A two-sex polygenic model for the evolution of premating isolation. I. Deterministic theory for natural populations

It is proposed that mating behavior is normally determined by independent genetic systems in the male and female. A specific model is put forward in which mating behavior is determined by additive gene contributions in both sexes, and the strength of mating attraction is maximized when mating "scores" in the two sexes are equalized. This type of model, which may be described as a "facilitation" model, is related to models proposed by a number of authors. It is pointed out that a second class of models exists, "avoidance" models, and that these, although less tractable analytically, could be more realistic.-An organism is assumed to be divided into two strains, and selection is introduced through lethality or sterility of the hybrid (postmating isolation). The selective tendency for divergence of mating behavior in one sex is then shown to be proportional to the amount of divergence that already exists in the opposite sex, multiplied by a quantity that can be described as the heritability of mating attraction. The situation in which no initial divergence exists in either sex constitutes an equilibrium that is unstable, but one that requires substantial deviations before any selective progress can be made. Thus, the evolution of premating isolation to reinforce postmating isolation may be an inefficient process. The process would occur much more efficiently if some initial chance divergence in mating behavior occurred during the period in which postmating isolation evolved.     

Dynamic properties of cardiovascular systems.

A recently derived mathematical model of an isolated heart is extended here to a closed-loop cardiovascular system. Taking the end-diastolic volume as state variable, the authors show that the closed-loop cardiovascular system can be described by a one-dimensional nonlinear discrete dynamical system that depends on parameters describing the systolic and diastolic properties of the heart, heart rate, total peripheral resistance, and arterial capacitance. Studies of this model show that the system possesses a rich spectrum of dynamical behavior, from stable points through stable cycles to a "chaotic" behavior. It is shown that such an analysis of dynamic behavior yields those domains in the parameter space that correspond to a normal and abnormal beating heart, when the heart ejects time-invariant and time-variant (periodic or aperiodic) stable stroke volumes, respectively. Determination of such domains may lead to better understanding of the specific pathologic mechanism involved in the evolution of an abnormal beating heart.     

Experimental analysis of a neural system: Two modeling approaches

The retinal neural system in the catfish which transforms light intensity temporal variations into the horizontal cell potential is experimentally analyzed and modeled by two distinct methods. The first method involves testing the system with gaussian white-noisemodulated light intensity and the subsequent derivation of a mathematical model in terms of a Wiener functional series. The second method involves testing of the system by step and sinewave stimuli and the postulation of a set of nonlinear differential equations which are designed to fit these stimulus-response data. In this latter approach, the differential equations describe the usually assumed dynamic behavior of the component subsystems, such as photoreceptor and horizontal cell membranes in terms of properties of membrance resistance and capacitance. The system behavior is found to exhibit certain small signal nonlinearities such as dynamic asymmetry in the response as well as certain large signal nonlinearities. The two modeling approaches and the resulting models are compared and it is found that the functional model derived from the white-noise experiment, while it does not attempt to describe the underlying system structure as the differential equation does, produced, in general, more satisfactory results as far as the input-output behavior of the system is concerned. It is suggested that combination of the two approaches could be very fruitful in modeling a particular system.     

A quantitative model of successive color induction in the honeybee

Intensity discrimination experiments are performed with individual walking honeybees trained to color stimuli (UV, blue and green) of constant intensity. The choice behavior to stimuli of identical wavelength spectrum but different intensities is tested. A graded choice behavior is found. The training intensity is chosen with the highest probability in most cases. Phototaxis as well as brightness discrimination can be excluded. The choice behavior is explained exclusively by discrimination of chromaticness (hue and saturation) according to the Bezold-Brücke shift.The bees adapt to the chromatic stimuli during their choices. From the behavioral data, it is concluded that in adaptation, adjustment in photoreceptor sensitivity in one receptor also affects the sensitivity of the other receptors (co-adaptation). The linear adaptation model corresponding to the von Kries Coefficient Law used up to now to describe adaptation to white light in the honeybee does not describe this type of adaptation.A quantitative model of adaptation to chromatic stimuli extending the linear adaptation model is developed.The most reasonable mechanism of co-adaptation is optical coupling by lateral filtering. Other mechanisms such as electrical coupling are unlikely, since their effects on color vision would lead to effects inconsistent with Graßmann's Laws.     

Frequency and burst duration in oscillating neurons and two-cell networks

We study the relationship of injected current to oscillator period in single neurons and two-cell model networks formed by reciprocal inhibitory synapses. Using a Morris-Lecar-like model, we identify two qualitative types of oscillatory behavior for single model neurons. The classical oscillator behavior is defined as type A. Here the burst duration is relatively constant and the frequency increases with depolarization. For oscillator type B, the frequency first increases and then decreases when depolarized, due to the variable burst duration. Our simulations show that relatively modest changes in the maximal inward and outward conductances can move the oscillator from one type to another. Cultured stomatogastric ganglion neurons exhibit both A and B type behaviors and can switch between the two types with pharmacological manipulation. Our simulations indicate that the stability of a two-cell network with injected current can be extended with inhibitory coupling. In addition, two-cell networks formed from type A or type B oscillators behave differently from each other at lower synaptic strengths.     

Pyrophosphate formation from phospho(enol)pyruvate adsorbed onto precipitated orthophosphate: A model for prebiotic catalysis of transphosphorylations

It has been postulated that adsorption and surface catalysis, as well as repeated drying and wetting cycles, were essential in the synthesis, interconversion and co-evolution of phosphorylated molecules, including energy-rich compounds. We have investigated the formation of pyrophosphate from phospho(enol)pyruvate and orthophosphate. The reaction occurred within hours at 37°C, required the adsorption of phospho(enol)pyruvate onto sedimented phosphate, exhibited Michaelian-like behavior and showed positive cooperativity with respect to divalent cation concentration. Thus in mild, near-equilibrium conditions, the de-solvated surfaces of phosphate crystals can catalyze the formation of pyrophosphate with a kinetic behavior similar to that found in contemporary enzymes. The experimental system we describe may represent a model for the prebiotic catalysis of transphosphorylations.     

Experimental investigation on the origin of the genetic code

Summary One of the essential relationships between nucleic acids and amino acids in present biological systems, and perhaps in precursors to these systems is expressed in binding interactions. Such interactions depend on the size, composition and conformation of the interacting species. A simplified model of such complex systems was tested in an attempt to assess first the compositional effect, i.e., the binding behavior of monomeric nucleic acid and protein components. Nine representative amino acids were immobilized individually on a prepared chromatographic support by the formation of an amide linkage. Selective binding of ribonucleoside 5-phosphates was exhibited by these amino acids under standardized conditions and the binding was characterized by a site-binding model. It was found that binding behavior was dependent of the nature of the base and the nature of the amino acid. Basic information is thus provided which should be useful in the interpretation of more complex nucleic acid-protein systems and the study of their role in the evolution of the cell.     

Electrogenic properties of the sodium-alanine cotransporter in pancreatic acinar cells: I. Tight-seal whole-cell recordings

Summary Electrical currents associated with sodium-coupled alanine transport in mouse pancreatic acinar cells were studied using the method of whole-cell recording with patch pipettes. Single cells or small clusters of (electrically coupled) cells were isolated by collagenase treatment. The composition of the intracellular solution could be controlled by internal perfusion of the patch pipette. In this way both inward and outward currents could be measured under zero-trans conditions, i.e., with finite concentrations of sodium andl-alanine on one side and zero concentrations on the other. Inward andoutward currents for equal but opposite concentration gradients were found to be of similar magnitude, meaning that the cotransporter is functionally nearly symmetric. The dependence of current on the concentrations of sodium andl-alanine exhibited a Michaelis-Menten behavior. From the sodium-concentration dependence of current as well as from the reversal potential of the current in the presence of an alanine-concentration, gradient, a sodium/alanine stoichiometric ratio of 1:1 can be inferred. The finding that N-methylated amino acids may substitute, forl-alanine, as well as the observed pH dependence of currents indicate that the pancreatic alanine transport system is similar to (or identical with) the A-system which is widespread in animal cells. The transport system is tightly coupled with respect to Na⁺; alanine-coupled inward flow of Na⁺ is at least 30 times higher than uncoupled Na⁺ flow mediated by the cotransporter. The current-voltage characteristic of the cotransporter could be (approximately) determined from the difference of transmembrane current in the presence and in the absence ofl-alanine. The sodium-concentration dependence of the current-voltage characteristic indicates that a Na⁺ ion approaching the binding site from the extracellular medium has to cross part of the transmembrane electric field.     

Reduction of a Hodgkin-Huxley-type model for a mammalian neuron at body temperature

Hodgkin-Huxley-type models mimick the electrical behavior of excitable membranes quite realistically. However, inclusion of many different ionic channels into such a model yields a highly complex set of differential equations. In this paper a reduction of a full Hodgkin-Huxley-type model based on voltage-clamp data from small rat neurons in the supraoptic nucleus area is introduced. It was found that two of the ionic channel gating variables of the full model preserved a rather close relationship during simulations. This allowed to express one of these gating variables in terms of the other one thus reducing the number of differential equations the model is based on. The behavior of the reduced model was very similar to that of the full model. In particular, important physiological features as spike shape and constant-input-to-interspike-interval relationship were (almost) identical in the full and the reduced model.     

Equilibrium amide hydrogen exchange and protein folding kinetics

The classical Linderstrøm-Lang hydrogen exchange (HX) model is extended to describe the relationship between the HX behaviors (EX1 and EX2) and protein folding kinetics for the amide protons that can only exchange by global unfolding in a three-state system including native (N), intermediate (I), and unfolded (U) states. For these slowly exchanging amide protons, it is shown that the existence of an intermediate (I) has no effect on the HX behavior in an off-pathway three-state system (IUN). On the other hand, in an on-pathway three-state system (UIN), the existence of a stable folding intermediate has profound effect on the HX behavior. It is shown that fast refolding from the unfolded state to the stable intermediate state alone does not guarantee EX2 behavior. The rate of refolding from the intermediate state to the native state also plays a crucial role in determining whether EX1 or EX2 behavior should occur. This is mainly due to the fact that only amide protons in the native state are observed in the hydrogen exchange experiment. These new concepts suggest that caution needs to be taken if one tries to derive the kinetic events of protein folding from equilibrium hydrogen exchange experiments.     

Folding of a model three-helix bundle protein: a thermodynamic and kinetic analysis.

The kinetics and thermodynamics of an off-lattice model for a three-helix bundle protein are investigated as a function of a bias gap parameter that determines the energy difference between native and non-native contacts. A simple dihedral potential is used to introduce the tendency to form right-handed helices. For each value of the bias parameter, 100 trajectories of up to one microsecond are performed. Such statistically valid sampling of the kinetics is made possible by the use of the discrete molecular dynamics method with square-well interactions. This permits much faster simulations for off-lattice models than do continuous potentials. It is found that major folding pathways can be defined, although ensembles with considerable structural variation are involved. The large gap models generally fold faster than those with a smaller gap. For the large gap models, the kinetic intermediates are non-obligatory, while both obligatory and non-obligatory intermediates are present for small gap models. Certain large gap intermediates have a two-helix microdomain with one helix extended outward (as in domain-swapped dimers); the small gap intermediates have more diverse structures. The importance of studying the kinetic, as well as the thermodynamics, of folding for an understanding of the mechanism is discussed and the relation between kinetic and equilibrium intermediates is examined. It is found that the behavior of this model system has aspects that encompass both the "new" view and the "old" view of protein folding.     

Anion transport across the red blood cell membrane mediated by dielectric pores

Summary The anion transport across the red blood cell membrane is assumed to occur by ionic diffusion through dielectric pores which are formed by protein molecules spanning the red blood cell membrane. The access of anions to the dielectric pores is regulated by anion adsorption sites positioned at the entrances of the pores. The adsorption of small inorganic anions to the adsorption sites is facilitated by ionizing cationic groups setting up a surface potential at the respective membrane surfaces. Applying the transition state theory of rate processes, flux equations for the unidirectional flux were derived expressing the unidirectional flux as a function of the fractional occupancies of anion adsorption sites at both membrane surfaces.The basic properties of the transport model were investigated. The concentration-dependence and the pH-dependence of the unidirectional fluxes were shown to depend upon the surface charge density and upon the affinity of the transported anion species to the anion binding sites. The concentration-response and the pH-response of the unidirectional fluxes of different anion species may differ substantially even if the anion species are transported by the same anion transport system. The model predicts a characteristic behavior of the Lineweaver-Burk plot and of the Dixon plot.A comparison between computer simulated and experimentally determined flux curves was made. By choosing a suitable set of parameters, the anion transport model is capable of simulating the concentration-dependencies and the pH-dependencies of the unidirectional sulfate and chloride flux. It is sufficient to change one single constant in order to convert the sulfate transport system into a chloride transport system. Furthermore, the model is capable of predicting the inhibitory action of chloride on the sulfate transport system. No attempts were made to fit the experimental data to the model. The behavior of the model was qualitatively in accordance with the experimental results.     

A dynamical neural network model for motor cortical activity during movement: population coding of movement trajectories

As a dynamical model for motor cortical activity during hand movement we consider an artificial neural network that consists of extensively interconnected neuron-like units and performs the neuronal population vector operations. Local geometrical parameters of a desired curve are introduced into the network as an external input. The output of the model is a time-dependent direction and length of the neuronal population vector which is calculated as a sum of the activity of directionally tuned neurons in the ensemble. The main feature of the model is that dynamical behavior of the neuronal population vector is the result of connections between directionally tuned neurons rather than being imposed externally. The dynamics is governed by a system of coupled nonlinear differential equations. Connections between neurons are assigned in the simplest and most common way so as to fulfill basic requirements stemming from experimental findings concerning the directional tuning of individual neurons and the stabilization of the neuronal population vector, as well as from previous theoretical studies. The dynamical behavior of the model reveals a close similarity with the experimentally observed dynamics of the neuronal population vector. Specifically, in the framework of the model it is possible to describe a geometrical curve in terms of the time series of the population vector. A correlation between the dynamical behavior of the direction and the length of the population vector entails a dependence of the neural velocity on the curvature of the tracing trajectory that corresponds well to the experimentally measured covariation between tangential velocity and curvature in drawing tasks.On leave of absencefrom the Institute of Molecular Genetics, Russian Academy of Sciences, Moscow, Russia.     

“Live” neuron and optimal learning rule

A concept of the live unit as an automatic regulation system with a few admissible states areas in the space of states is considered. Energetic profit of oscillatory behavior consisting in the consecutive transitions of system from one admissible states area to another is shown. It is stated, that external disturbances cause the energy consumption of oscillatory system to decrease. On the basis of this concept and some neurophysiological data, the live energy-consuming nonlinear three-state neuron model is proposed and the existence of energy optimal generation frequency v _opt is proved. For the realization of tendency to v _opt the optimal learning rule is proposed, which provides unsupervised learning and interlinked short-term and long-term memories with forgetting. The model proposed explains the genesis of neural network, is promising in the sense of network self-organization and allows to solve the problem of internal activity in the researches on artificial intelligence.     

Modulation of the B-A transition of DNA by potential antitumor antibiotics. Influence of the base composition of DNA

The B-A transition of DNA in oriented films of DNA-drug complexes is more or less restricted as a consequence of drug binding as revealed by infrared linear dichroism. A fraction of DNA is irreversibly locked into the B form. This behavior is described by the number of DNA base pairs "frozen" in the B form by one drug molecule. This quantity is dependent on the DNA sequence the drug is attached to. In this paper, drug complexes of oriented films of NaDNA with a GC content of 42% from calf thymus and a GC-rich DNA from Micrococcus lysodeikticus were compared. The restriction of the B-A transition of DNA complexes with two intercalating antibiotics, aclacinomycin A and violamycin BI, is not severely influenced by the base composition of DNA. By contrast, the strong groove binding oligopeptide antibiotics netropsin and distamycin A are much less effective to restrict the B-A transition of GC-rich DNA than of AT-rich DNA. This finding is in agreement with previous results by other methods which support a model based upon a strong preference of AT clusters by these two non-intercalating drugs.     

Adsorptive control of water in esterification with immobilized enzymes. Continuous operation in a periodic counter-current reactor

A periodic counter-current adsorptive-reactor system is developed to carry out continuous esterifications in organic solvents with immobilized enzymes. The system comprises a number of fixed-beds distributed between a reaction-adsorption zone and a regeneration zone and operated in a "merry-go-round" sequence. Water formed in the reaction is adsorbed preventing the formation of a free-water phase and deactivation of the biocatalyst. The adsorbed water is, in turn, recovered by desorption in the regeneration zone. The concept is tested experimentally on a laboratory-scale using, as a model, the esterification of isoamyl alcohol and propionic acid in hexane catalyzed by an immobilized lipase. Pure isoamyl alcohol is used as a regenerant to remove excess water from the biocatalyst. In the periodic steady-state, improvements in ester productivity greater than 50% over that achievable with a conventional fixed-bed reactor are demonstrated experimentally with just two beds in a series arrangement. Use of a water-selective adsorbent in conjunction with the biocatalyst provides further improvements by reducing accumulation of water on the enzyme. A mathematical model is also developed to predict the thermodynamic activity of water along the reactor and describe the dynamic behavior of the system. The model, based on independently developed rate and equilibrium parameters, successfully predicts the experimental behavior and provides an effective tool for scale-up and optimization.     

Analysis of membrane fusion as a two-state sequential process: evaluation of the stalk model

We propose a model that accounts for the time courses of PEG-induced fusion of membrane vesicles of varying lipid compositions and sizes. The model assumes that fusion proceeds from an initial, aggregated vesicle state ((A) membrane contact) through two sequential intermediate states (I(1) and I(2)) and then on to a fusion pore state (FP). Using this model, we interpreted data on the fusion of seven different vesicle systems. We found that the initial aggregated state involved no lipid or content mixing but did produce leakage. The final state (FP) was not leaky. Lipid mixing normally dominated the first intermediate state (I(1)), but content mixing signal was also observed in this state for most systems. The second intermediate state (I(2)) exhibited both lipid and content mixing signals and leakage, and was sometimes the only leaky state. In some systems, the first and second intermediates were indistinguishable and converted directly to the FP state. Having also tested a parallel, two-intermediate model subject to different assumptions about the nature of the intermediates, we conclude that a sequential, two-intermediate model is the simplest model sufficient to describe PEG-mediated fusion in all vesicle systems studied. We conclude as well that a fusion intermediate "state" should not be thought of as a fixed structure (e.g., "stalk" or "transmembrane contact") of uniform properties. Rather, a fusion "state" describes an ensemble of similar structures that can have different mechanical properties. Thus, a "state" can have varying probabilities of having a given functional property such as content mixing, lipid mixing, or leakage. Our data show that the content mixing signal may occur through two processes, one correlated and one not correlated with leakage. Finally, we consider the implications of our results in terms of the "modified stalk" hypothesis for the mechanism of lipid pore formation. We conclude that our results not only support this hypothesis but also provide a means of analyzing fusion time courses so as to test it and gauge the mechanism of action of fusion proteins in the context of the lipidic hypothesis of fusion.     

Two open states or two different Na channels in skeletal muscle fibers: Markov models of the decay of Na currents in frog skeletal muscle

The rate of sodium current decay at –140 mV was studied as a function of the duration and amplitude of the activating voltage pulse. These sodium current decays or tails of current showed a biexponential decline in amplitude which depended upon the duration of the activating pulse. At 12°C, the two exponential components of the Na tail currents exhibited time constants of 72 and 534 s. As the duration of an activating pulse was lengthened, the relative amplitude of the slow component of the decay increased compared to the fast component, without any changes in the fast and slow time constants. This slowing of the decay of current as a function of the duration of the activating pulse is found only in fibers with inactivation intact.A number of Markov models were tested for their ability to predict the biexponential decays found in muscle fibers with inactivation intact and removed. A homogeneous population of channels having only a single open state fails to predict the behavior. A homogeneous population of channels having two open states predicts the behavior. The behavior can also be predicted by two different types of single open-state sodium channels, with one ensemble of channels carrying a minority of the current and exhibiting a much slower closing rate. If a homogeneous population of channels is present, the simulations show that the observed changes in decay rates are driven by inactivation.     

Dynamic properties of polyelectrolyte calcium membranes

Summary Shashoua observed spontaneous oscillations in a polyelectrolyte membrane formed by interfacial precipitates of polyacid and polybase. We have here undertaken experimental and theoretical studies of polyglutamic acid-Ca⁺⁺ membrane in order to clarify the processes involved in this dynamic behavior. We find a region of distinct hysteresis in the voltage current curve for this system. A sharp transition from a state of low membrane resistance to one of high resistance occurs at a current density different from that of inverse transition.This membrane system is modeled as a two layer structure: a negatively charged layer made of ionized polyelectrolyte in series with a neutral region in which the polymeric ionic sites are masked by calcium ion. This structure results in a difference in the transference number for the mobile ions, causing salt accumulation at the interfacial region during a current flow in the to direction. This altered salt concentration induces a change of polymeric conformation, which in turn affects the membrane permeability and the rate of accumulation. Based upon nonequilibrium thermodynamic flow equations, and a two-state representation of membrane macromolecular conformation, this model displays a region of hysteresis in the current range of experimental observations.