Progeny counter mechanism in malaria parasites is linked to extracellular resources.

Malaria is caused by the rapid proliferation of Plasmodium parasites in patients and disease severity correlates with the number of infected red blood cells in circulation. Parasite multiplication within red blood cells is called schizogony and occurs through an atypical multinucleated cell division mode. The mechanisms regulating the number of daughter cells produced by a single progenitor are poorly understood. We investigated underlying regulatory principles by quantifying nuclear multiplication dynamics in Plasmodium falciparum and knowlesi using super-resolution time-lapse microscopy. This confirmed that the number of daughter cells was consistent with a model in which a counter mechanism regulates multiplication yet incompatible with a timer mechanism. P. falciparum cell volume at the start of nuclear division correlated with the final number of daughter cells. As schizogony progressed, the nucleocytoplasmic volume ratio, which has been found to be constant in all eukaryotes characterized so far, increased significantly, possibly to accommodate the exponentially multiplying nuclei. Depleting nutrients by dilution of culture medium caused parasites to produce fewer merozoites and reduced proliferation but did not affect cell volume or total nuclear volume at the end of schizogony. Our findings suggest that the counter mechanism implicated in malaria parasite proliferation integrates extracellular resource status to modify progeny number during blood stage infection.

Trade-offs between cost and information in cellular prediction.

Living cells can leverage correlations in environmental fluctuations to predict the future environment and mount a response ahead of time. To this end, cells need to encode the past signal into the output of the intracellular network from which the future input is predicted. Yet, storing information is costly while not all features of the past signal are equally informative on the future input signal. Here, we show for two classes of input signals that cellular networks can reach the fundamental bound on the predictive information as set by the information extracted from the past signal: Push-pull networks can reach this information bound for Markovian signals, while networks that take a temporal derivative can reach the bound for predicting the future derivative of non-Markovian signals. However, the bits of past information that are most informative about the future signal are also prohibitively costly. As a result, the optimal system that maximizes the predictive information for a given resource cost is, in general, not at the information bound. Applying our theory to the chemotaxis network of Escherichia coli reveals that its adaptive kernel is optimal for predicting future concentration changes over a broad range of background concentrations, and that the system has been tailored to predicting these changes in shallow gradients.

Quantitating CD8+ T cell memory development.

In acute immune responses to infection, memory T cells develop that can spawn recall responses. This process has not been observable directly in vivo. Here we highlight the utility of mathematical inference to derive quantitatively testable models of mammalian CD8+ T cell memory development from complex experimental data. Previous inference studies suggested that precursors of memory T cells arise early during the immune response. Recent work has both validated a crucial prediction of this T cell diversification model and refined the model. While multiple developmental routes to distinct memory subsets might exist, a branch point occurs early in proliferating T cell blasts, from which separate differentiation pathways emerge for slowly dividing precursors of re-expandable memory cells and rapidly dividing effectors.

Pyrimidine de novo synthesis inhibition selectively blocks effector but not memory T cell development.

Blocking pyrimidine de novo synthesis by inhibiting dihydroorotate dehydrogenase is used to treat autoimmunity and prevent expansion of rapidly dividing cell populations including activated T cells. Here we show memory T cell precursors are resistant to pyrimidine starvation. Although the treatment effectively blocked effector T cells, the number, function and transcriptional profile of memory T cells and their precursors were unaffected. This effect occurred in a narrow time window in the early T cell expansion phase when developing effector, but not memory precursor, T cells are vulnerable to pyrimidine starvation. This vulnerability stems from a higher proliferative rate of early effector T cells as well as lower pyrimidine synthesis capacity when compared with memory precursors. This differential sensitivity is a drug-targetable checkpoint that efficiently diminishes effector T cells without affecting the memory compartment. This cell fate checkpoint might therefore lead to new methods to safely manipulate effector T cell responses.

CycleFlow simultaneously quantifies cell-cycle phase lengths and quiescence in vivo.

Populations of stem, progenitor, or cancer cells show proliferative heterogeneity in vivo, comprising proliferating and quiescent cells. Consistent quantification of the quiescent subpopulation and progression of the proliferating cells through the individual phases of the cell cycle has not been achieved. Here, we describe CycleFlow, a method that robustly infers this comprehensive information from standard pulse-chase experiments with thymidine analogs. Inference is based on a mathematical model of the cell cycle, with realistic waiting time distributions for the G1, S, and G2/M phases and a long-term quiescent G0 state. We validate CycleFlow with an exponentially growing cancer cell line in vitro. Applying it to T cell progenitors in steady state in vivo, we uncover strong proliferative heterogeneity, with a minority of CD4+CD8+ T cell progenitors cycling very rapidly and then entering quiescence. CycleFlow is suitable as a routine method for quantitative cell-cycle analysis.

Fate mapping of hematopoietic stem cells reveals two pathways of native thrombopoiesis.

Hematopoietic stem cells (HSCs) produce highly diverse cell lineages. Here, we chart native lineage pathways emanating from HSCs and define their physiological regulation by computationally integrating experimental approaches for fate mapping, mitotic tracking, and single-cell RNA sequencing. We find that lineages begin to split when cells leave the tip HSC population, marked by high Sca-1 and CD201 expression. Downstream, HSCs either retain high Sca-1 expression and the ability to generate lymphocytes, or irreversibly reduce Sca-1 level and enter into erythro-myelopoiesis or thrombopoiesis. Thrombopoiesis is the sum of two pathways that make comparable contributions in steady state, a long route via multipotent progenitors and CD48hi megakaryocyte progenitors (MkPs), and a short route from HSCs to developmentally distinct CD48-/lo MkPs. Enhanced thrombopoietin signaling differentially accelerates the short pathway, enabling a rapid response to increasing demand. In sum, we provide a blueprint for mapping physiological differentiation fluxes from HSCs and decipher two functionally distinct pathways of native thrombopoiesis.

Asynchronous nuclear cycles in multinucleated Plasmodium falciparum facilitate rapid proliferation.

Malaria-causing parasites proliferate within erythrocytes through schizogony, forming multinucleated stages before cellularization. Nuclear multiplication does not follow a strict geometric 2n progression, and each proliferative cycle produces a variable number of progeny. Here, by tracking nuclei and DNA replication, we show that individual nuclei replicate their DNA at different times, despite residing in a shared cytoplasm. Extrapolating from experimental data using mathematical modeling, we provide strong indication that a limiting factor exists, which slows down the nuclear multiplication rate. Consistent with this prediction, our data show that temporally overlapping DNA replication events were significantly slower than partially overlapping or nonoverlapping events. Our findings suggest the existence of evolutionary pressure that selects for asynchronous DNA replication, balancing available resources with rapid pathogen proliferation.

Optimal ligand discrimination by asymmetric dimerization and turnover of interferon receptors.

In multicellular organisms, antiviral defense mechanisms evoke a reliable collective immune response despite the noisy nature of biochemical communication between tissue cells. A molecular hub of this response, the interferon I receptor (IFNAR), discriminates between ligand types by their affinity regardless of concentration. To understand how ligand type can be decoded robustly by a single receptor, we frame ligand discrimination as an information-theoretic problem and systematically compare the major classes of receptor architectures: allosteric, homodimerizing, and heterodimerizing. We demonstrate that asymmetric heterodimers achieve the best discrimination power over the entire physiological range of local ligand concentrations. This design enables sensing of ligand presence and type, and it buffers against moderate concentration fluctuations. In addition, receptor turnover, which drives the receptor system out of thermodynamic equilibrium, allows alignment of activation points for ligands of different affinities and thereby makes ligand discrimination practically independent of concentration. IFNAR exhibits this optimal architecture, and our findings thus suggest that this specialized receptor can robustly decode digital messages carried by its different ligands.

Single-molecule stretching experiments of flexible (wormlike) chain molecules in different ensembles: Theory and a potential application of finite chain length effects to nick-counting in DNA.

We propose a formalism for deriving force-elongation and elongation-force relations for flexible chain molecules from analytical expressions for their radial distribution function, which provides insight into the factors controlling the asymptotic behavior and finite chain length corrections. In particular, we apply this formalism to our previously developed interpolation formula for the wormlike chain end-to-end distance distribution. The resulting expression for the asymptotic limit of infinite chain length is of similar quality to the numerical evaluation of Marko and Siggia's variational theory and considerably more precise than their interpolation formula. A comparison to numerical data suggests that our analytical finite chain length corrections achieve a comparable accuracy. As an application of our results, we discuss the possibility of inferring the time-dependent number of nicks in single-molecule stretching experiments on double-stranded DNA from the accompanying changes in the effective chain length.

Single-Cell Tracing Dissects Regulation of Maintenance and Inheritance of Transcriptional Reinduction Memory.

Transcriptional memory of gene expression enables adaptation to repeated stimuli across many organisms. However, the regulation and heritability of transcriptional memory in single cells and through divisions remains poorly understood. Here, we combined microfluidics with single-cell live imaging to monitor Saccharomyces cerevisiae galactokinase 1 (GAL1) expression over multiple generations. By applying pedigree analysis, we dissected and quantified the maintenance and inheritance of transcriptional reinduction memory in individual cells through multiple divisions. We systematically screened for loss- and gain-of-memory knockouts to identify memory regulators in thousands of single cells. We identified new loss-of-memory mutants, which affect memory inheritance into progeny. We also unveiled a gain-of-memory mutant, elp6Δ, and suggest that this new phenotype can be mediated through decreased histone occupancy at the GAL1 promoter. Our work uncovers principles of maintenance and inheritance of gene expression states and their regulators at the single-cell level.

Hidden long-range memories of growth and cycle speed correlate cell cycles in lineage trees.

Cell heterogeneity may be caused by stochastic or deterministic effects. The inheritance of regulators through cell division is a key deterministic force, but identifying inheritance effects in a systematic manner has been challenging. Here, we measure and analyze cell cycles in deep lineage trees of human cancer cells and mouse embryonic stem cells and develop a statistical framework to infer underlying rules of inheritance. The observed long-range intra-generational correlations in cell-cycle duration, up to second cousins, seem paradoxical because ancestral correlations decay rapidly. However, this correlation pattern is naturally explained by the inheritance of both cell size and cell-cycle speed over several generations, provided that cell growth and division are coupled through a minimum-size checkpoint. This model correctly predicts the effects of inhibiting cell growth or cycle progression. In sum, we show how fluctuations of cell cycles across lineage trees help in understanding the coordination of cell growth and division.

eGFRD in all dimensions.

Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present "eGFRD2," a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions.

Stem cell homeostasis by integral feedback through the niche.

Hematopoiesis is a paradigm for tissue development and renewal from stem cells. Experiments show that the maintenance of hematopoietic stem cells (HSCs) relies on signals from niche cells. However, it is not known how the size of the HSC compartment is set. Competition by HSCs for niche access has been suggested, yet niche cells in the bone marrow outnumber HSCs. Here we propose a cooperative model of HSC homeostasis in which stem and niche cells mutually interact such that niche cells function as negative feedback regulators of HSC proliferation. This model explains puzzling experimental findings, including homeostatic recovery of the HSC compartment after irradiation versus apparent lack of recovery after HSC ablation. We show that bidirectional niche-stem cell regulation has properties of a proportional-integral feedback controller. Moreover, we predict that the outflux of differentiated cells from HSCs can be regulated by the affinity of HSCs for niche cells. Much effort has been devoted to elucidating niche cell signaling to stem cells; our theoretical insights indicate that studying the effect of stem cells on the niche may be equally important for understanding stem cell homeostasis.

Quantifying fluctuations in reversible enzymatic cycles and clocks.

Biochemical reactions are fundamentally noisy at a molecular scale. This limits the precision of reaction networks, but it also allows fluctuation measurements that may reveal the structure and dynamics of the underlying biochemical network. Here, we study nonequilibrium reaction cycles, such as the mechanochemical cycle of molecular motors, the phosphorylation cycle of circadian clock proteins, or the transition state cycle of enzymes. Fluctuations in such cycles may be measured using either of two classical definitions of the randomness parameter, which we show to be equivalent in general microscopically reversible cycles. We define a stochastic period for reversible cycles and present analytical solutions for its moments. Furthermore, we associate the two forms of the randomness parameter with the thermodynamic uncertainty relation, which sets limits on the timing precision of the cycle in terms of thermodynamic quantities. Our results should prove useful also for the study of temporal fluctuations in more general networks.

Optimal Prediction by Cellular Signaling Networks.

Living cells can enhance their fitness by anticipating environmental change. We study how accurately linear signaling networks in cells can predict future signals. We find that maximal predictive power results from a combination of input-noise suppression, linear extrapolation, and selective readout of correlated past signal values. Single-layer networks generate exponential response kernels, which suffice to predict Markovian signals optimally. Multilayer networks allow oscillatory kernels that can optimally predict non-Markovian signals. At low noise, these kernels exploit the signal derivative for extrapolation, while at high noise, they capitalize on signal values in the past that are strongly correlated with the future signal. We show how the common motifs of negative feedback and incoherent feed-forward can implement these optimal response functions. Simulations reveal that E. coli can reliably predict concentration changes for chemotaxis, and that the integration time of its response kernel arises from a trade-off between rapid response and noise suppression.

Rare switching events in non-stationary systems.

Physical systems with many degrees of freedom can often be understood in terms of transitions between a small number of metastable states. For time-homogeneous systems with short-term memory these transitions are fully characterized by a set of rate constants. We consider the question how to extend such a coarse-grained description to non-stationary systems and to systems with finite memory. We identify the physical regimes in which time-dependent rates are meaningful, and state microscopic expressions that can be used to measure both externally time-dependent and history-dependent rates in microscopic simulations. Our description can be used to generalize Markov state models to time-dependent Markovian or non-Markovian systems.

Non-stationary forward flux sampling.

We present a method, Non-Stationary Forward Flux Sampling, that allows efficient simulation of rare events in both stationary and non-stationary stochastic systems. The method uses stochastic branching and pruning to achieve uniform sampling of trajectories in phase space and time, leading to accurate estimates for time-dependent switching propensities and time-dependent phase space probability densities. It is suitable for equilibrium or non-equilibrium systems, in or out of stationary state, including non-Markovian or externally driven systems. We demonstrate the validity of the technique by applying it to a one-dimensional barrier crossing problem that can be solved exactly, and show its usefulness by applying it to the time-dependent switching of a genetic toggle switch.

From crystal and NMR structures, footprints and cryo-electron-micrographs to large and soft structures: nanoscale modeling of the nucleosomal stem.

The interaction of histone H1 with linker DNA results in the formation of the nucleosomal stem structure, with considerable influence on chromatin organization. In a recent paper [Syed,S.H., Goutte-Gattat,D., Becker,N., Meyer,S., Shukla,M.S., Hayes,J.J., Everaers,R., Angelov,D., Bednar,J. and Dimitrov,S. (2010) Single-base resolution mapping of H1-nucleosome interactions and 3D organization of the nucleosome. Proc. Natl Acad. Sci. USA, 107, 9620-9625], we published results of biochemical footprinting and cryo-electron-micrographs of reconstituted mono-, di- and tri-nucleosomes, for H1 variants with different lengths of the cationic C-terminus. Here, we present a detailed account of the analysis of the experimental data and we include thermal fluctuations into our nano-scale model of the stem structure. By combining (i) crystal and NMR structures of the nucleosome core particle and H1, (ii) the known nano-scale structure and elasticity of DNA, (iii) footprinting information on the location of protected sites on the DNA backbone and (iv) cryo-electron micrographs of reconstituted tri-nucleosomes, we arrive at a description of a polymorphic, hierarchically organized stem with a typical length of 20 ± 2 base pairs. A comparison to linker conformations inferred for poly-601 fibers with different linker lengths suggests, that intra-stem interactions stabilize and facilitate the formation of dense chromatin fibers.

Looping probabilities in model interphase chromosomes.

Fluorescence in-situ hybridization (FISH) and chromosome conformation capture (3C) are two powerful techniques for investigating the three-dimensional organization of the genome in interphase nuclei. The use of these techniques provides complementary information on average spatial distances (FISH) and contact probabilities (3C) for specific genomic sites. To infer the structure of the chromatin fiber or to distinguish functional interactions from random colocalization, it is useful to compare experimental data to predictions from statistical fiber models. The current estimates of the fiber stiffness derived from FISH and 3C differ by a factor of 5. They are based on the wormlike chain model and a heuristic modification of the Shimada-Yamakawa theory of looping for unkinkable, unconstrained, zero-diameter filaments. Here, we provide an extended theoretical and computational framework to explain the currently available experimental data for various species on the basis of a unique, minimal model of decondensing chromosomes: a kinkable, topologically constraint, semiflexible polymer with the (FISH) Kuhn length of l(K) = 300 nm, 10 kinks per Mbp, and a contact distance of 45 nm. In particular: 1), we reconsider looping of finite-diameter filaments on the basis of an analytical approximation (novel, to our knowledge) of the wormlike chain radial density and show that unphysically large contact radii would be required to explain the 3C data based on the FISH estimate of the fiber stiffness; 2), we demonstrate that the observed interaction frequencies at short genomic lengths can be explained by the presence of a low concentration of curvature defects (kinks); and 3), we show that the most recent experimental 3C data for human chromosomes are in quantitative agreement with interaction frequencies extracted from our simulations of topologically confined model chromosomes.

Comment on "Remeasuring the double helix".

Mathew-Fenn et al. (Reports, 17 October 2008, p. 446) reported unexpected distance fluctuations in short end-labeled DNA constructs and interpreted them as evidence for cooperative DNA stretching modes. We show that when accounting for a subtle linker leverage effect, their data can be understood within standard noncooperative DNA elasticity.