Correlations reveal the hierarchical organization of biological networks with latent variables.

Deciphering the functional organization of large biological networks is a major challenge for current mathematical methods. A common approach is to decompose networks into largely independent functional modules, but inferring these modules and their organization from network activity is difficult, given the uncertainties and incompleteness of measurements. Typically, some parts of the overall functional organization, such as intermediate processing steps, are latent. We show that the hidden structure can be determined from the statistical moments of observable network components alone, as long as the functional relevance of the network components lies in their mean values and the mean of each latent variable maps onto a scaled expectation of a binary variable. Whether the function of biological networks permits a hierarchical modularization can be falsified by a correlation-based statistical test that we derive. We apply the test to gene regulatory networks, dendrites of pyramidal neurons, and networks of spiking neurons.

Distributed coding of duration in rodent prefrontal cortex during time reproduction.

As we interact with the external world, we judge magnitudes from sensory information. The estimation of magnitudes has been characterized in primates, yet it is largely unexplored in nonprimate species. Here, we use time interval reproduction to study rodent behavior and its neural correlates in the context of magnitude estimation. We show that gerbils display primate-like magnitude estimation characteristics in time reproduction. Most prominently their behavioral responses show a systematic overestimation of small stimuli and an underestimation of large stimuli, often referred to as regression effect. We investigated the underlying neural mechanisms by recording from medial prefrontal cortex and show that the majority of neurons respond either during the measurement or the reproduction of a time interval. Cells that are active during both phases display distinct response patterns. We categorize the neural responses into multiple types and demonstrate that only populations with mixed responses can encode the bias of the regression effect. These results help unveil the organizing neural principles of time reproduction and perhaps magnitude estimation in general.

Tuft dendrites of pyramidal neurons operate as feedback-modulated functional subunits.

Dendrites of pyramidal cells exhibit complex morphologies and contain a variety of ionic conductances, which generate non-trivial integrative properties. Basal and proximal apical dendrites have been shown to function as independent computational subunits within a two-layer feedforward processing scheme. The outputs of the subunits are linearly summed and passed through a final non-linearity. It is an open question whether this mathematical abstraction can be applied to apical tuft dendrites as well. Using a detailed compartmental model of CA1 pyramidal neurons and a novel theoretical framework based on iso-response methods, we first show that somatic sub-threshold responses to brief synaptic inputs cannot be described by a two-layer feedforward model. Then, we relax the core assumption of subunit independence and introduce non-linear feedback from the output layer to the subunit inputs. We find that additive feedback alone explains the somatic responses to synaptic inputs to most of the branches in the apical tuft. Individual dendritic branches bidirectionally modulate the thresholds of their input-output curves without significantly changing the gains. In contrast to these findings for precisely timed inputs, we show that neuronal computations based on firing rates can be accurately described by purely feedforward two-layer models. Our findings support the view that dendrites of pyramidal neurons possess non-linear analog processing capabilities that critically depend on the location of synaptic inputs. The iso-response framework proposed in this computational study is highly efficient and could be directly applied to biological neurons.

Grid-Cell Activity on Linear Tracks Indicates Purely Translational Remapping of 2D Firing Patterns at Movement Turning Points.

Grid cells in rodent medial entorhinal cortex are thought to play a critical role for spatial navigation. When the animal is freely moving in an open arena the firing fields of each grid cell tend to form a hexagonal lattice spanning the environment. For movements along a linear track the cells seem to respond differently. They show multiple firing fields that are not periodically arranged and whose shape and position change when the running direction is reversed. In addition, peak firing rates vary widely from field to field. Measured along one running direction only, firing fields are, however, compatible with a slice through a two-dimensional (2D) hexagonal pattern. It is an open question, whether this is also true if leftward and rightward runs are jointly considered. By analyzing data from 15 male Long-Evans rats, we show that a single hexagonal firing pattern explains the linear-track data if translational shifts of the pattern are allowed at the movement turning points. A rotation or scaling of the grid is not required. The agreement is further improved if the peak firing rates of the underlying 2D grid fields can vary from field to field, as suggested by recent studies. These findings have direct consequences for experiments using linear tracks in virtual reality.SIGNIFICANCE STATEMENT Various types of neurons support spatial navigation. Their response properties are often studied in reduced settings and might change when the animal can freely explore its environment. Grid cells in rodents, for example, exhibit seemingly irregular firing fields when animal movement is restricted to a linear track but highly regular patterns in two-dimensional (2D) arenas. We show that linear-track responses of a cell for both leftward and rightward running directions can be explained as cuts through a single hexagonal pattern if translational remapping is allowed at movement turning points; neither rotations nor scale transformations are needed. These results provide a basis to quantify grid-cell activity in 1D virtual reality and could help to detect and categorize grid cells without experiments in 2D environments.

Heat Stress Dictates Microbial Lipid Composition along a Thermal Gradient in Marine Sediments.

Temperature exerts a first-order control on microbial populations, which constantly adjust the fluidity and permeability of their cell membrane lipids to minimize loss of energy by ion diffusion across the membrane. Analytical advances in liquid chromatography coupled to mass spectrometry have allowed the detection of a stunning diversity of bacterial and archaeal lipids in extreme environments such as hot springs, hydrothermal vents and deep subsurface marine sediments. Here, we investigated a thermal gradient from 18 to 101°C across a marine sediment field and tested the hypothesis that cell membrane lipids provide a major biochemical basis for the bioenergetics of archaea and bacteria under heat stress. This paper features a detailed lipidomics approach with the focus on membrane lipid structure-function. Membrane lipids analyzed here include polar lipids of bacteria and polar and core lipids of archaea. Reflecting the low permeability of their ether-linked isoprenoids, we found that archaeal polar lipids generally dominate over bacterial lipids in deep layers of the sediments influenced by hydrothermal fluids. A close examination of archaeal and bacterial lipids revealed a membrane quandary: not only low permeability, but also increased fluidity of membranes are required as a unified property of microbial membranes for energy conservation under heat stress. For instance, bacterial fatty acids were composed of longer chain lengths in concert with higher degree of unsaturation while archaea modified their tetraethers by incorporation of additional methyl groups at elevated sediment temperatures. It is possible that these configurations toward a more fluidized membrane at elevated temperatures are counterbalanced by the high abundance of archaeal glycolipids and bacterial sphingolipids, which could reduce membrane permeability through strong intermolecular hydrogen bonding. Our results provide a new angle for interpreting membrane lipid structure-function enabling archaea and bacteria to survive and grow in hydrothermal systems.

Cyanobacteria in Sulfidic Spring Microbial Mats Can Perform Oxygenic and Anoxygenic Photosynthesis Simultaneously during an Entire Diurnal Period.

We used microsensors to study the regulation of anoxygenic and oxygenic photosynthesis (AP and OP, respectively) by light and sulfide in a cyanobacterium dominating microbial mats from cold sulfidic springs. Both photosynthetic modes were performed simultaneously over all H2S concentrations (1-2200 µM) and irradiances (4-52 µmol photons m-2 s-1) tested. AP increased with H2S concentration while the sum of oxygenic and anoxygenic photosynthetic rates was constant at each light intensity. Thus, the total photosynthetically driven electron transport rate was solely controlled by the irradiance level. The partitioning between the rates of these two photosynthetic modes was regulated by both light and H2S concentration. The plastoquinone pool (PQ) receives electrons from sulfide:quinone:reductase (SQR) in AP and from photosystem II (PSII) in OP. It is thus the link in the electron transport chain where both pathways intersect, and the compound that controls their partitioning. We fitted our data with a model of the photosynthetic electron transport that includes the kinetics of plastoquinone reduction and oxidation. The model results confirmed that the observed partitioning between photosynthetic modes can be explained by a simple kinetic control based on the affinity of SQR and PSII toward PQ. The SQR enzyme and PSII have similar affinities toward PQ, which explains the concurrent OP and AP over an astonishingly wide range of H2S concentrations and irradiances. The elegant kinetic control of activity makes the cyanobacterium successful in the fluctuating spring environment. We discuss how these specific regulation mechanisms may have played a role in ancient H2S-rich oceans.

Structure and function of natural sulphide-oxidizing microbial mats under dynamic input of light and chemical energy.

We studied the interaction between phototrophic and chemolithoautotrophic sulphide-oxidizing microorganisms in natural microbial mats forming in sulphidic streams. The structure of these mats varied between two end-members: one characterized by a layer dominated by large sulphur-oxidizing bacteria (SOB; mostly Beggiatoa-like) on top of a cyanobacterial layer (B/C mats) and the other with an inverted structure (C/B mats). C/B mats formed where the availability of oxygen from the water column was limited (<5 µm). Aerobic chemolithotrophic activity of the SOB depended entirely on oxygen produced locally by cyanobacteria during high light conditions. In contrast, B/C mats formed at locations where oxygen in the water column was comparatively abundant (>45 µM) and continuously present. Here SOB were independent of the photosynthetic activity of cyanobacteria and outcompeted the cyanobacteria in the uppermost layer of the mat where energy sources for both functional groups were concentrated. Outcompetition of photosynthetic microbes in the presence of light was facilitated by the decoupling of aerobic chemolithotrophy and oxygenic phototrophy. Remarkably, the B/C mats conserved much less energy than the C/B mats, although similar amounts of light and chemical energy were available. Thus ecosystems do not necessarily develop towards optimal energy usage. Our data suggest that, when two independent sources of energy are available, the structure and activity of microbial communities is primarily determined by the continuous rather than the intermittent energy source, even if the time-integrated energy flux of the intermittent energy source is greater.

Sulfate reduction and sulfide oxidation in extremely steep salinity gradients formed by freshwater springs emerging into the Dead Sea.

Abundant microbial mats, recently discovered in underwater freshwater springs in the hypersaline Dead Sea, are mostly dominated by sulfur-oxidizing bacteria. We investigated the source of sulfide and the activity of these communities. Isotopic analysis of sulfide and sulfate in the spring water showed a fractionation of 39-50‰ indicative of active sulfate reduction. Sulfate reduction rates (SRR) in the spring sediment (< 2.8 nmol cm(-3) day(-1)) are too low to account for the measured sulfide flux. Thus, sulfide from the springs, locally reduced salinity and O2 from the Dead Sea water are responsible for the abundant microbial biomass around the springs. The springs flow is highly variable and accordingly the local salinities. We speculate that the development of microbial mats dominated by either Sulfurimonas/Sulfurovum-like or Thiobacillus/Acidithiobacillus-like sulfide-oxidizing bacteria, results from different mean salinities in the microenvironment of the mats. SRR of up to 10 nmol cm(-3) day(-1) detected in the Dead Sea sediment are surprisingly higher than in the less saline springs. While this shows the presence of an extremely halophilic sulfate-reducing bacteria community in the Dead Sea sediments, it also suggests that extensive salinity fluctuations limit these communities in the springs due to increased energetic demands for osmoregulation.

Oxygenic photosynthesis as a protection mechanism for cyanobacteria against iron-encrustation in environments with high Fe(2+) concentrations.

If O2 is available at circumneutral pH, Fe(2+) is rapidly oxidized to Fe(3+), which precipitates as FeO(OH). Neutrophilic iron oxidizing bacteria have evolved mechanisms to prevent self-encrustation in iron. Hitherto, no mechanism has been proposed for cyanobacteria from Fe(2+)-rich environments; these produce O2 but are seldom found encrusted in iron. We used two sets of illuminated reactors connected to two groundwater aquifers with different Fe(2+) concentrations (0.9 µM vs. 26 µM) in the Äspö Hard Rock Laboratory (HRL), Sweden. Cyanobacterial biofilms developed in all reactors and were phylogenetically different between the reactors. Unexpectedly, cyanobacteria growing in the Fe(2+)-poor reactors were encrusted in iron, whereas those in the Fe(2+)-rich reactors were not. In-situ microsensor measurements showed that O2 concentrations and pH near the surface of the cyanobacterial biofilms from the Fe(2+)-rich reactors were much higher than in the overlying water. This was not the case for the biofilms growing at low Fe(2+) concentrations. Measurements with enrichment cultures showed that cyanobacteria from the Fe(2+)-rich environment increased their photosynthesis with increasing Fe(2+) concentrations, whereas those from the low Fe(2+) environment were inhibited at Fe(2+) > 5 µM. Modeling based on in-situ O2 and pH profiles showed that cyanobacteria from the Fe(2+)-rich reactor were not exposed to significant Fe(2+) concentrations. We propose that, due to limited mass transfer, high photosynthetic activity in Fe(2+)-rich environments forms a protective zone where Fe(2+) precipitates abiotically at a non-lethal distance from the cyanobacteria. This mechanism sheds new light on the possible role of cyanobacteria in precipitation of banded iron formations.

Spatial distribution of diatom and cyanobacterial mats in the Dead Sea is determined by response to rapid salinity fluctuations.

Cyanobacteria and diatom mats are ubiquitous in hypersaline environments but have never been observed in the Dead Sea, one of the most hypersaline lakes on Earth. Here we report the discovery of phototrophic microbial mats at underwater freshwater seeps in the Dead Sea. These mats are either dominated by diatoms or unicellular cyanobacteria and are spatially separated. Using in situ and ex situ O2 microsensor measurements we show that these organisms are photosynthetically active in their natural habitat. The diatoms, which are phylogenetically associated to the Navicula genus, grew in culture at salinities up to 40 % Dead Sea water (DSW) (14 % total dissolved salts, TDS). The unicellular cyanobacteria belong to the extremely halotolerant Euhalothece genus and grew at salinities up to 70 % DSW (24.5 % TDS). As suggested by a variable O2 penetration depth measured in situ, the organisms are exposed to drastic salinity fluctuations ranging from brackish to DSW salinity within minutes to hours. We could demonstrate that both phototrophs are able to withstand such extreme short-term fluctuations. Nevertheless, while the diatoms recover better from rapid fluctuations, the cyanobacteria cope better with long-term exposure to DSW. We conclude that the main reason for the development of these microbial mats is a local dilution of the hypersaline Dead Sea to levels allowing growth. Their spatial distribution in the seeping areas is a result of different recovery rates from short or long-term fluctuation in salinity.

Microenvironments of reduced salinity harbour biofilms in Dead Sea underwater springs.

The Dead Sea is a hypersaline lake where only few types of organisms can grow. Recently, abundant and diverse microbial life was discovered in biofilms covering rocks and permeable sediments around underwater freshwater springs and seeps. We used a newly developed salinity mini-sensor (spatial resolution 300 µm) to investigate the salinity environment around these biofilms in a flume that simulates an underwater spring. Compared with the hypersaline bulk water, salinity at the sediment surface decreased to zero at seeping velocities of 7 cm s(-1). At similar flow velocities, salinity above rocks decreased to 100-200 g L(-1) at a distance of 300 µm from the surface. This depended on the position on the rock, and coincided with locations of natural biofilms. The salinity reduction substantially diminished at flow velocities of 3.5 cm s(-1). We suggest that locally decreased salinity due to freshwater input is one of the main factors that make areas around underwater freshwater springs and seeps in the Dead Sea more favourable for life. However, due to frequent fluctuations in the freshwater flow, the locally decreased salinity is unstable. Therefore, microorganisms that inhabit these environments must be capable of withstanding large and rapid salinity fluctuations.

Microbial and chemical characterization of underwater fresh water springs in the Dead Sea.

Due to its extreme salinity and high Mg concentration the Dead Sea is characterized by a very low density of cells most of which are Archaea. We discovered several underwater fresh to brackish water springs in the Dead Sea harboring dense microbial communities. We provide the first characterization of these communities, discuss their possible origin, hydrochemical environment, energetic resources and the putative biogeochemical pathways they are mediating. Pyrosequencing of the 16S rRNA gene and community fingerprinting methods showed that the spring community originates from the Dead Sea sediments and not from the aquifer. Furthermore, it suggested that there is a dense Archaeal community in the shoreline pore water of the lake. Sequences of bacterial sulfate reducers, nitrifiers iron oxidizers and iron reducers were identified as well. Analysis of white and green biofilms suggested that sulfide oxidation through chemolitotrophy and phototrophy is highly significant. Hyperspectral analysis showed a tight association between abundant green sulfur bacteria and cyanobacteria in the green biofilms. Together, our findings show that the Dead Sea floor harbors diverse microbial communities, part of which is not known from other hypersaline environments. Analysis of the water's chemistry shows evidence of microbial activity along the path and suggests that the springs supply nitrogen, phosphorus and organic matter to the microbial communities in the Dead Sea. The underwater springs are a newly recognized water source for the Dead Sea. Their input of microorganisms and nutrients needs to be considered in the assessment of possible impact of dilution events of the lake surface waters, such as those that will occur in the future due to the intended establishment of the Red Sea-Dead Sea water conduit.

Distributed fading memory for stimulus properties in the primary visual cortex.

It is currently not known how distributed neuronal responses in early visual areas carry stimulus-related information. We made multielectrode recordings from cat primary visual cortex and applied methods from machine learning in order to analyze the temporal evolution of stimulus-related information in the spiking activity of large ensembles of around 100 neurons. We used sequences of up to three different visual stimuli (letters of the alphabet) presented for 100 ms and with intervals of 100 ms or larger. Most of the information about visual stimuli extractable by sophisticated methods of machine learning, i.e., support vector machines with nonlinear kernel functions, was also extractable by simple linear classification such as can be achieved by individual neurons. New stimuli did not erase information about previous stimuli. The responses to the most recent stimulus contained about equal amounts of information about both this and the preceding stimulus. This information was encoded both in the discharge rates (response amplitudes) of the ensemble of neurons and, when using short time constants for integration (e.g., 20 ms), in the precise timing of individual spikes (