Sensing extracellular changes initiates signal transduction and is the first stage of cellular decision-making. Yet relatively little is known about why one form of sensing biochemistry has been selected over another. To gain insight into this question, we studied the sensing characteristics of one of the biochemically simplest of sensors: the allosteric transcription factor. Such proteins, common in microbes, directly transduce the detection of a sensed molecule to changes in gene regulation. Using the Monod-Wyman-Changeux model, we determined six sensing characteristics – the dynamic range, the Hill number, the intrinsic noise, the information transfer capacity, the static gain, and the mean response time – as a function of the biochemical parameters of individual sensors and of the number of sensors. We found that specifying one characteristic strongly constrains others. For example, a high dynamic range implies a high Hill number and a high capacity, and vice versa. Perhaps surprisingly, these constraints are so strong that most of the space of characteristics is inaccessible given biophysically plausible ranges of parameter values. Within our approximations, we can calculate the probability distribution of the numbers of input molecules that maximizes information transfer and show that a population of one hundred allosteric transcription factors can in principle distinguish between more than four bands of input concentrations. Our results imply that allosteric sensors are unlikely to have been selected for high performance in one sensing characteristic but for a compromise in the performance of many.

Author Summary

Sensing environmental changes is the first step in the process of cellular decision-making, but many different biochemical sensors exist and why one sensor is selected for a particular task over another is not known. Here we study the sensing properties of a simple and generic allosteric sensor to understand the effectiveness and limitations of its “design”. We begin by defining and calculating a set of six engineering-inspired characteristics of the sensor’s response and investigate how specifying a high performance in one characteristic constrains the sensor’s performance in others. We determine many such trade-offs and, perhaps surprisingly, that much of the space of characteristics is inaccessible given biophysically plausible ranges of parameters. Our results suggest that allosteric sensors are not under selection for high performance in one sensing characteristic but for a compromise in performance between many. Our approach provides both quantitative and qualitative insights about the function and robustness of allosteric sensors and as such is applicable to both the study of endogenous systems and the design of synthetic ones.

Background

Understanding biological networks requires identifying their elementary protein interactions and establishing the timing and strength of those interactions. Fluorescence microscopy and Förster resonance energy transfer (FRET) have the potential to reveal such information because they allow molecular interactions to be monitored in living cells, but it is unclear how best to analyze FRET data. Existing techniques differ in assumptions, manipulations of data and the quantities they derive. To address this variation, we have developed a versatile Bayesian analysis based on clear assumptions and systematic statistics.

Results

Our algorithm infers values of the FRET efficiency and dissociation constant, Kd, between a pair of fluorescently tagged proteins. It gives a posterior probability distribution for these parameters, conveying more extensive information than single-value estimates can. The width and shape of the distribution reflects the reliability of the estimate and we used simulated data to determine how measurement noise, data quantity and fluorophore concentrations affect the inference. We are able to show why varying concentrations of donors and acceptors is necessary for estimating Kd. We further demonstrate that the inference improves if additional knowledge is available, for example of the FRET efficiency, which could be obtained from separate fluorescence lifetime measurements.

Conclusions

We present a general, systematic approach for extracting quantitative information on molecular interactions from FRET data. Our method yields both an estimate of the dissociation constant and the uncertainty associated with that estimate. The information produced by our algorithm can help design optimal experiments and is fundamental for developing mathematical models of biochemical networks.

Much of the complexity of biochemical networks comes from the information-processing abilities of allosteric proteins, be they receptors, ion-channels, signalling molecules or transcription factors. An allosteric protein can be uniquely regulated by each combination of input molecules that it binds. This “regulatory complexity” causes a combinatorial increase in the number of parameters required to fit experimental data as the number of protein interactions increases. It therefore challenges the creation, updating, and re-use of biochemical models. Here, we propose a rule-based modelling framework that exploits the intrinsic modularity of protein structure to address regulatory complexity. Rather than treating proteins as “black boxes”, we model their hierarchical structure and, as conformational changes, internal dynamics. By modelling the regulation of allosteric proteins through these conformational changes, we often decrease the number of parameters required to fit data, and so reduce over-fitting and improve the predictive power of a model. Our method is thermodynamically grounded, imposes detailed balance, and also includes molecular cross-talk and the background activity of enzymes. We use our Allosteric Network Compiler to examine how allostery can facilitate macromolecular assembly and how competitive ligands can change the observed cooperativity of an allosteric protein. We also develop a parsimonious model of G protein-coupled receptors that explains functional selectivity and can predict the rank order of potency of agonists acting through a receptor. Our methodology should provide a basis for scalable, modular and executable modelling of biochemical networks in systems and synthetic biology.

Author Summary

The complexity of biochemical networks challenges our ability to create quantitative and predictive models of cellular responses to extracellular changes. In these networks, the regulation of allosteric receptors and proteins by multiple drugs or endogenous ligands introduces “regulatory complexity” because a large number of parameters is required to describe such interactions. Protein interactions also give rise to “combinatorial complexity” by generating large numbers of protein complexes and covalent modification states. To address these twin problems, we propose a modelling framework that combines a modular description of protein structure and function with a rule-based description of protein interactions. We define the input-output function of an allosteric protein through its thermodynamic properties and structural components. We show that our “biomolecule-centric” methodology, in contrast to ad hoc approaches that emphasize the regulatory logic of interactions, can reduce the number of parameters required to model experimental observations. We also demonstrate how the application of our framework gives insights into the assembly of macromolecular complexes and increases the predictive power of a standard model of G protein-coupled receptors. These benefits are possible in many systems, given the ubiquity of allostery in biochemical networks. Our research delineates a fundamental relationship between allostery, modularity, and complexity in biochemical networks.

Stochasticity pervades life at the cellular level. Cells receive stochastic signals, perform detection and transduction with stochastic biochemistry, and grow and die in stochastic environments. Here we review progress in going from the molecular details to the information-processing strategies cells use in their decision-making. Such strategies are fundamentally influenced by stochasticity. We argue that the cellular decision-making can only be probabilistic and occurs at three levels. First, cells must infer from noisy signals the probable current and anticipated future state of their environment. Second, they must weigh the costs and benefits of each potential response, given that future. Third, cells must decide in the presence of other, potentially competitive, decision-makers. In this context, we discuss cooperative responses where some individuals can appear to sacrifice for the common good. We believe that decision-making strategies will be conserved, with comparatively few strategies being implemented by different biochemical mechanisms in many organisms. Determining the strategy of a decision-making network provides a potentially powerful coarse-graining that links systems and evolutionary biology to understand biological design.

Background

To control and manipulate cellular signaling, we need to understand cellular strategies for information transfer, integration, and decision-making. A key feature of signal transduction is the generation of only a few intracellular messengers by many extracellular stimuli.

Methodology/Principal Findings

Here we model molecular cross-talk between two classic second messengers, cyclic AMP (cAMP) and calcium, and show that the dynamical complexity of the response of both messengers increases substantially through their interaction. In our model of a non-excitable cell, both cAMP and calcium concentrations can oscillate. If mutually inhibitory, cross-talk between the two second messengers can increase the range of agonist concentrations for which oscillations occur. If mutually activating, cross-talk decreases the oscillation range, but can generate ‘bursting’ oscillations of calcium and may enable better filtering of noise.

Conclusion

We postulate that this increased dynamical complexity allows the cell to encode more information, particularly if both second messengers encode signals. In their native environments, it is unlikely that cells are exposed to one stimulus at a time, and cross-talk may help generate sufficiently complex responses to allow the cell to discriminate between different combinations and concentrations of extracellular agonists.

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise', is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored'). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high-throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.

A basic assumption underlying synthetic biology is that analysis of genetic circuit elements, such as regulatory proteins and promoters, can be used to understand and predict the behavior of circuits containing those elements. To test this assumption, we used time-lapse fluorescence microscopy to quantitatively analyze two autoregulatory negative feedback circuits. By measuring the gene regulation functions of the corresponding repressor–promoter interactions, we accurately predicted the expression level of the autoregulatory feedback loops, in molecular units. This demonstration that quantitative characterization of regulatory elements can predict the behavior of genetic circuits supports a fundamental requirement of synthetic biology.

Background

A goal of systems biology is the quantitative modelling of biochemical networks. Yet for many biochemical systems, parameter values and even the existence of interactions between some chemical species are unknown. It is therefore important to be able to easily investigate the effects of adding or removing reactions and to easily perform a bifurcation analysis, which shows the qualitative dynamics of a model for a range of parameter values.

Results

We present Facile, a Perl command-line tool for analysing the dynamics of a systems biology model. Facile implements the law of mass action to automatically compile a biochemical network (written as, for example, E + S <-> C) into scripts for analytical analysis (Mathematica and Maple), for simulation (XPP and Matlab), and for bifurcation analysis (AUTO). Facile automatically identifies mass conservations and generates the reduced form of a model with the minimum number of independent variables. This form is essential for bifurcation analysis, and Facile produces a C version of the reduced model for AUTO.

Conclusion

Facile is a simple, yet powerful, tool that greatly accelerates analysis of the dynamics of a biochemical network. By acting at the command-line and because of its intuitive, text-based input, Facile is quick to learn and can be incorporated into larger programs or into automated tasks.