A kinetic model of RNA folding

The RNA folding process is represented as a Markov process with states corresponding to RNA secondary structures and transition probabilities corresponding to transformations of a secondary structure caused by formation or disintegration of a helix. Transition probabilities (kinetic constants) are determined. A notion of a group of structures is introduced, and it allows to reduce the state space. Energetic and kinetic parameters of pseudoknots are estimated. Algorithms for computation of a kinetic ensemble for structures and groups of structures are presented, as well as their modifications that take into account pseudoknots. The described algorithms are implemented as a procedure for prediction of RNA secondary structure that is included in the package DNA-SUN.     

A model for oscillatory kinetic systems

A kinetic model is proposed for oscillatory kinetic phenomena. The exact analytic solution is exhibited and shown to account for several features exhibited by oscillatory chemical and biological systems.     

A kinetic model for glutamate dehydrogenase

A model for the glutamate dehydrogenase reaction has been obtained that contains the reported intermediates suggested by binding and equilibrium isotope exchange methods. Calculated steady state-initial velocity rates using this model are quantitatively consistent with a wide range of nonlinear experimental data in both directions.     

A kinetic model for plasmid curing

A simple mathematical model of drug-induced plasmid elimination (curing) considering density-dependent growth rates and plasmid transfers is presented. It describes nonlinear population dynamics of conjugative plasmids during in vitro curing experiments in batch culture. The model was tested on kinetics of acridine orange curing of F'lac plasmid. Effects of density dependence, plasmid elimination, selection for plasmidless segregants, conjugation, initial and maximal population density, and postsegregational killing on curing kinetics are simulated and discussed.     

A kinetic model for calcium distribution

Models for the distribution of minerals in the body are of interest as they allow researchers to trace the effect of a dose on mineral levels in plasma, storage and other compartments. Limited models are available in the literature for tracing the distribution of a calcium dose through a short time period. We propose a more general kinetic model which includes both limited absorption through the gut and loss of calcium via excretion. This new method has the advantages of giving reasonable results over moderate time periods, and allowing the extrapolation of calcium levels in extracellular fluid and storage. We fit the model to published data in order to obtain typical parameter values. These values are then used to analyze the implications of the model regarding the effect of calcium dose on calcium levels in various compartments.     

A kinetic model for cell agglutination

A model of concanavalin A (ConA) mediated cell agglutination kinetics is proposed, in which the binding of the lectin, the agglutination of cells and the disintegration of cell clumps are discussed. This resulted in a differential equation, which is solved in terms of the average number of cells per cell clump as a function of time.     

A nonlinear dynamics model for simulating long range correlations of cognitive bistability

Simulation results of bistable perception due to ambiguous visual stimuli are presented which are obtained with a behavioral nonlinear dynamics model using perception–attention–memory coupling. This model provides an explanation of recent experimental results of Gao et al. (Cogn Process 7:105–112, 2006a) and it supports their speculation that the fractal character of perceptual dominance time series may be understood in terms of nonlinear and reentrant dynamics of brain processing. Percept reversals are induced by attention fatigue and noise, with an attention bias which balances the relative percept duration. Dynamical coupling of the attention bias to the perception state introduces memory effects leading to significant long range correlations of perceptual duration times as quantified by the Hurst parameter H > 0.5 (Mandelbrot, The fractal geometry of nature, 1991), in agreement with Gao et al. (Cogn Process 7:105–112, 2006a).     

A three-stage kinetic model of amyloid fibrillation

Amyloid fibrillation has been intensively studied because of its association with various neurological disorders. While extensive time-dependent fibrillation experimental data are available and appear similar, few mechanistic models have been developed to unify those results. The aim of this work was to interpret these experimental results via a rigorous mathematical model that incorporates the physical chemistry of nucleation and fibril growth dynamics. A three-stage mechanism consisting of protein misfolding, nucleation, and fibril elongation is proposed and supported by the features of homogeneous fibrillation responses. Estimated by nonlinear least-squares algorithms, the rate constants for nucleation were approximately 10,000,000 times smaller than those for fibril growth. These results, coupled with the positive feedback characteristics of the elongation process, account for the typical sigmoidal behavior during fibrillation. In addition, experiments with different proteins, various initial concentrations, seeding versus nonseeding, and several agitation rates were analyzed with respect to fibrillation using our new model. The wide applicability of the model confirms that fibrillation kinetics may be fairly similar among amyloid proteins and for different environmental factors. Recommendations on further experiments and on the possible use of molecular simulations to determine the desired properties of potential fibrillation inhibitors are offered.     

A kinetic model of coordinated myosin V

We present a kinetic model for the walking of myosin V on actin under conditions of zero external force. The model includes three pathways and the termination of the processivity. Experimentally measured kinetic parameters are used in the model to obtain quantitative results. Using the model and associated parameters, we compute the proportion of the pathway containing an intermediate state, as well as the walking velocities and run lengths at various concentrations of ATP and ADP. The resulting trends agree with experimental data. The model explains the surprising experimental finding that myosin walks at a faster speed but for a shorter distance as the ATP concentration increases in the absence of ADP. It also suggests that under physiological condition ([ADP] approximately 12-50 microM), myosin walks with a higher speed and for longer distances when ATP is more abundant.     

A kinetic model of the cytochrome bf complex. Evaluation of kinetic parameters

A kinetic model of the cytochrome bf complex was developed on the assumption that the Q-cycle operates. The bf complex was considered as a membrane enzyme catalyzing the electron transfer from plastoquinol to plastocyanine, which is coupled with proton translocation from the chloroplast stroma to the thylakoid lumen. The dependence of the electron transfer rates on the value of the transmembrane electric potential was taken into account. The model was applied to describe the experimental data on the flash-induced turnover of cytochromes b, plastocyanine, and the kinetics of proton deposition in the thylakoid lumen. The estimation of model parameters was performed.     

Chitin and chitinase: A kinetic model

A model is described for the action of insect molting chitinase on chitin microfibrils in cuticle. The model reconciles the disparate structures proposed for chitin in the literature. It also accounts for the kinetic characteristics of molting fluid chitinase insofar as known from in vitro studies, viz. positive co-operativity of possibly three catalytic sites, complexity, and processivity. These have hitherto been difficult to account for in vivo, given the arrangement of chitin in anhydrous microfibrils in arthropod cuticle.     

A kinetic model for subtractive hybridization.

Nucleic acid sequences that differ in abundance between two populations (target sequences) can be cloned by multiple rounds of subtractive hybridization and amplification by PCR. These sequences can be cDNAs representing up-regulated mRNAs, or genomic DNAs from deletion mutants. We have derived an equation that describes the recovery of such sequences, and have used this to simulate the outcome of up to 10 rounds of subtractive hybridization and PCR amplification. When the model was tested by comparing its predictions with the published results from genomic and cDNA subtractions, the predictions of the model were generally in good agreement with the published data. We have modelled the outcomes of genomic subtractions, for a variety of genomes, and have used it to compare various strategies for enriching targets. The model predicts that for genomes of less than 5 x 10(8) bp, deletions of as small as 1 kbp should represent > 99% of the DNA after three to six rounds of hybridization (depending on the enrichment procedure). As genomes increase in size, the kinetics of hybridization become an important limiting factor. However, even for genomes as large as 3 x 10(9) bp, it should be possible to isolate deletions of 5 kbp using the appropriate conditions. These simulations suggest that such methods offer a realistic alternative to chromosome walking for identifying genomic deletions for which there are known phenotypes, thereby considerably reducing time and effort. For cDNA subtractive hybridization, the model predicts that after six rounds of hybridization, sequences that do not differ in abundance between the tester and driver populations (the background) will represent < 1% of the subtracted population, and even quite modestly upregulated cDNAs should be successfully enriched. Where several up-regulated cDNAs are present, the predicted final representation is dependent on both the initial abundance and the degree of up-regulation.     

A kinetic model of non-photochemical quenching in cyanobacteria

High light poses a threat to oxygenic photosynthetic organisms. Similar to eukaryotes, cyanobacteria evolved a photoprotective mechanism, non-photochemical quenching (NPQ), which dissipates excess absorbed energy as heat. An orange carotenoid protein (OCP) has been implicated as a blue-green light sensor that induces NPQ in cyanobacteria. Discovered in vitro, this process involves a light-induced transformation of the OCP from its dark, orange form (OCP(o)) to a red, active form, however, the mechanisms of NPQ in vivo remain largely unknown. Here we show that the formation of the quenching state in vivo is a multistep process that involves both photoinduced and dark reactions. Our kinetic analysis of the NPQ process reveals that the light induced conversion of OCP(o) to a quenching state (OCP(q)) proceeds via an intermediate, non-quenching state (OCP(i)), and this reaction sequence can be described by a three-state kinetic model. The conversion of OCP(o) to OCP(i) is a photoinduced process with the effective absorption cross section of 4.5 × 10(-3)?2 at 470 nm. The transition from OCP(i) to OCP(q) is a dark reaction, with the first order rate constant of approximately 0.1s(-1) at 25°C and the activation energy of 21 kcal/mol. These characteristics suggest that the reaction rate may be limited by cis-trans proline isomerization of Gln224-Pro225 or Pro225-Pro226, located at a loop near the carotenoid. NPQ decreases the functional absorption cross-section of Photosystem II, suggesting that formation of the quenched centers reduces the flux of absorbed energy from phycobilisomes to the reaction centers by approximately 50%.     

A kinetic model of the agglutination process.

We propose a kinetic model of the aggregation process in a system consisting of two different types of particles. Aggregating particles (cells) are polyvalent and bear on the surface a huge number of binding sites for the other type of particles, ligands. The ligand is bivalent and has two identical active sites for binding to cells. The cross-linking of the cells by the ligands causes the aggregation phenomenon called agglutination. We obtained the analytical solution of this model task describing the time dependence of the aggregate mean size versus the composition of the system. The comparison of the analytical solution with the experimental data for the agglutination of bacterial cells by bivalent antibodies shows that the main factors affecting agglutination were correctly taken into account.     

A kinetic model describing the processivity of myosin-V

The precise details of how myosin-V coordinates the biochemical reactions and mechanical motions of its two head elements to engineer effective processive molecular motion along actin filaments remain unresolved. We compare a quantitative kinetic model of the myosin-V walk, consisting of five basic states augmented by two further states to allow for futile hydrolysis and detachments, with experimental results for run lengths, velocities, and dwell times and their dependence on bulk nucleotide concentrations and external loads in both directions. The model reveals how myosin-V can use the internal strain in the molecule to synchronize the motion of the head elements. Estimates for the rate constants in the reaction cycle and the internal strain energy are obtained by a computational comparison scheme involving an extensive exploration of the large parameter space. This scheme exploits the fact that we have obtained analytic results for our reaction network, e.g., for the velocity but also the run length, diffusion constant, and fraction of backward steps. The agreement with experiment is often reasonable but some open problems are highlighted, in particular the inability of such a general model to reproduce the reported dependence of run length on ADP concentration. The novel way that our approach explores parameter space means that any confirmed discrepancies should give new insights into the reaction network model.     

A mathematical model of muscle containing heterogeneous half-sarcomeres exhibits residual force enhancement

A skeletal muscle fiber that is stimulated to contract and then stretched from L₁ to L₂ produces more force after the initial transient decays than if it is stimulated at L₂. This behavior has been well studied experimentally, and is known as residual force enhancement. The underlying mechanism remains controversial. We hypothesized that residual force enhancement could reflect mechanical interactions between heterogeneous half-sarcomeres. To test this hypothesis, we subjected a computational model of interacting heterogeneous half-sarcomeres to the same activation and stretch protocols that produce residual force enhancement in real preparations. Following a transient period of elevated force associated with active stretching, the model predicted a slowly decaying force enhancement lasting >30 seconds after stretch. Enhancement was on the order of 13% above isometric tension at the post-stretch muscle length, which agrees well with experimental measurements. Force enhancement in the model was proportional to stretch magnitude but did not depend strongly on the velocity of stretch, also in agreement with experiments. Even small variability in the strength of half-sarcomeres (2.1% standard deviation, normally distributed) was sufficient to produce a 5% force enhancement over isometric tension. Analysis of the model suggests that heterogeneity in half-sarcomeres leads to residual force enhancement by storing strain energy introduced during active stretch in distributions of bound cross-bridges. Complex interactions between the heterogeneous half-sarcomeres then dissipate this stored energy at a rate much slower than isolated cross-bridges would cycle. Given the variations in half-sarcomere length that have been observed in real muscle preparations and the stochastic variability inherent in all biological systems, half-sarcomere heterogeneity cannot be excluded as a contributing source of residual force enhancement.