The Effect of the G 1 - S transition Checkpoint on an Age Structured Cell Cycle Model

Knowledge of how a population of cancerous cells progress through the cell cycle is vital if the population is to be treated effectively, as treatment outcome is dependent on the phase distributions of the population. Estimates on the phase distribution may be obtained experimentally however the errors present in these estimates may effect treatment efficacy and planning. If mathematical models are to be used to make accurate, quantitative predictions concerning treatments, whose efficacy is phase dependent, knowledge of the phase distribution is crucial. In this paper it is shown that two different transition rates at the - checkpoint provide a good fit to a growth curve obtained experimentally. However, the different transition functions predict a different phase distribution for the population, but both lying within the bounds of experimental error. Since treatment outcome is effected by the phase distribution of the population this difference may be critical in treatment planning. Using an age-structured population balance approach the cell cycle is modelled with particular emphasis on the - checkpoint. By considering the probability of cells transitioning at the - checkpoint, different transition functions are obtained. A suitable finite difference scheme for the numerical simulation of the model is derived and shown to be stable. The model is then fitted using the different probability transition functions to experimental data and the effects of the different probability transition functions on the model''s results are discussed.     

Evaluation of cooperativity for phase transitions in two- and three-dimensional systems

Use of the so-called "cooperative unit" (readily obtainable from the midpoint slope of phase transition curves) is discussed for the determination of cluster sizes and cooperative interaction energies. This quantity has been commonly employed in a rather empirical way since its correct interpretation is known only for some special cases (linear systems, all-or-none transitions). It is shown in the framework of a lattice model (Ising model) that the cooperative unit may be interpreted in terms of correlation functions and that it defines an average cluster corresponding to the patch size as obtained from scattering experiments. Relations between the cooperative unit and a cooperativity parameter are given for various lattices. Different types of transition curves are discussed using a simple analytical formalism, the quasichemical approximation. Some important nonideality effects are investigated which may lead to a "smearing-out" of first-order transitions.     

Theoretical calculation on the reaction of alkene molecules on H-terminated Si(100)-3×1 surface

A study on mechanisms of radical initiated surface chain reaction of ethylene molecule on H-terminated Si(100)-3 × 1 has been carried out in a supercell approach by using density functional theory and ab initio molecular dynamic method. On the H-terminated Si(100)-3 × 1 surface, one of the crucial steps of the surface chain reaction, namely, the abstraction of a H atom from a nearby surface hydride unit, is found to have a somewhat smaller activation energy from the nearest silicon site than from the next-nearest silicon site. From the intermediate state to the final state, the transition state has bigger activation energy. Ab initio molecular dynamics (MD) shows that the H-abstraction on Si(100)-3 × 1 surface bound organic group with a carbon-centered radical is very easy to be obtained from the transition state, and it also shows that the C…H bond at methyl group is formed in a very short MD time, and the Si…C bond between the Si surface and the alkyl chain oscillates with time evolution on Si(100)-3 × 1 surface.     

The role of agonist-independent conformational transformation (AICT) in IP₃ cluster behavior

Inositol 1,4,5-trisphosphate (IP(3)) receptor is a central unit in intracellular Ca(2+) signaling. Regulation of the IP? receptor by calcium is well characterized. High open probability values are reported for a single IP? receptor in nuclear patch clamp experiments. These experimental observations are in contrast with the lower open probability values of the lipid bilayer experiments. Most theoretical models do not account for high open probabilities of the receptor. But more recently, new models of the IP? receptor have been put forward which are constrained by single-channel nuclear patch clamp recordings, which generate the larger open probability with the aid of an additional agonist-independent conformational transformation (AICT)-'active' state. The main aim of this work is to constrain the AICT models with a wealth of experimental data characterizing calcium release from IP? receptor clusters. Our results suggest that consistency of cluster release between theory and experiments constrains the kinetics of the agonist-independent conformational transition rates (AICT) to values which lead to small open probabilities for the IP? receptor inconsistent with nuclear patch clamp experimental data.     

Temperature-dependent reversible transition of poly(dCdG) · poly(DcdG) in ethanolic and methanolic solutions

Using CD we investigated the transitions of poly(dCdG) · poly(dGdC) from B-to-Z form and from Z-to-Z′ form. We have found experimental conditions that allow the cooperative transition to occur as a function of temperature in ethanolic solutions. The transition is reversible and can be repeated as often as desired. There is no evidence of strand separation during the cooperative transition as monitored by absorbance. For purposes of calculation, we have assumed a two-state model for the B-to-Z transition, although the data indicate that such a model is too simplistic. The calculations allow the estimation of the change in enthalpy per mole of cooperative unit for the transition as a function of ethanol concentration. The values range from ±140 to ±200 kcal/mol for ethanol concentrations between 10 and 20%. Investigations of the noncooperative Z-to-Z′ transition show that it is a reversible two-state transition. The different forms of poly(dCdG) · poly(dGdC) give no scattering contributions to the CD as shown by fluorescent-detected CD or fluorscat techniques. This indicates that the CD spectra are true spectra, and contain no contributions from differential scattering of the polynucleotide. This is particularly significant in the case of the Z′ form, since it exists at high ethanol concentrations (80%) where condensation of polynucleotides can provide large contributions to the CD spectra. Analogous investigations using methanol show that the two transitions also occur, but the final Z′ form in methanol is qualitatively different from the ethanol form.     

AN EXTENDED TRANSITION PROBABILITY MODEL OF THE VARIABILITY OF CELL GENERATION TIMES

The transition probability model of variability of cell generation times is extended so that the rate constant for the transition from the A-state to the B-phase of the cell cycle depends on time which a particular cell has already spent in the A-state. A specific time dependence of this rate constant is introduced. It is determined by the value of one constant which is then an additional parameter of the model. The corresponding cell population kinetics are calculated and compared to existing experimental evidence. The model accounts satisfactorily for the generation time distribution function and for the shortening of the G₁ phase of binucleate cells. The time dependence of the transition probability is related to the cell kinetics of an hypothetical cell constituent. A possible relationship is proposed between the chemical parameters within the cell and the parameters of the cell population kinetics.     

Statistical Inference For Risk Difference in an Incomplete Correlated 2 × 2 Table

In some infectious disease studies and 2‐step treatment studies, 2 × 2 table with structural zero could arise in situations where it is theoretically impossible for a particular cell to contain observations or structural void is introduced by design. In this article, we propose a score test of hypotheses pertaining to the marginal and conditional probabilities in a 2 × 2 table with structural zero via the risk/rate difference measure. Score test‐based confidence interval will also be outlined. We evaluate the performance of the score test and the existing likelihood ratio test. Our empirical results evince the similar and satisfactory performance of the two tests (with appropriate adjustments) in terms of coverage probability and expected interval width. Both tests consistently perform well from small‐ to moderate‐sample designs. The score test however has the advantage that it is only undefined in one scenario while the likelihood ratio test can be undefined in many scenarios. We illustrate our method by a real example from a two‐step tuberculosis skin test study.     

The Quantum Casimir Effect May Be a Universal Force Organizing the Bilayer Structure of the Cell Membrane

A mathematic–physical model of the interaction between cell membrane bilayer leaflets is proposed based on the Casimir effect in dielectrics. This model explains why the layers of a lipid membrane gently slide one past another rather than penetrate each other. The presented model reveals the dependence of variations in the free energy of the system on the membrane thickness. This function is characterized by the two close minima corresponding to the different levels of interdigitation of the lipids from neighbor layers. The energy barrier of the compressing transition between the predicted minima is estimated to be 5.7 kT/lipid, and the return energy is estimated to be 3.1 kT/lipid. The proposed model enables estimation of the value of the membrane elastic thickness modulus of compressibility, which is 1.7 × 10⁹ N/m², and the value of the interlayer friction coefficient, which is 1.9 × 10⁸ Ns/m³.     

Quantification of the zygotic barrier between interbreeding taxa using gene flow data

Hybridization and introgression via interspecific gene flow are common processes in the plant kingdom. The effectiveness of these processes is governed by the strengths of multiple zygotic barriers. These barriers have often been quantified in artificial settings using laborious and time‐consuming hand‐pollination experiments, but their quantification is nonexistent in the landscape. In this study, we utilized gene flow data within a spatially explicit simulation to assess the strengths of zygotic barriers. Our model system consisted of Populus nigra and its hybrid, P. × canadensis, which interbreed under natural conditions. The study population was located in the floodplain of the Eder River in central Germany. Pollen‐mediated introgression rates from hybrid males into the seeds of individual female trees were used as the target pattern using an inverse modeling approach. Simulations that treated pollen from both taxa equally revealed a large discrepancy between the observed and modeled rates of introgression for both taxa. The discrepancy was reduced by introducing a zygotic barrier against the pollen from the hybrid males. The best model outcome values indicated comparably strong zygotic barriers acting against pollen‐mediated introgressive gene flow into the two parental taxa, P. nigra and P. × canadensis. The sensitivity of our model was tested by applying different dispersal functions. Four common probability density functions were used along with a pollen dispersal function that had previously been fitted to gene flow data from the same dataset. The best barrier value was almost independent of the dispersal functions used here. Moreover, it was within the range previously determined in hand‐pollination‐based investigations, validating our model. These data indicate that the inverse modeling approach is a powerful method for quantifying hidden processes, and we discuss its use as a valuable tool for generating new insights into plant mating systems that are relevant to evolutionary biology and risk analyses in conservation efforts.     

An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks

MOTIVATION: Probabilistic Boolean networks (PBNs) have been proposed to model genetic regulatory interactions. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution usually includes construction of the transition probability matrix and computation of the steady-state probability distribution. The size of the transition probability matrix is 2(n)-by-2(n) where n is the number of genes in the genetic network. Therefore, the computational costs of these two steps are very expensive and it is essential to develop a fast approximation method. RESULTS: In this article, we propose an approximation method for computing the steady-state probability distribution of a PBN based on neglecting some Boolean networks (BNs) with very small probabilities during the construction of the transition probability matrix. An error analysis of this approximation method is given and theoretical result on the distribution of BNs in a PBN with at most two Boolean functions for one gene is also presented. These give a foundation and support for the approximation method. Numerical experiments based on a genetic network are given to demonstrate the efficiency of the proposed method.     

Mathematical development of a physical model of some visco-elastic properties of the aorta

Visco-elastic properties of blood vessels, the aorta in particular, may be approximated by a suitable arrangement of two elastic rods and one viscous rod. This simple model is readily derived from models already proposed for individual components of the aortic wall: elastin, collagen, and smooth muscle. The model is even consistent with various results ofin vitro experimental data which have previously appeared uncorrelated, or even contradictory. What is more, when elastic and viscous coefficients of the model were calculated from these data, the density of each of the three histological components could be predicted for some specimens. The mathematical development of the model and the agreement with varied experiments justify use of the model for analysis ofin vivo aortic pressure curves in subsequent papers. The development also indicates the need for additional data from some simplein vitro experiments suggested by this analysis. Data from the suggested experiments may support the present model or require some modification of it.     

X-ray diffraction and electron microscopy of a light meromyosin tactoid

The structure of a tactoid of light meromyosin with a 43-nm periodicity was studied by both X-ray diffraction and electron microscopy. Such tactoids were formed from light meromyosin prepared by a short tryptic digestion (5 min) of myosin.A strong magnetic field (6 kgauss) was employed to obtain oriented specimens of tactoids for X-ray diffraction. The oriented tactoids gave equatorial reflections from a rectangular lattice with a unit cell of 6·5 nm × 3·9 nm (at pH 6·6) in a plane perpendicular to the long axis of the tactoid. This lattice shrank anisotropically when the pH was lowered. The meridional reflections could be indexed as orders of 42·93 ± 0·05 nm.The tactoids were frequently associated with sheet-like structures termed banded sheets. In negative stain these banded sheets showed the same band pattern as the tactoids with 10 nm wide light and 33 nm wide dark bands. However, in thin banded sheets the density of neighbouring dark bands alternated so that the true axial repeat was 86 nm. Optical diffraction showed that the face-on view of the banded sheet had a unit cell of 3·6 nm × 86 nm.From these observations a plausible model for the structure of the light meromyosin tactoid has been deduced. In this model the tactoid is made by a stacking of unit layers. A unit cell (6·5 nm × 3·9 nm × 86 nm) contains four light meromyosin molecules, each 90 nm long and packed co-planar, not all of which are in an identical environment. The molecules make parallel interactions with staggers of 86 and 43 nm and antiparallel interactions with overlaps of 84 and 41 nm.     

The Crystal Structure of Glutamine-binding Protein fromEscherichia coli

The crystal structure of the glutamine-binding protein (GlnBP) fromEscherichia coliin a ligand-free “open” conformational state has been determined by isomorphous replacement methods and refined to anR-value of 21.4% at 2.3 Å resolution. There are two molecules in the asymmetric unit, related by pseudo 4-fold screw symmetry. The refined model consists of 3587 non-hydrogen atoms from 440 residues (two monomers), and 159 water molecules. The structure has root-mean-square deviations of 0.013 Å from “deal” bond lengths and 1.5° from “ideal” bond angles.The GlnBP molecule has overall dimensions of approximately 60 Å × 40 Å × 35 Å and is made up of two domains (termed large and small), which exhibit a similar supersecondary structure, linked by two antiparallel β-strands. The small domain contains three α-helices and four parallel and one antiparallel β-strands. The large domain is similar to the small domain but contains two additional α-helices and three more short antiparallel β-strands. A comparison of the secondary structural motifs of GlnBP with those of other periplasmic binding proteins is discussed.A model of the “closed form” GlnBP-Gln complex has been proposed based on the crystal structures of the histidine-binding protein-His complex and “open form” GlnBP. This model has been successfully used as a search model in the crystal structure determination of the “closed form” GlnBP-Gln complex by molecular replacement methods. The model agrees remarkably well with the crystal structure of the Gln-GlnBP complex with root-mean-square deviation of 1.29 Å. Our study shows that, at least in our case, it is possible to predict one conformational state of a periplasmic binding protein from another conformational state of the protein. The glutamine-binding pockets of the model and the crystal structure are compared and the modeling technique is described.     

The statistics of unique native states for random peptides

Given a probability distribution from which the energy spectrum of a random peptide is to be sampled, we derive a general expression for the probability that such a peptide will fold to a unique native state and for the probability distribution of the native energy. This latter result allows us to localize the energy of folding based on model parameters and is one advantage of our formulation. Evidence from both the lattice theory of proteins and protein threading experiments suggest that the energy spectrum for the compact states of a peptide chain is Gaussian in form. For this reason we have derived from the more general framework the specific formulas that apply in the Gaussian case, where one requires only the number of states and the variance of the Gaussian distribution in order to apply the theory. This simplicity allows us to perform calculations that we compare with calculations previously made by others based on statistical thermodynamics. We find qualitative agreement, but a significant correction to prior estimates of folding probability derived from the Gaussian assumption is necessary. © 1996 John Wiley & Sons, Inc.     

Human Health Risk Assessment of Naturally Occurring Radioactive Materials in Produced Water—A Case Study

Human health effects from naturally occurring radioactive materials (NORM) in produced water are of concern due to their bioavailability and bioaccumulation characteristics in finfish and shellfish species used for human consumption. Being chemically similar to calcium, radium concentrates mostly in bones, shells, and exoskeletons. Previous studies have been based on the whole-body bioaccumulation of radium in fish where the distribution of radium in bone/exoskeleton and the edible parts of fish were not considered separately and thus the predicted risks were relatively high. In this article, the distribution of radium in the non-edible and edible parts of fish and the probability of exposure to a produced water plume have been studied in order to characterize human health risks. A probabilistic hydrodynamic model has been incorporated in this study. Using the concentration distribution approach, the mean cancer risks to humans were predicted in the range of 8.6 × 10^?7 to 9.5 × 10^?7, which were 2.6 to 2.7 times less than the risks predicted by using the whole body concentrations. The exceedence probability of maximum permissible human health cancer risk of 1 × 10^?4 is close to zero. At a risk level of 1 × 10^?6, the exceedence probability is 21% whereas in the whole body concentration approach it is between 45 to 49%. In this study, no effect on fish from exposure to NORM components in produced water was found.     

Photon correlation spectroscopy, total intensity light scattering with laser radiation, and hydrodynamic studies of a well fractionated DNA sample.

A Malvern laser light-scattering instrument has been modified for use at scattering angles down to 5° and both total intensity and quasi-elastic scattering experiments. A sample of sheared, length-fractionated calf-thymus DNA was characterized by sedimentation, viscosity and electron microscopy. Quasi-elastic scattering and absolute intensity determinations were performed with the laser instrument and intensity determinations only with a Fica conventional light-scattering photometer. The total intensity experiments gave M?_w = (3.75 ± 0.15) × 10⁶ and 〈R²〉^1/2_z = (206.9 ± 10.3) nm which yielded a value for the persistence length, allowing for polydispersity, of 66 ± 6nm. The quasi-elastic experiments at scattering angles below 20° gave D⁰_{20, w} = (2.23 ± 0.06) × 10^?8 cm²/sec which combined with S⁰_{20, w} = 15.6 in the Svedberg equation gave M?_w = (3.73 ± 0.18) × 10⁶. In addition, from the higher angle data we extracted a value of the longest intramolecular relaxation time, τ1 of 17.5 msec. This is not in particularly good agreement with τ1 predicted by the Zimm–Rouse theory using our other experimental parameters. The disagreement may be due to the restricted applicability of the Zimm–Rouse spring-bead model as a quantitative representation of DNA molecules. Alternatively, it may be due to present difficulties in the unambiguous interpretation of molecular motions from the experimental autocorrelation functions.     

A selective temperature-sensitive defect in viral RNA expression in cells infected with a ts transformation mutant of murine sarcoma virus

We investigated the nature of the defect in the temperature-sensitive mutant of Moloney murine sarcoma virus (Mo-MuSV), termed ts110. This mutant has a temperature-sensitive defect in a function required for maintenance of the transformed state. A nonproducer cell clone, 6m2, infected with ts110 expresses P85 and P58 at 33°C, the transformed temperature, but only P58 is detected at the restrictive temperature of 39°C. Shift-up (33°C → 39°C) and in vitro experiments have established that P85 is not thermolabile for immunoprecipitation. Previous temperature-shift experiments (39°C → 33°C) have shown that P85 synthesis resumes after a 2–3 hr lag period. Temperature shifts (39°C → 33°C) performed in the presence of actinomycin D prevented the synthesis of P85, whereas P58 synthesis did not decline for 5 hr, suggesting that P58 and P85 are translated from different mRNAs. The shift-up experiments also indicated that, once made, the RNA coding for P85 can function at the restrictive temperature for several hours. MuSV-ts110-infected cells superinfected with Mo-MuLV produced a ts110 MuSV-MuLV mixture. Sucrose gradient analysis of virus subunit RNAs revealed a ～28S and a ～35S peak. Electrophoresis of the ～28S poly(A)-containing RNA from ts110 virus in methyl mercuric hydroxide gels resolved two RNAs with estimated sizes of 1.9 × 10⁶ and 1.6 × 10⁶ daltons, both smaller than the wild type MuSV-349 genomic RNA (2.2 × 10⁶ daltons). RNA in the ～28S size class from virus preparations harvested at 33°C was found to translate from P85 and P58, whereas, the ～35S RNA yielded helper virus Pr63^gag. In contrast, virus harvested at 39°C was deficient in P85 coding RNA only. Peptide mapping experiments indicate that P85 contains P23 sequences, a candidate Moloney mouse sarcoma virus src gene product. Taken together, these results suggest that two virus-specific RNAs are present in ts 110-infected 6m2 cells and rescued ts110 pseudotype virions at 33°C, one coding for P85, whose expression can be interfered with by shifting the culture to 39°C; the other coding for P58, whose expression is unaffected by temperature shifts. P85 is a candidate gag-src fusion protein, while P58 contains gag sequences only.