A power law for cells

Darwin observed that multiple, lowly organized, rudimentary, or exaggerated structures show increased relative variability. However, the cellular basis for these laws has never been investigated. Some animals, such as the nematode Caenorhabditis elegans, are famous for having organs that possess the same number of cells in all individuals, a property known as eutely. But for most multicellular creatures, the extent of cell number variability is unknown. Here we estimate variability in organ cell number for a variety of animals, plants, slime moulds, and volvocine algae. We find that the mean and variance in cell number obey a power law with an exponent of 2, comparable to Taylor's law in ecological processes. Relative cell number variability, as measured by the coefficient of variation, differs widely across taxa and tissues, but is generally independent of mean cell number among homologous tissues of closely related species. We show that the power law for cell number variability can be explained by stochastic branching process models based on the properties of cell lineages. We also identify taxa in which the precision of developmental control appears to have evolved. We propose that the scale independence of relative cell number variability is maintained by natural selection.

Retinoic acid (RA) and As2O3 treatment in transgenic models of acute promyelocytic leukemia (APL) unravel the distinct nature of the leukemogenic process induced by the PML-RARα and PLZF-RARα oncoproteins

Acute promyelocytic leukemia (APL) is associated with chromosomal translocations always involving the RARα gene, which variably fuses to one of several distinct loci, including PML or PLZF (X genes) in t(15;17) or t(11;17), respectively. APL in patients harboring t(15;17) responds well to retinoic acid (RA) treatment and chemotherapy, whereas t(11;17) APL responds poorly to both treatments, thus defining a distinct syndrome. Here, we show that RA, As2O3, and RA + As2O3 prolonged survival in either leukemic PML-RARα transgenic mice or nude mice transplanted with PML-RARα leukemic cells. RA + As2O3 prolonged survival compared with treatment with either drug alone. In contrast, neither in PLZF-RARα transgenic mice nor in nude mice transplanted with PLZF-RARα cells did any of the three regimens induce complete disease remission. Unexpectedly, therapeutic doses of RA and RA + As2O3 can induce, both in vivo and in vitro, the degradation of either PML-RARα or PLZF-RARα proteins, suggesting that the maintenance of the leukemic phenotype depends on the continuous presence of the former, but not the latter. Our findings lead to three major conclusions with relevant therapeutic implications: (i) the X-RARα oncoprotein directly determines response to treatment and plays a distinct role in the maintenance of the malignant phenotype; (ii) As2O3 and/or As2O3 + RA combination may be beneficial for the treatment of t(15;17) APL but not for t(11;17) APL; and (iii) therapeutic strategies aimed solely at degrading the X-RARα oncoprotein may not be effective in t(11;17) APL.

Polymer Models of Meiotic and Mitotic Chromosomes

Polymers tied together by constraints exhibit an internal pressure; this idea is used to analyze physical properties of the bottle-brush–like chromosomes of meiotic prophase that consist of polymer-like flexible chromatin loops, attached to a central axis. Using a minimal number of experimental parameters, semiquantitative predictions are made for the bending rigidity, radius, and axial tension of such brushes, and the repulsion acting between brushes whose bristles are forced to overlap. The retraction of lampbrush loops when the nascent transcripts are stripped away, the oval shape of diplotene bivalents between chiasmata, and the rigidity of pachytene chromosomes are all manifestations of chromatin pressure. This two-phase (chromatin plus buffer) picture that suffices for meiotic chromosomes has to be supplemented by a third constituent, a chromatin glue to understand mitotic chromosomes, and explain how condensation can drive the resolution of entanglements. This process resembles a thermal annealing in that a parameter (the affinity of the glue for chromatin and/or the affinity of the chromatin for buffer) has to be tuned to achieve optimal results. Mechanical measurements to characterize this protein–chromatin matrix are proposed. Finally, the propensity for even slightly chemically dissimilar polymers to phase separate (cluster like with like) can explain the apparent segregation of the chromatin into A+T- and G+C-rich regions revealed by chromosome banding.

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

A comparison of the potential role of the tetrodotoxin-insensitive sodium channels, PN3/SNS and NaN/SNS2, in rat models of chronic pain

Alterations in sodium channel expression and function have been suggested as a key molecular event underlying the abnormal processing of pain after peripheral nerve or tissue injury. Although the relative contribution of individual sodium channel subtypes to this process is unclear, the biophysical properties of the tetrodotoxin-resistant current, mediated, at least in part, by the sodium channel PN3 (SNS), suggests that it may play a specialized, pathophysiological role in the sustained, repetitive firing of the peripheral neuron after injury. Moreover, this hypothesis is supported by evidence demonstrating that selective “knock-down” of PN3 protein in the dorsal root ganglion with specific antisense oligodeoxynucleotides prevents hyperalgesia and allodynia caused by either chronic nerve or tissue injury. In contrast, knock-down of NaN/SNS2 protein, a sodium channel that may be a second possible candidate for the tetrodotoxin-resistant current, appears to have no effect on nerve injury-induced behavioral responses. These data suggest that relief from chronic inflammatory or neuropathic pain might be achieved by selective blockade or inhibition of PN3 expression. In light of the restricted distribution of PN3 to sensory neurons, such an approach might offer effective pain relief without a significant side-effect liability.

Estimation of evolutionary distances under stationary and nonstationary models of nucleotide substitution

Estimation of evolutionary distances has always been a major issue in the study of molecular evolution because evolutionary distances are required for estimating the rate of evolution in a gene, the divergence dates between genes or organisms, and the relationships among genes or organisms. Other closely related issues are the estimation of the pattern of nucleotide substitution, the estimation of the degree of rate variation among sites in a DNA sequence, and statistical testing of the molecular clock hypothesis. Mathematical treatments of these problems are considerably simplified by the assumption of a stationary process in which the nucleotide compositions of the sequences under study have remained approximately constant over time, and there now exist fairly extensive studies of stationary models of nucleotide substitution, although some problems remain to be solved. Nonstationary models are much more complex, but significant progress has been recently made by the development of the paralinear and LogDet distances. This paper reviews recent studies on the above issues and reports results on correcting the estimation bias of evolutionary distances, the estimation of the pattern of nucleotide substitution, and the estimation of rate variation among the sites in a sequence.

Kinetics of hydrogen bond breakage in the process of unfolding of ribonuclease A measured by pulsed hydrogen exchange.

A sensitive test for kinetic unfolding intermediates in ribonuclease A (EC 3.1.27.5) is performed under conditions where the enzyme unfolds slowly (10 degrees C, pH 8.0, 4.5 M guanidinium chloride). Exchange of peptide NH protons (2H-1H) is used to monitor structural opening of individual hydrogen bonds during unfolding, and kinetic models are developed for hydrogen exchange during the process of protein unfolding. The analysis indicates that the kinetic process of unfolding can be monitored by EX1 exchange (limited by the rate of opening) for ribonuclease A in these conditions. Of the 49 protons whose unfolding/exchange kinetics was measured, 47 have known hydrogen bond acceptor groups. To test whether exchange during unfolding follows the EX2 (base-catalyzed) or the EX1 (uncatalyzed) mechanism, unfolding/exchange was measured both at pH 8.0 and at pH 9.0. A few faster-exchanging protons were found that undergo exchange by both EX1 and EX2 processes, but the 43 slower-exchanging protons at pH 8 undergo exchange only by the EX1 mechanism, and they have closely similar rates. Thus, it is likely that all 49 protons undergo EX1 exchange at the same rate. The results indicate that a single rate-limiting step in unfolding breaks the entire network of peptide hydrogen bonds and causes the overall unfolding of ribonuclease A. The additional exchange observed for some protons that follows the EX2 mechanism probably results from equilibrium unfolding intermediates and will be discussed elsewhere.