Modeling the dynamics of human hair cycles by a follicular automaton

The hair follicle cycle successively goes through the anagen, catagen, telogen, and latency phases, which correspond, respectively, to hair growth, arrest, shedding, and absence before a new anagen phase is initiated. Experimental observations collected over a period of 14 years in a group of 10 male volunteers, alopecic and nonalopecic, allowed us to determine the characteristics of scalp hair follicle cycles. On the basis of these observations, we propose a follicular automaton model to simulate the dynamics of human hair cycles. The automaton model is defined by a set of rules that govern the stochastic transitions of each follicle between the successive states anagen, telogen, and latency, and the subsequent return to anagen. The transitions occur independently for each follicle, after time intervals given stochastically by a distribution characterized by a mean and a variance. The follicular automaton model accounts both for the dynamical transitions observed in a single follicle and for the behavior of an ensemble of independently cycling follicles. Thus, the model successfully reproduces the evolution of the fractions of follicle populations in each of the three phases, which fluctuate around steady-state or slowly drifting values. We apply the follicular automaton model to the study of spatial patterns of follicular growth that result from a spatially heterogeneous distribution of parameters such as the mean duration of anagen phase. When considering that follicles die or miniaturize after going through a critical number of successive cycles, the model can reproduce the evolution to hair patterns similar to well known types of diffuse or androgenetic alopecia.

Crystal structure of Taq DNA polymerase in complex with an inhibitory Fab: The Fab is directed against an intermediate in the helix-coil dynamics of the enzyme

We report the crystal structure of Thermus aquaticus DNA polymerase I in complex with an inhibitory Fab, TP7, directed against the native enzyme. Some of the residues present in a helical conformation in the native enzyme have adopted a γ turn conformation in the complex. Taken together, structural information that describes alteration of helical structure and solution studies that demonstrate the ability of TP7 to inhibit 100% of the polymerase activity of the enzyme suggest that the change in conformation is probably caused by trapping of an intermediate in the helix-coil dynamics of this helix by the Fab. Antibodies directed against modified helices in proteins have long been anticipated. The present structure provides direct crystallographic evidence. The Fab binds within the DNA binding cleft of the polymerase domain, interacting with several residues that are used by the enzyme in binding the primer:template complex. This result unequivocally corroborates inferences drawn from binding experiments and modeling calculations that the inhibitory activity of this Fab is directly attributable to its interference with DNA binding by the polymerase domain of the enzyme. The combination of interactions made by the Fab residues in both the polymerase and the vestigial editing nuclease domain of the enzyme reveal the structural basis of its preference for binding to DNA polymerases of the Thermus species. The orientation of the structure-specific nuclease domain with respect to the polymerase domain is significantly different from that seen in other structures of this polymerase. This reorientation does not appear to be antibody-induced and implies remarkably high relative mobility between these two domains.

Linking topography of its potential surface with the dynamics of folding of a protein model

The “3-color, 46-bead” model of a folding polypeptide is the vehicle for adapting to proteins a mode of analysis used heretofore for atomic clusters, to relate the topography of the potential surface to the dynamics that lead to formation of selected structures. The analysis is based on sequences of stationary points—successive minima, joined by saddles—that rise monotonically in energy from basin bottoms. Like structure-seeking clusters, the potential surface of the model studied here is staircase-like, rather than sawtooth-like, with highly collective motions required for passage from one minimum to the next. The surface has several deep basins whose minima correspond to very similar structures, but which are separated by high energy barriers.

A theory for controlling cell cycle dynamics using a reversibly binding inhibitor

We demonstrate, by using mathematical modeling of cell division cycle (CDC) dynamics, a potential mechanism for precisely controlling the frequency of cell division and regulating the size of a dividing cell. Control of the cell cycle is achieved by artificially expressing a protein that reversibly binds and inactivates any one of the CDC proteins. In the simplest case, such as the checkpoint-free situation encountered in early amphibian embryos, the frequency of CDC oscillations can be increased or decreased by regulating the rate of synthesis, the binding rate, or the equilibrium constant of the binding protein. In a more complex model of cell division, where size-control checkpoints are included, we show that the same reversible binding reaction can alter the mean cell mass in a continuously dividing cell. Because this control scheme is general and requires only the expression of a single protein, it provides a practical means for tuning the characteristics of the cell cycle in vivo.

Singular value decomposition for genome-wide expression data processing and modeling

We describe the use of singular value decomposition in transforming genome-wide expression data from genes × arrays space to reduced diagonalized “eigengenes” × “eigenarrays” space, where the eigengenes (or eigenarrays) are unique orthonormal superpositions of the genes (or arrays). Normalizing the data by filtering out the eigengenes (and eigenarrays) that are inferred to represent noise or experimental artifacts enables meaningful comparison of the expression of different genes across different arrays in different experiments. Sorting the data according to the eigengenes and eigenarrays gives a global picture of the dynamics of gene expression, in which individual genes and arrays appear to be classified into groups of similar regulation and function, or similar cellular state and biological phenotype, respectively. After normalization and sorting, the significant eigengenes and eigenarrays can be associated with observed genome-wide effects of regulators, or with measured samples, in which these regulators are overactive or underactive, respectively.

Mantle dynamics and seismic tomography

Three-dimensional imaging of the Earth's interior, called seismic tomography, has achieved breakthrough advances in the last two decades, revealing fundamental geodynamical processes throughout the Earth's mantle and core. Convective circulation of the entire mantle is taking place, with subducted oceanic lithosphere sinking into the lower mantle, overcoming the resistance to penetration provided by the phase boundary near 650-km depth that separates the upper and lower mantle. The boundary layer at the base of the mantle has been revealed to have complex structure, involving local stratification, extensive structural anisotropy, and massive regions of partial melt. The Earth's high Rayleigh number convective regime now is recognized to be much more interesting and complex than suggested by textbook cartoons, and continued advances in seismic tomography, geodynamical modeling, and high-pressure–high-temperature mineral physics will be needed to fully quantify the complex dynamics of our planet's interior.

Host-parasite dynamics and outgrowth of virus containing a single K70R amino acid change in reverse transcriptase are responsible for the loss of human immunodeficiency virus type 1 RNA load suppression by zidovudine.

The association between human immunodeficiency virus type I (HIV-1) RNA load changes and the emergence of resistant virus variants was investigated in 24 HIV-1-infected asymptomatic persons during 2 years of treatment with zidovudine by sequentially measuring serum HIV-1 RNA load and the relative amounts of HIV-1 RNA containing mutations at reverse transcriptase (RT) codons 70 (K-->R), 41 (M-->L), and 215 (T-->Y/F). A mean maximum decline in RNA load occurred during the first month, followed by a resurgence between 1 and 3 months, which appeared independent of drug-resistance. Mathematical modeling suggests that this resurgence is caused by host-parasite dynamics, and thus reflects infection of the transiently increased numbers of CD4+ lymphocytes. Between 3 and 6 months of treatment, the RNA load returned to baseline values, which was associated with the emergence of virus containing a single lysine to arginine amino acid change at RT codon 70, only conferring an 8-fold reduction in susceptibility. Despite the relative loss of RNA load suppression, selection toward mutations at RT codons 215 and 41 continued. Identical patterns were observed in the mathematical model. While host-parasite dynamics and outgrowth of low-level resistant virus thus appear responsible for the loss of HIV-1 RNA load suppression, zidovudine continues to select for alternative mutations, conferring increasing levels of resistance.