Noise-driven growth rate gain in clonal cellular populations

Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a “speed limit” for proliferation.Cell growth is an important physiological process that underlies the fitness of organisms. In exponentially growing cell populations, proliferation is usually quantified using the bulk population growth rate, which is assumed to represent the average growth rate of single cells within a population. In addition, basic growth laws exist that relate ribosome function and metabolic efficiency, macromolecular composition, and cell size of the culture as a whole to the bulk population growth rate (1–3). Population growth rate is therefore a quantity of primary importance that reports cellular physiological states and fitness.However, at the single-cell level, growth-related parameters such as the division time interval and division cell size are heterogeneous even in a clonal population growing at a constant rate (4–9). Such “growth noise” causes concurrently living cells to compete within the population for representation among its future descendants. For example, if two sibling cells born from the same mother cell had different division intervals, the faster dividing sibling is likely to have more descendants in the future population compared with its slower dividing sister, despite the fact that progenies of both siblings may proliferate equally well (Fig. 1). Intrapopulation competition complicates single-cell analysis because any growth-correlated quantities measured over the population deviate from intrinsic single-cell properties (10–12). In the case of the toy model described in Fig. 1, cells are assumed to determine their generation times (division interval) randomly by roll of a dice. The mean of intrinsic cellular generation time is thus (1 + 2 +  ?  + 6)/6 = 3.5 h, but population doubling time, which is the time required for a population to double the number of cells, is in fact 3.2 h. This counterintuitive result is a direct consequence of growth noise in a population. Indeed, as we will see, the population doubling time can only equal the mean generation time when no variability of generation time exists at the single-cell level. Population growth rate is determined not only by an average of single cells but also by the details of heterogeneity within a population. Therefore, understanding how population growth rates and other properties arise from single-cell heterogeneity poses a fundamental challenge to single-cell biology.Open in a separate windowFig. 1.Competition within a population caused by growth noise and its consequence to population growth rate. (A) Toy model of cell proliferation. Here, we consider a model of cell proliferation in which all of the cells in a population determine their generation time (interdivision time) randomly by throwing a dice to learn the consequences of intrapopulation growth noise. In this setting, cells can take either of the six possible choices of generation time, τ=1,2,⋯,6 h, with the equal probability of 1/6. The mean generation time is thus ?τ?_g= 3.5 h. (B) Example of pedigree tree showing competition between sibling cells. In this tree, two sibling cells were born from the common mother cell at t = 0 h, and divided with different generation times (sibling cell 1: τ_s1 = 5 h; and sibling cell 2: τ_s2 = 2 h). The descendant cells from the both sibling cells follow the same rule of cell divisions irrespectively of the ancestral generation time. The difference of generation time between the sibling cells 1 and 2 was caused just by chance, but the expected number of descendant cells becomes larger for the fast dividing sibling cell. The ratio of the expected number of descendant cells from those sibling cells at a certain future time point is ?N₁?/?N₂? = e^{?Λ_p(τ_s1?τ_s2)}, where Λ_p is the population growth rate. (C) Growth of cell population. When all of the cells in the population follow the same division rule in A, the number of cells in the population grows exponentially. The rate of this exponential growth is the “population growth rate,” Λ_p. The time required for the population to double the number of cells is the “population doubling time,” T_d, i.e., N(t) = N(0)2^t/T_d. Therefore, T_d = ln2/Λ_p. An interesting consequence of stochasticity in generation time is that population doubling time becomes smaller than the mean generation time, i.e., T_d <?τ?_g. In the case of the dice population, T_d = 3.187 h, which is indeed smaller than ?τ?_g= 3.5 h.A classical study of theoretical and experimental microbiology attempted to reveal the discrepancies between mean cellular generation times and population doubling times in real bacterial populations (13). Experimental methods and techniques available at that time, however, hampered reliable tests. Recently, the techniques of single-cell time-lapse microscopy have advanced to a great extent, revealing the heterogeneous and stochastic nature of single-cell dynamics quantitatively (14). With the aid of microfluidic platforms, tracking single cells over many generations in controlled constant or changing environments has also become feasible, providing insights into the mechanisms of cell size homeostasis and stress responses (3, 6, 7, 9, 15–22).In this study, through microfluidics time-lapse microscopy and single-cell analysis on large-scale, single-cell lineage trees, we reveal that clonal populations of Escherichia coli indeed grow with a doubling time that is smaller than the mean doubling time of their constituent cells under broad, balanced-growth conditions. We show that the observed growth rate gains and population age structures are predictable from cellular generation time distributions based on a simple age-structured population model. Furthermore, we reveal unique features of long single-cell lineages within populations in competition, and provide a history-based formulation that connects growth rate gain with a measure of statistical deviation between isolated and competing lineages. Finally, we demonstrate a linear relation between the means and the variances of generation time across conditions, which constrains the maximum growth rate of this organism.     

Cleft palate and decreased brain γ-aminobutyric acid in mice lacking the 67-kDa isoform of glutamic acid decarboxylase

In addition to its role as an inhibitory neurotransmitter, γ-aminobutyric acid (GABA) is presumed to be involved in the development and plasticity of the nervous system. GABA is synthesized by glutamic acid decarboxylase (GAD), but the respective roles of its two isoforms (GAD65 and 67) have not been determined. The selective elimination of each GAD isoform by gene targeting is expected to clarify these issues. Recently we have produced GAD65 −/− mice and demonstrated that lack of GAD65 does not change brain GABA contents or animal behavior, except for a slight increase in susceptibility to seizures. Here we report the production of GAD67 −/− mice. These mice were born at the expected frequency but died of severe cleft palate during the first morning after birth. GAD activities and GABA contents were reduced to 20% and 7%, respectively, in the cerebral cortex of the newborn GAD67 −/− mice. Their brain, however, did not show any discernible defects. Previous pharmacological and genetic investigations have suggested the involvement of GABA in palate formation, but this is the first demonstration of a role for GAD67-derived GABA in the development of nonneural tissue.     

Microscopic polyangiitis associated with marked systemic bleeding tendency caused by disseminated intravascular coagulation

A 57-year-old woman was admitted to our hospital because of severe dyspnea due to pulmonary hemorrhage and rapidly progressive renal failure. The patient was positive for perinuclear pattern anti-neutrophil cytoplasmic antibody (p-ANCA) and was manifested with gastrointestinal bleeding and brain hemorrhage. Thus, she was diagnosed as having microscopic polyangiitis (MPA). Laboratory examination demonstrated severe thrombocytopenia, increased prothrombin time and a high concentration of fibrin degradation products. In addition, the elevated plasma levels of D-dimer, thrombin-antithrombin complex and plasmin-plasmin inhibitor complex led us to make a diagnosis of disseminated intravascular coagulation (DIC). Complication of DIC was considered to have caused further deterioration in bleeding tendency due to MPA in the present case. The patient was treated with plasma exchange, hemodialysis, administration of corticosteroid including pulse therapy and cyclophosphamide. Continuous infusion of gabexate mesilate proved effective for improvement of systemic bleeding tendency. However, she finally died of severe infectious diseases. In conclusion, it is suggested that ANCA-associated vasculitis could be accompanied by DIC and gabexate mesilate may be a useful therapeutic agent for these disorders.     

Globoid Cell Leucodystrophy (Krabbe''s Disease): Deficiency of Galactocerebroside β-Galactosidase

Profound deficiency of a specific enzyme, galactocerebroside beta-galactosidase, has been demonstrated in the brains, liver, and spleen of three patients with Krabbe's globoid cell leucodystrophy. The activity of this enzyme was normal in a variety of other cerebral diseases, including those with similarly devasted white matter. The lack of enzyme activity was not due to an inhibitor in the tissue, nor is it due to a shift in the pH optimum. The deficiency of galactocerebroside beta-galactosidase as the primary enzymatic defect can account for the morphological and biochemical characteristics of this disease better than the previously reported deficiency of cerebroside-sulfatide sulfotransferase.     

Aberrant hepatic duct connected with the main pancreatic duct by anomalous pancreato-biliary ductal union: Case report

An aberrant hepatic duct directly connected to the main pancreatic duct with anomalous arrangement of the pancreato-biliary ductal system is reported here, the first report of such a case, to our knowledge. A 53-year-old woman was admitted to our hospital because of cholecystolithiasis with abdominal pain in the right upper quadrant. Endoscopic retrograde cholangiopancreatography (ERCP) showed that an aberrant hepatic duct, which independently drained the right posterior segment of the liver, connected to the main pancreatic duct at a high insertion site distal to the sphincter area of the major papilla. The common bile duct (containing stones), on the other hand, united with the main pancreatic duct in a normal fashion. Cholecystectomy and bile duct lithotomy were performed. The aberrant hepatic duct was separated from the main pancreatic duct just above the junction, and was anastomosed side-by-side to the common hepatic duct. The embryologic development of this lesion is not clear, but is discussed in this report.     

The rs1333049 polymorphism on locus 9p21.3 and extreme longevity in Spanish and Japanese cohorts

GeroScience - The rs1333049 (G/C) polymorphism located on chromosome 9p21.3 is a candidate to influence extreme longevity owing to its association with age-related diseases, notably coronary artery...     

Accuracy of metabolic volume and total glycolysis among six threshold-based target segmentation algorithms

Annals of Nuclear Medicine - This study aimed to evaluate the accuracy of six threshold-based segmentation methods with different target-to-background ratios (TBR), images with different voxel...