Activation of Ras proteins underlies functional decisions in diverse cell types. Two molecules, RasGRP and SOS, catalyze Ras activation in lymphocytes. Binding of active Ras to SOS′ allosteric pocket markedly increases SOS′ activity establishing a positive feedback loop for SOS-mediated Ras activation. Integrating in silico and in vitro studies, we demonstrate that digital signaling in lymphocytes (cells are “on” or “off”) is predicated upon feedback regulation of SOS. SOS′ feedback loop leads to hysteresis in the dose-response curve, which can enable a capacity to sustain Ras activation as stimuli are withdrawn and exhibit “memory” of past encounters with antigen. Ras activation via RasGRP alone is analog (graded increase in amplitude with stimulus). We describe how complementary analog (RasGRP) and digital (SOS) pathways act on Ras to efficiently convert analog input to digital output. Numerous predictions regarding the impact of our findings on lymphocyte function and development are noted.

Living cells deploy many resources to sense their environments, including receptors, downstream signaling molecules, time, and fuel. However, it is not known which resources fundamentally limit the precision of sensing, like weak links in a chain, and which can compensate each other, leading to trade-offs between them. We present a theory for the optimal design of the large class of sensing systems in which a receptor drives a push-pull network. The theory identifies three classes of resources that are required for sensing: receptors and their integration time, readout molecules, and energy (fuel turnover). Each resource class sets a fundamental sensing limit, which means that the sensing precision is bounded by the limiting resource class and cannot be enhanced by increasing another class-the different classes cannot compensate each other. This result yields a previously unidentified design principle, namely that of optimal resource allocation in cellular sensing. It states that, in an optimally designed sensing system, each class of resources is equally limiting so that no resource is wasted. We apply our theory to what is arguably the best-characterized sensing system in biology, the chemotaxis network of Escherichia coli. Our analysis reveals that this system obeys the principle of optimal resource allocation, indicating a selective pressure for the efficient design of cellular sensing systems.cell signaling | thermodynamics | design principles | chemotaxis | information transmission B iochemical networks are the information-processing devices of life. Like any device, they require resources to be built and run. Components are needed to construct the network, space is required to accommodate the components, time is needed to process the information, and energy is required to make the components and operate the network. These resources constrain the design and performance of any biochemical network. However, it is not clear which resources are indispensable, thus fundamentally limiting the performance of the network, and which resources might trade-off against each other. Here, we consider the interplay among cellular resources, network design, and performance in a canonical biochemical function, namely sensing the environment.Living cells can measure chemical concentrations with extraordinary precision (1-3), raising the question what sets the fundamental limit to the accuracy of chemical sensing (1). Cells measure chemical concentrations via receptors on their surface. These measurements are inevitably corrupted by noise that arises from the stochastic arrival of ligand molecules by diffusion and from the stochastic binding of the ligand to the receptor. Berg and Purcell pointed out that the sensing error is fundamentally bounded by this noise extrinsic to the cell, but that cells can reduce the error by taking multiple independent measurements (1). One way to increase the number of measurements is to add more receptors (1, 4). Another is to take more measurements per receptor over time; here, the cell infe...

Two contrasting theories have emerged that attempt to describe T-cell ligand potency, one based on the t 1/2 of the interaction and the other based on the equilibrium affinity (K D ). Here, we have identified and studied an extensive set of T-cell receptor (TCR)-peptide-MHC (pMHC) interactions for CD4 + cells that have differential K D s and kinetics of binding. Our data indicate that ligands with a short t 1/2 can be highly stimulatory if they have fast onrates. Simple models suggest these fast kinetic ligands are stimulatory because the pMHCs bind and rebind the same TCR several times. Rebinding occurs when the TCR-pMHC on-rate outcompetes TCR-pMHC diffusion within the cell membrane, creating an aggregate t 1/2 (t a ) that can be significantly longer than a single TCRpMHC encounter. Accounting for t a , ligand potency is K D -based when ligands have fast on-rates (k on ) and t 1/2 -dependent when they have slow k on . Thus, TCR-pMHC k on allow high-affinity short t 1/2 ligands to follow a kinetic proofreading model.T cell receptors (TCRs) expressed on T cells bind host MHC proteins presenting both self-and foreign pathogen-derived peptides (pMHCs). Depending on the signal emanating from these interactions, diverse biological outcomes ensue. In the thymus, these TCR-pMHC-mediated signals shape the specificity of the mature T-cell repertoire and prevent overtly self-reactive T cells from escaping (1). In the periphery, naive T cells require continual TCR engagement with self-pMHC complexes to receive a homeostatic survival signal, whereas engagements with foreign peptides induce rapid T-cell division and the acquisition of effector functions (2). How T cells interpret the interaction between their TCR and pMHC ligands leading to these different biological outcomes is greatly debated.Two competing models of T-cell activation have been proposed, with ligand potency being a function of TCR-pMHC equilibrium affinity (K D ) (3-7) or t 1/2 (8-11). Evidence supporting K D -based receptor occupancy models of TCR signaling comes from sets of ligands that show a correlation between the K D and ligand potency (3, 5) and from the fact that ligands induce qualitatively distinct biological outcomes depending on their concentration (12).In sharp contrast to receptor occupancy models, t 1/2 -based kinetic proofreading models hypothesize that the TCR must be engaged long enough to complete a series of signaling events, including coreceptor recruitment and TCR phosphorylation (13). Increases in the t 1/2 of the TCR-pMHC engagement raise the probability that any single TCR-pMHC engagement will surpass the threshold amount of time required to initiate T-cell activation (14). Recently, this threshold amount of time has been predicted to be at least 2 s (9, 15). Whether there is, in addition, an optimal t 1/2 that balances these kinetic proofreading requirements and the serial triggering of TCRs has been debated (16,17).Further evidence supporting t 1/2 -based kinetic proofreading models arises from the discovery of antagonist pMHC l...

Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why?We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitatively distinct from and worse than implied by the bound, and more complex steady-state copy processes cannot perform better. Nonetheless, the cost remains close to the thermodynamic bound unless accuracy is extremely high. Additionally, we show that biomolecular reactions could be used in thermodynamically optimal devices under exogenous manipulation of chemical fuels, suggesting an experimental system for testing computational thermodynamics.If it were possible to perform many measurements using a single bit of memory without putting in work, Maxwell's Demon could use the information gained to violate the second law of thermodynamics and extract net work from an equilibrium system. Landauer's insight that computational processes require a physical instantiation and therefore have thermodynamic consequences 1-3 is key to exorcising the Demon, and the survival of the second law has been demonstrated in a range of physical models 2-4 . If, unlike Maxwell's thought experiment, the correlations generated by a measurement or copy are not used to perform work, the cycle increases the entropy of the universe (by at least k ln 2 if the measurement is binary, perfectly accurate and has a 50/50 outcome) 2,4,5 . Landauer and others have provided specific physical implementations of binary devices along with protocols that achieve the thermodynamic bound for measurement cycles 2,3 or memory erasure protocols 1,6-9 . Examples include magnetic systems 1,2,9 , or single particles in pistons 4,5,10-13 . Do biomolecules perform measurement and copying within this computational paradigm? Many biological processes involve creating long-lived molecular copies of other molecules 2,14,15 . Perhaps the most tantalising analogy is in the cellular sensing of external ligand concentrations. Following the seminal work of Berg and Purcell 16 , it has been shown that cells can reduce their sensing error by averaging a noisy receptor signal over time [17][18][19][20][21][22][23][24] . Recent studies claim that cells implement time integration by dissipatively copying receptor states into the chemical modification states of readout molecules 24-26 . Other authors have highlighted the necessity of dissipation in adaption 27-29 and kinetic proofreading 30,31 .While it has been noted that there is a connection between the dissipation present in cellular copying and the a) Electronic mail: t.ouldridge@impeial.ac.uk thermodynamics of computation 24-26 , the nature ...

Enhanced signaling by the small guanosine triphosphatase Ras is common in T cell acute lymphoblastic leukemia/lymphoma (T-ALL, but the underlying mechanisms are unclear. Here, we identified the guanine nucleotide exchange factor RasGRP1 (Rasgrp1 in mice) as a Ras activator that contributes to leukemogenesis. We found increased RasGRP1 expression in many pediatric T-ALL patients, which we did not observe in rare early T cell precursor (ETP) T-ALL patients with KRAS and NRAS mutations, such as K-RasG12D. Leukemia screens in wild-type mice, but not in mice expressing the mutant K-RasG12D that encodes a constitutively active Ras, yielded frequent retroviral insertions that led to increased Rasgrp1 expression. Rasgrp1 and oncogenic K-RasG12D promoted T-ALL through distinct mechanisms. In K-RasG12D T-ALLs, we found that enhanced Ras activation did not lead to cell cycle arrest. In mouse T-ALL cells with increased Rasgrp1 expression, we found that Rasgrp1 contributed to a previously uncharacterized cytokine receptor–activated Ras pathway that stimulated the proliferation of T-ALL cells in vivo, which was accompanied by dynamic patterns of activation of effector kinases downstream of Ras in individual T-ALLs. Reduction of Rasgrp1 abundance reduced cytokine-stimulated Ras signaling and decreased the proliferation of T-ALL in vivo, suggesting that patients with this cancer should be screened for increased abundance of RasGRP1 to customize treatment.