Exploring local and non-local interactions for protein stability by structural motif engineering

In order to probe the relative contribution of local and non-local interactions to the thermodynamic stability of proteins, we have devised an experimental approach based on a combination of motif engineering and sequence shuffling. Candidate chain segments in an immunoglobulin V(L) domain were identified whose conformation is proposed to be dominated by non-local interactions. Locally interacting structural motifs of a different conformation were then constructed as replacements, by introducing motif consensus sequences. We find that all nine replacements we constructed systematically reduce the folding cooperativity. By comparing this destabilising effect with the folding transitions of shuffled sequences for three of these motifs, we estimate the contribution of local, native interactions to the free energy of folding. Our results suggest that local and non-local interactions contribute to stability by an approximately equal amount, but that local interactions stabilise by increasing the resistance to denaturation while non-local interactions increase folding cooperativity. The systematic loss of stability by sequence shuffling in these host-guest experiments suggests that the designed interactions indeed are present in the native state, thus consensus sequence engineering may be a useful tool in structure design, but non-local interactions must be taken into account for global stability engineering. Statistical approaches are powerful tools for engineering protein structure and stability, but an analysis based on local sequence propensities alone does not adequately represent the balance of sequence and context in protein structures.     

Evolution of interactions in family-structured populations: mixed mating models

THE EFFECT OF INBREEDING ON SOCIALITY IS STUDIED THEORETICALLY FOR THE EVOLUTION OF INTERACTIONS BETWEEN SIBLINGS IN CERTAIN MIXED MATING SYSTEMS THAT GIVE RISE TO INBREEDING: sib with random mating and selfing with random mating. Two approaches are taken. First, specific models of altruism are studied for the various mating systems. In the case of the additive model, inbreeding facilitates the evolution of altruistic genes. Likewise, for the multiplicative model this is usually the case, as long as the costs of altruism are not too great. Second, the case of total altruism, in which the gene has zero individual fitness but increases the fitness of associates, is studied for a general fitness formulation. In this case, inbreeding often retards the ability of such genes to increase when rare, and the equilibrium frequency of those recessive genes that can increase is totally independent of the mating system and, consequently, of the amount of inbreeding. It appears from the results presented that inbreeding facilitates most forms of altruism, but retards extreme altruism. These results stem from the fact that inbreeding increases the within-family relatedness by increasing the between-family variance in allele frequency. In most cases this facilitates altruism. However, in the case of total altruism, only heterozygotes can pass on the altruistic allele, and inbreeding tends to decrease this heterozygote class. In either case, the important effect of inbreeding lies in altering the genotypic distribution of the interactions.     

Stability analysis of a two-species model with transitions between population interactions

Stability of a simple two-species system is investigated. This model assumes that the kind of inter-specific interactions is not fixed, and that it depends on the system state, i.e., undergoes transitions between different population interactions due to variation in population densities. The main goal is to show the effects of the transitions between different population interactions on the two-species coexistence, and on the stability conditions of multiple equilibria.     

Excitatory and inhibitory interactions in localized populations of model neurons

Coupled nonlinear differential equations are derived for the dynamics of spatially localized populations containing both excitatory and inhibitory model neurons. Phase plane methods and numerical solutions are then used to investigate population responses to various types of stimuli. The results obtained show simple and multiple hysteresis phenomena and limit cycle activity. The latter is particularly interesting since the frequency of the limit cycle oscillation is found to be a monotonic function of stimulus intensity. Finally, it is proved that the existence of limit cycle dynamics in response to one class of stimuli implies the existence of multiple stable states and hysteresis in response to a different class of stimuli. The relation between these findings and a number of experiments is discussed.     

The local and non-local components of the local field potential in awake primate visual cortex

The Local Field Potential (LFP) is the analog signal recorded from a microelectrode inserted into cortex, typically in the frequency band of approximately 1 to 200 Hz. Here visual stimuli were flashed on in the receptive fields of primary visual cortical neurons in awake behaving macaques, and both isolated single units (neurons) and the LFP signal were recorded from the same unipolar microelectrode. The fall-off of single unit activity as a visual stimulus was moved from near the center to near the edge of the receptive field paralleled the fall-off of the stimulus-locked (evoked) LFP response. This suggests that the evoked LFP strongly reflects local neuronal activity. However, the evoked LFP could be significant even when the visual stimulus was completely outside the receptive field and the single unit response had fallen to zero, although this phenomenon was variable. Some of the non-local components of the LFP may be related to the slow distributed, or non-retinotopic, LFP signal previously observed in anesthetized animals. The induced (not time-locked to stimulus onset) component of the LFP showed significant increases only for stimuli within the receptive field of the single units. While the LFP primarily reflects local neuronal activity, it can also reflect neuronal activity at more distant sites, although these non-local components are typically more variable, slower, and weaker than the local components.     

A model for complex sequence learning and reproduction in neural populations

Temporal patterns of activity which repeat above chance level in the brains of vertebrates and in the mammalian neocortex have been reported experimentally. This temporal structure is thought to subserve functions such as movement, speech, and generation of rhythms. Several studies aim to explain how particular sequences of activity are learned, stored, and reproduced. The learning of sequences is usually conceived as the creation of an excitation pathway within a homogeneous neuronal population, but models embodying the autonomous function of such a learning mechanism are fraught with concerns about stability, robustness, and biological plausibility. We present two related computational models capable of learning and reproducing sequences which come from external stimuli. Both models assume that there exist populations of densely interconnected excitatory neurons, and that plasticity can occur at the population level. The first model uses temporally asymmetric Hebbian plasticity to create excitation pathways between populations in response to activation from an external source. The transition of the activity from one population to the next is permitted by the interplay of excitatory and inhibitory populations, which results in oscillatory behavior that seems to agree with experimental findings in the mammalian neocortex. The second model contains two layers, each one like the network used in the first model, with unidirectional excitatory connections from the first to the second layer experiencing Hebbian plasticity. Input sequences presented in the second layer become associated with the ongoing first layer activity, so that this activity can later elicit the the presented sequence in the absence of input. We explore the dynamics of these models, and discuss their potential implications, particularly to working memory, oscillations, and rhythm generation.     

Phase transitions in nuclei and chromatin

Changes in the volume of rat liver nuclei have been monitored as a function of modifications in ionic environment (from 0 to 20 mM), temperature (from 4 to 37°C) and pH (from 1 to 8). An abrupt reduction of nuclear volume occurred with increasing ion concentration, this contraction being more pronounced with bivalent (either Ca²⁺ or Mg²⁺) than with monovalent (either Na⁺ or K⁺) cations. The lowering of pH produced a similar effect. Parallel changes in chromatin structure took place at the same time as phase-like transitions. Atomic absorption spectroscopy allowed determination of free and nuclei-bound ions, pointing to the presence of a sizeable number of free binding sites for chromatin-DNA even within intact nuclei. DNA-phosphate sites appear to be neutralized by ions strictly according to the size of the electric charge and polyelectrolyte theory. Partial digestion (by micrococcal nuclease) or simple breaks (by chemical carcinogens) of the chromatin-DNA fiber caused respectively elimination or reduction of the abrupt volume changes in the intact nuclei. The apparent role of chromatin structure versus nuclear matrix in determining the shape and volume of intact nuclei is briefly discussed.     

Sequential configuration model for firing patterns in local neural networks

This paper presents a sequential configuration model to represent the coordinated firing patterns of memory traces in groups of neurons in local networks. Computer simulations are used to study the dynamic properties of memory traces selectively retrieved from networks in which multiple memory traces have been embedded according to the sequential configuration model. Distinct memory traces which utilize the same neurons, but differ only in temporal sequencing are selectively retrievable. Firing patterns of constituent neurons of retrieved memory traces exhibit the main properties of neurons observed in multi microelectrode recordings. The paper shows how to adjust relative synaptic weightings so as to control the disruptive influences of cross-talk in multipy-embedded networks. The theoretical distinction between (primarily anatomical) beds and (primarily physiological) realizations underlines the fundamentally stochastic nature of network firing patterns, and allows the definition of 4 degrees of clarity of retrieved memory traces.     

Equilibrium and local stability in a logistic matrix model for age-structured populations

A logistic matrix model for age-structured population dynamics is constructed. This model discretizes a continuous, density-dependent model with age structure, i.e. it is an extension of the logistic model to the case of age-dependence. We prove the existence and uniqueness of its equilibrium and give a necessary and sufficient condition for the local stability of the equilibrium.     

Phase transitions and molecular motion in the cell.

The cytoplasm exhibits all of the signature characteristics of a gel. The thesis put forth here is that the cytoplasm's gel-like character is central to the generation of biological movement. In artificial gels, a common vehicle for generating movement is the polymer-gel phase-transition. By undergoing phase-transition, gels produce motion of both solvent and solutes. It is argued that cells do the same. Three examples are given: the secretory system, the muscle contraction system and the biological streaming system. In each case it is shown that the characteristic motions may be created as proteins and water undergo transition from an expanded, hydrated state to a contracted, dehydrated state--or the reverse. These changes shift solutes and solvent in a characteristic way that depends on the respective organelle's structure. Phase-transitions are simple, powerful mechanisms that may be responsible for many, if not all, biological motions.     

A prototype model structure for mixed microbial populations in homogeneous food products

An important factor which has not been included in many models in the field of predictive microbiology is the influence of a background of microflora in a food product. It is however generally known that the growth of a microorganism as a pure culture can be substantially different from its growth in a mixed culture, due to microbial interactions. Because of the importance of these interactions and the lack of suitable modeling techniques in the field of predictive microbiology to describe them, the potential of models in other research fields-namely ecology-to deal with interactions is explored in previous work of the authors. However, a model structure for microbial growth in food products cannot simply be copied from those elaborated in ecology. The structure of a predictive growth model is indeed typical, primarily due to the explicit modeling of a lag phase. The current paper proposes a prototype model structure for growth of mixed microbial populations in homogeneous food products. The model is able to describe a lag phase and reduces to a classical predictive growth model in the special case of single-species growth.     

A kinetic model for Ascaridia galli populations in chickens treated with mixed salts of copper and zinc.

The action of mixed salts of copper and zinc (basic and neutral) on Hisex chickens experimentally infected with Ascaridia galli has been studied. The data show that the lowest host mortality and decrease in body weight gain and the highest reduction in nematode loading occurs in infected chickens treated with basic salts (in comparison with infected chickens, untreated or treated with neutral salts). A mathematical model has been proposed to provide a quantitative interpretation of the observed results. The model solutions of the kinetics of parasite numbers and of the gain in body weight are in a good agreement with the experimental data. One of the kinetic parameters in the model is defined as a phenomenological constant of the host immune response. Its value is determined in the case of infected and untreated chickens.     

Interaction ofBdellovibrio with Its prey in mixed microbial populations

The interaction ofBdellovibrio with its prey can be affected by the presence of other microorganisms regardless of whether they serve as a prey for the bdellovibrios. This was shown in a system in which the fate of one prey could be followed in mixed bacterial populations thanks to a specific trait, bioluminescence. The attacking bdellovibrio causes decay of bioluminescence, and the rate of light decay of the population indicates the rate at which the luminous bacteria are attacked. Using this system it was found that different bacteria affected the predatorprey interaction in different ways: some competed with the original prey for the predator; others enhanced the activity of the predator toward the original prey, and others inhibited it. The significance of these findings in relation to the distribution and activity ofBdellovibrio in the natural ecosystem is discussed.     

A neural model of interactions subserving prey-predator discrimination and size preference in anuran amphibia

The model described is an extension of a previous model of the optic tectum (Arbib & Lara, 1982; Lara, Arbib & Cromarty, 1982; Lara & Arbib, 1982) and takes into consideration anatomical, physiological and behavioral studies in anurans, as well as earlier modelling efforts (Ewert & Von Seelen, 1974; Didday, 1976). Computer simulations were conducted to analyze how interactions among retina, optic tectum and pretectum may give frogs and toads the ability to discriminate between prey and predator stimuli. Results from simulations have allowed us to reproduce empirical observations, to suggest new experiments, and to postulate what neural mechanisms might be involved in some phenomena related to prey-catching orienting behavior, with direction invariance of prey-predator recognition being a consequence of tectal architecture, and size preference and response latency depending on the motivational state of the animal.     

Cell interactions within nascent neural crest cell populations transiently promote death of neurogenic precursors

We have previously shown that cultured trunk neural crest cell populations irreversibly lose neurogenic ability when dispersal is prevented or delayed, while the ability to produce other crest derivatives is retained (Vogel, K. S. and Weston, J. A. (1988) Neuron 1, 569-577). Here, we show that when crest cells are prevented from dispersing, cell death is increased and neurogenesis is decreased in the population, as a result of high cell density. Control experiments to characterize the effects of high cell density on environmental conditions in culture suggest that reduced neurogenesis is the result of cell-cell interactions and not changes (conditioning or depletion) of the culture medium. Additionally, we show that the caspase inhibitor zVAD-fmk, which blocks developmentally regulated cell death, rescues the neurogenic ability of high density cultures, without any apparent effect on normal, low-density cultures. We conclude, therefore, that increased cell interaction at high cell densities results in the selective death of neurogenic precursors in the nascent crest population. Furthermore, we show that neurogenic cells in cultured crest cell populations that have dispersed immediately are not susceptible to contact-mediated death, even if they are subsequently cultured at high cell density. Since most early migrating avian crest cells express Notch1, and a subset expresses Delta1 (Wakamatsu, Y., Maynard, T. M. and Weston, J. A. (2000) Development 127, 2811-2821), we tested the possibility that the effects of cell contact were mediated by components of a Notch signaling pathway. We found that neurogenic precursors are eliminated when crest cells are co-cultured with exogenous Delta1-expressing cells immediately after they segregate from the neural tube, although not after they have previously dispersed. We conclude that early and prolonged cell interactions, mediated at least in part by Notch signaling, can regulate the survival of neurogenic cells within the nascent crest population. We suggest that a transient episode of cell contact-mediated death of neurogenic cells may serve to eliminate fate-restricted neurogenic cells that fail to disperse promptly in vivo.