Existence and stability criteria for phase-locked modes in ring neural networks based on the spike time resetting curve method

We developed a systematic and consistent mathematical approach to predicting 1:1 phase-locked modes in ring neural networks of spiking neurons based on the open loop spike time resetting curve (STRC) and its almost equivalent counterpart—the phase resetting curve (PRC). The open loop STRCs/PRCs were obtained by injecting into an isolated model neuron a triangular shaped time-dependent stimulus current closely resembling an actual synaptic input. Among other advantages, the STRC eliminates the confusion regarding the undefined phase for stimuli driving the neuron outside of the unperturbed limit cycle. We derived both open loop PRC and STRC-based existence and stability criteria for 1:1 phase-locked modes developed in ring networks of spiking neurons. Our predictions were in good agreement with the closed loop numerical simulations. Intuitive graphical methods for predicting phase-locked modes were also developed both for half-centers and for larger ring networks.     

Phase-Locked Loop Technique to Record Resonance Frequency of Plant Tissue

An apparatus based on the phase-locked loop technique has been developed in order to record automatically the resonance frequency of a mechanically vibrating plant specimen. Hereby changes in the elasticity of the plant material can be continuously recorded. In order to demonstrate the use of the apparatus, elasticity changes of Avena coleoptiles due to exchange of the root medium were continuously recorded.     

Mathematical modelling of the agr operon in Staphylococcus aureus

Staphylococcus aureus is a pathogenic bacterium that utilises quorum sensing (QS), a cell-to-cell signalling mechanism, to enhance its ability to cause disease. QS allows the bacteria to monitor their surroundings and the size of their population, and S. aureus makes use of this to regulate the production of virulence factors. Here we describe a mathematical model of this QS system and perform a detailed time-dependent asymptotic analysis in order to clarify the roles of the distinct interactions that make up the QS process, demonstrating which reactions dominate the behaviour of the system at various timepoints. We couple this analysis with numerical simulations and are thus able to gain insight into how a large population of S. aureus shifts from a relatively harmless state to a highly virulent one, focussing on the need for the three distinct phases which form the feedback loop of this particular QS system.     

Fault tolerance in the cardiac ganglion of the lobster

Canavier et al. (1997) used phase response curves (PRCs) of individual oscillators to characterize the possible modes of phase-locked entrainment of an N-oscillator ring network. We extend this work by developing a mathematical criterion to determine the local stability of such a mode based on the PRCs. Our method does not assume symmetry; neither the oscillators nor their connections need be identical. To use these techniques for predicting modes and determining their stability, one need only determine the PRC of each oscillator in the ring either experimentally or from a computational model. We show that network stability cannot be determined by simply testing the ability of each oscillator to entrain the next. Stability depends on the number of neurons in the ring, the type of mode, and the slope of each PRC at the point of entrainment of the respective neuron. We also describe simple criteria which are either necessary or sufficient for stability and examine the implications of these results. Received: 2 April 1998 / Accepted in revised form: 2 July 1998     

Calcium oscillations in a triplet of pancreatic acinar cells

We use a mathematical model of calcium dynamics in pancreatic acinar cells to investigate calcium oscillations in a ring of three coupled cells. A connected group of cells is modeled in two different ways: 1), as coupled point oscillators, each oscillator being described by a spatially homogeneous model; and 2), as spatially distributed cells coupled along their common boundaries by gap-junctional diffusion of inositol trisphosphate and/or calcium. We show that, although the point-oscillator model gives a reasonably accurate general picture, the behavior of the spatially distributed cells cannot always be predicted from the simpler analysis; spatially distributed diffusion and cell geometry both play important roles in determining behavior. In particular, oscillations in which two cells are in synchrony, with the third phase-locked but not synchronous, appears to be more dominant in the spatially distributed model than in the point-oscillator model. In both types of model, intercellular coupling leads to a variety of synchronous, phase-locked, or asynchronous behaviors. For some parameter values there are multiple, simultaneous stable types of oscillation. We predict 1), that intercellular calcium diffusion is necessary and sufficient to coordinate the responses in neighboring cells; 2), that the function of intercellular inositol trisphosphate diffusion is to smooth out any concentration differences between the cells, thus making it easier for the diffusion of calcium to synchronize the oscillations; 3), that groups of coupled cells will tend to respond in a clumped manner, with groups of synchronized cells, rather than with regular phase-locked periodic intercellular waves; and 4), that enzyme secretion is maximized by the presence of a pacemaker cell in each cluster which drives the other cells at a frequency greater than their intrinsic frequency.     

A model of the nystagmus induced by off vertical axis rotation

A three-dimensional model is proposed that accounts for a number of phenomena attributed to the otoliths. It is constructed by extending and modifying a model of vestibular velocity storage. It is proposed that the otolith information about the orientation of the head to gravity changes the time constant of vestibular responses by modulating the gain of the velocity storage feedback loop. It is further proposed that the otolith signals, such as those that generate L-nystagmus (linear acceleration induced nystagmus), are partially coupled to the vestibular system via the velocity storage integrator. The combination of these two hypotheses suggests that a vestibular neural mechanism exists that performs correlation in the mathematical sense which is multiplication followed by integration. The multiplication is performed by the otolith modulation of the velocity storage feedback loop gain and the integration is performed by the velocity storage mechanism itself. Correlation allows calculation of the degree to which two signals are related and in this context provides a simple method of determining head angular velocity from the components of linear acceleration induced by off-vertical axis rotation. Correlation accounts for the otolith supplementation of the VOR and the sustained nystagmus generated by off-vertical axis rotation. The model also predicts the cross-coupling of horizontal and vertical optokinetic afternystagmus that occurs in head-lateral positions and the reported effects of tilt on vestibular responses.     

Modelling of the regulation of the hilA promoter of type three secretion system of Salmonella enterica serovar Typhimurium

One of the most common modes of secretion of toxins in gram-negative bacteria is via the type three secretion system (TTSS), which enables the toxins to be specifically exported into the host cell. The hilA gene product is a key regulator of the expression of the TTSS located on the pathogenicity island (SPI-1) of Salmonella enterica serovar Typhimurium. It has been proposed earlier that the regulation of HilA expression is via a complex feedforward loop involving the transactivators HilD, HilC and RtsA. In this paper, we have constructed a mathematical model of regulation of hilA-promoter by all the three activators using two feedforward loops. We have modified the model to include additional complexities in regulation such as the proposed positive feedback and cross regulations of the three transactivators. Results of the various models indicate that the basic model involving two Type I coherent feedforward loops with an OR gate is sufficient to explain the published experimental observations. We also discuss two scenarios where the regulation can occur via monomers or heterodimers of the transactivators and propose experiments that can be performed to distinguish the two modes of regulator function. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

A kLa identification technique for a dynamic model of the coupled system: Air-lift fermenter — oxygen probes

The time delay of oxygen probe response to the signal from a fermenter makes identification of the volumetric oxygen transfer coefficient k_La by the dynamic method more complicated. A coupled model involving the transient-state oxygen balance of the fermenter together with the dynamic model of the oxygen probe must be then formulated, solved and identified. In this paper two simple models of air-lift loop fermenters have been proposed and a coupled mathematical model of the fermenter – oxygen probe system has been developed. The identification procedure was used to estimate k_La values in the fermenter with internal circulation flow on the basis of experimental measurements. A comparison of evaluated and experimental indications of the probes placed at various heights of the column proves that the model presented gives a possibility of the first-step approximation of k_La in loop fermenters.     

Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm

A mechanism for generating circadian rhythms has been of major interest in recent years. After the discovery of per and tim, a model with a simple feedback loop involving per and tim has been proposed. However, it is recognized that the simple feedback model cannot account for phenotypes generated by various mutants. A recent report by Glossop, Lyons & Hardin [Science286, 766 (1999)] on Drosophila suggests involvement of another feedback loop by dClk that is interlocked with per-tim feedback loop. In order to examine whether interlocked feedback loops can be a basic mechanism for circadian rhythms, a mathematical model was created and examined. Through extensive simulation and mathematical analysis, it was revealed that the interlocked feedback model accounts for the observations that are not explained by the simple feedback model. Moreover, the interlocked feedback model has robust properties in oscillations.     

Damped oscillations in the adaptive response of the iron homeostasis network of E. coli

Living organisms often have to adapt to sudden environmental changes and reach homeostasis. To achieve adaptation, cells deploy motifs such as feedback in their genetic networks, endowing the cellular response with desirable properties. We studied the iron homeostasis network of E. coli, which employs feedback loops to regulate iron usage and uptake, while maintaining intracellular iron at non‐toxic levels. Using fluorescence reporters for iron‐dependent promoters in bulk and microfluidics‐based, single‐cell experiments, we show that E. coli cells exhibit damped oscillations in gene expression, following sudden reductions in external iron levels. The oscillations, lasting for several generations, are independent of position along the cell cycle. Experiments with mutants in network components demonstrate the involvement of iron uptake in the oscillations. Our findings suggest that the response is driven by intracellular iron oscillations large enough to induce nearly full network activation/deactivation. We propose a mathematical model based on a negative feedback loop closed by rapid iron uptake, and including iron usage and storage, which captures the main features of the observed behaviour. Taken together, our results shed light on the control of iron metabolism in bacteria and suggest that the oscillations represent a compromise between the requirements of stability and speed of response.     

ACA‐specific RNA sequence recognition is acquired via the loop 2 region of MazF mRNA interferase

MazF is an mRNA interferase that cleaves mRNAs at a specific RNA sequence. MazF from E. coli (MazF‐ec) cleaves RNA at A and CA. To date, a large number of MazF homologs that cleave RNA at specific three‐ to seven‐base sequences have been identified from bacteria to archaea. MazF‐ec forms a dimer, in which the interface between the two subunits is known to be the RNA substrate‐binding site. Here, we investigated the role of the two loops in MazF‐ec, which are closely associated with the interface of the MazF‐ec dimer. We examined whether exchanging the loop regions of MazF‐ec with those from other MazF homologs, such as MazF from Myxococcus xanthus (MazF‐mx) and MazF from Mycobacterium tuberculosis (MazF‐mt3), affects RNA cleavage specificity. We found that exchanging loop 2 of MazF‐ec with loop 2 regions from either MazF‐mx or MazF‐mt3 created a new cleavage sequence at (A/U)(A/U)AA and C in addition to the original cleavage site, A and CA, whereas exchanging loop 1 did not alter cleavage specificity. Intriguingly, exchange of loop 2 with 8 or 12 consecutive Gly residues also resulted in a new RNA cleavage site at (A/U)(A/U)AA and C. The present study suggests a method for expanding the RNA cleavage repertoire of mRNA interferases, which is crucial for potential use in the regulation of specific gene expression and for biotechnological applications. Proteins 2013. © 2012 Wiley Periodicals, Inc.     

Dynamics of the active site loops in catalyzing aminoacylation reaction in seryl and histidyl tRNA synthetases

Aminoacylation reaction is the first step of protein biosynthesis. The catalytic reorganization at the active site of aminoacyl tRNA synthetases (aaRSs) is driven by the loop motions. There remain lacunae of understanding concerning the catalytic loop dynamics in aaRSs. We analyzed the functional loop dynamics in seryl tRNA synthetase from Methanopyrus kandleri (^mkSerRS) and histidyl tRNA synthetases from Thermus thermophilus (^ttHisRS), respectively, using molecular dynamics. Results confirm that the motif 2 loop and other active site loops are flexible spots within the catalytic domain. Catalytic residues of the loops form a network of interaction with the substrates to form a reactive state. The loops undergo transitions between closed state and open state and the relaxation of the constituent residues occurs in femtosecond to nanosecond time scale. Order parameters are higher for constituent catalytic residues which form a specific network of interaction with the substrates to form a reactive state compared to the Gly residues within the loop. The development of interaction is supported from mutation studies where the catalytic domain with mutated loop exhibits unfavorable binding energy with the substrates. During the open-close motion of the loops, the catalytic residues make relaxation by ultrafast librational motion as well as fast diffusive motion and subsequently relax rather slowly via slower diffusive motion. The Gly residues act as a hinge to facilitate the loop closing and opening by their faster relaxation behavior. The role of bound water is analyzed by comparing implicit solvent-based and explicit solvent-based simulations. Loops fail to form catalytically competent geometry in absence of water. The present result, for the first time reveals the nature of the active site loop dynamics in aaRS and their influence on catalysis.     

Intersubunit communication in the dihydroorotase–aspartate transcarbamoylase complex of Aquifex aeolicus

Aspartate transcarbamoylase and dihydroorotase, enzymes that catalyze the second and third step in de novo pyrimidine biosynthesis, are associated in dodecameric complexes in Aquifex aeolicus and many other organisms. The architecture of the dodecamer is ideally suited to channel the intermediate, carbamoyl aspartate from its site of synthesis on the ATC subunit to the active site of DHO, which catalyzes the next step in the pathway, because both reactions occur within a large, internal solvent‐filled cavity. Channeling usually requires that the reactions of the enzymes are coordinated so that the rate of synthesis of the intermediate matches its rate of utilization. The linkage between the ATC and DHO subunits was demonstrated by showing that the binding of the bisubstrate analog, N‐phosphonacetyl‐L ‐aspartate to the ATC subunit inhibits the activity of the distal DHO subunit. Structural studies identified a DHO loop, loop A, interdigitating between the ATC domains that would be expected to interfere with domain closure essential for ATC catalysis. Mutation of the DHO residues in loop A that penetrate deeply between the two ATC domains inhibits the ATC activity by interfering with the normal reciprocal linkage between the two enzymes. Moreover, a synthetic peptide that mimics that part of the DHO loop that binds between the two ATC domains was found to be an allosteric or noncompletive ATC inhibitor (K_i = 22 μM). A model is proposed suggesting that loop A is an important component of the functional linkage between the enzymes.     

A critical role of water in the specific cleavage of the anticodon loop of some eukaryotic methionine initiator tRNAs

We have noticed that during a long storage and handling, the plant methionine initiator tRNA is spontaneously hydrolyzed within the anticodon loop at the C34-A35 phosphodiester bond. A literature search indicated that there is also the case for human initiator tRNA^Met but not for yeast tRNA^Met _i or E. coli tRNA^Met _f. All these tRNAs have an identical nucleotide sequence of the anticodon stems and loops with only one difference at position 33 within the loop. It means that cytosine 33 (C33) makes the anticodon loop of plant and human tRNA^Met _i susceptible to the specific cleavage reaction. Using crystallographic data of tRNA^Met _f of E. coli with U33, we modeled the anticodon loop of this tRNA with C33. We found that C33 within the anticodon loop creates a pocket that can accomodate a hydrogen bonded water molecule that acts as a general base and catalyzes a hydrolysis of C-A bond. We conclude that a single nucleotide change in the primary structure of tRNA^Met _i made changes in hydration pattern and readjustment in hydrogen bonding which lead to a cleavage of the phosphodiester bond.     

Kinetic characterization of the double mutant R148A/E182S of glycogen phosphorylase kinase catalytic subunit: the role of the activation loop

Many protein kinases are activated by phosphorylation in a highly conserved region of their catalytic subunit, termed activation loop. Phosphorylase kinase is constitutively active without the requirement for phosphorylation of residues in the activation loop. The residue which plays an analogous role to the phosphorylatable residues in other protein kinases is Glu182, which makes contacts to a highly conserved Arg148. In turn, Arg148 adjacent to the catalytic Asp149, enabling information to be transmitted from the activation loop to the catalytic machinery. The double mutant R148A/E182S has been kinetically characterized. The mutation resulted in an approximate 16- to 22-fold decrease in the k _cat/K _m value of the enzyme. The kinetic data, discussed in the light of the structural data from previously determined complexes of the enzyme, lead to the suggestion that the activation loop has a major role in substrate binding but also in correct orientation of the groups participating in catalysis.     

A mathematical model for the decay of short-term memory with age

A mathematical neural net model based on our previous studies (Anninos et al, 1970; Anninos, 1972) is proposed here to show that the short-term memory of events decays with man age. In particular, in this work we try to explain why recent memories die out with age before the establishment of permanent memory. As it was shown we lose some connections due to the loss of a large number of neurons with age, and in our model this corresponds to a smaller hysteresis loop which, according to our assumption, represents the short-term memory of an event. Thus we showed that if we decrease the number of connections even further the hysteresis loop will vanish to a single curve which, according to Katchalsky & Oplatka (1969), corresponds to a memory-less system.     

Molecular structure of the lampbrush loops nooses of the Y chromosome of Drosophila hydei

The molecular structure of the lampbrush loopforming fertility gene nooses from the short arm of the Y chromosome of Drosophila hydei is described on the basis of cloned DNA sequences which are characteristic for the sequence organization in the lampbrush loop. Y chromosomal lampbrush loops are organized into tandem repeat clusters of loop-specific repetitive DNA sequences and in interspersed repetitive DNA sequences with homologies elsewhere in the genome. In this paper, the basic properties of a repeat unit of the tandemly repeated sequence family ay1 are described. Moreover, it is shown that a loop contains several different domains carrying repeat clusters of the same repeated DNA family but with divergent sequence character. One of these clusters is characterized by an internal duplication of the basic repeat unit. We propose that the tandem repeat DNA family ay1 forms a frame of the lampbrush loop which is required for structural and functional reasons.     

Role of connecting loop I in catalysis and allosteric regulation of human glucokinase

Glucokinase (GCK, hexokinase IV) is a monomeric enzyme with a single glucose binding site that displays steady‐state kinetic cooperativity, a functional characteristic that affords allosteric regulation of GCK activity. Structural evidence suggests that connecting loop I, comprised of residues 47–71, facilitates cooperativity by dictating the rate and scope of motions between the large and small domains of GCK. Here we investigate the impact of varying the length and amino acid sequence of connecting loop I upon GCK cooperativity. We find that sequential, single amino acid deletions from the C‐terminus of connecting loop I cause systematic decreases in cooperativity. Deleting up to two loop residues leaves the k_cat value unchanged; however, removing three or more residues reduces k_cat by 1000‐fold. In contrast, the glucose K_0.5 and K_D values are unaffected by shortening the connecting loop by up to six residues. Substituting alanine or glycine for proline‐66, which adopts a cis conformation in some GCK crystal structures, does not alter cooperativity, indicating that cis/trans isomerization of this loop residue does not govern slow conformational reorganizations linked to hysteresis. Replacing connecting loop I with the corresponding loop sequence from the catalytic domain of the noncooperative isozyme human hexokinase I (HK‐I) eliminates cooperativity without impacting the k_cat and glucose K_0.5 values. Our results indicate that catalytic turnover requires a minimal length of connecting loop I, whereas the loop has little impact upon the binding affinity of GCK for glucose. We propose a model in which the primary structure of connecting loop I affects cooperativity by influencing conformational dynamics, without altering the equilibrium distribution of GCK conformations.