approach to multi-level model abstraction for simplifying ODE models of biological networks and a case study: The G1/S Checkpoint/DNA damage signalling pathways of mammalian cell cycle.

Model reduction is an important topic in studies of biological systems. By reducing the complexity of large models through multi-level models while keeping the essence (biological meaning) of the model, model reduction can help answer many important questions about these systems. In this paper, we present a new reduction method based on hierarchical representation and a lumping approach. We used G1/S checkpoint pathway represented in Ordinary Differential Equations (ODE) in Iwamoto et al. (2011) as a case study to present this reduction method. The approach consists of two parts; the first part represents the biological network as a hierarchy (multiple levels) based on protein binding relations, which allowed us to model the biological network at different levels of abstraction. The second part applies different levels (level 1, 2 and 3) of lumping the species together depending on the level of the hierarchy, resulting in a reduced and transformed model for each level. The model at each level is a representation of the whole system and can address questions pertinent to that level. We develop and simulate reduced models for levels-1, 2 and 3 of lumping for the G1/S checkpoint pathway and evaluate the biological plausibility of the proposed method by comparing the results with the original ODE model of Iwamoto et al. (2011). The results for continuous dynamics of the G1/S checkpoint pathway with or without DNA-damage for reduced models of level- 1, 2 and 3 of lumping are in very good agreement and consistent with the original model results and with biological findings. Therefore, the reduced models (level-1, 2 and 3) can be used to study cell cycle progression in G1 and the effects of DNA damage on it. It is suitable for reducing complex ODE biological network models while retaining accurate continuous dynamics of the system. The 3 levels of the reduced models respectively achieved 20%, 26% and 31% reduction of the base model. Moreover, the reduced model is more efficient to run (30%, 44% and 52% time reduction for the three levels) and generate solutions than the original ODE model. Simplification of complex mathematical models is possible and the proposed reduction method has the potential to make an impact across many fields of biomedical research.

Functional repertoire of protein kinases and phosphatases in synaptic plasticity and associated neurological disorders.

Protein phosphorylation and dephosphorylation are two essential and vital cellular mechanisms that regulate many receptors and enzymes through kinases and phosphatases. Ca2+- dependent kinases and phosphatases are responsible for controlling neuronal processing; balance is achieved through opposition. During molecular mechanisms of learning and memory, kinases generally modulate positively while phosphatases modulate negatively. This review outlines some of the critical physiological and structural aspects of kinases and phosphatases involved in maintaining postsynaptic structural plasticity. It also explores the link between neuronal disorders and the deregulation of phosphatases and kinases.

Modeling protein-protein interactions in axon initial segment to understand their potential impact on action potential initiation.

The axon initial segment (AIS) region is crucial for action potential initiation due to the presence of high-density AIS protein voltage-gated sodium channels (Nav). Nav channels comprise several serine residues responsible for the recruitment of Nav channels into the structure of AIS through interactions with ankyrin-G (AnkG). In this study, a series of computational experiments are performed to understand the role of AIS proteins casein kinase 2 and AnkG on Nav channel recruitment into the AIS. The computational simulation results using Virtual cell software indicate that Nav channels with all serine sites available for phosphorylation bind to AnkG with strong affinity. At the low initial concentration of AnkG and casein kinase 2, the concentration of Nav channels reduces significantly, suggesting the importance of casein kinase 2 and AnkG in the recruitment of Nav channels.

An unbiased sensitivity analysis reveals important parameters controlling periodicity of circadian clock.

To assess the importance of model parameters in kinetic models, sensitivity analysis is generally employed to provide key measures. However, it is quite often that no information is available for a significant number of parameters in biochemical models. Therefore, the results of sensitivity analysis that heavily rely on the accuracy of parameters are largely ambiguous. In this study, we propose a computational approach to determine the relative importance of parameters controlling the performance of the circadian clock in Drosophila. While previous attempts to sensitivity analysis largely depend on the knowledge of model parameters which are generally unknown, our study depicts a consistent picture of sensitivity assessment for a large number of parameters, even when the values of these parameters are not available in vivo. The resulting parametric sensitivity analysis suggests that PER/TIM negative loop is critical to maintain the stable periodicity of the circadian clock, which is consistent to the previously experimental and computational findings. Furthermore, our analysis generates a rich hypothesis of important parameters in the circadian clock that can be further tested experimentally. This approach can also be extended to assess the sensitivity of parameters in any biochemical system where a large number of parameters have unknown values.

Detection of mastitis and its stage of progression by automatic milking systems using artificial neural networks.

Two types of artificial neural networks, multilayer perceptron (MLP) and self-organizing feature map (SOM) were used to detect mastitis by automatic milking systems (AMS) using a new mastitis indicator that combined two previously reported indicators based on higher electrical conductivity (EC) and lower quarter yield (QY). Four MLPs with four combinations of inputs were developed to detect infected quarters. One input combination involved principal components (PC) adopted for addressing multi-collinearity in the data. The PC-based MLP model was superior to other non-PC-based models in terms of less complexity and higher predictive accuracy. The overall correct classification rate (CCR), sensitivity and specificity of this model were 90.74%, 86.90% and 91.36%, respectively. The SOM detected the stage of progression of mastitis in a quarter within the mastitis spectrum and revealed that quarters form three clusters: healthy, moderately ill and severely ill. The clusters were validated using k-means clustering, ANOVA and least significant difference. Clusters reflected the characteristics of healthy and subclinical and clinical mastitis, respectively. We conclude that the PC based model based on EC and QY can be used in AMS to detect mastitis with high accuracy and that the SOM model can be used to monitor the health status of the herd for early intervention and possible treatment.

Using activity time windows and logical representation to reduce the complexity of biological network models: G1/S checkpoint pathway with DNA damage.

Biological systems are difficult to understand complex systems. Scientists continue to create models to simulate biological systems but these models are complex too; for this reason, new reduction methods to simplify complex biological models into simpler ones are increasingly needed. In this paper, we present a way of reducing complex quantitative (continuous) models into logical models based on time windows of system activity and logical (Boolean) models. Time windows were used to define slow and fast activity areas. We use the proposed approach to reduce a continuous ODE model into a logical model describing the G1/S checkpoint with and without DNA damage as a case study. We show that the temporal unfolding of this signalling system can be broken down into three time windows where only two display high level of activity and the other shows little or no activity. The two active windows represent a cell committing to cell cycle and making the G1/S transition, respectively, the two most important high level functions of cell cycle in the G1 phase. Therefore, we developed two models to represent these time windows to reduce time complexity and used Boolean approach to reduce interaction complexity in the ODE model in the respective time windows. The developed reduced models correctly produced the commitment to cell cycle and G1/S transfer through the expected behavior of signalling molecules involved in these processes. As most biological models have a large number of fast reactions and a relatively smaller number of slow reactions, we believe that the proposed approach could be suitable for representing many, if not all biological signalling networks. The approach presented in this study greatly helps in simplifying complex continuous models (ODE models) into simpler models. Moreover, it will also assist scientists build models concentrating on understanding and representing system behavior rather than setting values for a large number of kinetic parameters.