Predicting chemical environments of bacteria from receptor signaling

Sensory systems have evolved to respond to input stimuli of certain statistical properties, and to reliably transmit this information through biochemical pathways. Hence, for an experimentally well-characterized sensory system, one ought to be able to extract valuable information about the statistics of the stimuli. Based on dose-response curves from in vivo fluorescence resonance energy transfer (FRET) experiments of the bacterial chemotaxis sensory system, we predict the chemical gradients chemotactic Escherichia coli cells typically encounter in their natural environment. To predict average gradients cells experience, we revaluate the phenomenological Weber's law and its generalizations to the Weber-Fechner law and fold-change detection. To obtain full distributions of gradients we use information theory and simulations, considering limitations of information transmission from both cell-external and internal noise. We identify broad distributions of exponential gradients, which lead to log-normal stimuli and maximal drift velocity. Our results thus provide a first step towards deciphering the chemical nature of complex, experimentally inaccessible cellular microenvironments, such as the human intestine.Comment: DG and GM contributed equally to this wor

Input-output relations in biological systems: measurement, information and the Hill equation

Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system's overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.Comment: Biology Direct 8:3

Allosteric proteins as logarithmic sensors

Many sensory systems, from vision and hearing in animals to signal transduction in cells, respond to fold changes in signal relative to background. Responding to fold change requires that the system senses signal on a logarithmic scale, responding identically to a change in signal level from 1 to 3, or from 10 to 30. It is an ongoing search in the field to understand the ways in which a logarithmic sensor can be implemented at the molecular level. In this work, we present evidence that logarithmic sensing can be implemented with a single protein, by means of allosteric regulation. Specifically, we find that mathematical models show that allosteric proteins can respond to stimuli on a logarithmic scale. Next, we present evidence from measurements in the literature that some allosteric proteins do operate in a parameter regime that permits logarithmic sensing. Finally, we present examples suggesting that allosteric proteins are indeed used in this capacity: allosteric proteins play a prominent role in systems where fold-change detection has been proposed. This finding suggests a role as logarithmic sensors for the many allosteric proteins across diverse biological processes

Rescaling of spatio-temporal sensing in eukaryotic chemotaxis

Eukaryotic cells respond to a chemoattractant gradient by forming intracellular gradients of signaling molecules that reflect the extracellular chemical gradient - an ability called directional sensing. Quantitative experiments have revealed two characteristic input-output relations of the system: First, in a static chemoattractant gradient, the shapes of the intracellular gradients of the signaling molecules are determined by the relative steepness, rather than the absolute concentration, of the chemoattractant gradient along the cell body. Second, upon a spatially homogeneous temporal increase in the input stimulus, the intracellular signaling molecules are transiently activated such that the response magnitudes are dependent on fold changes of the stimulus, not on absolute levels. However, the underlying mechanism that endows the system with these response properties remains elusive. Here, by adopting a widely used modeling framework of directional sensing, local excitation and global inhibition (LEGI), we propose a hypothesis that the two rescaling behaviors stem from a single design principle, namely, invariance of the governing equations to a scale transformation of the input level. Analyses of the LEGI-based model reveal that the invariance can be divided into two parts, each of which is responsible for the respective response properties. Our hypothesis leads to an experimentally testable prediction that a system with the invariance detects relative steepness even in dynamic gradient stimuli as well as in static gradients. Furthermore, we show that the relation between the response properties and the scale invariance is general in that it can be implemented by models with different network topologies

Allosteric proteins as logarithmic sensors

Many sensory systems, from vision and hearing in animals to signal transduction in cells, respond to fold changes in signal relative to background. Responding to fold change requires that the system senses signal on a logarithmic scale, responding identically to a change in signal level from 1 to 3, or from 10 to 30. It is an ongoing search in the field to understand the ways in which a logarithmic sensor can be implemented at the molecular level. In this work, we present evidence that logarithmic sensing can be implemented with a single protein, by means of allosteric regulation. Specifically, we find that mathematical models show that allosteric proteins can respond to stimuli on a logarithmic scale. Next, we present evidence from measurements in the literature that some allosteric proteins do operate in a parameter regime that permits logarithmic sensing. Finally, we present examples suggesting that allosteric proteins are indeed used in this capacity: allosteric proteins play a prominent role in systems where fold-change detection has been proposed. This finding suggests a role as logarithmic sensors for the many allosteric proteins across diverse biological processes

Network motifs emerge from interconnections that favour stability

The microscopic principles organizing dynamic units in complex networks—from proteins to power generators—can be understood in terms of network ‘motifs’: small interconnection patterns that appear much more frequently in real networks than expected in random networks. When considered as small subgraphs isolated from a large network, these motifs are more robust to parameter variations, easier to synchronize than other possible subgraphs, and can provide specific functionalities. But one can isolate these subgraphs only by assuming, for example, a significant separation of timescales, and the origin of network motifs and their functionalities when embedded in larger networks remain unclear. Here we show that most motifs emerge from interconnection patterns that best exploit the intrinsic stability characteristics at different scales of interconnection, from simple nodes to whole modules. This functionality suggests an efficient mechanism to stably build complex systems by recursively interconnecting nodes and modules as motifs. We present direct evidence of this mechanism in several biological networks

A temporal model for early vision that explains detection thresholds for light pulses on flickering backgrounds

A model is presented for the early (retinal) stages of temporal processing of light inputs in the visual system. The model consists of a sequence of three adaptation processes, with two instantaneous nonlinearities in between. The three adaptation processes are, in order of processing of the light input: a divisive light adaptation, a subtractive light adaptation, and a contrast gain control. Divisive light adaptation is modeled by two gain controls. The first of these is a fast feedback loop with square-root behavior, the second a slow feedback loop with logarithm-like behavior. This can explain several aspects of the temporal behavior of photoreceptor outputs. Subtractive light adaptation is modeled by a high-pass filter equivalent to a fractional differentiation, and it can explain the attenuation of low frequencies observed in ganglion cell responses. Contrast gain control in the model is fast, and can explain the decreased detectability of test signals that are superimposed on dynamic backgrounds. We determine psychophysical detection thresholds for brief test pulses that are presented on flickering backgrounds, for a wide range of temporal modulation frequencies of these backgrounds. The model can explain the psychophysical data for the full range of modulation frequencies tested, as well as detection thresholds obtained for test pulses on backgrounds with increment and decrement steps in intensity.