Distinguishing excess mutations and increased cell death based on variant allele frequencies.

Tumors often harbor orders of magnitude more mutations than healthy tissues. The increased number of mutations may be due to an elevated mutation rate or frequent cell death and correspondingly rapid cell turnover, or a combination of the two. It is difficult to disentangle these two mechanisms based on widely available bulk sequencing data, where sequences from individual cells are intermixed and, thus, the cell lineage tree of the tumor cannot be resolved. Here we present a method that can simultaneously estimate the cell turnover rate and the rate of mutations from bulk sequencing data. Our method works by simulating tumor growth and finding the parameters with which the observed data can be reproduced with maximum likelihood. Applying this method to a real tumor sample, we find that both the mutation rate and the frequency of death may be high.

A compartment size-dependent selective threshold limits mutation accumulation in hierarchical tissues.

Cancer is a genetic disease fueled by somatic evolution. Hierarchical tissue organization can slow somatic evolution by two qualitatively different mechanisms: by cell differentiation along the hierarchy "washing out" harmful mutations and by limiting the number of cell divisions required to maintain a tissue. Here we explore the effects of compartment size on somatic evolution in hierarchical tissues by considering cell number regulation that acts on cell division rates such that the number of cells in the tissue has the tendency to return to its desired homeostatic value. Introducing mutants with a proliferative advantage, we demonstrate the existence of a third fundamental mechanism by which hierarchically organized tissues are able to slow down somatic evolution. We show that tissue size regulation leads to the emergence of a threshold proliferative advantage, below which mutants cannot persist. We find that the most significant determinant of the threshold selective advantage is compartment size, with the threshold being higher the smaller the compartment. Our results demonstrate that, in sufficiently small compartments, even mutations that confer substantial proliferative advantage cannot persist, but are expelled from the tissue by differentiation along the hierarchy. The resulting selective barrier can significantly slow down somatic evolution and reduce the risk of cancer by limiting the accumulation of mutations that increase the proliferation of cells.

Nanotubes connecting B lymphocytes: High impact of differentiation-dependent lipid composition on their growth and mechanics.

Nanotubes (NTs) are thin, long membranous structures forming novel, yet poorly known communication pathways between various cell types. Key mechanisms controlling their growth still remained poorly understood. Since NT-forming capacity of immature and mature B cells was found largely different, we investigated how lipid composition and molecular order of the membrane affect NT-formation. Screening B cell lines with various differentiation stages revealed that NT-growth linearly correlates with membrane ganglioside levels, while it shows maximum as a function of cholesterol level. NT-growth of B lymphocytes is promoted by raftophilic phosphatidylcholine and sphingomyelin species, various glycosphingolipids, and docosahexaenoic acid-containing inner leaflet lipids, through supporting membrane curvature, as demonstrated by comparative lipidomic analysis of mature versus immature B cell membranes. Targeted modification of membrane cholesterol and sphingolipid levels altered NT-forming capacity confirming these findings, and also highlighted that the actual lipid raft number may control NT-growth via defining the number of membrane-F-actin coupling sites. Atomic force microscopic mechano-manipulation experiments further proved that mechanical properties (elasticity or bending stiffness) of B cell NTs also depend on the actual membrane lipid composition. Data presented here highlight importance of the lipid side in controlling intercellular, nanotubular, regulatory communications in the immune system.

Effective temperature of mutations.

Biological macromolecules experience two seemingly very different types of noise acting on different time scales: (i) point mutations corresponding to changes in molecular sequence and (ii) thermal fluctuations. Examining the secondary structures of a large number of microRNA precursor sequences and model lattice proteins, we show that the effects of single point mutations are statistically indistinguishable from those of an increase in temperature by a few tens of kelvins. The existence of such an effective mutational temperature establishes a quantitative connection between robustness to genetic (mutational) and environmental (thermal) perturbations.

Development of hat-shaped liposomes on solid supports.

We introduce a simple dynamical model which can explain the development of hat-shaped surface attached liposomes by taking membrane self-adhesion into account. The model reveals that hat formation is a general phenomenon, although it is difficult to observe experimentally. We show under what conditions hat-shaped vesicles can become observable. One such scenario, in consistency with AFM measurements, is that the dynamics is slowed down by the low rate of the outflow of the internal fluid of the vesicle through the narrow space between the two bilayers of the brim.

Viscosity dependence of passage through a fluctuating bottleneck.

We generalize the model of a rate process involving the passage of an object through a fluctuating bottleneck. The rate of passage is considered to be proportional to a power function of the radius of the bottleneck with exponent α > 0. The fluctuations of the bottleneck are coupled to the motion of the surrounding medium and governed by Langevin dynamics. We show numerically and also explain analytically that for slow bottleneck fluctuations the long time decay rate of the process has a fractional power law dependence on the solvent viscosity with exponent α/(α + 2). The results are consistent with the experimental data on ligand binding to myoglobin, and might also be relevant to other reactions for which exponents between 0 and 1 were reported.

How mutation accumulation depends on the structure of the cell lineage tree.

All the cells of a multicellular organism are the product of cell divisions that trace out a single binary tree, the so-called cell lineage tree. Because cell divisions are accompanied by replication errors, the shape of the cell lineage tree is a key determinant of how somatic evolution, which can potentially lead to cancer, proceeds. Carcinogenesis requires the accumulation of a certain number of driver mutations. By mapping the accumulation of mutations into a graph theoretical problem, we present an exact numerical method to calculate the probability of collecting a given number of mutations and show that for low mutation rates it can be approximated with a simple analytical formula, which depends only on the distribution of the lineage lengths, and is dominated by the longest lineages. Our results are crucial in understanding how natural selection can shape the cell lineage trees of multicellular organisms and curtail somatic evolution.

Internal friction in enzyme reactions.

The empirical concept of internal friction was introduced 20 years ago. This review summarizes the results of experimental and theoretical studies that help to uncover the nature of internal friction. After the history of the concept, we describe the experimental challenges in measuring and interpreting internal friction based on the viscosity dependence of enzyme reactions. We also present speculations about the structural background of this viscosity dependence. Finally, some models about the relationship between the energy landscape and internal friction are outlined. Alternative concepts regarding the viscosity dependence of enzyme reactions are also discussed.

The structure of the hematopoietic system can explain chronic myeloid leukemia progression.

Almost all cancer types share the hallmarks of cancer and a similar tumor formation: fueled by stochastic mutations in somatic cells. In case of chronic myeloid leukemia (CML), this evolutionary process can be tracked from an asymptomatic long-lasting chronic phase to a final rapidly evolving blast phase. Somatic evolution in CML occurs in the context of healthy blood production, a hierarchical process of cell division; initiated by stem cells that self-renew and differentiate to produce mature blood cells. Here we introduce a general model of hierarchical cell division explaining the particular progression of CML as resulting from the structure of the hematopoietic system. Driver mutations confer a growth advantage to the cells carrying them, for instance, the BCR::ABL1 gene, which also acts as a marker for CML. We investigated the relation of the BCR::ABL1 mutation strength to the hematopoietic stem cell division rate by employing computer simulations and fitting the model parameters to the reported median duration for the chronic and accelerated phases. Our results demonstrate that driver mutations (additional to the BCR::ABL1 mutation) are necessary to explain CML progression if stem cells divide sufficiently slowly. We observed that the number of mutations accumulated by cells at the more differentiated levels of the hierarchy is not affected by driver mutations present in the stem cells. Our results shed light on somatic evolution in a hierarchical tissue and show that the clinical hallmarks of CML progression result from the structural characteristics of blood production.

Temperature dependence of internal friction in enzyme reactions.

Our aim was to elucidate the physical background of internal friction of enzyme reactions by investigating the temperature dependence of internal viscosity. By rapid transient kinetic methods, we directly measured the rate constant of trypsin 4 activation, which is an interdomain conformational rearrangement, as a function of temperature and solvent viscosity. We found that the apparent internal viscosity shows an Arrhenius-like temperature dependence, which can be characterized by the activation energy of internal friction. Glycine and alanine mutations were introduced at a single position of the hinge of the interdomain region to evaluate how the flexibility of the hinge affects internal friction. We found that the apparent activation energies of the conformational change and the internal friction are interconvertible parameters depending on the protein flexibility. The more flexible a protein was, the greater proportion of the total activation energy of the reaction was observed as the apparent activation energy of internal friction. Based on the coupling of the internal and external movements of the protein during its conformational change, we constructed a model that quantitatively relates activation energy, internal friction, and protein flexibility.

Streamlined determination of processive run length and mechanochemical coupling of nucleic acid motor activities.

Quantitative determination of enzymatic rates, processivity and mechanochemical coupling is a key aspect in characterizing nucleotide triphosphate (NTP)-driven nucleic acid motor enzymes, for both basic research and technological applications. Here, we present a streamlined analytical method suitable for the determination of all key functional parameters based on measurement of NTP hydrolysis during interaction of motor enzymes with the nucleic acid track. The proposed method utilizes features of kinetic time courses of NTP hydrolysis that have not been addressed in previous analyses, and also accounts for the effect of protein traps used in kinetic experiments on processivity. This analysis is suitable for rapid and precise assessment of the effects of mutations, physical conditions, binding partners and other effectors on the functioning of translocases, helicases, polymerases and other NTP-consuming processive nucleic acid motors.

Trade-off between reducing mutational accumulation and increasing commitment to differentiation determines tissue organization.

Species-specific differences control cancer risk across orders of magnitude variation in body size and lifespan, e.g., by varying the copy numbers of tumor suppressor genes. It is unclear, however, how different tissues within an organism can control somatic evolution despite being subject to markedly different constraints, but sharing the same genome. Hierarchical differentiation, characteristic of self-renewing tissues, can restrain somatic evolution both by limiting divisional load, thereby reducing mutation accumulation, and by increasing cells' commitment to differentiation, which can "wash out" mutants. Here, we explore the organization of hierarchical tissues that have evolved to limit their lifetime incidence of cancer. Estimating the likelihood of cancer in the presence of mutations that enhance self-proliferation, we demonstrate that a trade-off exists between mutation accumulation and the strength of washing out. Our results explain differences in the organization of widely different hierarchical tissues, such as colon and blood.

Neck-linker docking coordinates the kinetics of kinesin's heads.

Conventional kinesin is a two-headed homodimeric motor protein, which is able to walk along microtubules processively by hydrolyzing ATP. Its neck linkers, which connect the two motor domains and can undergo a docking/undocking transition, are widely believed to play the key role in the coordination of the chemical cycles of the two motor domains and, consequently, in force production and directional stepping. Although many experiments, often complemented with partial kinetic modeling of specific pathways, support this idea, the ultimate test of the viability of this hypothesis requires the construction of a complete kinetic model. Considering the two neck linkers as entropic springs that are allowed to dock to their head domains, and incorporating only the few most relevant kinetic and structural properties of the individual heads, we develop here the first, to our knowledge, detailed, thermodynamically consistent model of kinesin that can 1), explain the cooperation of the heads (including their gating mechanisms) during walking, and 2), reproduce much of the available experimental data (speed, dwell-time distribution, randomness, processivity, hydrolysis rate, etc.) under a wide range of conditions (nucleotide concentrations, loading force, neck-linker length and composition, etc.). Besides revealing the mechanism by which kinesin operates, our model also makes it possible to look into the experimentally inaccessible details of the mechanochemical cycle and predict how certain changes in the protein affect its motion.

Uncovering the overlapping community structure of complex networks in nature and society.

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.

Congruent evolution of genetic and environmental robustness in micro-RNA.

Genetic robustness, the preservation of an optimal phenotype in the face of mutations, is critical to the understanding of evolution as phenotypically expressed genetic variation is the fuel of natural selection. The origin of genetic robustness, whether it evolves directly by natural selection or it is a correlated byproduct of other phenotypic traits, is, however, unresolved. Examining micro-RNA (miRNA) genes of several eukaryotic species, Borenstein and Ruppin (Borenstein E, Ruppin E. 2006. Direct evolution of genetic robustness in microRNA. Proc Natl Acad Sci USA. 103: 6593) showed that the structure of miRNA precursor stem loops exhibits significantly increased mutational robustness in comparison with a sample of random RNA sequences with the same stem-loop structure. The observed robustness was found to be uncorrelated with traditional measures of environmental robustness-implying that miRNA sequences show evidence of the direct evolution of genetic robustness. These findings are surprising as theoretical results indicate that the direct evolution of robustness requires high mutation rates and/or large effective population sizes only found among RNA viruses, not multicellular eukaryotes. We demonstrate that the sampling method used by Borenstein and Ruppin introduced significant bias that lead to an overestimation of robustness. Introducing a novel measure of environmental robustness based on the equilibrium thermodynamic ensemble of secondary structures of the miRNA precursor sequences, we demonstrate that the biophysics of RNA folding induces a high level of correlation between genetic (mutational) and environmental (thermodynamic) robustness, as expected from the theory of plastogenetic congruence introduced by Ancel and Fontana (Ancel LW, Fontana W. 2000. Plasticity, evolvability, and modularity in RNA. J Exp Zool. 288: 242-283). In light of theoretical considerations, we believe that this correlation strongly suggests that genetic robustness observed in miRNA sequences is the byproduct of selection for environmental robustness.

Self-division of giant vesicles driven by an internal enzymatic reaction.

Self-division is one of the most common phenomena in living systems and one of the most important properties of life driven by internal mechanisms of cells. Design and engineering of synthetic cells from abiotic components can recreate a life-like function thus contributing to the understanding of the origin of life. Existing methods to induce the self-division of vesicles require external and non-autonomous triggers (temperature change and the addition of membrane precursors). Here we show that pH-responsive giant unilamellar vesicles on the micrometer scale can undergo self-division triggered by an internal autonomous chemical stimulus driven by an enzymatic (urea-urease) reaction coupled to a cross-membrane transport of the substrate, urea. The bilayer of the artificial cells is composed of a mixture of phospholipids (POPC, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine) and oleic acid molecules. The enzymatic reaction increases the pH in the lumen of the vesicles, which concomitantly changes the protonation state of the oleic acid in the inner leaflet of the bilayer causing the removal of the membrane building blocks into the lumen of the vesicles thus decreasing the inner membrane area with respect to the outer one. This process coupled to the osmotic stress (responsible for the volume loss of the vesicles) leads to the division of a mother vesicle into two smaller daughter vesicles. These two processes must act in synergy; none of them alone can induce the division. Overall, our self-dividing system represents a step forward in the design and engineering of a complex autonomous model of synthetic cells.

Adhesion force measurements on functionalized microbeads: An in-depth comparison of computer controlled micropipette and fluidic force microscopy.

Characterization of the binding of functionalized microparticles to surfaces with a specific chemistry sheds light on molecular scale interactions. Polymer or protein adsorption are often monitored by colloid particle deposition. Force measurements on microbeads by atomic force microscopy (AFM) or optical tweezers are standard methods in molecular biophysics, but typically have low throughput. Washing and centrifuge assays with (bio)chemically decorated microbeads provide better statistics, but only qualitative results without a calibrated binding force or energy value. In the present work we demonstrate that a computer controlled micropipette (CCMP) is a straightforward and high-throughput alternative to quantify the surface adhesion of functionalized microparticles. However, being an indirect force measurement technique, its in-depth comparison with a direct force measurement is a prerequisite of applications requiring calibrated adhesion force values. To this end, we attached polystyrene microbeads to a solid support by the avidin-biotin linkage. We measured the adhesion strength of the microbeads with both a specialized robotic fluid force microscope (FluidFM BOT) and CCMP. Furthermore, the bead-support contact zone was directly characterized on an optical waveguide biosensor to determine the density of avidin molecules. Distribution of the detachment force recorded on ∼50 individual beads by FluidFM BOT was compared to the adhesion distribution obtained from CCMP measurements on hundreds of individual beads. We found that both methods provide unimodal histograms. We conclude that FluidFM BOT can directly measure the detachment force curve of 50 microbeads in 150 min. CCMP can provide calibrated binding/adhesion force values of 120 microbeads in an hour.

Evolutionary games on minimally structured populations.

Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects have, however, proved to be sensitive to the details of the underlying topology and dynamics. Here we introduce a minimal population structure that is described by two distinct hierarchical levels of interaction, similar to the structured metapopulation concept of ecology and island models in population genetics. We believe this model is able to identify effects of spatial structure that do not depend on the details of the topology. While effects depending on such details clearly lie outside the scope of our approach, we expect that those we are able to reproduce should be generally applicable to a wide range of models. We derive the dynamics governing the evolution of a system starting from fundamental individual level stochastic processes through two successive mean-field approximations. In our model of population structure the topology of interactions is described by only two parameters: the effective population size at the local scale and the relative strength of local dynamics to global mixing. We demonstrate, for example, the existence of a continuous transition leading to the dominance of cooperation in populations with hierarchical levels of unstructured mixing as the benefit to cost ratio becomes smaller then the local population size. Applying our model of spatial structure to the repeated prisoner's dilemma we uncover a counterintuitive mechanism by which the constant influx of defectors sustains cooperation. Further exploring the phase space of the repeated prisoner's dilemma and also of the "rock-paper-scissor" game we find indications of rich structure and are able to reproduce several effects observed in other models with explicit spatial embedding, such as the maintenance of biodiversity and the emergence of global oscillations.

The relevance of neck linker docking in the motility of kinesin.

Conventional kinesin is a motor protein, which is able to walk along a microtubule processively. The exact mechanism of the stepping motion and force generation of kinesin is still far from clear. In this paper we argue that neck linker docking is a crucial element of this mechanism, without which the experimentally observed dwell times of the steps could not be explained under a wide range of loading forces. We also show that the experimental data impose very strict constraints on the lengths of both the neck linker and its docking section, which are compatible with the known structure of kinesin.

The effect of recombination on the neutral evolution of genetic robustness.

Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure only through neutral mutations can evolve mutational robustness [E. van Nimwegen, J.P. Crutchfield, M. Huynen, Neutral evolution of mutational robustness, Proc. Natl. Acad. Sci. USA 96(17), 9716-9720 (1999)], by concentrating the population on regions of high neutrality. Introducing recombination we demonstrate, through numerically calculating the stationary distribution of an infinite population on ensembles of random neutral networks that mutational robustness is significantly enhanced and further that the magnitude of this enhancement is sensitive to details of the neutral network topology. Through the simulation of finite populations of genotypes evolving on random neutral networks and a scaled down microRNA neutral network, we show that even in finite populations recombination will still act to focus the population on regions of locally high neutrality.