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Fundamental mechanisms governing cell size control and homeostasis are still poorly understood. The relationship between sizes at division and birth in single cells is used as a metric to categorize the basis of size homeostasis. Cells dividing at a fixed size regardless of birth size (sizer) are expected to show a division-birth slope of zero, whereas cells dividing after growing for a fixed size increment (adder) have an expected slope of +1. These two theoretical values are, however, rarely experimentally observed. For example, rod-shaped fission yeast Schizosaccharomyces pombe cells, which divide at a fixed surface area, exhibit a division-birth slope for cell lengths of 0.25 ± 0.02, significantly different from the expected sizer value of zero. Here, we investigate possible reasons for this discrepancy by developing a mathematical model of sizer control including the relevant sources of variation. Our results support pure sizer control and show that deviation from zero slope is exaggerated by measurement of an inappropriate geometrical quantity (e.g., length instead of area), combined with cell-to-cell radius variability. The model predicts that mutants with greater errors in size sensing or septum positioning paradoxically appear to behave as better sizers. Furthermore, accounting for cell width variability, we show that pure sizer control can in some circumstances reproduce the apparent adder behavior observed in Escherichia coli. These findings demonstrate that analysis of geometric variation can lead to new insights into cell size control.

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How cell size is determined and maintained remains unclear, even in simple model organisms. In proliferating cells, cell size is regulated by coordinating growth and division through sizer, adder, or timer mechanisms or through some combination [1, 2]. Currently, the best-characterized example of sizer behavior is in fission yeast, Schizosaccharomyces pombe, which enters mitosis at a minimal cell size threshold. The peripheral membrane kinase Cdr2 localizes in clusters (nodes) on the medial plasma membrane and promotes mitotic entry [3]. Here, we show that the Cdr2 nodal density, which scales with cell size, is used by the cell to sense and control its size. By analyzing cells of different widths, we first show that cdr2+ cells divide at a fixed cell surface area. However, division in the cdr2Δ mutant is more closely specified by cell volume, suggesting that Cdr2 is essential for area sensing and supporting the existence of a Cdr2-independent secondary sizer mechanism more closely based on volume. To investigate how Cdr2 nodes may sense area, we derive a minimal mathematical model that incorporates the cytoplasmic kinase Ssp1 as a Cdr2 activator. The model predicts that a cdr2 mutant in an Ssp1 phosphorylation site (cdr2-T166A) [4] should form nodes whose density registers cell length. We confirm this prediction experimentally and find that thin cells now follow this new scaling by dividing at constant length instead of area. This work supports the role of Cdr2 as a sizer factor and highlights the importance of studying geometrical aspects of size control.

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Drug-resistant bacterial pathogens pose an urgent public-health crisis. Here, we report the discovery, from microbial-extract screening, of a nucleoside-analog inhibitor that inhibits bacterial RNA polymerase (RNAP) and exhibits antibacterial activity against drug-resistant bacterial pathogens: pseudouridimycin (PUM). PUM is a natural product comprising a formamidinylated, N-hydroxylated Gly-Gln dipeptide conjugated to 6'-amino-pseudouridine. PUM potently and selectively inhibits bacterial RNAP in vitro, inhibits bacterial growth in culture, and clears infection in a mouse model of Streptococcus pyogenes peritonitis. PUM inhibits RNAP through a binding site on RNAP (the NTP addition site) and mechanism (competition with UTP for occupancy of the NTP addition site) that differ from those of the RNAP inhibitor and current antibacterial drug rifampin (Rif). PUM exhibits additive antibacterial activity when co-administered with Rif, exhibits no cross-resistance with Rif, and exhibits a spontaneous resistance rate an order-of-magnitude lower than that of Rif. PUM is a highly promising lead for antibacterial therapy.

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Cell size is partly determined through coordination between cell growth and division. How this coordination is achieved mechanistically remains mostly unknown. However, quantitative experiments together with computational modelling have reinvigorated the field and are elucidating underlying molecular processes. Size homeostasis may be achieved through different modes of regulation, including "sizers", "adders" and "timers." For sizer regulation, the cell division cycle does not proceed until a minimal size has been reached, requiring that the cell monitors its own size. Here, we highlight progress in defining sizer mechanisms in fission and budding yeasts showing how accumulation or dilution of key molecules can be used to monitor cell size during growth. We also discuss a potential role for sizers in bacterial size control.

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A way to decipher the complexity of the cellular metabolism is to study the effect of different external perturbations. Through an analysis over a sufficiently large set of gene knockouts and growing conditions, one aims to find a unifying principle that governs the metabolic regulation. For instance, it is known that the cessation of the microorganism proliferation after a gene deletion is only transient. However, we do not know the guiding principle that determines the partial or complete recovery of the growth rate, the corresponding redistribution of the metabolic fluxes and the possible different phenotypes. In spite of this large variety in the observed metabolic adjustments, we show that responses of E. coli to several different perturbations can always be derived from a sequence of greedy and myopic resilencings. This simple mechanism provides a detailed explanation for the experimental dynamics both at cellular (proliferation rate) and molecular level ((13)C-determined fluxes), also in case of appearance of multiple phenotypes. As additional support, we identified an example of a simple network motif that is capable of implementing this myopic greediness in the regulation of the metabolism.

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In simple organisms like E.coli, the metabolic response to an external perturbation passes through a transient phase in which the activation of a number of latent pathways can guarantee survival at the expenses of growth. Growth is gradually recovered as the organism adapts to the new condition. This adaptation can be modeled as a process of repeated metabolic adjustments obtained through the resilencings of the non-essential metabolic reactions, using growth rate as selection probability for the phenotypes obtained. The resulting metabolic adaptation process tends naturally to steer the metabolic fluxes towards high growth phenotypes. Quite remarkably, when applied to the central carbon metabolism of E.coli, it follows that nearly all flux distributions converge to the flux vector representing optimal growth, i.e., the solution of the biomass optimization problem turns out to be the dominant attractor of the metabolic adaptation process.

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Rod photoreceptors consist of an outer segment (OS) and an inner segment. Inside the OS a biochemical machinery transforms the rhodopsin photoisomerization into electrical signal. This machinery has been treated as and is thought to be homogenous with marginal inhomogeneities. To verify this assumption, we developed a methodology based on special tapered optical fibers (TOFs) to deliver highly localized light stimulations. By using these TOFs, specific regions of the rod OS could be stimulated with spots of light highly confined in space. As the TOF is moved from the OS base toward its tip, the amplitude of saturating and single photon responses decreases, demonstrating that the efficacy of the transduction machinery is not uniform and is 5-10 times higher at the base than at the tip. This gradient of efficacy of the transduction machinery is attributed to a progressive depletion of the phosphodiesterase along the rod OS. Moreover we demonstrate that, using restricted spots of light, the duration of the photoresponse along the OS does not increase linearly with the light intensity as with diffuse light.

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MOTIVATION: Within Flux Balance Analysis, the investigation of complex subtasks, such as finding the optimal perturbation of the network or finding an optimal combination of drugs, often requires to set up a bilevel optimization problem. In order to keep the linearity and convexity of these nested optimization problems, an ON/OFF description of the effect of the perturbation (i.e. Boolean variable) is normally used. This restriction may not be realistic when one wants, for instance, to describe the partial inhibition of a reaction induced by a drug. RESULTS: In this paper we present a formulation of the bilevel optimization which overcomes the oversimplified ON/OFF modeling while preserving the linear nature of the problem. A case study is considered: the search of the best multi-drug treatment which modulates an objective reaction and has the minimal perturbation on the whole network. The drug inhibition is described and modulated through a convex combination of a fixed number of Boolean variables. The results obtained from the application of the algorithm to the core metabolism of E.coli highlight the possibility of finding a broader spectrum of drug combinations compared to a simple ON/OFF modeling. CONCLUSIONS: The method we have presented is capable of treating partial inhibition inside a bilevel optimization, without loosing the linearity property, and with reasonable computational performances also on large metabolic networks. The more fine-graded representation of the perturbation allows to enlarge the repertoire of synergistic combination of drugs for tasks such as selective perturbation of cellular metabolism. This may encourage the use of the approach also for other cases in which a more realistic modeling is required.

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MOTIVATION: A gene regulatory network in which the modes (activation/inhibition) of the transcriptional regulations are known and in which gene expression assumes boolean values can be treated as a system of linear equations over a binary field, i.e. as a constraint satisfaction problem for an information code. RESULTS: For currently available gene networks, we show in this article that the distortion associated with the corresponding information code is much lower than expected from null models, and that it is close to (when not lower than) the Shannon bound determined by the rate-distortion theorem. This corresponds to saying that the distribution of regulatory modes is highly atypical in the networks, and that this atypicality greatly helps in avoiding contradictory transcriptional actions. Choosing a boolean formalism to represent the gene networks, we also show how to formulate criteria for the selection of gates that maximize the compatibility with the empirical information available on the transcriptional regulatory modes. Proceeding in this way, we obtain in particular that non-canalizing gates are upper-bounded by the distortion, and hence that the boolean gene networks are more canalizing than expected from null models.

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Sensory systems adapt, i.e., they adjust their sensitivity to external stimuli according to the ambient level. In this paper we show that single cell electrophysiological responses of vertebrate olfactory receptors and of photoreceptors to different input protocols exhibit several common features related to adaptation, and that these features can be used to investigate the dynamical structure of the feedback regulation responsible for the adaptation. In particular, we point out that two different forms of adaptation can be observed, in response to steps and to pairs of pulses. These two forms of adaptation appear to be in a dynamical trade-off: the more adaptation to a step is close to perfect, the slower is the recovery in adaptation to pulse pairs and viceversa. Neither of the two forms is explained by the dynamical models currently used to describe adaptation, such as the integral feedback model.

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This note presents a review of recent work by the authors on angiogenesis, as a case study for analyzing the role of randomness in the formation of biological patterns. The mathematical description of the formation of new vessels is presented, based on a system of stochastic differential equations, coupled with a branching process, both of them driven by a set of relevant chemotactic underlying fields. A discussion follows about the possible reduction of complexity of the above approach, by mean field approximations of the underlying fields. The crucial role of randomness at the microscale is observed in order to obtain nontrivial realistic vessel networks.

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BACKGROUND: In the field of drug discovery, assessing the potential of multidrug therapies is a difficult task because of the combinatorial complexity (both theoretical and experimental) and because of the requirements on the selectivity of the therapy. To cope with this problem, we have developed a novel method for the systematic in silico investigation of synergistic effects of currently available drugs on genome-scale metabolic networks. RESULTS: The algorithm finds the optimal combination of drugs which guarantees the inhibition of an objective function, while minimizing the side effect on the other cellular processes. Two different applications are considered: finding drug synergisms for human metabolic diseases (like diabetes, obesity and hypertension) and finding antitumoral drug combinations with minimal side effect on the normal human cell. The results we obtain are consistent with some of the available therapeutic indications and predict new multiple drug treatments. A cluster analysis on all possible interactions among the currently available drugs indicates a limited variety on the metabolic targets for the approved drugs. CONCLUSION: The in silico prediction of drug synergisms can represent an important tool for the repurposing of drugs in a realistic perspective which considers also the selectivity of the therapy. Moreover, for a more profitable exploitation of drug-drug interactions, we have shown that also experimental drugs which have a different mechanism of action can be reconsider as potential ingredients of new multicompound therapeutic indications. Needless to say the clues provided by a computational study like ours need in any case to be thoroughly evaluated experimentally.

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Structural balance theory affirms that signed social networks (i.e., graphs whose signed edges represent friendly/hostile interactions among individuals) tend to be organized so as to avoid conflictual situations, corresponding to cycles of negative parity. Using an algorithm for ground-state calculation in large-scale Ising spin glasses, in this paper we compute the global level of balance of very large online social networks and verify that currently available networks are indeed extremely balanced. This property is explainable in terms of the high degree of skewness of the sign distributions on the nodes of the graph. In particular, individuals linked by a large majority of negative edges create mostly "apparent disorder," rather than true "frustration."

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The chemotactic response of cells to graded fields of chemical cues is a complex process that requires the coordination of several intracellular activities. Fundamental steps to obtain a front vs. back differentiation in the cell are the localized distribution of internal molecules and the amplification of the external signal. The goal of this work is to develop a mathematical and computational model for the quantitative study of such phenomena in the context of axon chemotactic pathfinding in neural development. In order to perform turning decisions, axons develop front-back polarization in their distal structure, the growth cone. Starting from the recent experimental findings of the biased redistribution of receptors on the growth cone membrane, driven by the interaction with the cytoskeleton, we propose a model to investigate the significance of this process. Our main contribution is to quantitatively demonstrate that the autocatalytic loop involving receptors, cytoplasmic species and cytoskeleton is adequate to give rise to the chemotactic behavior of neural cells. We assess the fact that spatial bias in receptors is a precursory key event for chemotactic response, establishing the necessity of a tight link between upstream gradient sensing and downstream cytoskeleton dynamics. We analyze further crosslinked effects and, among others, the contribution to polarization of internal enzymatic reactions, which entail the production of molecules with a one-to-more factor. The model shows that the enzymatic efficiency of such reactions must overcome a threshold in order to give rise to a sufficient amplification, another fundamental precursory step for obtaining polarization. Eventually, we address the characteristic behavior of the attraction/repulsion of axons subjected to the same cue, providing a quantitative indicator of the parameters which more critically determine this nontrivial chemotactic response.

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