Biological systems often have to measure extremely low concentrations of chemicals with high precision. When dealing with such small numbers of molecules, the inevitable randomness of physical transport processes and binding reactions will limit the precision with which measurements can be made. An important question is what the lower bound on the noise would be in such measurements. Using the theory of diffusion-influenced reactions, we derive an analytical expression for the precision of concentration estimates that are obtained by monitoring the state of a receptor to which a diffusing ligand can bind. The variance in the estimate consists of two terms, one resulting from the intrinsic binding kinetics and the other from the diffusive arrival of ligand at the receptor. The latter term is identical to the fundamental limit derived by Berg and Purcell (Biophys. J., 1977), but disagrees with a more recent expression by Bialek and Setayeshgar. Comparing the theoretical predictions against results from particle-based simulations confirms the accuracy of the resulting expression and reaffirms the fundamental limit established by Berg and Purcell.
In biochemical signaling, information is often encoded in oscillatory signals. However, the advantages of such a coding strategy over an amplitude-encoding scheme of constant signals remain unclear. Here we study the dynamics of a simple model gene promoter in response to oscillating and constant transcription factor signals. We find that in biologically relevant parameter regimes an oscillating input can produce a more constant protein level than a constant input. Our results suggest that oscillating signals may be used to minimize noise in gene regulation.
In this Letter we show that living cells can multiplex biochemical signals, i.e., transmit multiple signals through the same signaling pathway simultaneously, and yet respond to them very specifically. We demonstrate how two binary input signals can be encoded in the concentration of a common signaling protein, which is then decoded such that each of the two output signals provides reliable information about one corresponding input. Under biologically relevant conditions the network can reach the maximum amount of information that can be transmitted, which is 2 bits. DOI: 10.1103/PhysRevLett.107.048101 PACS numbers: 87.18.Mp, 87.18.Cf, 87.18.Tt Cells continually have to respond to a myriad of signals. One strategy for transmitting distinct stimuli is to use distinct signal transduction networks. It is, however, increasingly recognized that components are often shared between pathways [1]. Moreover, cells can transmit different signals through one and the same pathway, and yet respond to them specifically. In rat cells, for instance, neuronal growth factor and epidermal growth factor stimuli are transmitted through the same MAPK (mitogenactivated protein kinase) pathway, yet give rise to different cell fates, differentiation and proliferation, respectively [2]. These observations suggest that cells are able to transmit multiple messages through the same signal transduction network, just as many telephone calls can be transmitted via a single wire. Indeed, the intriguing question arises whether biochemical networks, like electronic circuits, can multiplex signals: can multiple input signals be combined (encoded) simultaneously in the dynamics of a common signaling pathway, and then decoded such that cells can respond specifically to each signal (see Fig. 1)?An open question in biology is how cells transduce multiple signals via pathways that share components, since sharing components may lead to unwanted cross talk between the different signals. In recent years, several mechanisms for ensuring signaling specificity have been proposed. One is spatial insulation, where the shared components are incorporated into distinct macromolecular complexes on scaffold proteins [1,3], leading effectively to independent communication channels for the transmission of the respective signals. Other proposals are based on the temporal dynamics of the system, such as crosspathway inhibition [4] and kinetic insulation [5]. With these mechanisms the system cannot be decomposed into independent pathways for the transmission of the respective signals. Yet, these studies suggest that multiple messages cannot be transmitted simultaneously because one pathway tends to dominate the response. Here we demonstrate that cells can truly multiplex signals: we show that they can transmit at least two signals simultaneously through a common pathway, and yet respond specifically to each of them.Cells employ a number of coding strategies for transducing signals, such as encoding stimuli in the temporal dynamics, like the duration [2] or frequency ...
Information processing and decision-making is based upon logic operations, which in cellular networks has been well characterized at the level of transcription. In recent years, however, both experimentalists and theorists have begun to appreciate that cellular decision-making can also be performed at the level of a single protein, giving rise to the notion of protein logic. Here we systematically explore protein logic using a well-known statistical mechanical model. As an example system, we focus on receptors that bind either one or two ligands, and their associated dimers. Notably, we find that a single heterodimer can realize any of the 16 possible logic gates, including the XOR gate, by variation of biochemical parameters. We then introduce what to our knowledge is a novel idea: that a set of receptors with fixed parameters can encode functionally unique logic gates simply by forming different dimeric combinations. An exhaustive search reveals that the simplest set of receptors (two single-ligand receptors and one double-ligand receptor) can realize several different groups of three unique gates, a result for which the parametric analysis of single receptors and dimers provides a clear interpretation. Both results underscore the surprising functional freedom readily available to cells at the single-protein level.
In recent years it has been increasingly recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that the protein signaling network of living cells has a bow-tie structure and that components are often shared between different signaling pathways. Here we show by mathematical modeling that living cells can multiplex a constant and an oscillatory signal: they can transmit these two signals simultaneously through a common signaling pathway, and yet respond to them specifically and reliably. We find that information transmission is reduced not only by noise arising from the intrinsic stochasticity of biochemical reactions, but also by crosstalk between the different channels. Yet, under biologically relevant conditions more than 2 bits of information can be transmitted per channel, even when the two signals are transmitted simultaneously. These observations suggest that oscillatory signals are ideal for multiplexing signals.
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