A Mechanistic Model of Perceptual Binding Predicts That Binding Mechanism Is Robust against Noise.

The concept of the brain's own time and space is central to many models and theories that aim to explain how the brain generates consciousness. For example, the temporo-spatial theory of consciousness postulates that the brain implements its own inner time and space for conscious processing of the outside world. Furthermore, our perception and cognition of time and space can be different from actual time and space. This study presents a mechanistic model of mutually connected processes that encode phenomenal representations of space and time. The model is used to elaborate the binding mechanism between two sets of processes representing internal space and time, respectively. Further, a stochastic version of the model is developed to investigate the interplay between binding strength and noise. Spectral entropy is used to characterize noise effects on the systems of interacting processes when the binding strength between them is varied. The stochastic modeling results reveal that the spectral entropy values for strongly bound systems are similar to those for weakly bound or even decoupled systems. Thus, the analysis performed in this study allows us to conclude that the binding mechanism is noise-resilient.

Mathematical Modeling in Systems Biology.

Mathematical modeling is a key tool used in the field of systems biology to determine the mechanisms with which the elements of biological systems interact to produce complex dynamic behavior [...].

A continuous-time stochastic Boolean model provides a quantitative description of the budding yeast cell cycle.

The cell division cycle is regulated by a complex network of interacting genes and proteins. The control system has been modeled in many ways, from qualitative Boolean switching-networks to quantitative differential equations and highly detailed stochastic simulations. Here we develop a continuous-time stochastic model using seven Boolean variables to represent the activities of major regulators of the budding yeast cell cycle plus one continuous variable representing cell growth. The Boolean variables are updated asynchronously by logical rules based on known biochemistry of the cell-cycle control system using Gillespie's stochastic simulation algorithm. Time and cell size are updated continuously. By simulating a population of yeast cells, we calculate statistical properties of cell cycle progression that can be compared directly to experimental measurements. Perturbations of the normal sequence of events indicate that the cell cycle is 91% robust to random 'flips' of the Boolean variables, but 9% of the perturbations induce lethal mistakes in cell cycle progression. This simple, hybrid Boolean model gives a good account of the growth and division of budding yeast cells, suggesting that this modeling approach may be as accurate as detailed reaction-kinetic modeling with considerably less demands on estimating rate constants.

Mathematical Models of Death Signaling Networks.

This review provides an overview of the progress made by computational and systems biologists in characterizing different cell death regulatory mechanisms that constitute the cell death network. We define the cell death network as a comprehensive decision-making mechanism that controls multiple death execution molecular circuits. This network involves multiple feedback and feed-forward loops and crosstalk among different cell death-regulating pathways. While substantial progress has been made in characterizing individual cell death execution pathways, the cell death decision network is poorly defined and understood. Certainly, understanding the dynamic behavior of such complex regulatory mechanisms can be only achieved by applying mathematical modeling and system-oriented approaches. Here, we provide an overview of mathematical models that have been developed to characterize different cell death mechanisms and intend to identify future research directions in this field.

Crosstalk between Plk1, p53, cell cycle, and G2/M DNA damage checkpoint regulation in cancer: computational modeling and analysis.

Different cancer cell lines can have varying responses to the same perturbations or stressful conditions. Cancer cells that have DNA damage checkpoint-related mutations are often more sensitive to gene perturbations including altered Plk1 and p53 activities than cancer cells without these mutations. The perturbations often induce a cell cycle arrest in the former cancer, whereas they only delay the cell cycle progression in the latter cancer. To study crosstalk between Plk1, p53, and G2/M DNA damage checkpoint leading to differential cell cycle regulations, we developed a computational model by extending our recently developed model of mitotic cell cycle and including these key interactions. We have used the model to analyze the cancer cell cycle progression under various gene perturbations including Plk1-depletion conditions. We also analyzed mutations and perturbations in approximately 1800 different cell lines available in the Cancer Dependency Map and grouped lines by genes that are represented in our model. Our model successfully explained phenotypes of various cancer cell lines under different gene perturbations. Several sensitivity analysis approaches were used to identify the range of key parameter values that lead to the cell cycle arrest in cancer cells. Our resulting model can be used to predict the effect of potential treatments targeting key mitotic and DNA damage checkpoint regulators on cell cycle progression of different types of cancer cells.

Modeling and analysis of the macronutrient signaling network in budding yeast.

Adaptive modulation of the global cellular growth state of unicellular organisms is crucial for their survival in fluctuating nutrient environments. Because these organisms must be able to respond reliably to ever varying and unpredictable nutritional conditions, their nutrient signaling networks must have a certain inbuilt robustness. In eukaryotes, such as the budding yeast Saccharomyces cerevisiae, distinct nutrient signals are relayed by specific plasma membrane receptors to signal transduction pathways that are interconnected in complex information-processing networks, which have been well characterized. However, the complexity of the signaling network confounds the interpretation of the overall regulatory "logic" of the control system. Here, we propose a literature-curated molecular mechanism of the integrated nutrient signaling network in budding yeast, focusing on early temporal responses to carbon and nitrogen signaling. We build a computational model of this network to reconcile literature-curated quantitative experimental data with our proposed molecular mechanism. We evaluate the robustness of our estimates of the model's kinetic parameter values. We test the model by comparing predictions made in mutant strains with qualitative experimental observations made in the same strains. Finally, we use the model to predict nutrient-responsive transcription factor activities in a number of mutant strains undergoing complex nutrient shifts.

Implications of Noise on Neural Correlates of Consciousness: A Computational Analysis of Stochastic Systems of Mutually Connected Processes.

Random fluctuations in neuronal processes may contribute to variability in perception and increase the information capacity of neuronal networks. Various sources of random processes have been characterized in the nervous system on different levels. However, in the context of neural correlates of consciousness, the robustness of mechanisms of conscious perception against inherent noise in neural dynamical systems is poorly understood. In this paper, a stochastic model is developed to study the implications of noise on dynamical systems that mimic neural correlates of consciousness. We computed power spectral densities and spectral entropy values for dynamical systems that contain a number of mutually connected processes. Interestingly, we found that spectral entropy decreases linearly as the number of processes within the system doubles. Further, power spectral density frequencies shift to higher values as system size increases, revealing an increasing impact of negative feedback loops and regulations on the dynamics of larger systems. Overall, our stochastic modeling and analysis results reveal that large dynamical systems of mutually connected and negatively regulated processes are more robust against inherent noise than small systems.

Dynamical analysis of the fission yeast cell cycle via Markov chain.

The cell cycle is a complex network involved in the regulation of cell growth and proliferation. Intrinsic molecular noise in gene expression in the cell cycle network can generate fluctuations in protein concentration. How the cell cycle network maintains its robust transitions between cell cycle phases in the presence of these fluctuations remains unclear. To understand the complex and robust behavior of the cell cycle system in the presence of intrinsic noise, we developed a Markov model for the fission yeast cell cycle system. We quantified the effect of noise on gene and protein activity and on the probability of transition between different phases of the cell cycle. Our analysis shows how network perturbations decide the fate of the cell. Our model predicts that the cell cycle pathway (subsequent transitions from [Formula: see text]) is the most robust and probable pathway among all possible trajectories in the cell cycle network. We performed a sensitivity analysis to find correlations between protein interaction weights and transition probabilities between cell cycle phases. The sensitivity analysis predicts how network perturbations affect the transition probability between different cell cycle phases and, consequently, affect different cell fates, thus, forming testable in vitro/in vivo hypotheses. Our simulation results agree with published experimental findings and reveal how noise in the cell cycle regulatory network can affect cell cycle progression.

A systems biology approach to discovering pathway signaling dysregulation in metastasis.

Total metastatic burden is the primary cause of death for many cancer patients. While the process of metastasis has been studied widely, much remains to be understood. Moreover, few agents have been developed that specifically target the major steps of the metastatic cascade. Many individual genes and pathways have been implicated in metastasis but a holistic view of how these interact and cooperate to regulate and execute the process remains somewhat rudimentary. It is unclear whether all of the signaling features that regulate and execute metastasis are yet fully understood. Novel features of a complex system such as metastasis can often be discovered by taking a systems-based approach. We introduce the concepts of systems modeling and define some of the central challenges facing the application of a multidisciplinary systems-based approach to understanding metastasis and finding actionable targets therein. These challenges include appreciating the unique properties of the high-dimensional omics data often used for modeling, limitations in knowledge of the system (metastasis), tumor heterogeneity and sampling bias, and some of the issues key to understanding critical features of molecular signaling in the context of metastasis. We also provide a brief introduction to integrative modeling that focuses on both the nodes and edges of molecular signaling networks. Finally, we offer some observations on future directions as they relate to developing a systems-based model of the metastatic cascade.

Genetic interactions derived from high-throughput phenotyping of 6589 yeast cell cycle mutants.

Over the last 30 years, computational biologists have developed increasingly realistic mathematical models of the regulatory networks controlling the division of eukaryotic cells. These models capture data resulting from two complementary experimental approaches: low-throughput experiments aimed at extensively characterizing the functions of small numbers of genes, and large-scale genetic interaction screens that provide a systems-level perspective on the cell division process. The former is insufficient to capture the interconnectivity of the genetic control network, while the latter is fraught with irreproducibility issues. Here, we describe a hybrid approach in which the 630 genetic interactions between 36 cell-cycle genes are quantitatively estimated by high-throughput phenotyping with an unprecedented number of biological replicates. Using this approach, we identify a subset of high-confidence genetic interactions, which we use to refine a previously published mathematical model of the cell cycle. We also present a quantitative dataset of the growth rate of these mutants under six different media conditions in order to inform future cell cycle models.

Modeling the dynamic behavior of biochemical regulatory networks.

Strategies for modeling the complex dynamical behavior of gene/protein regulatory networks have evolved over the last 50 years as both the knowledge of these molecular control systems and the power of computing resources have increased. Here, we review a number of common modeling approaches, including Boolean (logical) models, systems of piecewise-linear or fully non-linear ordinary differential equations, and stochastic models (including hybrid deterministic/stochastic approaches). We discuss the pro's and con's of each approach, to help novice modelers choose a modeling strategy suitable to their problem, based on the type and bounty of available experimental information. We illustrate different modeling strategies in terms of some abstract network motifs, and in the specific context of cell cycle regulation.

CrossPlan: systematic planning of genetic crosses to validate mathematical models.

Motivation: Mathematical models of cellular processes can systematically predict the phenotypes of novel combinations of multi-gene mutations. Searching for informative predictions and prioritizing them for experimental validation is challenging since the number of possible combinations grows exponentially in the number of mutations. Moreover, keeping track of the crosses needed to make new mutants and planning sequences of experiments is unmanageable when the experimenter is deluged by hundreds of potentially informative predictions to test. Results: We present CrossPlan, a novel methodology for systematically planning genetic crosses to make a set of target mutants from a set of source mutants. We base our approach on a generic experimental workflow used in performing genetic crosses in budding yeast. We prove that the CrossPlan problem is NP-complete. We develop an integer-linear-program (ILP) to maximize the number of target mutants that we can make under certain experimental constraints. We apply our method to a comprehensive mathematical model of the protein regulatory network controlling cell division in budding yeast. We also extend our solution to incorporate other experimental conditions such as a delay factor that decides the availability of a mutant and genetic markers to confirm gene deletions. The experimental flow that underlies our work is quite generic and our ILP-based algorithm is easy to modify. Hence, our framework should be relevant in plant and animal systems as well. Availability and implementation: CrossPlan code is freely available under GNU General Public Licence v3.0 at https://github.com/Murali-group/crossplan. Supplementary information: Supplementary data are available at Bioinformatics online.

GraphSpace: stimulating interdisciplinary collaborations in network biology.

SUMMARY: Networks have become ubiquitous in systems biology. Visualization is a crucial component in their analysis. However, collaborations within research teams in network biology are hampered by software systems that are either specific to a computational algorithm, create visualizations that are not biologically meaningful, or have limited features for sharing networks and visualizations. We present GraphSpace, a web-based platform that fosters team science by allowing collaborating research groups to easily store, interact with, layout and share networks. AVAILABILITY AND IMPLEMENTATION: Anyone can upload and share networks at http://graphspace.org. In addition, the GraphSpace code is available at http://github.com/Murali-group/graphspace if a user wants to run his or her own server. CONTACT: murali@cs.vt.edu. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Engineered Tug-of-War Between Kinesin and Dynein Controls Direction of Microtubule Based Transport In Vivo.

Bidirectional transport of membrane organelles along microtubules (MTs) is driven by plus-end directed kinesins and minus-end directed dynein bound to the same cargo. Activities of opposing MT motors produce bidirectional movement of membrane organelles and cytoplasmic particles along MT transport tracks. Directionality of MT-based transport might be controlled by a protein complex that determines which motor type is active at any given moment of time, or determined by the outcome of a tug-of-war between MT motors dragging cargo organelles in opposite directions. However, evidence in support of each mechanisms of regulation is based mostly on the results of theoretical analyses or indirect experimental data. Here, we test whether the direction of movement of membrane organelles in vivo can be controlled by the tug-of-war between opposing MT motors alone, by attaching a large number of kinesin-1 motors to organelles transported by dynein to minus-ends of MTs. We find that recruitment of kinesin significantly reduces the length and velocity of minus-end-directed dynein-dependent MT runs, leading to a reversal of the overall direction of dynein-driven organelles in vivo. Therefore, in the absence of external regulators tug-of-war between opposing MT motors alone is sufficient to determine the directionality of MT transport in vivo.

From START to FINISH: computational analysis of cell cycle control in budding yeast.

In the cell division cycle of budding yeast, START refers to a set of tightly linked events that prepare a cell for budding and DNA replication, and FINISH denotes the interrelated events by which the cell exits from mitosis and divides into mother and daughter cells. On the basis of recent progress made by molecular biologists in characterizing the genes and proteins that control START and FINISH, we crafted a new mathematical model of cell cycle progression in yeast. Our model exploits a natural separation of time scales in the cell cycle control network to construct a system of differential-algebraic equations for protein synthesis and degradation, post-translational modifications, and rapid formation and dissociation of multimeric complexes. The model provides a unified account of the observed phenotypes of 257 mutant yeast strains (98% of the 263 strains in the data set used to constrain the model). We then use the model to predict the phenotypes of 30 novel combinations of mutant alleles. Our comprehensive model of the molecular events controlling cell cycle progression in budding yeast has both explanatory and predictive power. Future experimental tests of the model's predictions will be useful to refine the underlying molecular mechanism, to constrain the adjustable parameters of the model, and to provide new insights into how the cell division cycle is regulated in budding yeast.

Regulation of microtubule-based transport by MAP4.

Microtubule (MT)-based transport of organelles driven by the opposing MT motors kinesins and dynein is tightly regulated in cells, but the underlying molecular mechanisms remain largely unknown. Here we tested the regulation of MT transport by the ubiquitous protein MAP4 using Xenopus melanophores as an experimental system. In these cells, pigment granules (melanosomes) move along MTs to the cell center (aggregation) or to the periphery (dispersion) by means of cytoplasmic dynein and kinesin-2, respectively. We found that aggregation signals induced phosphorylation of threonine residues in the MT-binding domain of the Xenopus MAP4 (XMAP4), thus decreasing binding of this protein to MTs. Overexpression of XMAP4 inhibited pigment aggregation by shortening dynein-dependent MT runs of melanosomes, whereas removal of XMAP4 from MTs reduced the length of kinesin-2-dependent runs and suppressed pigment dispersion. We hypothesize that binding of XMAP4 to MTs negatively regulates dynein-dependent movement of melanosomes and positively regulates kinesin-2-based movement. Phosphorylation during pigment aggregation reduces binding of XMAP4 to MTs, thus increasing dynein-dependent and decreasing kinesin-2-dependent motility of melanosomes, which stimulates their accumulation in the cell center, whereas dephosphorylation of XMAP4 during dispersion has an opposite effect.

Stimulation of the CLIP-170--dependent capture of membrane organelles by microtubules through fine tuning of microtubule assembly dynamics.

Cytoplasmic microtubules (MTs) continuously grow and shorten at their free plus ends, a behavior that allows them to capture membrane organelles destined for MT minus end-directed transport. In Xenopus melanophores, the capture of pigment granules (melanosomes) involves the +TIP CLIP-170, which is enriched at growing MT plus ends. Here we used Xenopus melanophores to test whether signals that stimulate minus end MT transport also enhance CLIP-170-dependent binding of melanosomes to MT tips. We found that these signals significantly (>twofold) increased the number of growing MT plus ends and their density at the cell periphery, thereby enhancing the likelihood of interaction with dispersed melanosomes. Computational simulations showed that local and global increases in the density of CLIP-170-decorated MT plus ends could reduce the half-time of melanosome aggregation by ~50%. We conclude that pigment granule aggregation signals in melanophores stimulate MT minus end-directed transport by the increasing number of growing MT plus ends decorated with CLIP-170 and redistributing these ends to more efficiently capture melanosomes throughout the cytoplasm.

Diffusion amid random overlapping obstacles: similarities, invariants, approximations.

Efficient and accurate numerical techniques are used to examine similarities of effective diffusion in a void between random overlapping obstacles: essential invariance of effective diffusion coefficients (D(eff)) with respect to obstacle shapes and applicability of a two-parameter power law over nearly entire range of excluded volume fractions (φ), except for a small vicinity of a percolation threshold. It is shown that while neither of the properties is exact, deviations from them are remarkably small. This allows for quick estimation of void percolation thresholds and approximate reconstruction of D(eff) (φ) for obstacles of any given shape. In 3D, the similarities of effective diffusion yield a simple multiplication "rule" that provides a fast means of estimating D(eff) for a mixture of overlapping obstacles of different shapes with comparable sizes.

Quantifying a pathway: kinetic analysis of actin dendritic nucleation.

Progress in uncovering the reaction networks that underlie important cell functions is laying the groundwork for quantitative identification of protein-interaction pathways. Since direct measurement of rate constants is not always feasible, the parameters are often inferred from multiple pieces of data using kinetic analyses based on appropriate mathematical models. The success of this approach relies on the sufficiency of available experimental data for a unique parameterization of the network. The concept of a rate-limiting step is applied to the analysis of experimental data that are usually used to quantify a pathway of actin dendritic nucleation, the Arp2/3-mediated mechanism that enables rapid changes of cell shape in response to external cues. The method yields analytical descriptions of the dynamics of polymerized actin and provides insights into how the experimental curves should be analyzed. It is shown that dynamics measured by pyrene-labeled actin assays with varying Arp2/3 concentrations are equally well described by two different rate-limiting steps: 1), binding of a nucleating complex to the side of a preexisting filament; or 2), its subsequent activation. To distinguish between the alternatives, we propose experiments with varying concentrations of actin monomers, taking advantage of the fact that the number of branches in the two cases depends differently on the initial monomer concentration. The idea is tested by simulating the proposed experiments with the use of spatial stochastic modeling.