Identification of alterations in the Jacobian of biochemical reaction networks from steady state covariance data at two conditions

Model building of biochemical reaction networks typically involves experiments in which changes in the behavior due to natural or experimental perturbations are observed. Computational models of reaction networks are also used in a systems biology approach to study how transitions from a healthy to a diseased state result from changes in genetic or environmental conditions. In this paper we consider the nonlinear inverse problem of inferring information about the Jacobian of a Langevin type network model from covariance data of steady state concentrations associated to two different experimental conditions. Under idealized assumptions on the Langevin fluctuation matrices we prove that relative alterations in the network Jacobian can be uniquely identified when comparing the two data sets. Based on this result and the premise that alteration is locally confined to separable parts due to network modularity we suggest a computational approach using hybrid stochastic-deterministic optimization for the detection of perturbations in the network Jacobian using the sparsity promoting effect of $\ell _p$ -penalization. Our approach is illustrated by means of published metabolomic and signaling reaction networks.     

Behaviour of a Premixed Flame Subjected to Acoustic Oscillations

In this paper, a one dimensional premixed laminar methane flame is subjected to acoustic oscillations and studied. The purpose of this analysis is to investigate the effects of acoustic perturbations on the reaction rates of different species, with a view to their respective contribution to thermoacoustic instabilities. Acoustically transparent non reflecting boundary conditions are employed. The flame response has been studied with acoustic waves of different frequencies and amplitudes. The integral values of the reaction rates, the burning velocities and the heat release of the acoustically perturbed flame are compared with the unperturbed case. We found that the flame''s sensitivity to acoustic perturbations is greatest when the wavelength is comparable to the flame thickness. Even in this case, the perturbations are stable with time. We conclude that acoustic fields acting on the chemistry do not contribute significantly to the emergence of large amplitude pressure oscillations.     

A chemical instability mechanism for asymmetric cell differentiation

We propose a mechanism of asymmetric mitosis applicable for cells even without inherent architectural asymmetry and in the presence of symmetric conditions such as a homogeneous environment. The theory is based on the instability of the symmetric development in time of the prospective daughters of a cell in mitosis. The macroscopic equations of chemical reaction, diffusion, and permeation of the various chemical species in the cell are given formal expression, and are then linearized about the symmetric development in order to test the stability to asymmetric perturbations. Instability to such perturbations indicates the deterministic onset of asymmetric division (differentiation). Only small external gradients of concentration, temperature, light, etc. are necessary to polarize the asymmetry for the purpose of a particular morphology. The theory is compared qualitatively with experiments on melanocytogenesis, is used to suggest new experiments, and is proposed as a possible alternative to other mechanisms. Possible application of the theory to the experiments on the first division in the egg of Fucus is considered. Finally, a simple model of a product-enhanced reaction mechanism is developed in detail which shows that the history of the initial preparation of the cell prior to mitosis may play a role in determining the possibility of asymmetric division.     

Quantification of Excluded Volume Effects on the Folding Landscape of Pseudomonas aeruginosa Apoazurin In Vitro

Proteins fold and function inside cells that are crowded with macromolecules. Here, we address the role of the resulting excluded volume effects by in vitro spectroscopic studies of Pseudomonas aeruginosa apoazurin stability (thermal and chemical perturbations) and folding kinetics (chemical perturbation) as a function of increasing levels of crowding agents dextran (sizes 20, 40, and 70 kDa) and Ficoll 70. We find that excluded volume theory derived by Minton quantitatively captures the experimental effects when crowding agents are modeled as arrays of rods. This finding demonstrates that synthetic crowding agents are useful for studies of excluded volume effects. Moreover, thermal and chemical perturbations result in free energy effects by the presence of crowding agents that are identical, which shows that the unfolded state is energetically the same regardless of method of unfolding. This also underscores the two-state approximation for apoazurin’s unfolding reaction and suggests that thermal and chemical unfolding experiments can be used in an interchangeable way. Finally, we observe increased folding speed and invariant unfolding speed for apoazurin in the presence of macromolecular crowding agents, a result that points to unfolded-state perturbations. Although the absolute magnitude of excluded volume effects on apoazurin is only on the order of 1–3 kJ/mol, differences of this scale may be biologically significant.     

Complex dynamics of mass-closed coupled autocatalytic systems in response to minute asymmetric perturbations

The role of kinetic coupling in catering to a remote-control mechanism for the onset and regulation of self-organization phenomena in a multicompartmental biochemical system has been examined. Using two cyclic autocatalytic reaction networks operating in two chambers separated by a membrane and coupled through a common cofactor, it has been demonstrated that (i) in response to asymmetric perturbations, the coupled reaction networks exhibit a variety of temporal self-organization phenomena such as bistability, multiple periodicity, hard excitation and coexistence of aperiodic oscillation with limit cycle even in mass-closed conditions; (ii) without disturbing a network directly, its dynamic behaviour can be regulated by perturbing some other network kinetically coupled to it and (iii) the dynamics of two coupled networks can be made to flip-flop between oscillatory and steady-states simply by modulating the time of application of external perturbations. The extreme sensitivity of this model to minute asymmetric fluctuations in the environment can predict how the impact of local changes in physico-chemical conditions can be transmitted from one compartment to another through coupled biochemical pathways in a living cell.     

Quantification of Excluded Volume Effects on the Folding Landscape of Pseudomonas aeruginosa Apoazurin In?Vitro

Proteins fold and function inside cells that are crowded with macromolecules. Here, we address the role of the resulting excluded volume effects by in vitro spectroscopic studies of Pseudomonas aeruginosa apoazurin stability (thermal and chemical perturbations) and folding kinetics (chemical perturbation) as a function of increasing levels of crowding agents dextran (sizes 20, 40, and 70 kDa) and Ficoll 70. We find that excluded volume theory derived by Minton quantitatively captures the experimental effects when crowding agents are modeled as arrays of rods. This finding demonstrates that synthetic crowding agents are useful for studies of excluded volume effects. Moreover, thermal and chemical perturbations result in free energy effects by the presence of crowding agents that are identical, which shows that the unfolded state is energetically the same regardless of method of unfolding. This also underscores the two-state approximation for apoazurin’s unfolding reaction and suggests that thermal and chemical unfolding experiments can be used in an interchangeable way. Finally, we observe increased folding speed and invariant unfolding speed for apoazurin in the presence of macromolecular crowding agents, a result that points to unfolded-state perturbations. Although the absolute magnitude of excluded volume effects on apoazurin is only on the order of 1–3 kJ/mol, differences of this scale may be biologically significant.     

Electromagnetic induced kinetic effects on charged substrates in localized enzyme systems.

An analytical expression for the rate efficiency factor of planar localized enzyme systems is derived. The derivation takes into account the isothermal kinetic effect under the externally imposed perturbation of combined electrostatic and high frequency time-varying fields. The contribution of each individual field to the enzyme reaction is examined through the basic mechanism in which charged substrates interact with the specific perturbing field. The interaction mechanisms for the electrostatic and for the time-varying fields are found to be different. This difference regulates the different manners in which enzymatic reaction rates are altered. Enzymatic reactions under electrostatic perturbation can be retarded or enhanced depending on the field polarization. At sufficiently high field intensities the reaction rate may approach zero or approach a maximum value equal to the turnover number of the enzyme. Time-varying field perturbations, on the other hand, always enhance the enzymatic reactions if bunching effects are negligible. At sufficiently high field intensities, the reaction may approach a value equal to that of the free enzyme system. Several typical numerical examples on pure eletrostatic field perturbations, pure time-varying field perturbations, and combined field perturbations are also presented.     

Complexes of mismatched and complementary DNA with minor groove binders. Structures at nucleotide resolution via an improved hydroxyl radical cleavage methodology

Tumor cell lines can replicate faster than normal cells and many also have defective DNA repair pathways. This has lead to the investigation of the inhibition of DNA repair proteins as a means of therapeutic intervention. An alternative approach is to hide or mask damaged DNA from the repair systems. We have developed a protocol to investigate the structures of the complexes of damaged DNA with drug like molecules. Nucleotide resolution structural information can be obtained using an improved hydroxyl radical cleavage protocol. The use of a dT(n) tail increases the length of the smallest fragments of interest and allows efficient co-precipitation of the fragments with poly(A). The use of a fluorescent label, on the 5' end of the dT(n) tail, in conjunction with modified cleavage reaction conditions, avoids the lifetime and other problems with (32)P labeling. The structures of duplex DNAs containing AC and CC mismatches in the presence and absence of minor groove binders have been investigated as have those of the fully complementary DNA. The results indicate that the structural perturbations of the mismatches are localized, are sequence dependent and that the presence of a mismatch can alter the binding of drug like molecules.     

Amplitude effects of medio-lateral mechanical and visual perturbations on gait

Falls during walking are a major contributor to accidental deaths and injuries that can result in debilitating hospitalization costs, lost productivity, and diminished quality of life. To reduce these losses, we must develop a more profound understanding of the characteristic responses to perturbations similar to those encountered in daily life. This study addresses this issue by building on our earlier studies that examined mechanical and visual perturbations in the same environment by applying the same continuous pseudo-random perturbations at multiple (3 mechanical, 5 visual) amplitudes. Walking variability during mechanical perturbations increased significantly with amplitude for all subjects and differences as measured by variabilities of step width, COM position, and COM velocity. These parameters were the only ones sensitive to the presence of visual perturbations, but none of them changed significantly with perturbation amplitude. Additionally, visual perturbation effects were far less consistent across participants, with several who were essentially unaffected by visual perturbations at any level. The homogeneity of the mechanical perturbation effects demonstrates that human responses to mechanical perturbations are similar because they are driven by kinetics that require similar corrections that must be made in order to maintain balance. Conversely, responses to visual perturbations are driven by the perceived need to make corrections and this perception is not accurate enough to produce amplitude-related corrections, even for a single participant, nor is this perception consistent across individuals. This latter finding is likely to be relevant to future visual perturbation studies and the diagnosis and rehabilitation of gait and balance disorders.     

A possible mechanism for the generation and motion of blobs in tokamaks

A possible mechanism for the generation and motion of so-called blobs—peculiar perturbations that are observed in a tokamak edge plasma—is proposed. It is suggested that blobs are self-contracting plasma filaments generated either by the thermal-radiative instability of a plasma with impurities or by the nonradiative resonant charge-exchange instability resulting from the presence of neutral hydrogen atoms near the tokamak wall. Instability occurs in a narrow temperature range in which pressure is a decreasing function of density. Under these conditions, the most typical perturbations are the local ones that originate spontaneously in the form of separate growing hills and wells in the density. The temperature at the centers of the hills is lower than that in the surrounding plasma, but they are denser and, consequently, brighter than the background. The (denser) hills should move (“sink”) toward the separatrix, while the (less dense) wells should “rise” in the opposite direction, as is observed in experiments. It may even be said that they behave in accordance with a peculiar Archimedes' principle.     

On performing experimental studies on transient states of continuous-flow methanogenic reactors

One approach to exploring the behavior of microbial cultures during transient conditions of unbalanced growth is to experimentally observe continuous-flow biological reactors which have been subjected to perturbations in the influent flowrate and/or concentration of growth-limiting substrate. Proper interpretation of such experiments requires that appropriate account be taken of reaction stoichiometry, the distribution and abundance of microbial populations within the reactor, and the nonideality of mixing and flow distribution in the reactor. These aspects of proper experimental design are particularly critical when the system of interest involves methanogenic consortia and is not a completely-mixed, suspended-growth reactor.     

Development of a novel fluorescence assay for studying lipid bilayer perturbation induced by amyloidogenic peptides using cell plasma membrane vesicles

Numerous pathophysiological conditions are associated with the misfolding and aggregation of proteins into insoluble amyloid fibrils. The mechanisms by which this process leads to cellular dysfunction remain elusive, though several hypotheses point toward the perturbation of the cell plasma membrane by pre-fibrillar intermediates and/or amyloid growth. However, current models to study membrane perturbations are largely limited to synthetic lipid vesicles and most of experimental approaches cannot be transposed to complex cell-derived plasma membrane systems. Herein, vesicles originating from the plasma membrane of erythrocytes and β-pancreatic cells were used to study the perturbations induced by an amyloidogenic peptide, the islet amyloid polypeptide (IAPP). These biologically relevant lipid vesicles displayed a characteristic clustering in the presence of the amyloidogenic peptide, which was able to rupture membranes. By exploiting Förster resonance energy transfer (FRET), a rapid, simple, and potentially high-throughput assay to detect membrane perturbations of intact mammalian cell plasma membrane vesicles was implemented. The FRET kinetics of membrane perturbations closely correlated with the kinetics of thioflavin-T fluorescence associated with amyloid formation. This novel kinetics assay expands the toolbox available to study amyloid-associated membrane damage, bridging the gap between synthetic lipid vesicles and living cells.     

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

Quantitative determination of conformations of flexible molecules in solution using lanthanide ions as nuclear magnetic resonance probes: application to adenosine-5'-monophosphate

A procedure is described here whereby the conformation, of a flexible molecule in solution can be found. The method depends on the study of the nuclear magnetic resonance spectrum of the molecule in the presence of perturbations due to specifically bound lanthanide cations. The magnetic perturbations are of two kinds: shifts of nuclear magnetic resonance spectral lines in the presence of cations such as Eu³⁺ and changes in relaxation rates of the nuclear magnetic resonance excitations in the presence of cations such as Gd³⁺. Suitable expressions are given for the relation between the magnitude of the perturbations and the geometry of the lanthanide complex in the absence of through-bond perturbations and for an axially symmetric system. It is proved that the spectral changes described here are not due to through-bond (contact) effects. The circumstances, in which the anisotropy of the magnetic susceptibility tensor, as seen in the nuclear magnetic resonance spectra, is of axial symmetry, are defined. The experimental systems described are of this kind. A computer program has been devised that searches for the conformations of the molecule which fit the nuclear magnetic resonance data.We outline here the principles of the method and how we have used a combination of relaxation and shift probes to obtain the conformation of adenosine-5′-monophosphate at pH 2. It is shown that a small family of closely related conformations fit the nuclear magnetic resonance data. These conformations are very similar to that of the crystal structure of AMP.     

Effect of urea on the partial reactions and crystallization pattern of sarcoplasmic reticulum adenosine triphosphatase

Steady-state ATPase activity, calcium binding, formation of phosphorylated enzyme intermediate with ATP in the presence of Ca2+, or with Pi in the absence of Ca2+, and association of ATPase molecules into bidimensional crystals, were studied using vesicular fragments of sarcoplasmic reticulum. The vesicles were exposed to increasing concentrations of urea in order to produce stepwise perturbations of protein structure and to test the effect of such perturbations on the partial reactions and crystallization pattern of sarcoplasmic reticulum ATPase. It was found that low concentrations of urea produce specific inhibition of Pi binding and enzyme phosphorylation with Pi (but not with ATP). Intermediate concentrations of urea reduce calcium binding affinity and cooperativity, while the ability of the enzyme to be phosphorylated with ATP and to form dimeric arrays is retained. These observations demonstrate that the sarcoplasmic reticulum ATPase is sensitive to physical perturbations producing specific and reversible changes in the Pi and calcium binding domains. These changes interfere with enzyme turnover, indicating that conformational effects related to binding and dissociation of Pi and calcium are tightly coupled to catalysis and energy transduction. Higher concentrations of urea produce irreversible denaturation, accompanied by total inhibition of calcium binding, enzyme phosphorylation with ATP, and association of ATPase chains in bidimensional crystals. Under these conditions, protein unfolding is manifested by a sharp reduction in the fluorescence of intrinsic tryptophan residues and of a covalently bound probe. These observations suggest that dimeric association and a tendency to form bidimensional crystals correspond to a basic property of the enzyme, which is linked to its native structure and whose character may change in the presence of ligands and/or during the catalytic cycle. On the other hand, the decavanadate-induced crystallization pattern cannot be interpreted in terms of a mechanistic relationship of ATPase dimerization with one of the intermediate states of the catalytic cycle.     

Kinetic asymmetry as a key source of functional diversity in biochemical networks

From the analysis of the dynamic properties of various symmetric and asymmetric kinetic schemes, the present report demonstrates that all kinetic schemes, which can be hypothetically divided into two equal halves about an axis of mirror symmetry, are endowed with structural metastability under mass-closed conditions. In mass-closed symmetric schemes, absolute symmetry in reaction conditions in two halves is essential for the occurrence of ordered dynamic behaviour. Even an infinitesimal deviation from the symmetry relations instantaneously drives such systems from limit-cycles to turbulence. Reaction schemes with no axes of symmetry may exhibit a large variety of complex, structurally stable temporal order for wide ranges of values of system parameters and variables. Kinetic asymmetry, therefore, may confer to biochemical networks the functional diversity as well as stability against environmental perturbations.     

Pattern formation in one- and two-dimensional shape-space models of the immune system.

A large-scale model of the immune network is analyzed, using the shape-space formalism. In this formalism, it is assumed that the immunoglobulin receptors on B cells can be characterized by their unique portions, or idiotypes, that have shapes that can be represented in a space of a small finite dimension. Two receptors are assumed to interact to the extent that the shapes of their idiotypes are complementary. This is modeled by assuming that shapes interact maximally whenever their coordinates in the space-space are equal and opposite, and that the strength of interaction falls off for less complementary shapes in a manner described by a Gaussian function of the Euclidean "distance" between the pair of interacting shapes. The degree of stimulation of a cell when confronted with complementary idiotypes is modeled using a log bell-shaped interaction function. This leads to three possible equilibrium states for each clone: a virgin, an immune, and a suppressed state. The stability properties of the three possible homogeneous steady states of the network are examined. For the parameters chosen, the homogeneous virgin state is stable to both uniform and sinusoidal perturbations of small amplitude. A sufficiently large perturbation will, however, destabilize the virgin state and lead to an immune reaction. Thus, the virgin system is both stable and responsive to perturbations. The homogeneous immune state is unstable to both uniform and sinusoidal perturbations, whereas the homogeneous suppressed state is stable to uniform, but unstable to sinusoidal, perturbations. The non-uniform patterns that arise from perturbations of the homogeneous states are examined numerically. These patterns represent the actual immune repertoire of an animal, according to the present model. The effect of varying the standard deviation sigma of the Gaussian is numerically analyzed in a one-dimensional model. If sigma is large compared to the size of the shape-space, the system attains a fixed non-uniform equilibrium. Conversely if sigma is small, the system attains one out of many possible non-uniform equilibria, with the final pattern depending on the initial conditions. This demonstrates the plasticity of the immune repertoire in this shape-space model. We describe how the repertoire organizes itself into large clusters of clones having similar behavior. These results are extended by analyzing pattern formation in a two-dimensional (2-D) shape-space.(ABSTRACT TRUNCATED AT 400 WORDS)     

Persistence despite perturbations for interacting populations

Two definitions of persistence despite perturbations in deterministic models are presented. The first definition, persistence despite frequent small perturbations, is shown to be equivalent to the existence of a positive attractor i.e. an attractor bounded away from extinction. The second definition, persistence despite rare large perturbations, is shown to be equivalent to permanence i.e. a positive attractor whose basin of attraction includes all positive states. Both definitions set up a natural dichotomy for classifying models of interacting populations. Namely, a model is either persistent despite perturbations or not. When it is not persistent, it follows that all initial conditions are prone to extinction due to perturbations of the appropriate type. For frequent small perturbations, this method of classification is shown to be generically robust: there is a dense set of models for which persistent (respectively, extinction prone) models lies within an open set of persistent (resp. extinction prone) models. For rare large perturbations, this method of classification is shown not to be generically robust. Namely, work of Josef Hofbauer and the author have shown there are open sets of ecological models containing a dense sets of permanent models and a dense set of extinction prone models. The merits and drawbacks of these different definitions are discussed.     

Multistability and dynamic transitions of intracellular Min protein patterns

Cells owe their internal organization to self‐organized protein patterns, which originate and adapt to growth and external stimuli via a process that is as complex as it is little understood. Here, we study the emergence, stability, and state transitions of multistable Min protein oscillation patterns in live Escherichia coli bacteria during growth up to defined large dimensions. De novo formation of patterns from homogenous starting conditions is observed and studied both experimentally and in simulations. A new theoretical approach is developed for probing pattern stability under perturbations. Quantitative experiments and simulations show that, once established, Min oscillations tolerate a large degree of intracellular heterogeneity, allowing distinctly different patterns to persist in different cells with the same geometry. Min patterns maintain their axes for hours in experiments, despite imperfections, expansion, and changes in cell shape during continuous cell growth. Transitions between multistable Min patterns are found to be rare events induced by strong intracellular perturbations. The instances of multistability studied here are the combined outcome of boundary growth and strongly nonlinear kinetics, which are characteristic of the reaction–diffusion patterns that pervade biology at many scales.     

A Basic Set of Homeostatic Controller Motifs

Adaptation and homeostasis are essential properties of all living systems. However, our knowledge about the reaction kinetic mechanisms leading to robust homeostatic behavior in the presence of environmental perturbations is still poor. Here, we describe, and provide physiological examples of, a set of two-component controller motifs that show robust homeostasis. This basic set of controller motifs, which can be considered as complete, divides into two operational work modes, termed as inflow and outflow control. We show how controller combinations within a cell can integrate uptake and metabolization of a homeostatic controlled species and how pathways can be activated and lead to the formation of alternative products, as observed, for example, in the change of fermentation products by microorganisms when the supply of the carbon source is altered. The antagonistic character of hormonal control systems can be understood by a combination of inflow and outflow controllers.