A simple model of dynamic receptor pattern generation

A dynamic pattern generating automaton has been constructed. The rules controlling its function furnish the non-random generation of sub-patterns in consecutive cycles, within a large plane area, covered by four different classes of units of constant mean frequency in each class (standard system). The stabilization of certain specific sub-patterns over 100 subsequent cycles of pattern generation (modified systems) resulted in the modification of the frequency and frequency distribution of the sub-patterns relative to the standard system. Some new types of sub-patterns, not encountered in the standard system, also made appearance in the modified systems. The functioning of the standard and modified systems was analyzed and compared by the methods of mathematical statistics. The automaton was used to model certain features of the cytoplasmic membrane. The latter was regarded as a device by which the cell collects information about its environment. The dynamic generation of sub-patterns was taken as the cell's manner of asking questions, and the complementary chemical structures present in the environment were treated as possible answers to these. The irreversible question-answer interactions were regarded as signals and were modelled by the stabilization of specific sub-patterns. It was found that in a dynamic system like the model presented, it is not necessary to code each possible sub-pattern individually. Precise coding of the relative frequency of units per class and of their possible interactions is sufficient to furnish statistically constant mean frequencies for a given range of sub-patterns. In a dynamic system, the actual range of sub-patterns arisen in a population of identical individuals depends only on the size of the population. If the latter is appropriately large, all possible sub-patterns may be simultaneously present at any time at the average frequencies characteristic of each. Stabilized sub-patterns (signals) seem to modify specifically the frequencies of the other sub-patterns generated by the normal automaton. Some sub-patterns may disappear permanently, while others (new ones) may turn up and persist at given frequencies. Missense signals may definitively put the automaton out of order, i.e. result in the cell's complete misorientation in respect of its relations to the normal tissue structure.Reader of publications in physics, Gondolat Publishing House, Budapest, Hungary     

Metastable equilibrium with random local fluctuations: Simulations of dynamic receptor pattern generation in a fluid mosaic membrane

The generation of receptors in the animal cell's membrane was simulated by a model consisting of units in four possible states within a hexagonal area (playboard) ofn units of a triangular network. The state of each unit was determined by the previous state or itself and of its six nearest neighbours, as regulated by a set of transition rules, which kept the mean relative frequency (m.r.f.) of each state constant. The transition rules were applied to the system exactlyn times, regardedless whether this involved selection of a unit on 0, 1, 2 or more occasions (programme random selection with repeat; RS-R). Comparison to previous results obtained by other ways of application of the rules has shown that the RS-R programme accounted for the highest m.r.f. of quiet (Q) units and Q clusters (sub-patterns), and also for the longest survival of Q configurations through several generations. Functioning of the model under the RS-R programme simulates an integrated system in metastable equilibrium with random local fluctuations, such as the cytoplasmic membrane is imagined to be in standardized environmental conditions. The formation-persistence-disintegration cycle of the sub-patterns is believed to simulate the dynamic generation of transitory receptor configurations in the cell membrane.     

A model of pattern generation of cockroach walking reconsidered

Cockroaches that have been decapitated or that have cut thoracic connectives can show rhythmic bursting in motoneurons to intrinsic leg muscles. These preparations have been studied as models for walking and to evaluate the functions of leg proprioceptors. The present study demonstrates that headless cockroaches walk extremely poorly and slowly with considerable discoordination of motoneuronal activity, these preparations show rhythmic motoneuron bursting that is similar to righting responses (attempts to turn upright) of intact animals when placed on their backs, and bursting is inhibited when a headless animal is turned or turns itself upright. Thus, rhythmic motoneuron activity of these preparations is most probably attempted righting rather than walking. It is concluded that the headless cockroach is useful for understanding the motor mechanisms underlying righting and walking but is not of value in assessing the functions of proprioceptive feedback.     

A dynamic model of the meningococcal transferrin receptor.

Iron is an essential nutrient for all organisms and consequently, the ability to bind transferrin and sequester iron from his source constitutes a distinct advantage to a blood-borne bacterial pathogen. Levels of free iron are strictly limited in human serum, largely through the action of the iron-binding protein transferrin. The acquisition of trasferrin-iron is coincident with pathogenicity among Neisseria species and a limited number of other pathogens of human and veterinary significance. In Neisseria meningitidis, transferrin binding relies on two co-expressed, outer membrane proteins distinct in aspects of both structure and function. These proteins are independently and simultaneously capable of binding human transferrin and both are required for the optimal uptake of iron from this source. It has been established that transferrin-binding proteins (designated TbpA and TbpB) form a discrete, specific complex which may be composed of a transmembrane species (composed of the TbpA dimer) associated with a single surface-exposed lipoprotein (TbpB). This more exposed protein is capable of selectively binding iron-saturated transferrin and the receptor complex has ligand-binding properties which are distinct from either of its components. Previous in vivo analyses of N. gonorrhoeae, which utilizes a closely related transferrin-iron uptake system, indicated that this receptor exists in several conformations influenced in part by the presence (or absence) of transferrin.Here we propose a dynamic model of the meningococcal transferrin receptor which is fully consistent with the current data concerning this subject. We suggest that TbpB serves as the initial binding site for iron-saturated transferrin and brings this ligand close to the associated transmembrane dimer, enabling additional binding events and orientating transferrin over the dual TbpA pores. The antagonistic association of these receptor proteins with a single ligand molecule may also induce conformational change in transferrin, thereby favouring the release of iron. As, in vivo, transferrin may have iron in one or both lobes, this dynamic molecular arrangement would enable iron uptake from either iron-binding site. In addition, the predicted molecular dimensions of the putative TbpA dimer and hTf are fully consistent with these proposals. Given the diverse data used in the formulation of this model and the consistent characteristics of transferrin binding among several significant Gram-negative pathogens, we speculate that such receptor-ligand interactions may be, at least in part, conserved between species. Consequently, this model may be applicable to bacteria other than N. meningitidis.     

A joint model of the contractile system of striated muscle (dynamic version)

The Joint Model of the Contractile System of Muscle is a theoretical construction and the question is whether it may express adequately some aspects of the biological original. In addition to the previous results which presented preliminary calculations, simulation experiments have been performed with a dynamic version of the model. The relations found between the variables studied (length, shortening velocity, isotonic contraction load, shortening heat production rate and excess of effective activity), did not essentially differ from those established by preliminary calculations; the choice of appropriate parameter values and the introduction of some additional features in the system made it possible to obtain a better approximation of relations known from measurements on the biological object. The model discloses some relevant general aspects of the contractile system of "independent" generators of force and thus contributes to a specification of the relationships between molecular and macroscopic levels of contraction phenomena. Future development or correction of the concepts under consideration depend on more suitable empirical data and further simulation experiments.     

Fighting for food: a dynamic version of the Hawk-Dove game

Summary The Hawk-Dove game (Maynard Smith, 1982) has been used to analyse conflicts over resources such as food. At the evolutionarily stable strategy (ESS), either a proportionp* of animals always play Hawk, or each animal has a probabilityp* of playing Hawk. We modify the standard Hawk-Dove game to include a state variable,x, that represents the animal's level of energy reserves. A strategy is now a rule for choosing an action as a function ofx and time of day. We consider a non-reproductive period and adopt the criterion of minimizing mortality over this period. We find the ESS, which has the form play Hawk if reserves are belowc* (t) at timet, otherwise play Dove. This ESS is very different from the ESS in the standard Hawk-Dove game. It is a pure ESS that depends on the animal's state and on time. Furthermore, it is characterized by the strong condition that any single mutant that does not adopt the ESS suffers a reduction in fitness. The standard Hawk-Dove game assumes pay-offs that are related to fitness; our approach starts from a definition of fitness and derives the pay-offs in the process of finding the ESS. When the environment becomes worse (e.g. food becomes less reliable or energy expenditure increases) the ESS changes in such a way as to increase the proportion of animals that will play Hawk.     

An integral dynamic model for the UASB reactor

In this article a dynamic model of a continuous working UASB reactor is described. It results from the integration of the fluid flow pattern in the reactor, the kinetic behavior of the bacteria (where inhibition and limitation were taken into account), and the mass transport phenomena between different compartments and different phases. The mathematical equations underlying the model and describing the important mechanisms were programmed and prepared for computations and simulations by computer. The settler efficiency has to be over 99% to prevent the reactor from wash-out. When the settler efficiency is over 99%, the total sludge content of the reactor increases steadily, so the reactor is hardly ever in a steady state. This implies dynamic modeling. The model is able to predict the various observable and nonobservable or difficult to observe state variables, e.g., the sludge bed height, the sludge blanket concentration, the short-circuiting flows over bed and blanket, and the effluent COD concentration as a function of the hydrodynamic load, COD load, pH, and settler efficiency. The optimal pH value is between 6.0 and 8.0; fatty acid shock loadings are difficult to handle outside this optimal pH range.     

The hot IVGTT two-compartment minimal model: an improved version

The two-compartment minimal model (2CMM) interpretation of a labeled intravenous glucose tolerance test (IVGTT) is a powerful tool to assess glucose metabolism in a single individual. It has been reported that a derived 2CMM parameter describing the proportional effect of glucose on insulin-independent glucose disposal can take physiologically unplausible negative values. In addition, precision of 2CMM parameter estimates is sometimes not satisfactory. Here we resolve the above issues by presenting an improved version of 2CMM that relies on a new assumption on the constant component R(d0) of insulin-independent glucose disposal. Here R(d0) is not fixed to 1 mg x kg(-1) x min(-1) but instead is expressed as a fraction of steady-state glucose disposal. The new 2CMM is identified on the same stable labeled IVGTT data base on which the original 2CMM was formulated. A more reliable insulin-independent glucose disposal portrait is obtained while that of insulin action remains unchanged. The new 2CMM also improves the precision with which model parameters and metabolic indexes are estimated.     

Type specification and spatial pattern formation of floral organs: A dynamic development model

A mathematical model simulating spatial pattern formation (positioning) of floral organs is proposed. Computer experiment with this model demonstrated the following sequence of spatial pattern formation in a typical cruciferous flower: medial sepals, carpels, lateral sepals, long stamens, petals, and short stamens. The positioning was acropetal for the perianth organs and basipetal for the stamens and carpels. Organ type specification and positioning proceed non-simultaneously in different floral parts and organ type specification goes ahead of organ spatial pattern formation. Computer simulation of flower development in several mutants demonstrated that the AG and AP2 genes determine both organ type specification and formation of the zones for future organ development. The function of the AG gene is to determine the basipetal patterning zones for the development of the reproductive organs, while the AP2 gene maintains proliferative activity of the meristem establishing the acropetal patterning zone for the development of the perianth organs.     

A structural and dynamic model for the nicotinic acetylcholine receptor

Folding of the five polypeptide subunits (alpha 2 beta gamma delta) of the nicotinic acetylcholine receptor (AChR) into a functional structural model is described. The principles used to arrange the sequences into a structure include: (1) hydrophobicity----membrane-crossing segments; (2) amphipathic character----ion-carrying segments (ion channel with single group rotations); (3) molecular shape (elongated, pentagonal cylinder)----folding dimensions of exobilayer portion; (4) choice of acetylcholine binding sites----specific folding of exobilayer segments; (5) location of reducible disulfides (near agonist binding site)----additional specification of exobilayer arrangement; (6) genetic homology----consistency of functional group choices; (7) noncompetitive antagonist labeling----arrangement of bilayer helices. The AChR model is divided into three parts: (a) exobilayer consisting of 11 antiparallel beta-strands from each subunit; (b) bilayer consisting of four hydrophobic and one amphiphilic alpha-helix from each subunit; (c) cytoplasmic consisting of one (folded) loop from each subunit. The exobilayer strands can form a closed 'flower' (the 'resting state') which is opened ('activated') by agonists bound perpendicular to the strands. Rearrangement of the agonists to a strand-parallel position and partial closing of the 'flower' leads to a desensitized receptor. The actions of acetylcholine and succinoyl and suberoyl bis-cholines are clarified by the model. The opening and closing of the exobilayer 'flower' controls access to the ion channel which is composed of the five amphiphilic bilayer helices. A molecular mechanism for ion flow in the channel is given. Openings interrupted by short duration closings (50 microseconds) depend upon channel group motions. The unusual photolabeling of intrabilayer serines in alpha, beta and delta subunits but not in gamma subunits near the binding site for non-competitive antagonists is explained along with a mechanism for the action of these antagonists such as phencyclidine. The unusual alpha 192Cys-193Cys disulfide may have a special peptide arrangement, such as a cis-peptide bond to a following proline (G.A. Petsko and E.M. Kosower, unpublished results). The position of phosphorylatable sites and proline-rich segments are noted for the cytoplasmic loops. The dynamic behavior of the AChR channel and many different experimental results can be interpreted in terms of the model. An example is the lowering of ionic conductivity on substitution of bovine for Torpedo delta M2 segment. The model represents a useful construct for the design of experiments on AChR.     

A coherent wave model for pattern generation during the aggregation of slime mould amoeba

In this paper we examine the finite difference equation describing the acrasin concentration as used by Parnas and Segel [11] in a computer simulation of the aggregation of slime mould amoeba. We consider the corresponding differential equation in two spatial dimensions rather than the single dimension used in [11]. We solve this equation along a spiral curve to within a quadrature and for low concentrations (in keeping with the simulation conditions) we extract an analytical form for the traveling wave. For a quantized relationship between the period of this wave and the refractory period of the amoeba we show the creation of an aggregation process along the spiral curve.We introduce a thermodynamic analysis from which we show that the production of the above acrasin wave is a typical symmetry breaking phenomenon dependent upon the amount of nutrients (bacteria) in the medium. This phase transition displays a critical exponent of 1/2 dependent upon the deviation of the bacterial concentration from its critical value. We are able to show that the broken symmetry state possesses lower free energy than a homogenous state. We also show, from a linear stability analysis, that this state is not destroyed by environmental perturbations.By utilizing the free energy expression in a time dependent Landau-Ginzburg type model we make contact with other well known physical phenomena such as rouleaux formation and superconductivity. This approach immediately opens up the possibility of examining the problem from a more general perspective.     

The contribution of sensory inputs to the pattern generation of breathing

Current concepts of the basic neural control system and its modulation by afferent inputs are reviewed. It is emphasized that, in analogy with locomotion, the central pattern generator (CPG) for automatic metabolic respiration does not depend on any afferent feedback from receptors sensitive to the movements of the "pump," or the streams of pumped air, for its production of a rhythmic motor output provides the CPG receives some "drive" inputs above threshold and adequate bias. The operation for a variety of reflexes and feedback loops is of fundamental importance, however, for adapting the breathing pattern to the varying requirements for gas exchange to the many behavioural, nonmetabolic demands on the breathing apparatus which are competing with its primary metabolic control functions. The presentation is focussed also on available evidence that the respiratory CPG exerts powerful modulations on the transmission in these reflex pathways controlling the pattern of breathing and adjusting it to the various metabolic and behavioural demands. Mechanisms for "gating," "phasic gain changes," and "phase-dependent reflex reversal" are exemplified.     

An extended dynamic model of oxidative phosphorylation.

The presented model based on an earlier one (Korzeniewski, B. and Froncisz, W. (1989) Studia Biophys. 132, 173-187) simulates concentration changes in time of chemical compounds and thermodynamic forces during respiration of cell suspension in a closed chamber. A set of differential equations solved numerically describes the utilization of oxygen up to anaerobiosis and the behaviour of the system after a sudden pulse of oxygen. Flux control coefficients for most important reactions (enzymes) of oxidative phosphorylation were calculated. A good qualitative and (when a direct comparison is possible) quantitative agreement with experimental results can be observed. The following conclusions can be drawn from the simulation: (1) Wilson's steady state model is not in contradiction with sharing of the control over the respiration between some steps and displacement of the ATP/ADP carrier from equilibrium. (2) The overshoot characteristics of the delta microH+ time-course after reoxygenation can be explained without using the lag-phase kinetics of ATP-synthetase. (3) A 'hot region' (sharp changes of many parameters) can be distinguished when the oxygen concentration approaches zero; only cytochrome oxidase is clearly sensitive on oxygen concentration in all its range. (4) Control over oxidative phosphorylation is shared mainly between inputs of the system (ATP utilization and substrate dehydrogenation) and the proton leak.     

A cell pattern generation model based on an extended artificial regulatory network

Cell pattern generation has a fundamental role in both artificial and natural development. This paper presents results from a model in which a genetic algorithm (GA) was used to evolve an artificial regulatory network (ARN) to produce predefined 2D cell patterns through the selective activation and inhibition of genes. The ARN used in this work is an extension of a model previously used to create simple geometrical patterns. The GA worked by evolving the gene regulatory network that was used to control cell reproduction, which took place in a testbed based on cellular automata (CA). After the final chromosomes were produced, a single cell in the middle of the CA lattice was allowed to replicate controlled by the ARN found by the GA, until the desired cell pattern was formed. The model was applied to the problem of generating a French flag pattern.     

The fictively breathing tadpole brainstem preparation as a model for the development of respiratory pattern generation and central chemoreception

Spontaneous high-frequency, low-amplitude and low-frequency, high-amplitude efferent bursting patterns of cranial and spinal motor nerve activity in the in vitro brainstem preparation of the bullfrog tadpole Rana catesbeiana have been characterized as fictive gill and lung ventilation, respectively (Gdovin MJ, Torgerson CS, Remmers JE). Characterization of gill and lung ventilatory activity in cranial nerves in the spontaneously breathing tadpole Rana catesbeiana, FASEB J 1996;10(3):A642; Gdovin MJ, Torgerson CS, Remmers JE. Neurorespiratory pattern of gill and lung ventilation in the decerebrate spontaneously breathing tadpole, Respir Physiol 1998;113:135 146; Pack AI, Galante RJ, Walker RE, Kubin LK, Fishman AP. Comparative approach to neural control of respiration, In: Speck DF, Dekin MS, Revelette WR, Frazier DT, editors. Respiratory Control Central and Peripheral Mechanisms. Lexington: University of Kentucky Press, 1993:52-57). In addition, the ontogenetic dependence of central respiratory chemoreceptor stimulation on fictive gill and lung ventilation has been previously described (Torgerson CS, Gdovin MJ, Remmers JE. Fictive gill and lung ventilation in the pre- and post-metamorphic tadpole brainstem, J Neurophysiol 1998, in press). To investigate the neural substrates responsible for central respiratory rhythm generation of gill and lung ventilation in the developing tadpole, we recorded efferent activities of cranial nerve (CN) V, VII, and X and spinal nerve (SN) II during changes in superfusate PCO2 before and after multiple transection of the in vitro brainstem. The brainstem was transected between CN VIII and IX and the response to changes in PCO2 was recorded. A second transection was then made between the caudal margin of CN X and rostral to SN II. Preliminary data reveal that robust gill ventilation was recorded consistently only if the segment of brainstem included CN X, whereas the loci capable of eliciting fictive lung bursting patterns appeared to differ depending on developmental stage. These data demonstrate that the neural substrate required for fictive gill and lung ventilation exists in anatomically separate regions such that the gill central pattern generator (CPG) is located in the caudal medulla at the level of CN X throughout development, whereas the location of the lung CPG is located more rostrally at the level of CN VII in the post-metamorphic larva. Both in vivo and in vitro studies revealed two distinct neural bursting patterns associated with gill and lung ventilation. Sequential activation of CN V, VII, X were observed during gill ventilation of in vivo and fictive gill ventilation in vitro, whereas these nerve activities, along with SN II displayed more synchronous bursting patterns of activation during lung ventilation and fictive lung breaths.     

The Thai version of the PSS-10: An Investigation of its psychometric properties

Background  

Among the stress instruments that measure the degree to which life events are perceived as stressful, the Perceived Stress Scale (PSS) is widely used. The goal of this study was to examine the psychometric properties of a Thai version of the PSS-10 (T-PSS-10) with a clinical and non-clinical sample. Internal consistency, test-retest reliability, concurrent validity, and the factorial structure of the scale were tested.     

A dynamic,genome-scale flux model of Lactococcus lactis to increase specific recombinant protein expression

Recently, lactic acid bacteria (LAB) have attracted a great deal of interest because of their potential to serve as oral delivery vehicles for recombinant protein vaccines. An important limitation to their use is the typically low level of heterologous expression obtained in LAB. To address this, a dynamic flux balance analysis (DFBA) model was used to identify gene targets for increasing specific expression of Green Fluorescent Protein (GFP), a model heterologous protein, in Lactococcus lactis IL1403. Two strains, each targeting one of the top model-identified genes, were constructed and tested in vivo. Data show that both strains, by a conservative estimate, achieved 15% higher GFP per cell than the control strain, a qualitative confirmation of the model predictions. A genome-scale DFBA model for L. lactis growing on M17 medium is presented along with the procedure for screening gene targets and a powerful method for visualizing fluxes in genome-scale metabolic networks.