Invariant characteristics of horizontal-plane minimum-torque-change movements with one mechanical degree of freedom

 Uno et al. (1989) suggested that movements are organized such that the squared change of torque is minimized over time. Although influential, this theory has attracted much less attention from experimental researchers than the competing minimum-jerk model (Flash and Hogan 1985). One reason for this relative neglect has been the lack of general quantitative predictions, which results from the belief that minimum-torque-change trajectories have to be computed numerically for individual movements and arm-dynamical parameters. In the present paper, we show that for an important special case, that of planar horizontal movements with one mechanical degree of freedom (DOF), it is actually possible to find an analytic expression for the predicted minimum-torque-change trajectories. Based on this mathematical result, we derive a set of properties which are characteristic of these trajectories and compare them to experimental data which have not previously been related to the minimum-torque-change model. Certain discrepancies between these experimental data and minimum-torque-change model predictions are revealed. Received: 3 September 1996 / Accepted in revised form: 7 January 1997     

A manipulative test of competing theories for metabolic scaling

The reasons why metabolic rate (B) scales allometrically with body mass (M) remain hotly debated. The field is dominated by correlational analyses of the relationship between B and M; these struggle to disentangle competing explanations because both B and M are confounded with ontogeny, life history, and ecology. Here, we overcome these problems by using an experimental approach to test among competing metabolic theories. We examined the scaling of B in size-manipulated and intact colonies of a bryozoan and show that B scales with M(0.5). To explain this, we apply a general model based on the dynamic energy budget theory for metabolic organization that predicts B on the basis of energy allocation to assimilation, maintenance, growth, and maturation. Uniquely, this model predicts the absolute value of B, emphasizes that there is no single scaling exponent of B, and demonstrates that a single model can explain the variation in B seen in nature.     

Pyruvate metabolism in rat liver mitochondria. What is optimized at steady state?

A representative model of mitochondrial pyruvate metabolism was broken down into its extremal independent currents and compared with experimental data obtained from liver mitochondria incubated with pyruvate as a substrate but in the absence of added adenosine diphosphate. Assuming no regulation of enzymatic activities, the free-flow prediction for the output of the model shows large discrepancies with the experimental data. To study the objective of the incubated mitochondria, we calculate the conversion cone of the model, which describes the possible input/output behaviour of the network. We demonstrate the consistency of the experimental data with the model because all measured data are within this cone. Because they are close to the boundary of the cone, we deduce that pyruvate is converted very efficiently (93%) to produce the measured extramitochondrial metabolites. We find that the main function of the incubated mitochondria is the production of malate and citrate, supporting the anaplerotic pathways in the cytosol, notably gluconeogenesis and fatty acid synthesis. Finally, we show that the major flow through the enzymatic steps of the mitochondrial pyruvate metabolism can be reliably predicted based on the stoichiometric model plus the measured extramitochondrial products. A major advantage of this method is that neither kinetic simulations nor radioactive tracers are needed.     

Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions

Cells grow by oxidizing nutrients using a complex network of biochemical reactions. During this process new biological material is produced along with energy used for maintaining cellular organization. Because the metabolic network is highly branched, these tasks can be accomplished using a wide variety of unique reaction sequences. However, evolutionary pressures under carbon-limited growth conditions likely select organisms that utilize highly efficient pathways. Using elementary-mode analysis, we demonstrate that the metabolism of the bacterium Escherichia coli contains four unique pathways that most efficiently convert glucose and oxygen into new cells and maintenance energy under any level of oxygen limitation. Observed regulatory patterns and experimental findings suggest growing cells use these highly efficient pathways. It is predicted that five knockout mutations generate a strain that supports growth using only the most efficient reaction sequence. The analysis approach should be generally useful for predicting metabolic capabilities and efficient network designs based on only genomic information.     

Theoretical analysis of biochemical pathways of nitric oxide release from vascular endothelial cells

Vascular endothelium expressing endothelial nitric oxide synthase (eNOS) produces nitric oxide (NO), which has a number of important physiological functions in the microvasculature. The rate of NO production by the endothelium is a critical determinant of NO distribution in the vascular wall. We have analyzed the biochemical pathways of NO synthesis and formulated a model to estimate NO production by the microvascular endothelium under physiological conditions. The model quantifies the NO produced by eNOS based on the kinetics of NO synthesis and the availability of eNOS and its intracellular substrates. The predicted NO production from microvessels was in the range of 0.005-0.1 microM/s. This range of predicted values is in agreement with some experimental values but is much lower than other rates previously measured or estimated from experimental data with the help of mathematical modeling. Paradoxical discrepancies between the model predictions and previously reported results based on experimental measurements of NO concentration in the vicinity of the arteriolar wall suggest that NO can also be released through eNOS-independent mechanisms, such as catalysis by neuronal NOS (nNOS). We also used our model to test the sensitivity of NO production to substrate availability, eNOS concentration, and potential rate-limiting factors. The results indicated that the predicted low level of NO production can be attributed primarily to a low expression of eNOS in the microvascular endothelial cells.     

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike–timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146–154, 2008a; J Neurophysiol 99:155–165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike–timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.     

Data-Derived Modeling Characterizes Plasticity of MAPK Signaling in Melanoma

The majority of melanomas have been shown to harbor somatic mutations in the RAS-RAF-MEK-MAPK and PI3K-AKT pathways, which play a major role in regulation of proliferation and survival. The prevalence of these mutations makes these kinase signal transduction pathways an attractive target for cancer therapy. However, tumors have generally shown adaptive resistance to treatment. This adaptation is achieved in melanoma through its ability to undergo neovascularization, migration and rearrangement of signaling pathways. To understand the dynamic, nonlinear behavior of signaling pathways in cancer, several computational modeling approaches have been suggested. Most of those models require that the pathway topology remains constant over the entire observation period. However, changes in topology might underlie adaptive behavior to drug treatment. To study signaling rearrangements, here we present a new approach based on Fuzzy Logic (FL) that predicts changes in network architecture over time. This adaptive modeling approach was used to investigate pathway dynamics in a newly acquired experimental dataset describing total and phosphorylated protein signaling over four days in A375 melanoma cell line exposed to different kinase inhibitors. First, a generalized strategy was established to implement a parameter-reduced FL model encoding non-linear activity of a signaling network in response to perturbation. Next, a literature-based topology was generated and parameters of the FL model were derived from the full experimental dataset. Subsequently, the temporal evolution of model performance was evaluated by leaving time-defined data points out of training. Emerging discrepancies between model predictions and experimental data at specific time points allowed the characterization of potential network rearrangement. We demonstrate that this adaptive FL modeling approach helps to enhance our mechanistic understanding of the molecular plasticity of melanoma.     

Boosting Probabilistic Graphical Model Inference by Incorporating Prior Knowledge from Multiple Sources

Inferring regulatory networks from experimental data via probabilistic graphical models is a popular framework to gain insights into biological systems. However, the inherent noise in experimental data coupled with a limited sample size reduces the performance of network reverse engineering. Prior knowledge from existing sources of biological information can address this low signal to noise problem by biasing the network inference towards biologically plausible network structures. Although integrating various sources of information is desirable, their heterogeneous nature makes this task challenging. We propose two computational methods to incorporate various information sources into a probabilistic consensus structure prior to be used in graphical model inference. Our first model, called Latent Factor Model (LFM), assumes a high degree of correlation among external information sources and reconstructs a hidden variable as a common source in a Bayesian manner. The second model, a Noisy-OR, picks up the strongest support for an interaction among information sources in a probabilistic fashion. Our extensive computational studies on KEGG signaling pathways as well as on gene expression data from breast cancer and yeast heat shock response reveal that both approaches can significantly enhance the reconstruction accuracy of Bayesian Networks compared to other competing methods as well as to the situation without any prior. Our framework allows for using diverse information sources, like pathway databases, GO terms and protein domain data, etc. and is flexible enough to integrate new sources, if available.     

Inferring differences in the distribution of reaction rates across conditions

Elucidating changes in the distribution of reaction rates in metabolic pathways under different conditions is a central challenge in systems biology. Here we present a method for inferring regulation mechanisms responsible for changes in the distribution of reaction rates across conditions from correlations in time-resolved data. A reversal of correlations between conditions reveals information about regulation mechanisms. With the use of a small in silico hypothetical network, based on only the topology and directionality of a known pathway, several regulation scenarios can be formulated. Confronting these scenarios with experimental data results in a short list of possible pathway regulation mechanisms associated with the reversal of correlations between conditions. This procedure allows for the formulation of regulation scenarios without detailed prior knowledge of kinetics and for the inference of reaction rate changes without rate information. The method was applied to experimental time-resolved metabolomics data from multiple short-term perturbation-response experiments in S. cerevisiae across aerobic and anaerobic conditions. The method's output was validated against a detailed kinetic model of glycolysis in S. cerevisiae, which showed that the method can indeed infer the correct regulation scenario.     

Exploring the Conformational Transitions of Biomolecular Systems Using a Simple Two-State Anisotropic Network Model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.     

Microbial catabolic activities are naturally selected by metabolic energy harvest rate

The fundamental trade-off between yield and rate of energy harvest per unit of substrate has been largely discussed as a main characteristic for microbial established cooperation or competition. In this study, this point is addressed by developing a generalized model that simulates competition between existing and not experimentally reported microbial catabolic activities defined only based on well-known biochemical pathways. No specific microbial physiological adaptations are considered, growth yield is calculated coupled to catabolism energetics and a common maximum biomass-specific catabolism rate (expressed as electron transfer rate) is assumed for all microbial groups. Under this approach, successful microbial metabolisms are predicted in line with experimental observations under the hypothesis of maximum energy harvest rate. Two microbial ecosystems, typically found in wastewater treatment plants, are simulated, namely: (i) the anaerobic fermentation of glucose and (ii) the oxidation and reduction of nitrogen under aerobic autotrophic (nitrification) and anoxic heterotrophic and autotrophic (denitrification) conditions. The experimentally observed cross feeding in glucose fermentation, through multiple intermediate fermentation pathways, towards ultimately methane and carbon dioxide is predicted. Analogously, two-stage nitrification (by ammonium and nitrite oxidizers) is predicted as prevailing over nitrification in one stage. Conversely, denitrification is predicted in one stage (by denitrifiers) as well as anammox (anaerobic ammonium oxidation). The model results suggest that these observations are a direct consequence of the different energy yields per electron transferred at the different steps of the pathways. Overall, our results theoretically support the hypothesis that successful microbial catabolic activities are selected by an overall maximum energy harvest rate.     

Van't Hoff and calorimetric enthalpies from isothermal titration calorimetry: are there significant discrepancies?

The enthalpy of a reaction is most often determined through one of two means; it can be determined directly using calorimetry or indirectly by measuring the temperature dependence of the equilibrium constant (i.e., the van't Hoff method). Recently, discrepancies have been noted between the enthalpy measured by calorimetry, and the enthalpy determined by the van't Hoff method,. This has been suggested to indicate that the binding reaction is more complex than the simple one-to-one binding model used to describe the data. To better understand possible discrepancies between and, we have undertaken both experimental studies using isothermal titration calorimetry to measure the binding energetics of Ba(2+) binding 18-crown-6 ether and 2'-CMP binding RNase A, along with a simulation of a system involving a molecule in conformational equilibrium coupled with binding. We find that when experimental setup and analysis are correctly performed, no statistically significant discrepancies between and exist even for the linked system.     

Network-Based Data Integration for Selecting Candidate Virulence Associated Proteins in the Cereal Infecting Fungus Fusarium graminearum

The identification of virulence genes in plant pathogenic fungi is important for understanding the infection process, host range and for developing control strategies. The analysis of already verified virulence genes in phytopathogenic fungi in the context of integrated functional networks can give clues about the underlying mechanisms and pathways directly or indirectly linked to fungal pathogenicity and can suggest new candidates for further experimental investigation, using a ‘guilt by association’ approach. Here we study 133 genes in the globally important Ascomycete fungus Fusarium graminearum that have been experimentally tested for their involvement in virulence. An integrated network that combines information from gene co-expression, predicted protein-protein interactions and sequence similarity was employed and, using 100 genes known to be required for virulence, we found a total of 215 new proteins potentially associated with virulence of which 29 are annotated as hypothetical proteins. The majority of these potential virulence genes are located in chromosomal regions known to have a low recombination frequency. We have also explored the taxonomic diversity of these candidates and found 25 sequences, which are likely to be fungal specific. We discuss the biological relevance of a few of the potentially novel virulence associated genes in detail. The analysis of already verified virulence genes in phytopathogenic fungi in the context of integrated functional networks can give clues about the underlying mechanisms and pathways directly or indirectly linked to fungal pathogenicity and can suggest new candidates for further experimental investigation, using a ‘guilt by association’ approach.     

A modelling-experimental approach reveals insulin receptor substrate (IRS)-dependent regulation of adenosine monosphosphate-dependent kinase (AMPK) by insulin

Mammalian target of rapamycin (mTOR) kinase responds to growth factors, nutrients and cellular energy status and is a central controller of cellular growth. mTOR exists in two multiprotein complexes that are embedded into a complex signalling network. Adenosine monophosphate-dependent kinase (AMPK) is activated by energy deprivation and shuts off adenosine 5'-triphosphate (ATP)-consuming anabolic processes, in part via the inactivation of mTORC1. Surprisingly, we observed that AMPK not only responds to energy deprivation but can also be activated by insulin, and is further induced in mTORC1-deficient cells. We have recently modelled the mTOR network, covering both mTOR complexes and their insulin and nutrient inputs. In the present study we extended the network by an AMPK module to generate the to date most comprehensive data-driven dynamic AMPK-mTOR network model. In order to define the intersection via which AMPK is activated by the insulin network, we compared simulations for six different hypothetical model structures to our observed AMPK dynamics. Hypotheses ranking suggested that the most probable intersection between insulin and AMPK was the insulin receptor substrate (IRS) and that the effects of canonical IRS downstream cues on AMPK would be mediated via an mTORC1-driven negative-feedback loop. We tested these predictions experimentally in multiple set-ups, where we inhibited or induced players along the insulin-mTORC1 signalling axis and observed AMPK induction or inhibition. We confirmed the identified model and therefore report a novel connection within the insulin-mTOR-AMPK network: we conclude that AMPK is positively regulated by IRS and can be inhibited via the negative-feedback loop.     

Importance of sequence specificity for predicting protein folding pathways: perturbed Gaussian chain model

Recent experimental and theoretical studies suggest that rates and pathways of protein folding are largely decided by topology of the native structures, at least for small proteins. However, some exceptions are known; for example, protein L and protein G have the same topology, but exhibit different characteristics of the TSE. Thus, folding pathways of some proteins are critically affected by detailed information on amino acid sequences. To investigate the sequence specificity, we calculate folding pathways of 20 small proteins using the perturbed Gaussian chain model developed by Portman et al. (Phys Rev Lett 1998;81:5237-5240; J Chem Phys 2001;114:5069-5081). Characteristics of the TSE predicted by the model are in good agreement with experimental phi-value data for many proteins at coarse-grained level. Especially, estimation of folding TSE for protein G and protein L based on both topology and additional sequence information are consistent with experimental phi-value data. With only topology information, however, the model predicts the TSE of protein G incorrectly. Moreover, the model that uses topology and sequence information describes free energy profiles of two-state and three-state folders consistently with experiment, whereas the topology only model predicts free energy profiles of some proteins incorrectly. This indicates that sequence specificity also has critical roles in determining the folding pathways for some proteins.     

Constitutive Model of Erythrocyte Membranes with Distributions of Spectrin Orientations and Lengths

We present an analytical hyperelastic constitutive model of the red blood cell (erythrocyte) membrane based on recently improved characterizations of density and microscopic structure of its spectrin network from proteomics and cryo-electron tomography. The model includes distributions of both orientations and natural lengths of spectrin and updated copy numbers of proteins. By applying finite deformation to the spectrin network, we obtain the total free energy and stresses in terms of invariants of shear and area deformation. We generalize an expression of the initial shear modulus, which is independent of the number of molecular orientations within the network and also derive a simplified version of the model. We apply the model and its simplified version to analyze micropipette aspiration computationally and analytically and explore the effect of local cytoskeletal density change. We also explore the discrepancies among shear modulus values measured using different experimental techniques reported in the literature. We find that the model exhibits hardening behavior and can explain many of these discrepancies. Moreover, we find that the distribution of natural lengths plays a crucial role in the hardening behavior when the correct copy numbers of proteins are used. The initial shear modulus values we obtain using our current model (5.9–15.6 pN/μm) are close to the early estimates (6–9 pN/μm). This new, to our knowledge, constitutive model establishes a direct connection between the molecular structure of spectrin networks and constitutive laws and also defines a new picture of a much denser spectrin network than assumed in prior studies.     

Native richness and species level trophic traits predict establishment of alien freshwater fishes

Community level ecological traits are thought to affect invasibility as more diverse communities with complex trophic interactions may be associated with greater biotic resistance. Elucidation of the nature of this relationship is often hampered by difficulties in characterising food webs, particularly where field data are lacking. We attempted to overcome this by coupling food web modelling with information-theoretic analysis of the modelled webs. In addition, we also investigated the possibility that species level trends in trophic traits of established aliens might reflect exploitation of empty niches. We constructed hypothetical food webs of 26 natural and artificial lentic habitats from a data set consisting of 370 fish species representing 71 families. Using these food webs, we investigated associations at the community level between food web traits and network topology and number of alien fish species using an information-theoretic approach based on a set of competing a priori hypotheses. At the species level, we similarly tested for trends in trophic traits of established alien fishes using the information-theoretic approach in addition to nMDS of diet data. We found that native species richness in a community was the most important determinant of the number of alien fish taxa, displaying an inverse relationship. Our data also show that alien fish generally feed lower down the food web. Our findings suggest that the biotic resistance hypothesis, though scale dependent, can result in observable effects in animal communities. Moreover, we also found that the ability to exploit low energy yield food sources could favour the establishment of alien species via avoidance of resistive forces from native taxa.     

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.