A systems model for the pupil size effect

The human pupillary control system is a paradigm for linearized biological control systems. It also exhibits a series of interesting nonlinear behaviors, particularly asymmetry, “pupillary escape”, and “pupillary capture.” We present a nonlinear model in which a signal dependent upon pupil size is fed back internally to cause a change in system parameters related to gains and rates of light adaptation. The model was simulated on a digital computer, a variety of experimental data was well matched, and improvements over previous pupil models demonstrated. A candidate physiological mechanism for adaptive components of the model might have the form of an inverse “Henneman coded” neuronal pool.     

Visual motion,binocular correspondence and binocular rivalry

The human pupillary control system has been the subject of interest to biologists and engineers as an example of a sensorimotor reflex which can be embedded in a control system paradigm. We present a nonlinear feedback model whose compact structure allows us to hypothesize possible physiological mechanisms which generate the proper behavior of the pupil system. The important pupil responses, including pupil size effect, asymmetry, and response to high-frequency stimuli, are defined. This model was simulated on a digital computer and comparisons to the paradigm experimental responses were performed, demonstrating a fit to each of the observed conditions. Improvements on previous models are discussed.     

Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes

A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the “inputs” and “outputs”, respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The “scaling-up” issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models.     

The possible role of “sibling neurite bias” in the coordination of neurite extension,branching, and survival

In this review we consider a novel mechanism, “sibling neurite bias,” which may explain aspects of the coordination of elongation, branching, and resorption among different neurites growing from the same neuronal cell body. In this model, growing neurites which incorporate structural precursors at higher rates would deplete the cellular pool of precursors available to their “sibling” neurites; neurites would compete for survival, but in addition they would bias each other's behavior during active growth. Evidence is reviewed that “sibling neurite bias” may contribute to the establishment and stabilization of specific neural connections. Specific examples examined include the loss of polyinnervation at the developing neuromuscular junction, contextual mapping in the retino-tectal system, and selective neurite growth patterns and synaptic connections in nerve tissue culture model systems.     

Complete parameter bounds and quasiidentifiability conditions for a class of unidentifiable linear systems

Lack of unique structural identifiability for parameters of dynamic system models is a very common situation with practical experimental schemes, particularly when studying biological systems. However, for well-structured (e.g., multicompartmental) models, it is often possible to localize unidentifiable parameters between finite limits (“interval identifiability”), using the same data base, and under certain conditions these limits nearly coincide. Two new results in this area are presented: (1) The smallest ranges on all unidentifiable rate constants and pool sizes of the most general n-compartment mammillary system are derived, in an easy-to-program algorithmic form, for the common case of input forcing and output measurements in the central pool only. From these results we see why elimination rate constants (“leaks”) are difficult to distinguish from zero, whereas exchange rate constants between pools, and pool sizes, may be bounded very tightly in certain circumstances. (2) The notion of quasiidentifiability, or sufficient identifiability for practical purposes, is introduced to quantify these circumstances. Each of the rate constants between central and peripheral pools, and all pool sizes, are quasiidentifiable if the magnitude of the ratio of the coefficient to the eigenvalue of the slowest mode is very much greater than the largest coefficient in the sum-of-exponentials response function. Also quasiidentifiability is a necessary condition for applicability of noncompartmental analysis to estimate pool sizes and residence times of mammillary systems with “leaky” noncentral pools.     

Modeling convergent ON and OFF pathways in the early visual system

For understanding the computation and function of single neurons in sensory systems, one needs to investigate how sensory stimuli are related to a neuron’s response and which biological mechanisms underlie this relationship. Mathematical models of the stimulus–response relationship have proved very useful in approaching these issues in a systematic, quantitative way. A starting point for many such analyses has been provided by phenomenological “linear–nonlinear” (LN) models, which comprise a linear filter followed by a static nonlinear transformation. The linear filter is often associated with the neuron’s receptive field. However, the structure of the receptive field is generally a result of inputs from many presynaptic neurons, which may form parallel signal processing pathways. In the retina, for example, certain ganglion cells receive excitatory inputs from ON-type as well as OFF-type bipolar cells. Recent experiments have shown that the convergence of these pathways leads to intriguing response characteristics that cannot be captured by a single linear filter. One approach to adjust the LN model to the biological circuit structure is to use multiple parallel filters that capture ON and OFF bipolar inputs. Here, we review these new developments in modeling neuronal responses in the early visual system and provide details about one particular technique for obtaining the required sets of parallel filters from experimental data.     

瞳孔光反应系统的空间分布式神经网络模型

为模拟刺激光空间分布变化引起瞳孔反应的实验现象,本文建立了空间分布式神经网络瞳孔模型。它是在瞳孔双通道模型基础上,借鉴Ｃａｎｎｏｎ－Ｒｏｂｉｎｓｏｎ的Ｏｃｕｌｏｍｏｔｏｒ模型的双层网络结构和视网膜的镶嵌式特点,经空间延括而成。空间各部位信号经第一层神经元处理得到对应各部位的线性ＤＣ和非线性ＡＣ输出,在第二层神经元进行空间综合,再经第三层神经元复合去控制效应器官虹膜肌的反应。该分布式部位机制模型能解释多种瞳孔实验现象。     

Level dependent signal flow in the light pupil reflex

Latency of pupillary responses to light stimuli are smaller for larger steps of light, and larger for smaller steps of light (Alpern 1954; Lowenstein et al. 1964; Lee et al. 1969; Terdiman et al. 1969; Cibis et al. 1977; and many others). Miller and Thompson (1978), however, reported negligible change in pupil cycle time (period of high gain instability oscillations) with increased mean brightness. Sandberg and Stark (1968) reportd a negligible reduction in phase lag of pupillary responses to sinusoidal light stimuli as the modulation coefficient (m) increased. To resolve the inconsistency between the well-documented dependence of latency upon brightness, and the apparent absence of level dependence in the phase characteristics (as reflected directly in the responses to sinusoidal stimuli and indirectly in pupil cycle time experiments) we measured: 1. Latency to step stimuli of light, 2. Phase of responses to sinusoidal light stimuli and 3. Period (pupil cycle time) of high gain instability oscillations. The dependence of pupillary latency upon stimulus level (both light and accommodation) and the interaction between accommodation and light responses were investigated. We show that most of the level dependence of light-pupil latency resides in the afferent path. In the companion papers, we demonstrate that: 1. Phase of pupillary response to sinusoidal light stimuli is reduced by increased mean light level, but is independent of pupil size and accommodative stimulus level; and 2. The period of high gain oscillations is shown to decrease with increased mean light level. Taken together, these results imply the existence of a Level Dependent Signal Flow (LDSF) operator that resides in the light-pupil pathway, but not in the accommodation-pupil pathway. We propose a systems model of this operator in which the neural signals controlling pupil size are treated as waves whose phase velocity increases in response to brighter stimuli, and decreases in response to dimmer stimuli. When parameters of the model are adjusted to fit measured pupillary latency over a range of light levels, the model exhibits reduced phase lag in response to increased mean light level in the sinusoidal paradigm, and it exhibits reduced pupil cycle time in the high-gain oscillation paradigm. The model exhibits saturation of the LDSF effect in all paradigms at high light levels, as do experimental results. It simulates directional asymmetry of pupillary response to positive and negative steps of light, with constriction more rapid than dilatation. Finally, it simulates tonic pupillary constriction in response to modulation of a light simulus without changing average light level (Varju 1964; Troelstra 1968). All of these stimulated results are in accord with experimental observation.     

Identification of nonlinear models of biological membranes using the voltage-clamp method

The method for identification of nonlinear systems proposed in 1952 by Hodgkin and Huxley is mathematically justified. A procedure for the application of this method is developed, including the development of the structure of a mathematical model, carrying out a series of tests with special chosen signals, and determination of unknown parameters. Basic requirements for the admissible sets of input and output signals and to the system operator have been determined. It is shown that this operator should be totally continuous and that the minimum number of unknown parameters and the minimum complexity of the operator structure should give an approximation of the necessary quality. The pros and cons of the Hodgkin-Huxley and Noble mathematical models and the methods used for their development are discussed. A structure for the operator for the identification of mathematical models of excitable membranes with a large number of membrane currents is proposed. It is found that the nonlinear electrical properties of biological membranes can be identified using tests with other types of “clamped” parameters, such as the current, ramp voltage, etc.     

A linear chromatic mechanism drives the pupillary response.

Previous studies have shown that a chromatic mechanism can drive pupil responses. The aim of this research was to clarify whether a linear or nonlinear chromatic mechanism drives pupillary responses by using test stimuli of various colours that are defined in cone contrast space. The pupil and accommodation responses evoked by these test stimuli were continuously and simultaneously objectively measured by photorefraction. The results with isochromatic and isoluminant stimuli showed that the accommodative level remained approximately constant (< 0.25 D change in mean level) even when the concurrent pupillary response was large (ca. 0.30 mm). The pupillary response to an isoluminant grating was sustained, delayed (by ca. 60 ms) and larger in amplitude than that for a isochromatic uniform stimulus, which supports previous work suggesting that the chromatic mechanism contributes to the pupillary response. In a second experiment, selected chromatic test gratings were used and isoresponse contours in cone contrast space were obtained. The results showed that the isoresponse contour in cone contrast space is well described (r(2) = 0.99) by a straight line with a positive slope. The results indicate that a /L - M/ linear chromatic mechanism, whereby a signal from the long wavelength cone is subtracted from that of the middle wavelength cone and vice versa, drives pupillary responses.     

Critical analysis of methods for analysing human calcium kinetics

A comparison has been made between several different compartmental and non-compartmental methods for analyzing human calcium kinetics. Using data from studies in six normal subjects, plus a computer-generated set of “error-free” data, the bone accretion rate and the exchangeable calcium pool size have been calculated by each method, along with their corresponding uncertainties. The effects of selective deletions of data have also been determined for the various methods.The results are highly dependent upon the model employed and the parameter investigated. In general, the non-compartmental models provide accretion rates which are less sensitive to measurement errors, and have less stringent requirements as to the necessary duration of an experimental study. Among compartmental models, a three-compartment model based on data collected from two hours to twenty days after isotopic calcium injection gives estimates of skeletal accretion rate and exchangeable pool size very similar to those resulting from a four-compartment model that includes additional earlier data.The relative advantages of various compartmental and non-compartmental methods of analysis are discussed in relation to these results, and practical recommendations offered to the clinical investigator.     

Pupil Dilation Co-Varies with Memory Strength of Individual Traces in a Delayed Response Paired-Associate Task

Studies on cognitive effort have shown that pupil dilation is a reliable indicator of memory load. However, it is conceivable that there are other sources of effort involved in memory that also affect pupil dilation. One of these is the ease with which an item can be retrieved from memory. Here, we present the results of an experiment in which we studied the way in which pupil dilation acts as an online marker for memory processing during the retrieval of paired associates while reducing confounds associated with motor responses. Paired associates were categorized into sets containing either 4 or 7 items. After learning the paired associates once, pupil dilation was measured during the presentation of the retrieval cue during four repetitions of each set. Memory strength was operationalized as the number of repetitions (frequency) and set-size, since having more items per set results in a lower average recency. Dilation decreased with increased memory strength, supporting the hypothesis that the amplitude of the evoked pupillary response correlates positively with retrieval effort. Thus, while many studies have shown that “memory load” influences pupil dilation, our results indicate that the task-evoked pupillary response is also sensitive to the experimentally manipulated memory strength of individual items. As these effects were observed well before the response had been given, this study also suggests that pupil dilation can be used to assess an item’s memory strength without requiring an overt response.     

The anthropological genetics of the Black Caribs “Garifuna” of Central America and the Caribbean

The Black Caribs “Garifuna” originated on St. Vincent Island, in the West Indies, as a cultural and biological amalgam between Amerindians “Arawak and Island Caribs” and West Africans. A total of 2,026 of the Black Caribs were deported by the British in 1797 to the Bay Islands, from which they further emigrated to Honduras, Central America. The Garifuna provide an example of evolutionary success by a colonizing population with one of the highest observed fertility levels “a mean of 10.9 children per woman 45 years of age or older” in the world. The Central American Black Carib population has increased from fewer than 2,000 persons in 1800 to approximately 70,000 at present. It has been estimated that an additional 20,000 Black Caribs have immigrated to England, the United States, and other parts of the world. This review focuses upon the observed genetic variation and population structure of the Black Caribs. The population structure is characterized by a series of fissions and fusions of the gene pool. Fusion and genetic hybridization play a major role in the early development of this society. Subdivision of the hybrid gene pool occurs as the Black Caribs colonize the coast of Central America, rapidly expanding their domain to an area over 1,000 kilometers of the coast. Blood genetic analyses reveal that the St. Vincent Black Caribs' gene pool contains the highest proportion of Amerindian genes “approximately 50%”, while the coastal communities exhibit a more African ancestry “up to 80%”. This apparent discrepancy can be explained in one of three ways: “1” the original Black Caribs of St. Vincent had a higher proportion of Amerindian genes. However, gene flow and incorporation of African populations residing along the coast into the Black Carib gene pool resulted in more African coastal groups; “2” those Black Caribs displaying African phenotypes were selectively deported; “3” that natural selection, in a malarial environment, operated in favor of those individuals with the more African phenotypes and resistance to Plasmodium falciparum.     

Relating Pupil Dilation and Metacognitive Confidence during Auditory Decision-Making

The sources of evidence contributing to metacognitive assessments of confidence in decision-making remain unclear. Previous research has shown that pupil dilation is related to the signaling of uncertainty in a variety of decision tasks. Here we ask whether pupil dilation is also related to metacognitive estimates of confidence. Specifically, we measure the relationship between pupil dilation and confidence during an auditory decision task using a general linear model approach to take into account delays in the pupillary response. We found that pupil dilation responses track the inverse of confidence before but not after a decision is made, even when controlling for stimulus difficulty. In support of an additional post-decisional contribution to the accuracy of confidence judgments, we found that participants with better metacognitive ability – that is, more accurate appraisal of their own decisions – showed a tighter relationship between post-decisional pupil dilation and confidence. Together our findings show that a physiological index of uncertainty, pupil dilation, predicts both confidence and metacognitive accuracy for auditory decisions.     

Postgenomic futures: translations across the machine-nature border in systems biology

Abstract

This article discusses the production of new “postgenomic” knowledges that aim to be more ecological and “wholistic” than the reductionist genetics of the last forty years. It examines systems biology and, briefly, developmental systems theory, which are two approaches that attempt to model complexities in biology. System biological metaphors and languages have been in part taken from engineering models of automobiles, airplanes and robots and then applied to complex living systems. Systems biology is only the most recent example and perhaps an excellent case in which to study this movement back and forth across the machine-living organism border in Euro-American biology to track how what we know to be nature and machine is constituted. This article argues for a careful analysis of this historical production specifically around the question of what is lost in translation at these border crossings and their potential consequences.     

When will evolution lead to deceptive signaling in the Sir Philip Sidney game?

Sir Philip Sidney games are a widely used model of simple signaling. Johnstone and Grafen [Johnstone, R.A., Grafen, A., 1993. Dishonesty and the handicap principle. Animal Behaviour 46, 759–764] present a version in which the Evolutionarily Stable Strategy (ESS) is for most signalers to “honestly” signal, with a small minority of signalers who “cheat”. This model is among the most frequently cited papers on the topic of “dishonest” signaling and supports the view that signals may be “dishonest” as long as they are “honest on average”. Using genetic algorithms, we demonstrate that another solution exists to the game, an evolutionarily stable set of Nash equilibria in which members of the set never signal and all donors give their resource. Payoffs to players using this set of strategies is greater those when playing the “dishonest” signaling ESS. We demonstrate that a random population is far more likely to evolve to this non-communicating strategy set than the “dishonest” signaling ESS. We also discuss the dynamics of biological game theory models and the advances of genetic algorithms as a heuristic solution method for these models.     

A general-purpose electronic model for arbitrary configurations of neurons

This paper describes a general-purpose electronic model for simulating the electrical activity in small groups of nerve cells arranged in arbitrary configurations. The model consists of 44 realizations of two basic modules (the “cell”, and the “axon with synapses”) which can be connected together in various arrangements by way of snapper-capped wires. The activity of the individual units is displayed via flashing lights atop the constituent cells; also there are taps on each cell from which one can obtain and display more detailed information concerning the electrical activity of each and all cells, including the graded “generator” potential of the triggering section, on for example an oscilloscope. The modules include realistic approximations to basic mechanisms of neuronal activity, but the main advance over previous models is the emphasis on and ability to deal with the network context of neuroelectric signals.Illustrative applications to mutually-inhibiting centers and to our ladder net theory for reticular-like networks are presented. The primary advantages of the electronic model are: actual physical representation of various configurations, asynchronous timing, flexibility with respect to overall configuration and with respect to network parameters, immediate turnaround, and cost.     

Predictive landscapes hidden beneath biological cellular automata

To celebrate Hans Frauenfelder’s achievements, we examine energy(-like) “landscapes” for complex living systems. Energy landscapes summarize all possible dynamics of some physical systems. Energy(-like) landscapes can explain some biomolecular processes, including gene expression and, as Frauenfelder showed, protein folding. But energy-like landscapes and existing frameworks like statistical mechanics seem impractical for describing many living systems. Difficulties stem from living systems being high dimensional, nonlinear, and governed by many, tightly coupled constituents that are noisy. The predominant modeling approach is devising differential equations that are tailored to each living system. This ad hoc approach faces the notorious “parameter problem”: models have numerous nonlinear, mathematical functions with unknown parameter values, even for describing just a few intracellular processes. One cannot measure many intracellular parameters or can only measure them as snapshots in time. Another modeling approach uses cellular automata to represent living systems as discrete dynamical systems with binary variables. Quantitative (Hamiltonian-based) rules can dictate cellular automata (e.g., Cellular Potts Model). But numerous biological features, in current practice, are qualitatively described rather than quantitatively (e.g., gene is (highly) expressed or not (highly) expressed). Cellular automata governed by verbal rules are useful representations for living systems and can mitigate the parameter problem. However, they can yield complex dynamics that are difficult to understand because the automata-governing rules are not quantitative and much of the existing mathematical tools and theorems apply to continuous but not discrete dynamical systems. Recent studies found ways to overcome this challenge. These studies either discovered or suggest an existence of predictive “landscapes” whose shapes are described by Lyapunov functions and yield “equations of motion” for a “pseudo-particle.” The pseudo-particle represents the entire cellular lattice and moves on the landscape, thereby giving a low-dimensional representation of the cellular automata dynamics. We outline this promising modeling strategy.

     

Ecological Stability: Reality,Misconceptions, and Implications for Risk Assessment

Over a long time frame, an ecological system may not exhibit constancy due to successional and evolutionary changes in the species composing the system. However, over shorter time frames an ecological system exhibits a certain degree of constancy (i.e., varies within defined bounds). Traditionally, ecologists considered this short-term constancy to reflect a “balance of nature,” which was viewed akin to the simple homeostatic dynamics of physiological systems. This is an appealing perspective because the disruption of the system's “balance” (i.e., its ”health“) can be ascertained by comparing the system's current state after the imposition of a perturbation with the societally desired state (i.e., baseline). Recently, ecologists have started to develop a much more complex, and perhaps more realistic, perspective regarding ecosystem dynamics, which does not depend upon homeostasis with a single baseline state. This new view includes stochastic variation, nonlinear dynamics and alternative states, and poses a challenge for assessing environmental “health” and the risk of creating “unhealthy” ecological systems