Beta Process Research Articles

Development of enriched 106CdWO 4 crystal scintillators to search for double β decay processes in 106Cd

A cadmium tungstate crystal scintillator enriched in 106Cd was developed for an experiment to search for double beta processes in 106Cd. With this aim samples of cadmium with natural isotopic composition and enriched in 106Cd were purified by vacuum distillation. Cadmium tungstate compounds were synthesized from solutions. The absolute isotopic composition of the enriched cadmium was accurately determined as 66.4% by thermal ionisation mass-spectrometry. A 106CdWO 4 crystal boule was grown by the low-thermal-gradient Czochralski technique. The total irrecoverable loss of the enriched cadmium in all the stages of the crystal scintillator production does not exceed 2.3%. The produced 106CdWO 4 crystal scintillator with mass of 216 g exhibits good optical and scintillation properties.

In Silico Analysis of the Apolipoprotein E and the Amyloid β Peptide Interaction: Misfolding Induced by Frustration of the Salt Bridge Network

The relationship between Apolipoprotein E (ApoE) and the aggregation processes of the amyloid β (Aβ) peptide has been shown to be crucial for Alzheimer's disease (AD). The presence of the ApoE4 isoform is considered to be a contributing risk factor for AD. However, the detailed molecular properties of ApoE4 interacting with the Aβ peptide are unknown, although various mechanisms have been proposed to explain the physiological and pathological role of this relationship. Here, computer simulations have been used to investigate the process of Aβ interaction with the N-terminal domain of the human ApoE isoforms (ApoE2, ApoE3 and ApoE4). Molecular docking combined with molecular dynamics simulations have been undertaken to determine the Aβ peptide binding sites and the relative stability of binding to each of the ApoE isoforms. Our results show that from the several ApoE isoforms investigated, only ApoE4 presents a misfolded intermediate when bound to Aβ. Moreover, the initial α-helix used as the Aβ peptide model structure also becomes unstructured due to the interaction with ApoE4. These structural changes appear to be related to a rearrangement of the salt bridge network in ApoE4, for which we propose a model. It seems plausible that ApoE4 in its partially unfolded state is incapable of performing the clearance of Aβ, thereby promoting amyloid forming processes. Hence, the proposed model can be used to identify potential drug binding sites in the ApoE4-Aβ complex, where the interaction between the two molecules can be inhibited.

An electrical circuit model of the alpha-beta merging seen in dielectric relaxation of ultraviscous liquids

We present a new model for dielectric data in the alpha-beta merging region. The model is constructed using electrical circuit analogies. It leads to an interpretation of the merging region as one where the total relaxation upon cooling separates in two relaxation processes, consistent with a view where the relaxing entities involved are the same for the two processes. We use this alpha-beta model to fit dielectric data in the merging region of two different molecular liquids. These fits are performed under the assumption that the intrinsic high-frequency behavior of the alpha relaxation is a -1/2 power law and that both the alpha and the beta process separately obey time temperature superposition. We get good quality fits in the entire frequency and temperature range studied. This supports the view that alpha relaxation high-frequency slopes that are found to be numerically smaller than 1/2 can be attributed to the influence of the beta relaxation.

Search for double beta decay of zinc and tungsten with low background ZnWO4 crystal scintillators

Double beta processes in 64Zn, 70Zn, 180W, and 186W have been searched for with the help of low background ZnWO4 crystal scintillators at the Gran Sasso National Laboratories of the INFN (Italy). The total measurement time exceeds ten thousand hours. New improved half-life (T1/2) limits on double electron capture and electron capture with positron emission in 64Zn have been set. New T1/2 bounds were also set on different modes of 2β processes in 70Zn, 180W, and 186W. Future perspectives are considered.

A class of neutral to the right priors induced by superposition of beta processes

A random distribution function on the positive real line which belongs to the class of neutral to the right priors is defined. It corresponds to the superposition of independent beta processes at the cumulative hazard level. The definition is constructive and starts with a discrete time process with random probability masses obtained from suitably defined products of independent beta random variables. The continuous time version is derived as the corresponding infinitesimal weak limit and is described in terms of completely random measures. It takes the interpretation of the survival distribution resulting from independent competing failure times. We discuss prior specification and illustrate posterior inference on a real data example.

Distinct β‐clamp interactions govern the activities of the Y family PolIV DNA polymerase

The prototypic Y family DNA polymerase IV (PolIV) of Escherichia coli is involved in multiple replication-associated processes including spontaneous mutagenesis, translesion synthesis (TLS), cell fitness, survival under stressful conditions and checkpoint like functions. It interacts physically and functionally with the replisome's beta processivity clamp through the canonical PolIV C-terminal peptide (CTP). A second interaction that involves a portion of the little finger (LF) domain of PolIV has been structurally described. Here we show that the LF-beta interaction stabilizes the clamp-polymerase complex in vitro and is necessary for the access of PolIV to ongoing replication forks in vivo. However, in contrast to the CTP-beta, the LF-beta interaction is dispensable for the role of the polymerase in TLS. This discloses two independent modes of action for PolIV and, in turn, uncovers a novel way by which the cell may regulate the potentially deleterious effect of such low fidelity polymerases during replication.

Characterization of Novel Alleles of the Escherichia coli umuDC Genes Identifies Additional Interaction Sites of UmuC with the Beta Clamp

Translesion synthesis is a DNA damage tolerance mechanism by which damaged DNA in a cell can be replicated by specialized DNA polymerases without being repaired. The Escherichia coli umuDC gene products, UmuC and the cleaved form of UmuD, UmuD', comprise a specialized, potentially mutagenic translesion DNA polymerase, polymerase V (UmuD'(2)C). The full-length UmuD protein, together with UmuC, plays a role in a primitive DNA damage checkpoint by decreasing the rate of DNA synthesis. It has been proposed that the checkpoint is manifested as a cold-sensitive phenotype that is observed when the umuDC gene products are overexpressed. Elevated levels of the beta processivity clamp along with elevated levels of the umuDC gene products, UmuD'C, exacerbate the cold-sensitive phenotype. We used this observation as the basis for genetic selection to identify two alleles of umuD' and seven alleles of umuC that do not exacerbate the cold-sensitive phenotype when they are present in cells with elevated levels of the beta clamp. The variants were characterized to determine their abilities to confer the umuD'C-specific phenotype UV-induced mutagenesis. The umuD variants were assayed to determine their proficiencies in UmuD cleavage, and one variant (G129S) rendered UmuD noncleaveable. We found at least two UmuC residues, T243 and L389, that may further define the beta binding region on UmuC. We also identified UmuC S31, which is predicted to bind to the template nucleotide, as a residue that is important for UV-induced mutagenesis.

Temperature-Dependent Mechanisms for the Dynamics of Protein-Hydration Waters: A Molecular Dynamics Simulation Study

Molecular dynamics simulations are performed to study the temperature-dependent dynamics and structures of the hydration shells of elastin-like and collagen-like peptides. For both model peptides, it is consistently observed that, upon cooling, the mechanisms for water dynamics continuously change from small-step diffusive motion to large-step jump motion, the temperature dependence of water dynamics shows a weak crossover from fragile behavior to strong behavior, and the order of the hydrogen-bond network increases. The temperature of the weak crossover from fragile to strong behavior is found to coincide with the temperature at which maximum possible order of the hydrogen-bond network is reached so that the structure becomes temperature independent. In the strong regime, the temperature dependence of water translation and rotational dynamics is characterized by an activation energy of E(a) approximately 0.43 eV, consistent with results from previous dielectric spectroscopy (DS) and nuclear magnetic resonance (NMR) studies on protein hydration waters. At these temperatures, a distorted pi-flip motion about the 2-fold molecular symmetry axes, i.e., a water-specific beta process, is an important aspect of water dynamics, at least at the water-peptide interfaces. In addition, it is shown that the hydration waters exhibit pronounced dynamical heterogeneities, which can be traced back to a strong slowdown of water motion in the immediate vicinity of peptide molecules due to formation of water-peptide hydrogen bonds.

Search for double beta decay of zinc and tungsten with low background ZnWO 4 crystal scintillators

Double beta processes in 64Zn, 70Zn, 180W, and 186W have been searched for with the help of large volume (0.1–0.7 kg) low background ZnWO 4 crystal scintillators at the Gran Sasso National Laboratories of the INFN (Italy). The total measurement time exceeds ten thousand hours. New improved half-life limits on double electron capture and electron capture with positron emission in 64Zn have been set, in particular (all the limits are at 90% C.L.): T 1 / 2 0 ν 2 ε ⩾ 1.1 × 10 20 yr , T 1 / 2 2 ν ε β + ⩾ 7.0 × 10 20 yr , and T 1 / 2 0 ν ε β + ⩾ 4.3 × 10 20 yr . In addition, new T 1 / 2 bounds were set for different modes of 2 β processes in 70Zn, 180W, and 186W at the level of 10 17–10 20 yr.

Steric Gate Variants of UmuC Confer UV Hypersensitivity onEscherichia coli

Y family DNA polymerases are specialized for replication of damaged DNA and represent a major contribution to cellular resistance to DNA lesions. Although the Y family polymerase active sites have fewer contacts with their DNA substrates than replicative DNA polymerases, Y family polymerases appear to exhibit specificity for certain lesions. Thus, mutation of the steric gate residue of Escherichia coli DinB resulted in the specific loss of lesion bypass activity. We constructed variants of E. coli UmuC with mutations of the steric gate residue Y11 and of residue F10 and determined that strains harboring these variants are hypersensitive to UV light. Moreover, these UmuC variants are dominant negative with respect to sensitivity to UV light. The UV hypersensitivity and the dominant negative phenotype are partially suppressed by additional mutations in the known motifs in UmuC responsible for binding to the beta processivity clamp, suggesting that the UmuC steric gate variant exerts its effects via access to the replication fork. Strains expressing the UmuC Y11A variant also exhibit decreased UV mutagenesis. Strikingly, disruption of the dnaQ gene encoding the replicative DNA polymerase proofreading subunit suppressed the dominant negative phenotype of a UmuC steric gate variant. This could be due to a recruitment function of the proofreading subunit or involvement of the proofreading subunit in a futile cycle of base insertion/excision with the UmuC steric gate variant.

Regulation of DNA damage responses by the polymerase manager proteins UmuD and UmuD′

Organisms experience DNA damage from numerous sources. When bacterial cells experience DNA damage and other stresses, the SOS response is induced, leading to upregulation of at least 50 genes in E. coli. Among the upregulated genes are specialized Y family DNA polymerases, which replicate damaged DNA and play a role in tolerance to DNA damage. The activity of these potentially mutagenic proteins is tightly regulated. The manager proteins UmuD2 and the cleaved form UmuD'2 provide one regulatory mechanism. The umuD gene products interact with both Y family polymerases, the replicative DNA polymerase, and the beta processivity clamp. The goal of this study is to determine how the conformation and dynamics of the umuD gene products regulate the cellular response to DNA damage. We are characterizing the effects of UmuD and UmuD' on DNA polymerase III activity and probing their conformations using fluorescence resonance energy transfer (FRET) and hydrogen‐deuterium exchange mass spectrometry (HXMS). In HXMS experiments, backbone amide hydrogens that are solvent‐accessible exchange with deuterium over time, whereas inaccessible hydrogens do not exchange. Our HXMS results reveal that the N‐terminal arm of UmuD, which is not present in the cleaved form UmuD′, exhibits local partial unfolding. Additionally, there are substantial regions of stable conformation in both proteins.This work is funded by a Dreyfus Foundation New Faculty Award.

Regulation Of The DNA Damage Response By The DNA Polymerase Manager Protein UmuD

Organisms experience DNA damage from environmental as well as endogenous sources. When bacterial cells experience DNA damage DNA and other stresses, the SOS response is induced, leading to upregulation of at least 50 genes in E. coli. Many of the genes whose expression is induced as part of the SOS response are responsible for DNA repair and cell cycle regulation. Another group of genes, specialized Y family DNA polymerases with the ability to replicate damaged DNA, play a role in tolerance to DNA damage at a potentially mutagenic cost. Multiple layers of regulation control the activity of these potentially mutagenic proteins. The function of Y family DNA polymerases is regulated by UmuD, a manager protein, and its cleaved form, UmuD'. The umuD gene products directly interact with both Y family polymerases as well as the beta processivity clamp. The goal of this study is to determine the conformation and dynamics of the umuD gene products in order to understand how they regulate the cellular response to DNA damage. We are using fluorescence resonance energy transfer (FRET) and hydrogen-deuterium exchange mass spectrometry (HXMS) to probe the conformations of UmuD and UmuD'. In HXMS experiments, backbone amide hydrogens that are solvent-accessible become labeled with deuterium over time, whereas those are are not accessible do not become labeled. Our HXMS results reveal that the N-terminal arm of UmuD, which is not present in the cleaved form UmuD', exhibits local partial unfolding. Residues that contact the N-terminal arm show large differences between UmuD and UmuD'. Additionally, there are substantial regions of stable conformation in both proteins. Complete characterization of UmuD and UmuD' dynamics is currently in progress.

Study of supercooled orientationally disordered binary solid solutions II: cyclohexyl derivatives, neopentanol and neopentylglycol

The main aim of the present investigation is to see how various relaxation processes including the chair-chair transformation (as found by earlier researchers at room temperature in mechanical relaxation spectroscopy) in cyclohexane derivatives evolve as the temperature is lowered. For this purpose, four remarkable (two-component) solid solutions that are orientationally disordered are investigated, where the first three systems are hydrogen (H-) bonded pairs, and the fourth is a non-H bonded pair. The former group is the two-component system of cyclohexanol (CHXOL) + 2,2-dimethyl-1-propanol or neopentanol (NPOL); cyclohexanol (CHXOL) + cycloheptanol (CHPOL) & neopentanol (NPOL) + neopentylglycol (NPGOL) systems, and the lone non H-bonded pair that has been studied is cyanocyclohexane (CNCH) and cyclohexylchloride (CHC). In all these cases, the liquid mixtures on cooling form orientationally disordered phases which are a solid solution of the corresponding pure phases. The feature is common to all the four systems studied here, but in CHXOL + CHPOL, the phase I of CHXOL beyond x(m) > or = 0.1 only forms a solid solution (designated as S(I')) with the phase I of CHPOL. In CNCH + CHC the solid phase is stable for the concentration range 0 < or = x(m) < or = 0.4 (without transition to any other phase). The above solid phase I (or I') has been investigated at low temperatures and for several concentrations, by means of dielectric spectroscopy and differential scanning calorimetry (DSC). Depending upon the concentration, this phase reveals a glass transition in the temperature range 116-150 K and associated with this is a pronounced relaxation process identifiable with the so called alpha-process. The dielectric spectra of this process is found to follow the Havriliak-Negami (HN) equation. In context of the binary system study here, the analysis of the various parameters obtained show an isomorphic relationship between the phases of the pure components through a continuous change of parameters. Another process of much smaller magnitude designated as the alpha'-process was also found in systems consisting of cyclohexyl derivatives above the glass transition temperature T(g) which kinetically freezes around 170 K. This process interestingly, is also non-Arrhenius in nature, becomes increasingly weaker with increase in the second component, and may be identified with (axial) chair-(equatorial) chair transformation. In addition in all these systems, a weak high-frequency process and a clear sub-T(g) process, are found which are designated as the beta- & gamma-processes respectively. The beta-process may be identified with Johari-Goldstein (JG) or beta(JG) process as it is found to follow the predictions of the coupling model proposed by Ngai. However, the identification of the gamma-process with internal degrees of freedom are fraught with some problems in the interpretation of the experimental data that are highlighted. The kinetic freezing of the various dielectric processes have been critically examined in relation to the T(g) found in the DSC experiments.

Non-parametric Bayesian analysis of clustered survival data

Clustered survival data are often modelled with frailty models which incorporate frailties to model the cluster specific heterogeneity and the dependence between observations in the same cluster. For the analysis of the frailty models, we propose Bayesian modelling with beta process prior on the cumulative hazard function and describe the details of the posterior computation. We demonstrate the method with two data sets using three different frailty distributions: gamma, log-normal and log-logistic distributions. We also empirically demonstrate the difficulty in checking the assumed frailty distribution with the posterior sample of the frailties.

The Glass Transition and Dielectric Secondary Relaxation of Fructose−Water Mixtures

Broad-band dielectric measurements for fructose-water mixtures with fructose concentrations between 70.0 and 94.6 wt% were carried out in the frequency range of 2 mHz to 20 GHz in the temperature range of -70 to 45 degrees C. Two relaxation processes, the alpha process at lower frequency and the secondary beta process at higher frequency, were observed. The dielectric relaxation time of the alpha process was 100 s at the glass transition temperature, T(g), determined by differential scanning calorimetry (DSC). The relaxation time and strength of the beta process changed from weaker temperature dependences of below T(g) to a stronger one above T(g). These changes in behaviors of the beta process in fructose-water mixtures upon crossing the T(g) of the mixtures is the same as that found for the secondary process of water in various other aqueous mixtures with hydrogen-bonding molecular liquids, polymers, and nanoporous systems. These results lead to the conclusion that the primary alpha process of fructose-water mixtures results from the cooperative motion of water and fructose molecules, and the secondary beta process is the Johari-Goldstein process of water in the mixture. At temperatures near and above T(g) where both the alpha and the beta processes were observed and their relaxation times, tau(alpha) and tau(beta), were determined in some mixtures, the ratio tau(alpha)/tau(beta) is in accord with that predicted by the coupling model. Fixing tau(alpha) at 100 s, the ratio tau(alpha)/tau(beta) decreases with decreasing concentration of fructose in the mixtures. This trend is also consistent with that expected by the coupling model from the decrease of the intermolecular coupling parameter upon decreasing fructose concentration.

The Bernstein–von Mises theorem in semiparametric competing risks models

Semiparametric Bayesian models are nowadays a popular tool in event history analysis. An important area of research concerns the investigation of frequentist properties of posterior inference. In this paper, we propose novel semiparametric Bayesian models for the analysis of competing risks data and investigate the Bernstein–von Mises theorem for differentiable functionals of model parameters. The model is specified by expressing the cause-specific hazard as the product of the conditional probability of a failure type and the overall hazard rate. We take the conditional probability as a smooth function of time and leave the cumulative overall hazard unspecified. A prior distribution is defined on the joint parameter space, which includes a beta process prior for the cumulative overall hazard. We first develop the large-sample properties of maximum likelihood estimators by giving simple sufficient conditions for them to hold. Then, we show that, under the chosen priors, the posterior distribution for any differentiable functional of interest is asymptotically equivalent to the sampling distribution derived from maximum likelihood estimation. A simulation study is provided to illustrate the coverage properties of credible intervals on cumulative incidence functions.

On the Enhanced Reverse Beta Processes in Graphene-Iron Composite Nanostructures at High Temperatures in Strong Magnetic Field

Strong dense many-spin interactions have been proposed to organize novel orbital dynamics (the Little Effect) for novel chemical and catalytic phenomena. The recent determinations of the relativistic and quantum Hall effects of car- riers in graphene under strong magnetic confinement have substantiated the Little Effect. Moreover such nonclassical phenomena under the stronger magnetic confinement of ferro-nanocatalysts are here shown to organize reverse beta proc- esses and possibly pycnonuclear reactions under high temperature and high-pressure conditions. Such processes have im- plications for reverse beta reactions and nuclear reactions within the earth's interior and new technologies for carbon nanotube-ferrometal and nanographene-ferrometal composites.

Study of secondary relaxation in disordered plastic crystals of isocyanocyclohexane, cyanocyclohexane, and 1-cyanoadamantane

In the present communication, dielectric relaxation investigations on three interesting supercooled plastic crystalline substances, i.e., isocyanocyclohexane (ICNCH), cyanocyclohexane (CNCH), and 1-cyanoadamantane (CNADM) are reported. All of these have the main dipole moment situated in their side group- C[Triple Bond]N or- N[Triple Bond]C. Differential scanning calorimetry (DSC) was also employed as a supporting technique. Glassy crystal were easily formed in the first two samples by slowly cooling the plastic phase, but in CNADM it was formed by rapidly quenching the room temperature plastic phase. In addition to the so called alpha process that can reasonably be described by a Havriliak-Negami (HN) shape function, a secondary (or beta) relaxation process is found in all the materials. The beta process in CNADM has an activation energy (DeltaE(beta)) of about approximately 13.8+/-1 kJmol, and is present even in the corresponding ordered crystalline phase, i.e., in its monoclinic phase. On the other hand, the magnitude of DeltaE(beta) in both the isomers of cyanocyclohexane, i.e., ICNCH and CNCH, is similar and is about 21.1 and 23.4 kJmol, respectively. Unlike CNADM, the cyclohexane derivatives are capable of exhibiting additional intramolecular process due to chair-chair conversion (i.e., in addition to the rotational motion of the side group- C[Triple Bond]N or- N[Triple Bond]C). Therefore, the secondary process of these systems is compared to that occuring in the binary liquid glass formed by dispersing a small quantity of these dipolar liquids in nearly nonpolar orthoterphenyl (OTP). Measurements were also made in the supercooled binary mixures of other cyclohexyl derivatives like cyclohexylchloride and cyclohexylbromide with OTP which lack a flexible side group. The sub-T(g) relaxation process exhibited in all these cases have almost similar activation energy as in case of pure ICNCH and CNCH. These observations together with the fact that the activation energy for this process is much below that of chair-chair conversion which is about 43 kJmol leads us to the conclusion that sub-T(g) relaxation process in the binary mixtures is JG type, and perhaps beta relaxation process in phase I of ICNCH and CNCH is also similar. With the help of semiemperical calculations of the dipolemoments for the axial and equitorial confirmers, it is concluded that the process associated with the chair-chair may not be dielectrically very active and, hence, should be relatively weaker in magnitude. The beta process in CNADM has an activation energy (DeltaE(beta)) of about 13.8+/-1 kJmol, and is present even in the corresponding ordered crystalline phase indicating that it may not be characteristic of the glass formation of phase I. The molecular structure of CNADM is such that it does not possess other intramolecular degrees of freedom of the type equitorial to axial (or chair-chair) transformation. Our experimental finding that JG relaxation for CNADM dispersed in glassy OTP matrix is about 31 kJmol, indicating that the well resolved sub-T(g) process in CNADM is due to the small side group, i.e., -C[Triple Bond]N and JG relaxation in phase I of CNADM is perhaps not resolvable or too small to be detected.

Influence of structural chemical characteristics on polymer chain dynamics

A comparative study of the dielectric relaxation behavior of two structurally close polymers containing aliphatic-aromatic side groups was carried out in order to get a better understanding on how slight differences in chemical structure affect the molecular responses to perturbation fields. Specifically, chain dynamics of poly(2-acryloyloxyethyl-2-naphthalene-2-ylacetate) and poly(2-methacryloyloxyethyl-2-naphthalene-2-ylacetate) were studied by broadband dielectric spectroscopy in the frequency range of 10(-2)-10(8) Hz and temperature window of 298-403 K. Also, the relaxation behavior of (2-acetyloxyethyl-2-naphthalene-2-ylacetate), model compound of the polymer side groups, was analyzed. The isotherms representing the dielectric loss in the frequency domain show important conductive contributions, especially at high temperature, which hide the low frequency side of the alpha relaxation. Conductivity also increases the real component of the complex permittivity in the low frequencies region. Retardation spectra were obtained by minimizing the sum of the squares of the difference between the experimental values of the complex permittivity for each frequency and the analytical ones, predicted by the linear phenomenological theory, using a Tikhonov regularization technique. The spectra present an apparent alpha peak with an excess wing at short time side resulting from the overlapping of the true alpha relaxation and a beta process. Three absorptions, named in increasing order of time gamma, beta, and alpha relaxations, are separated by deconvolution methods. The activation energies associated with the gamma process are 70.0+/-1.8, 68.0+/-1.4, and 74.8+/-0.8 kJ mol(-1) for (2-acetyloxyethyl-2-naphthalene-2-yl acetate), poly(2-acryloyloxyethyl-2-naphthalene-2-yl acetate) and poly(2-methacryloyloxyethyl-2-naphthalene-2-yl acetate), respectively. The respective activation energies associated with the beta relaxation are 121.7+/-2.4, 135.3+/-1.4, and 141.6+/-1.3 kJ mol(-1). Values of the shape parameters and the strengths of the relaxation processes were obtained as a function of temperature. The dynamic fragility of the polymers and the model compound was studied and compared with that reported for macromolecular and monomeric systems. Also, the evolution of the size of the correlated domains associated with the alpha relaxation was estimated. Finally, the gamma relaxation rather than the beta absorption obeys the criteria apparently held by the Johari-Goldstein beta processes.

Fock representation of the renormalized higher powers of White noise and the centreless Virasoro (or Witt)–Zamolodchikov–w∞*-Lie algebra

The identification of the *-Lie algebra of the renormalized higher powers of White noise (RHPWN) and the analytic continuation of the second quantized centreless Virasoro (or Witt)–Zamolodchikov–w∞*-Lie algebra of conformal field theory and high-energy physics, was recently established in [5] based on results obtained in [3] and [4]. In the present paper, we show how the RHPWN Fock kernels must be truncated in order to be positive semi-definite and we obtain a Fock representation of the two algebras. We show that the truncated renormalized higher powers of White noise (TRHPWN) Fock spaces of order ⩾2 host the continuous binomial and beta processes.