Spatiotemporal frequency responses of cat retinal ganglion cells

Spatiotemporal frequency responses were measured at different levels of light adaptation for cat X and Y retinal ganglion cells. Stationary sinusoidal luminance gratings whose contrast was modulated sinusoidally in time or drifting gratings were used as stimuli. Under photopic illumination, when the spatial frequency was held constant at or above its optimum value, an X cell's responsivity was essentially constant as the temporal frequency was changed from 1.5 to 30 Hz. At lower temporal frequencies, responsivity rolled off gradually, and at higher ones it rolled off rapidly. In contrast, when the spatial frequency was held constant at a low value, an X cell's responsivity increased continuously with temporal frequency from a very low value at 0.1 Hz to substantial values at temporal frequencies higher than 30 Hz, from which responsivity rolled off again. Thus, 0 cycles X deg-1 became the optimal spatial frequency above 30 Hz. For Y cells under photopic illumination, the spatiotemporal interaction was even more complex. When the spatial frequency was held constant at or above its optimal value, the temporal frequency range over which responsivity was constant was shorter than that of X cells. At lower spatial frequencies, this range was not appreciably different. As for X cells, 0 cycles X deg-1 was the optimal spatial frequency above 30 Hz. Temporal resolution (defined as the high temporal frequency at which responsivity had fallen to 10 impulses X s-1) for a uniform field was approximately 95 Hz for X cells and approximately 120 Hz for Y cells under photopic illumination. Temporal resolution was lower at lower adaptation levels. The results were interpreted in terms of a Gaussian center-surround model. For X cells, the surround and center strengths were nearly equal at low and moderate temporal frequencies, but the surround strength exceeded the center strength above 30 Hz. Thus, the response to a spatially uniform stimulus at high temporal frequencies was dominated by the surround. In addition, at temporal frequencies above 30 Hz, the center radius increased.     

Density of founder cells affects spatial pattern formation and cooperation in Bacillus subtilis biofilms

In nature, most bacteria live in surface-attached sedentary communities known as biofilms. Biofilms are often studied with respect to bacterial interactions. Many cells inhabiting biofilms are assumed to express ‘cooperative traits'', like the secretion of extracellular polysaccharides (EPS). These traits can enhance biofilm-related properties, such as stress resilience or colony expansion, while being costly to the cells that express them. In well-mixed populations cooperation is difficult to achieve, because non-cooperative individuals can reap the benefits of cooperation without having to pay the costs. The physical process of biofilm growth can, however, result in the spatial segregation of cooperative from non-cooperative individuals. This segregation can prevent non-cooperative cells from exploiting cooperative neighbors. Here we examine the interaction between spatial pattern formation and cooperation in Bacillus subtilis biofilms. We show, experimentally and by mathematical modeling, that the density of cells at the onset of biofilm growth affects pattern formation during biofilm growth. At low initial cell densities, co-cultured strains strongly segregate in space, whereas spatial segregation does not occur at high initial cell densities. As a consequence, EPS-producing cells have a competitive advantage over non-cooperative mutants when biofilms are initiated at a low density of founder cells, whereas EPS-deficient cells have an advantage at high cell densities. These results underline the importance of spatial pattern formation for competition among bacterial strains and the evolution of microbial cooperation.     

Emergence of Spatial Structure in Cell Groups and the Evolution of Cooperation

On its own, a single cell cannot exert more than a microscopic influence on its immediate surroundings. However, via strength in numbers and the expression of cooperative phenotypes, such cells can enormously impact their environments. Simple cooperative phenotypes appear to abound in the microbial world, but explaining their evolution is challenging because they are often subject to exploitation by rapidly growing, non-cooperative cell lines. Population spatial structure may be critical for this problem because it influences the extent of interaction between cooperative and non-cooperative individuals. It is difficult for cooperative cells to succeed in competition if they become mixed with non-cooperative cells, which can exploit the public good without themselves paying a cost. However, if cooperative cells are segregated in space and preferentially interact with each other, they may prevail. Here we use a multi-agent computational model to study the origin of spatial structure within growing cell groups. Our simulations reveal that the spatial distribution of genetic lineages within these groups is linked to a small number of physical and biological parameters, including cell growth rate, nutrient availability, and nutrient diffusivity. Realistic changes in these parameters qualitatively alter the emergent structure of cell groups, and thereby determine whether cells with cooperative phenotypes can locally and globally outcompete exploitative cells. We argue that cooperative and exploitative cell lineages will spontaneously segregate in space under a wide range of conditions and, therefore, that cellular cooperation may evolve more readily than naively expected.     

Visual sensitivity of ground squirrels to spatial and temporal luminance variations

Summary We have investigated the visual sensitivity of the California ground squirrel (Speromphilus beecheyi) to spatial and temporal luminance patterns. Spatial contrast sensitivity functions were determined in behavioral discrimination experiments in which the stimuli were sinusoidally-modulated luminance gratings. These squirrels were found to be maximally sensitive to spatial frequencies of about 0.7 cycles/ degree (c/d), and they are unable to discriminate gratings whose frequencies exceed 4 c/d. Similar results were obtained in electrophysiological experiments when the visually evoked cortical potential (VECP) was recorded from anesthetized squirrels. A third experiment involved tests of the ability of ground squirrels to discriminate square-wave gratings of much higher luminance (340 cd/m²). The finest gratings which were discriminable at this luminance level did not exceed 3.9–4.3 c/d and, thus, we conclude that the maximal spatial resolution of the California ground squirrel is about 4 c/d (corresponding to a bar separation of 7.5). In another behavioral experiment the abilities of ground squirrels to discriminate sinusoidally flickering lights (mean luminance = 3.4 cd/m²) was measured. The results show that ground squirrels are maximally sensitive to lights flickering at a rate of about 18 Hz, and that the highest rates that are still discriminable are slightly above 60 Hz.Abbreviations c/d cycles/degree - CFF critical flicker frequency - VECP visually evoked cortical potential This research was supported by Grant EY 00105 from the National Eye Institute. We thank David Birch who participated in some preliminary behavioral experiments and Kenneth Long who provided the histological material from which measurements of receptor spacing were made.     

Social setting,intuition and experience in laboratory experiments interact to shape cooperative decision-making

Recent studies suggest that cooperative decision-making in one-shot interactions is a history-dependent dynamic process: promoting intuition versus deliberation typically has a positive effect on cooperation (dynamism) among people living in a cooperative setting and with no previous experience in economic games on cooperation (history dependence). Here, we report on a laboratory experiment exploring how these findings transfer to a non-cooperative setting. We find two major results: (i) promoting intuition versus deliberation has no effect on cooperative behaviour among inexperienced subjects living in a non-cooperative setting; (ii) experienced subjects cooperate more than inexperienced subjects, but only under time pressure. These results suggest that cooperation is a learning process, rather than an instinctive impulse or a self-controlled choice, and that experience operates primarily via the channel of intuition. Our findings shed further light on the cognitive basis of human cooperative decision-making and provide further support for the recently proposed social heuristics hypothesis.     

Visual acuity of the midland banded water snake estimated from evoked telencephalic potentials

The visual acuity of seven midland banded water snakes was measured by recording evoked responses from telencephalon to temporally modulated square wave grating patterns. Using conventional electrophysiological techniques and signal averaging, high contrast square wave gratings of different spatial frequencies were presented. Acuity was estimated by extrapolating relative response amplitude/log₁₀ spatial frequency functions which yielded an average acuity of 4.25 cycles/degree. Refractive state was also estimated by recording evoked potentials to intermediate spatial frequencies with different lenses in front of the eye. Polynomial fits indicated that under the experimental conditions the snakes were around 6.4 diopters hyperopic suggesting a corrected acuity of 4.89 cycles/degree. Reduction of grating luminance resulted in a reduction in evoked potential acuity measurements. These results indicate that the spatial resolution of midland banded water snakes is the equal of cat; about 20/120 in human clinical terms.     

Relation of spatial and temporal frequencies to vernier acuity

Vernier thresholds were measured with a pair of vertical sinusoidal gratings of one and a half cycles as targets. The amplitude was weighted by a one-dimensional Gaussian and contrast was set one log unit above contrast threshold. The vernier thresholds were estimated with the method of constant stimuli. Temporal frequency effects were introduced by movement of the vernier targets. It was found that vernier thresholds expressed in phase angle were unchanged in the effective range of spatial frequencies provided that the temporal frequency and the visibility were unchanged, and that thresholds deteriorated by increasing the temporal frequency. It is suggested that the detection of relative phase may be involved in the discrimination of vernier offsets and that it may be mediated by a sustained unit. Three possible types of mechanisms, edge-localization processes, orientation-selective units and phase-sensitive units, were considered in relation to vernier acuity.     

Dependence of the threshold of sinusoidal grating displacement on its spatial frequency characteristics

The threshold of detection of sinusoidal grating displacement was studied under conditions of the absence of apparent movement. It was shown that the threshold rises with the pattern size and depends on the number of grating cycles at a constant stimulus magnitude. The stimulus size in 2–3 periods is optimal for its localization. The results suggest that objects in the visual field are localized by mechanisms tuned to a certain spatial frequency and selective to a certain image size. The size of the analyzed part of the visual field requires respective frequency tuning of the mechanism.     

A frequency view of colour: measuring the human sensitivity to square-wave spectral power distributions.

We have measured the chromatic threshold sensitivity to stimuli with spectral composition determined by a periodic function of energy over wavelength. This approach is analogous to frequency studies of spatial vision for the study of colour. A device was constructed permitting the synthesis of illuminants over the entire visible range (400-700 nm) in which phase, frequency and amplitude can be independently controlled. We have used 12 frequencies of square-wave functions (from 0.5 to 3.6 cycles/300 nm) and seven values of phase (between 0 degrees and 180 degrees) to obtain the contrast sensitivity function of the chromatic system in three normal trichromats. The results show maximum sensitivity around 1.5 cycles/300 nm and a high-frequency cut-off at 3.6 cycles/300 nm. These empirical values are compared with the predictions obtained from three current psychophysical models of opponent-colour process.     

Evolution of cooperation with shared costs and benefits

The quest to determine how cooperation evolves can be based on evolutionary game theory, in spite of the fact that evolutionarily stable strategies (ESS) for most non-zero-sum games are not cooperative. We analyse the evolution of cooperation for a family of evolutionary games involving shared costs and benefits with a continuum of strategies from non-cooperation to total cooperation. This cost-benefit game allows the cooperator to share in the benefit of a cooperative act, and the recipient to be burdened with a share of the cooperator's cost. The cost-benefit game encompasses the Prisoner's Dilemma, Snowdrift game and Partial Altruism. The models produce ESS solutions of total cooperation, partial cooperation, non-cooperation and coexistence between cooperation and non-cooperation. Cooperation emerges from an interplay between the nonlinearities in the cost and benefit functions. If benefits increase at a decelerating rate and costs increase at an accelerating rate with the degree of cooperation, then the ESS has an intermediate level of cooperation. The game also exhibits non-ESS points such as unstable minima, convergent-stable minima and unstable maxima. The emergence of cooperative behaviour in this game represents enlightened self-interest, whereas non-cooperative solutions illustrate the Tragedy of the Commons. Games having either a stable maximum or a stable minimum have the property that small changes in the incentive structure (model parameter values) or culture (starting frequencies of strategies) result in correspondingly small changes in the degree of cooperation. Conversely, with unstable maxima or unstable minima, small changes in the incentive structure or culture can result in a switch from non-cooperation to total cooperation (and vice versa). These solutions identify when human or animal societies have the potential for cooperation and whether cooperation is robust or fragile.     

A quantitative test of population genetics using spatiogenetic patterns in bacterial colonies

It is widely accepted that population-genetics theory is the cornerstone of evolutionary analyses. Empirical tests of the theory, however, are challenging because of the complex relationships between space, dispersal, and evolution. Critically, we lack quantitative validation of the spatial models of population genetics. Here we combine analytics, on- and off-lattice simulations, and experiments with bacteria to perform quantitative tests of the theory. We study two bacterial species, the gut microbe Escherichia coli and the opportunistic pathogen Pseudomonas aeruginosa, and show that spatiogenetic patterns in colony biofilms of both species are accurately described by an extension of the one-dimensional stepping-stone model. We use one empirical measure, genetic diversity at the colony periphery, to parameterize our models and show that we can then accurately predict another key variable: the degree of short-range cell migration along an edge. Moreover, the model allows us to estimate other key parameters, including effective population size (density) at the expansion frontier. While our experimental system is a simplification of natural microbial community, we argue that it constitutes proof of principle that the spatial models of population genetics can quantitatively capture organismal evolution.     

Kinesin-1 (uKHC/KIF5B) is required for bidirectional motility of ER exit sites and efficient ER-to-Golgi transport

Transport of proteins and lipids between intracellular compartments is fundamental to the organization and function of eukaryotic cells. The efficiency of this process is greatly enhanced through coupling of membranes to microtubules. This serves two functions, organelle positioning and vesicular transport. In this study, we show that in addition to the well-known role for the minus-end motor dynein in endoplasmic reticulum (ER)-to-Golgi transport, the plus-end-directed motor kinesin-1 is involved in positioning coat protein II-coated ER exit sites (ERES) in cells as well as the formation of transport carriers and their movement to the Golgi. Using two-dimensional Gaussian fitting to determine their location at high spatial resolution, we show that ERES undergo short-range bidirectional movements. Bidirectionality depends on both kinesin-1 and dynein. Suppression of kinesin-1 (KIF5B) also inhibits ER-to-Golgi transport and affects the morphology of ER-to-Golgi transport carriers. Furthermore, we show that suppression of dynein heavy chain expression increases the range of movement of ERES, suggesting that dynein might anchor ERES, or the ER itself, to microtubules. These data implicate kinesin-1 in the spatial organization of the ER/Golgi interface as well as in traffic outside the ER.     

Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.     

Spatial segregation and cooperation in radially expanding microbial colonies under antibiotic stress

Antibiotic resistance in microbial communities reflects a combination of processes operating at different scales. In this work, we investigate the spatiotemporal dynamics of bacterial colonies comprised of drug-resistant and drug-sensitive cells undergoing range expansion under antibiotic stress. Using the opportunistic pathogen Enterococcus faecalis with plasmid-encoded β-lactamase, we track colony expansion dynamics and visualize spatial patterns in fluorescently labeled populations exposed to antibiotics. We find that the radial expansion rate of mixed communities is approximately constant over a wide range of drug concentrations and initial population compositions. Imaging of the final populations shows that resistance to ampicillin is cooperative, with sensitive cells surviving in the presence of resistant cells at otherwise lethal concentrations. The populations exhibit a diverse range of spatial segregation patterns that depend on drug concentration and initial conditions. Mathematical models indicate that the observed dynamics are consistent with global cooperation, despite the fact that β-lactamase remains cell-associated. Experiments confirm that resistant colonies provide a protective effect to sensitive cells on length scales multiple times the size of a single colony, and populations seeded with (on average) no more than a single resistant cell can produce mixed communities in the presence of the drug. While biophysical models of drug degradation suggest that individual resistant cells offer only short-range protection to neighboring cells, we show that long-range protection may arise from synergistic effects of multiple resistant cells, providing surprisingly large protection zones even at small population fractions.Subject terms: Microbial ecology, Antibiotics, Population dynamics     

Evolutionary dynamics of the continuous iterated prisoner's dilemma

The iterated prisoner's dilemma (IPD) has been widely used in the biological and social sciences to model dyadic cooperation. While most of this work has focused on the discrete prisoner's dilemma, in which actors choose between cooperation and defection, there has been some analysis of the continuous IPD, in which actors can choose any level of cooperation from zero to one. Here, we analyse a model of the continuous IPD with a limited strategy set, and show that a generous strategy achieves the maximum possible payoff against its own type. While this strategy is stable in a neighborhood of the equilibrium point, the equilibrium point itself is always vulnerable to invasion by uncooperative strategies, and hence subject to eventual destabilization. The presence of noise or errors has no effect on this result. Instead, generosity is favored because of its role in increasing contributions to the most efficient level, rather than in counteracting the corrosiveness of noise. Computer simulation using a single-locus infinite alleles Gaussian mutation model suggest that outcomes ranging from a stable cooperative polymorphism to complete collapse of cooperation are possible depending on the magnitude of the mutational variance. Also, making the cost of helping a convex function of the amount of help provided makes it more difficult for cooperative strategies to invade a non-cooperative equilibrium, and for the cooperative equilibrium to resist destabilization by non-cooperative strategies. Finally, we demonstrate that a much greater degree of assortment is required to destabilize a non-cooperative equilibrium in the continuous IPD than in the discrete IPD. The continuous model outlined here suggests that incremental amounts of cooperation lead to rapid decay of cooperation and thus even a large degree of assortment will not be sufficient to allow cooperation to increase when cooperators are rare. The extreme degree of assortment required to destabilize the non-cooperative equilibrium, as well as the instability of the cooperative equilibrium, may help explain why cooperation in Prisoner's Dilemmas is so rare in nature.     

The binding of synthetic triiodo l-thyronine analogs to human transthyretin: molecular basis of cooperative and non-cooperative ligand recognition

Transthyretin (TTR) is a tetrameric β-sheet-rich transporter protein directly involved in human amyloid diseases. Several classes of small molecules can bind to TTR delaying its amyloid fibril formation, thus being promising drug candidates to treat TTR amyloidoses. In the present study, we characterized the interactions of the synthetic triiodo L-thyronine analogs and thyroid hormone nuclear receptor TRβ-selective agonists GC-1 and GC-24 with the wild type and V30M variant of human transthyretin (TTR). To achieve this aim, we conducted in vitro TTR acid-mediated aggregation and isothermal titration calorimetry experiments and determined the TTR:GC-1 and TTR:GC-24 crystal structures. Our data indicate that both GC-1 and GC-24 bind to TTR in a non-cooperative manner and are good inhibitors of TTR aggregation, with dissociation constants for both hormone binding sites (HBS) in the low micromolar range. Analysis of the crystal structures of TTRwt:GC-1(24) complexes and their comparison with the TTRwt X-ray structure bound to its natural ligand thyroxine (T4) suggests, at the molecular level, the basis for the cooperative process displayed by T4 and the non-cooperative process provoked by both GC-1 and GC-24 during binding to TTR.     

Nucleotide binding to the chaperonin GroEL: non-cooperative binding of ATP analogs and ADP, and cooperative effect of ATP

Chaperonin-assisted protein folding proceeds through cycles of ATP binding and hydrolysis by GroEL, which undergoes a large structural change by the ATP binding or hydrolysis. One of the main concerns of GroEL is the mechanism of the productive and cooperative structural change of GroEL induced by the nucleotide. We studied the cooperative nature of GroEL by nucleotide titration using isothermal titration calorimetry and fluorescence spectroscopy. Our results indicated that the binding of ADP and ATP analogs to a single ring mutant (SR1), as well as that to GroEL, was non-cooperative. Only ATP induces an apparently cooperative conformational change in both proteins. Furthermore, the fluorescence changes of pyrene-labeled GroEL indicated that GroEL has two kinds of nucleotide binding sites. The fluorescence titration result fits well with a model in which two kinds of binding sites are both non-cooperative and independent of each other. These results suggest that the binding and hydrolysis of ATP may be necessary for the cooperative transition of GroEL.     

Collective Cell Movement Promotes Synchronization of Coupled Genetic Oscillators

Collective cell movement is a crucial component of embryonic development. Intercellular interactions regulate collective cell movement by allowing cells to transfer information. A key question is how collective cell movement itself influences information flow produced in tissues by intercellular interactions. Here, we study the effect of collective cell movement on the synchronization of locally coupled genetic oscillators. This study is motivated by the segmentation clock in zebrafish somitogenesis, where short-range correlated movement of cells has been observed. We describe the segmentation clock tissue by a Voronoi diagram, cell movement by the force balance of self-propelled and repulsive forces between cells, the dynamics of the direction of self-propelled motion, and the synchronization of genetic oscillators by locally coupled phase oscillators. We find that movement with a correlation length of about 2 ∼ 3 cell diameters is optimal for the synchronization of coupled oscillators. Quantification of cell mixing reveals that this short-range correlation of cell movement allows cells to exchange neighbors most efficiently. Moreover, short-range correlated movement strongly destabilizes nonuniform spatial phase patterns, further promoting global synchronization. Our theoretical results suggest that collective cell movement may enhance the synchronization of the segmentation clock in zebrafish somitogenesis. More generally, collective cell movement may promote information flow in tissues by enhancing cell mixing and destabilizing spurious patterns.     

Stationary pattern adaptation and the early components in human visual evoked potentials

Pattern-onset visual evoked potentials were elicited from humans by sinusoidal gratings of 0.5, 1, 2 and 4 cpd (cycles/degree) following adaptation to a blank field or one of the gratings. The wave forms recorded after blank field adaptation showed an early positive component, P0, which decreased in amplitude with spatial frequency, whereas the immediately succeeding negative component, N1, increased in amplitude with spatial frequency. P0 and N1 components of comparable size were recorded at 1 cpd. Stationary pattern adaptation to a grating of the same spatial frequency as the test grating significantly reduced N1 amplitude at 4, 2 and 1 cpd. The N1 component elicited at 4 cpd was attenuated in log-linear fashion as the spatial frequency of the adaptation grating increased. P0, on the other hand, was unaffected by stationary pattern adaptation at all combinations of test and adapting spatial frequencies, although P0 amplitude is known to be attenuated by adaptation to a drifting grating. Since N1, but not P0, was significantly attenuated following adaptation and testing at 1 cpd, it was concluded that the neurons generating these components are functionally distinct. The use of a common adaptation grating discounted the possibility that N1, but not P0, was affected due to a difference in the rates of retinal image modulation caused by eye movements made while viewing adaptation gratings of different spatial frequencies. The neurons generating N1 were adapted at a lower rate of retinal image modulation than that apparently required for adaptation of the neurons generating P0, which suggests a difference between these neurons in the rate of stimulus modulation necessary for activation.