An information-theoretic characterization of the optimal gradient sensing response of cells

Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient-for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.     

Biodiversity enhancement induced by environmental noise

Recent research in ecology has concentrated on the effect of environmental changes on ecosystem structure and function. In most cases the focus has been on how ecosystems respond to changes in the mean values of environmental parameters, while the impact of changes in the variance has seldom been studied. However, changes in environmental variability may be important. For example, recent climate change predictions indicate that, in addition to trends in the mean values of climate variables, an increase in interannual variability is expected to occur in the near future. How will this increase in the variance of environmental parameters affect the dynamics of terrestrial and aquatic ecosystems? Environmental fluctuations are usually believed to play a "destructive role" in ecosystem dynamics and to act as a source of disturbance, which perturbs the state of a system. However, noise is also known for its "constructive role", i.e., for the ability to create new ordered states in dynamical systems. Here we show that environmental noise may also enhance biodiversity. To this end we develop a conceptual model to show how random environmental fluctuations may favor biodiversity. Noise-induced biodiversity is observed for moderate levels of noise intensity, while it disappears with stronger environmental fluctuations, consistently with the notion underlying the "intermediate disturbance hypothesis".     

Propagation of photon noise and information transfer in visual motion detection

The extraction of the direction of motion from the time varying retinal images is one of the most basic tasks any visual system is confronted with. However, retinal images are severely corrupted by photon noise, in particular at low light levels, thus limiting the performance of motion detection mechanisms of what sort so ever. Here, we study how photon noise propagates through an array of Reichardt-type motion detectors that are commonly believed to underlie fly motion vision. We provide closed-form analytical expressions of the signal and noise spectra at the output of such a motion detector array. We find that Reichardt detectors reveal favorable noise suppression in the frequency range where most of the signal power resides. Most notably, due to inherent adaptive properties, the transmitted information about stimulus velocity remains nearly constant over a large range of velocity entropies. Action editor: Matthew Wiener     

Quantum nature of photon signal emitted by Xanthoria parietina and its implications to biology

The properties of living systems are usually described in the semi-classical framework that makes phenomenological division of properties into four classes--matter, psyche, soft consciousness and hard consciousness. Quantum framework provides a scientific basis of this classification of properties. The scientific basis requires the existence of macroscopic quantum entity entangled with quantum photon field of a living system. Every living system emits a photon signal with features indicating its quantum nature. Quantum nature of the signal emitted by a sample of X. parietina is confirmed by analysing photo count distributions obtained in 20000 measurements of photon number in contiguous bins of sizes of 50, 100, 200, 300 and 500 ms. The measurements use a broadband detector sensitive in 300-800 nm range (Photo count distributions of background noise and observed signal are measured similarly. These measurements background noise corrected squeezed state parameters of the signal. The parameters are signal strength expressed in counts per bin, r = 0.06, theta = 2.76 and phi = 0.64. The parameters correctly reproduce photo count distribution of any bin size in 50 ms-6 s range. The reproduction of photo count distributions is a credible evidence of spontaneous emission of photon signal in a quantum squeezed state for macroscopic time by the sample. The evidence is extrapolated to other living systems emitting similar photon signals. It is suggested that every living system is associated with a photon field in squeezed state. The suggestion has far reaching implications to biology and provides two ways of observing and manipulating a living system--either through matter or field or a combination of the two. Some implications and possible scenarios are elaborated.     

A differential amplifier circuit for reducing noise in axial light loss measurements

Simplified electronics have been developed for reducing laser excitation source light intensity fluctuations in flow cytometric axial light loss (extinction) measurements. By continuously monitoring the laser output with a photodiode detector and combining it with the axial light loss signal from a second detector using a high-speed differential amplifier, background interference is reduced 10 to 40 dB. Oscilloscope waveforms and frequency distribution histograms recorded from uniform-size polystyrene latex spheres and human mononuclear blood cells are used to illustrate the noise reduction capabilities.     

Correlation versus gradient type motion detectors: the pros and cons

Visual motion contains a wealth of information about self-motion as well as the three-dimensional structure of the environment. Therefore, it is of utmost importance for any organism with eyes. However, visual motion information is not explicitly represented at the photoreceptor level, but rather has to be computed by the nervous system from the changing retinal images as one of the first processing steps. Two prominent models have been proposed to account for this neural computation: the Reichardt detector and the gradient detector. While the Reichardt detector correlates the luminance levels derived from two adjacent image points, the gradient detector provides an estimate of the local retinal image velocity by dividing the spatial and the temporal luminance gradient. As a consequence of their different internal processing structure, both the models differ in a number of functional aspects such as their dependence on the spatial-pattern structure as well as their sensitivity to photon noise. These different properties lead to the proposal that an ideal motion detector should be of Reichardt type at low luminance levels, but of gradient type at high luminance levels. However, experiments on the fly visual systems provided unambiguous evidence in favour of the Reichardt detector under all luminance conditions. Does this mean that the fly nervous system uses suboptimal computations, or is there a functional aspect missing in the optimality criterion? In the following, I will argue in favour of the latter, showing that Reichardt detectors have an automatic gain control allowing them to dynamically adjust their input–output relationships to the statistical range of velocities presented, while gradient detectors do not have this property. As a consequence, Reichardt detectors, but not gradient detectors, always provide a maximum amount of information about stimulus velocity over a large range of velocities. This important property might explain why Reichardt type of computations have been demonstrated to underlie the extraction of motion information in the fly visual system under all luminance levels.     

A method improving the accuracy of fluorescence recovery after photobleaching analysis

Fluorescence recovery after photobleaching has been an established technique of quantifying the mobility of molecular species in cells and cell membranes for more than 30 years. However, under nonideal experimental conditions, the current methods of analysis still suffer from occasional problems; for example, when the signal/noise ratio is low, when there are temporal fluctuations in the illumination, or when there is bleaching during the recovery process. We here present a method of analysis that overcomes these problems, yielding accurate results even under nonideal experimental conditions. The method is based on circular averaging of each image, followed by spatial frequency analysis of the averaged radial data, and requires no prior knowledge of the shape of the bleached area. The method was validated using both simulated and experimental fluorescence recovery after photobleaching data, illustrating that the diffusion coefficient of a single diffusing component can be determined to within ∼1%, even for small signal levels (100 photon counts), and that at typical signal levels (5000 photon counts) a system with two diffusion coefficients can be analyzed with <10% error.     

Electrical coupling between mammalian cones

BACKGROUND: Cone photoreceptors are noisy because of random fluctuations of photon absorption, signaling molecules, and ion channels. However, each cone's noise is independent of the others, whereas their signals are partially shared. Therefore, electrically coupling the synaptic terminals prior to forward transmission and subsequent nonlinear processing can appreciably reduce noise relative to the signal. This signal-processing strategy has been demonstrated in lower vertebrates with rather coarse vision, but its occurrence in mammals with fine acuity has been doubted (even though gap junctions are present) because coupling would blur the neural image. RESULTS: In ground squirrel retina, whose triangular cone lattice resembles the human fovea, paired electrical recordings from adjacent cones demonstrated electrical coupling with an average conductance of approximately 320 pS. Blur caused by this degree of coupling had a space constant of approximately 0.5 cone diameters. Psychophysical measurements employing laser interferometry to bypass the eye's optics suggest that human foveal cones experience a similar degree of neural blur and that it is invariant with light intensity. This neural blur is narrower than the eye's optical blur, and we calculate that it should improve the signal-to-noise ratio at the cone terminal by about 77%. CONCLUSIONS: We conclude that the gap junctions observed between mammalian cones, including those in the human fovea, represent genuine electrical coupling. Because the space constant of the resulting neural blur is less than that of the optical blur, the signal-to-noise ratio can be markedly improved before the nonlinear stages with little compromise to visual acuity.     

Listening to the noise: random fluctuations reveal gene network parameters

The cellular environment is abuzz with noise originating from the inherent random motion of reacting molecules in the living cell. In this noisy environment, clonal cell populations show cell‐to‐cell variability that can manifest significant phenotypic differences. Noise‐induced stochastic fluctuations in cellular constituents can be measured and their statistics quantified. We show that these random fluctuations carry within them valuable information about the underlying genetic network. Far from being a nuisance, the ever‐present cellular noise acts as a rich source of excitation that, when processed through a gene network, carries its distinctive fingerprint that encodes a wealth of information about that network. We show that in some cases the analysis of these random fluctuations enables the full identification of network parameters, including those that may otherwise be difficult to measure. This establishes a potentially powerful approach for the identification of gene networks and offers a new window into the workings of these networks.     

The photon counting histogram in fluorescence fluctuation spectroscopy.

Fluorescence correlation spectroscopy (FCS) is generally used to obtain information about the number of fluorescent particles in a small volume and the diffusion coefficient from the autocorrelation function of the fluorescence signal. Here we demonstrate that photon counting histogram (PCH) analysis constitutes a novel tool for extracting quantities from fluorescence fluctuation data, i.e., the measured photon counts per molecule and the average number of molecules within the observation volume. The photon counting histogram of fluorescence fluctuation experiments, in which few molecules are present in the excitation volume, exhibits a super-Poissonian behavior. The additional broadening of the PCH compared to a Poisson distribution is due to fluorescence intensity fluctuations. For diffusing particles these intensity fluctuations are caused by an inhomogeneous excitation profile and the fluctuations in the number of particles in the observation volume. The quantitative relationship between the detected photon counts and the fluorescence intensity reaching the detector is given by Mandel's formula. Based on this equation and considering the fluorescence intensity distribution in the two-photon excitation volume, a theoretical expression for the PCH as a function of the number of molecules in the excitation volume is derived. For a single molecular species two parameters are sufficient to characterize the histogram completely, namely the average number of molecules within the observation volume and the detected photon counts per molecule per sampling time epsilon. The PCH for multiple molecular species, on the other hand, is generated by successively convoluting the photon counting distribution of each species with the others. The influence of the excitation profile upon the photon counting statistics for two relevant point spread functions (PSFs), the three-dimensional Gaussian PSF conventionally employed in confocal detection and the square of the Gaussian-Lorentzian PSF for two photon excitation, is explicitly treated. Measured photon counting distributions obtained with a two-photon excitation source agree, within experimental error with the theoretical PCHs calculated for the square of a Gaussian-Lorentzian beam profile. We demonstrate and discuss the influence of the average number of particles within the observation volume and the detected photon counts per molecule per sampling interval upon the super-Poissonian character of the photon counting distribution.     

The photon counting histogram in fluorescence fluctuation spectroscopy with non-ideal photodetectors

Fluorescence fluctuation spectroscopy utilizes the signal fluctuations of single molecules for studying biological processes. Information about the biological system is extracted from the raw data by statistical methods such as used in fluctuation correlation spectroscopy or photon counting histogram (PCH) analysis. Since detectors are never ideal, it is crucial to understand the influence of photodetectors on signal statistics to correctly interpret the experimental data. Here we focus on the effects of afterpulsing and detector dead-time on PCH statistics. We determine the dead-time and afterpulse probability for our detectors experimentally and show that afterpulsing can be neglected for most experiments. Dead-time effects on the PCH are concentration-dependent and become significant when more than one molecule is present in the excitation volume. We develop a new PCH theory that includes dead-time effects and verify it experimentally. Additionally, we derive a simple analytical expression that accurately predicts the effect of dead-time on the molecular brightness. Corrections for non-ideal detector effects extend the useful concentration range of PCH experiments and are crucial for the interpretation of titration and dilution experiments.     

Optimal noise filtering in the chemotactic response of Escherichia coli

Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.     

Initial studies of the application of the linear signal transfer theory in evaluating diaphanoscopic examinations exemplified by rheumatism diagnosis]

Rheumatoid arthritis affecting the small joints--in particular the fingers--has advantageous geometry for the transmission of near-infrared (NIR) light. Examination of the optical properties of tissues has revealed that as a result of changes to the capsule and synovial fluid there is a considerable increase in photon scattering already in the early stages of the disease--in particular around 685 nm. This suggests the appropriateness of analysing the photon density profile resulting from punctiform irradiation of the joint. In a first approximation, the point spread function of transmitted photon density is confirmed to be proportional to a Gauss distribution, as suggested by Arridge. In accordance with the linear signal transfer theory, therefore, it is possible to establish a virtual transfer system described by a first-order differential equation. (The tissue optical conditions mu a < mu's and mu a = constant (mu a = absorption coefficient) were assumed). The parameter mu's (= reduced scattering coefficient) was determined by linear approximation of the Gauss distribution to the calculated or measured point spread function. For selected patient data, the mu's was determined in healthy and diseased finger joints (e.g. 10.1 cm-1 and 26.8 cm-1, respectively), and the results were in good agreement with those obtained experimentally.     

Enhanced potential for metabolic studies using narrow-band sensitized FT-IR microspectroscopy.

The ability to detect and measure the relative concentration of deuterated substance found in tissue specimens is enhanced by adding a custom made-to-order 50 microm narrow MCT band that has an optimized response profile for the CD, ND and OH absorption bands. In the short range of interest it has a 2:1 signal advantage over the stock MCT detector and the steep cut off before the finger print region significantly diminishing the noise. The result is that levels of specific deuterated compounds experimentally administered to biological systems and dispersed by the host organism can be detected and measured The custom small target size narrow-band detector with increased signal and reduced noise enhances the potential for the use of FT-IR microspectoscopy as a novel way to study metabolism without the use of radioactive materials.     

Inferences about membrane properties from electrical noise measurements

Four sources of electrical noise in biological membranes, each with a different physical basis, are discussed; the analysis of each type of noise potentially yields a different sort of information about membrane properties. (a) From the thermal noise spectrum, the passive membrane impedance may be obtained, so that thermal noise measurements are essentially equivalent to the type of since wave analysis carried out by Cole and Curtis. (b) If adequately high frequency measurements could be made, the shot noise spectrum should give information about the average motion of a single ion within the membrane. (c) The number of charge carriers and single ion mobilities within the membrane can possibly be inferred from measurements of noise with a 1/f spectrum. Available data indicate, for example, that increases in axon membrane conductance are not achieved by modulations in the mobility of ions within the membrane. (d) Fluctuations arising from the mechanisms normally responsible for membrane conductance changes can produce a type of electrical noise. Analysis of such conductance fluctuations provides a way to assess the validity of various microscopic models for the behavior of individual channels. Two different probabilistic interpretations of the Hodgkin-Huxley equations are investigated here and shown to yield different predictions about the spectrum of conductance fluctuations; thus, appropriate noise measurements may serve to eliminate certain classes of microscopic models for membrane conductance changes. Further, it is shown how the analysis of conductance fluctuations can, in some circumstances, provide an estimate of the conductance of a single channel.     

Biophoton emission

The phenomenon of ultraweak photon emission from living systems was further investigated in order to elucidate the physical properties of this radiation and its possible source. We obtained evidence that the light has a high degree of coherence because of (1) its photon count statistics, (2) its spectral distribution, (3) its decay behavior after exposure to light illumination, and (4) its transparency through optically thick materials. Moroever, DNA is apparently at least an important source, since conformational changes induced with ethidium bromide in vivo are clearly reflected by changes of the photon emission of cells. The physical properties of the radiation are described, taking DNA as an exciplex laser system, where a stable state can be reached far from thermal equilibrium at threshold.     

Light adaptation in Drosophila photoreceptors: I. Response dynamics and signaling efficiency at 25 degrees C

Besides the physical limits imposed on photon absorption, the coprocessing of visual information by the phototransduction cascade and photoreceptor membrane determines the fidelity of photoreceptor signaling. We investigated the response dynamics and signaling efficiency of Drosophila photoreceptors to natural-like fluctuating light contrast stimulation and intracellular current injection when the cells were adapted over a 4-log unit light intensity range at 25 degrees C. This dual stimulation allowed us to characterize how an increase in the mean light intensity causes the phototransduction cascade and photoreceptor membrane to produce larger, faster and increasingly accurate voltage responses to a given contrast. Using signal and noise analysis, this appears to be associated with an increased summation of smaller and faster elementary responses (i.e., bumps), whose latency distribution stays relatively unchanged at different mean light intensity levels. As the phototransduction cascade increases, the size and speed of the signals (light current) at higher adapting backgrounds and, in conjunction with the photoreceptor membrane, reduces the light-induced voltage noise, and the photoreceptor signal-to-noise ratio improves and extends to a higher bandwidth. Because the voltage responses to light contrasts are much slower than those evoked by current injection, the photoreceptor membrane does not limit the speed of the phototransduction cascade, but it does filter the associated high frequency noise. The photoreceptor information capacity increases with light adaptation and starts to saturate at approximately 200 bits/s as the speed of the chemical reactions inside a fixed number of transduction units, possibly microvilli, is approaching its maximum.