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Background: Inhibition of PCSK9 (proprotein convertase subtilisin/kexin type 9)-low density lipoprotein receptor interaction with injectable monoclonal antibodies or small interfering RNA lowers plasma low density lipoprotein-cholesterol, but despite nearly 2 decades of effort, an oral inhibitor of PCSK9 is not available. Macrocyclic peptides represent a novel approach to target proteins traditionally considered intractable to small-molecule drug design. Methods: Novel mRNA display screening technology was used to identify lead chemical matter, which was then optimized by applying structure-based drug design enabled by novel synthetic chemistry to identify macrocyclic peptide (MK-0616) with exquisite potency and selectivity for PCSK9. Following completion of nonclinical safety studies, MK-0616 was administered to healthy adult participants in a single rising-dose Phase 1 clinical trial designed to evaluate its safety, pharmacokinetics, and pharmacodynamics. In a multiple-dose trial in participants taking statins, MK-0616 was administered once daily for 14 days to characterize the safety, pharmacokinetics, and pharmacodynamics (low density lipoprotein cholesterol). Results: MK-0616 displayed high affinity ( K i = 5pM) for PCSK9 in vitro and sufficient safety and oral bioavailability preclinically to enable advancement into the clinic. In Phase 1 clinical studies in healthy adults, single oral doses of MK-0616 were associated with >93% geometric mean reduction (95% CI, 84–103) of free, unbound plasma PCSK9; in participants on statin therapy, multiple–oral-dose regimens provided a maximum 61% geometric mean reduction (95% CI, 43–85) in low density lipoprotein cholesterol from baseline after 14 days of once-daily dosing of 20 mg MK-0616. Conclusions: This work validates the use of mRNA display technology for identification of novel oral therapeutic agents, exemplified by the identification of an oral PCSK9 inhibitor, which has the potential to be a highly effective cholesterol lowering therapy for patients in need.

Proprotein convertase subtilisin-like/kexin type 9 (PCSK9) is a key regulator of plasma LDL-cholesterol (LDL-C) and a clinically validated target for the treatment of hypercholesterolemia and coronary artery disease. Starting from second-generation lead structures such as 2, we were able to refine these structures to obtain extremely potent bi- and tricyclic PCSK9 inhibitor peptides. Optimized molecules such as 44 demonstrated sufficient oral bioavailability to maintain therapeutic levels in rats and cynomolgus monkeys after dosing with an enabled formulation. We demonstrated target engagement and LDL lowering in cynomolgus monkeys essentially identical to those observed with the clinically approved, parenterally dosed antibodies. These molecules represent the first report of highly potent and orally bioavailable macrocyclic peptide PCSK9 inhibitors with overall profiles favorable for potential development as once-daily oral lipid-lowering agents. In this manuscript, we detail the design criteria and multiparameter optimization of this novel series of PCSK9 inhibitors.

Let $K$ be the function field of a smooth, irreducible curve defined over $\overline{\mathbb{Q}}$. Let $f\in K[x]$ be of the form $f(x)=x^q+c$ where $q = p^{r}, r \ge 1,$ is a power of the prime number $p$, and let $\beta\in \overline{K}$. For all $n\in\mathbb{N}\cup\{\infty\}$, the Galois groups $G_n(\beta)=\mathop{\rm{Gal}}(K(f^{-n}(\beta))/K(\beta))$ embed into $[C_q]^n$, the $n$-fold wreath product of the cyclic group $C_q$. We show that if $f$ is not isotrivial, then $[[C_q]^\infty:G_\infty(\beta)], Comment: 20 pages

We advance a new conjecture in the spirit of the dynamical Manin–Mumford conjecture. We show that our conjecture holds for all polarisable endomorphisms of abelian varieties and for all polarisable endomorphisms of $(\mathbb{P}^{1})^{N}$. Furthermore, we show various examples which highlight the restrictions one would need to consider in formulating any general conclusion in the dynamical Manin–Mumford conjecture.

Arithmetic dynamics is the study of number theoretic properties of dynamical systems. A relatively new field, it draws inspiration partly from dynamical analogues of theorems and conjectures in classical arithmetic geometry and partly from p p -adic analogues of theorems and conjectures in classical complex dynamics. In this article we survey some of the motivating problems and some of the recent progress in the field of arithmetic dynamics.

Pathway activating mutations of the transcription factor NRF2 and its negative regulator KEAP1 are strongly correlative with poor clinical outcome with pemetrexed/carbo(cis)platin/pembrolizumab (PCP) chemo-immunotherapy in lung cancer. Despite the strong genetic support and therapeutic potential for a NRF2 transcriptional inhibitor, currently there are no known direct inhibitors of the NRF2 protein or its complexes with MAF and/or DNA. Herein we describe the design of a novel and high-confidence homology model to guide a medicinal chemistry effort that resulted in the discovery of a series of peptides that demonstrate high affinity, selective binding to the Antioxidant Response Element (ARE) DNA and thereby displace NRF2-MAFG from its promoter, which is an inhibitory mechanism that to our knowledge has not been previously described. In addition to their activity in electrophoretic mobility shift (EMSA) and TR-FRET-based assays, we show significant dose-dependent ternary complex disruption of NRF2-MAFG binding to DNA by SPR, as well as cellular target engagement by thermal destabilization of HiBiT-tagged NRF2 in the NCI–H1944 NSCLC cell line upon digitonin permeabilization, and SAR studies leading to improved cellular stability. We report the characterization and unique profile of lead peptide 18, which we believe to be a useful in vitro tool to probe NRF2 biology in cancer cell lines and models, while also serving as an excellent starting point for additional in vivo optimization toward inhibition of NRF2-driven transcription to address a significant unmet medical need in non-small cell lung cancer (NSCLC).

Let $K$ be a number field or a function field. Let $f\in K(x)$ be a rational function of degree $d\geq 2$, and let $\beta\in\mathbb{P}^1(K)$. For all $n\in\mathbb{N}\cup\{\infty\}$, the Galois groups $G_n(\beta)=\text{Gal}(K(f^{-n}(\beta))/K)$ embed into $\text{Aut}(T_n)$, the automorphism group of the $d$-ary rooted tree of level $n$. A major problem in arithmetic dynamics is the arboreal finite index problem: determining when $[\text{Aut}(T_\infty):G_\infty], Comment: 36 pages, 4 figures

Given a smooth projective curve C defined over a number field and given two elliptic surfaces E_1/C and E_2/C along with sections P_i and Q_i of E_i (for i = 1,2), we prove that if there exist infinitely many algebraic points t on C such that for some integers m_{1,t} and m_{2,t}, we have that [m_{i,t}](P_i)_t = (Q_i)_t on E_i (for i = 1,2), then at least one of the following conclusions must hold: either (i) there exists an isogeny f between E_1 and E_2 and also there exists a nontrivial endomorphism g of E_2 such that f(P_1) = g(P_2); or (ii) Q_i is a multiple of P_i for some i = 1,2. A special case of our result answers a conjecture made by Silverman.

Let K be a number field or a function field of characteristic 0. If K is a number field, assume the abc-conjecture for K. We prove a variant of Zsigmondy's theorem for ramified primes in preimage fields of rational functions in K ( x ) that are not postcritically finite. For example, suppose K is a number field and f ∈ K [ x ] is not postcritically finite, and let K n be the field generated by the nth iterated preimages under f of β ∈ K . We show that for all large n, there is a prime of K that ramifies in K n and does not ramify in K m for any m n .

Let a and b be algebraic numbers such that exactly one of a and b is an algebraic integer, and let f_t(z):=z^2+t be a family of polynomials parametrized by t. We prove that the set of all algebraic numbers t for which there exist positive integers m and n such that f_t^m(a)=f_t^n(b) has bounded Weil height. This is a special case of a more general result supporting a new bounded height conjecture in dynamics. Our results fit into the general setting of the principle of unlikely intersections in arithmetic dynamics.

We formulate a general question regarding the size of the iterated Galois groups associated to an algebraic dynamical system and then we discuss some special cases of our question., 18 pages. arXiv admin note: text overlap with arXiv:1810.00990

Glucagon and insulin maintain blood glucose homeostasis and are used to treat hypoglycemia and hyperglycemia, respectively, in patients with diabetes. Whereas insulin is stable for weeks in its solution formulation, glucagon fibrillizes rapidly at the acidic pH required for solubility and is therefore formulated as a lyophilized powder that is reconstituted in an acidic solution immediately before use. Here we use solid-state NMR to determine the atomic-resolution structure of fibrils of synthetic human glucagon grown at pharmaceutically relevant low pH. Unexpectedly, two sets of chemical shifts are observed, indicating the coexistence of two β-strand conformations. The two conformations have distinct water accessibilities and intermolecular contacts, indicating that they alternate and hydrogen bond in an antiparallel fashion along the fibril axis. Two antiparallel β-sheets assemble with symmetric homodimer cross sections. This amyloid structure is stabilized by numerous aromatic, cation-π, polar and hydrophobic interactions, suggesting mutagenesis approaches to inhibit fibrillization could improve this important drug., National Institutes of Health (U.S.) (Grant AG059661), National Institutes of Health (U.S.). Ruth L. Kirschstein National Research Service Award (1F31AI133989)

Let K be a function field over an algebraically closed field k of characteristic 0, let ϕ ∈ K(z) be a rational function of degree at least equal to 2 for which there is no point at which ϕ is totally ramified and let α ∈ K. We show that for all but finitely many pairs (m, n) ∈ $\mathbb{Z}$⩾0 × $\mathbb{N}$ there exists a place $\mathfrak{p}$ of K such that the point α has preperiod m and minimum period n under the action of ϕ. This answers a conjecture made by Ingram–Silverman [13] and Faber–Granville [8]. We prove a similar result, under suitable modification, also when ϕ has points where it is totally ramified. We give several applications of our result, such as showing that for any tuple (c0, . . ., cd−2) ∈ kd−1 and for almost all pairs (mi, ni) ∈ $\mathbb{Z}$⩾0 × $\mathbb{N}$ for i = 0, . . ., d − 2, there exists a polynomial f ∈ k[z] of degree d in normal form such that for each i = 0, . . ., d − 2, the point ci has preperiod mi and minimum period ni under the action of f.

Previous work has suggested that activation of mGlu5 receptor augments NMDA receptor function and thereby may constitute a rational approach addressing glutamate hypofunction in schizophrenia and a target for novel antipsychotic drug development. Here, we report the in vitro activity, in vivo efficacy and safety profile of 5PAM523 (4-Fluorophenyl){(2R,5S)-5-[5-(5-fluoropyridin-2-yl)-1,2,4-oxadiazol-3-yl]-2-methylpiperidin-1-yl}methanone), a structurally novel positive allosteric modulator selective of mGlu5. In cells expressing human mGlu5 receptor, 5PAM523 potentiated threshold responses to glutamate in fluorometric calcium assays, but does not have any intrinsic agonist activity. 5PAM523 acts as an allosteric modulator as suggested by the binding studies showing that 5PAM523 did not displace the binding of the orthosteric ligand quisqualic acid, but did partially compete with the negative allosteric modulator, MPyEP. In vivo, 5PAM523 reversed amphetamine-induced locomotor activity in rats. Therefore, both the in vitro and in vivo data demonstrate that 5PAM523 acts as a selective mGlu5 PAM and exhibits anti-psychotic like activity. To study the potential for adverse effects and particularly neurotoxicity, brain histopathological exams were performed in rats treated for 4 days with 5PAM523 or vehicle. The brain exam revealed moderate to severe neuronal necrosis in the rats treated with the doses of 30 and 50 mg/kg, particularly in the auditory cortex and hippocampus. To investigate whether this neurotoxicity is mechanism specific to 5PAM523, similar safety studies were carried out with three other structurally distinct selective mGlu5 PAMs. Results revealed a comparable pattern of neuronal cell death. Finally, 5PAM523 was tested in mGlu5 knock-out (KO) and wild type (WT) mice. mGlu5 WT mice treated with 5PAM523 for 4 days at 100 mg/kg presented significant neuronal death in the auditory cortex and hippocampus. Conversely, mGlu5 KO mice did not show any neuronal loss by histopathology, suggesting that enhancement of mGlu5 function is responsible for the toxicity of 5PAM523. This study reveals for the first time that augmentation of mGlu5 function with selective allosteric modulators results in neurotoxicity.

The synthesis, computer modeling, and biological activity of an octawalled molecular umbrella short interfacing RNA (siRNA) conjugate is described. This molecular umbrella-siRNA conjugate exhibited mRNA knockdown activity in vitro in the absence of a transfection reagent. Evaluation of this molecular umbrella conjugate in vivo, using the rat eye via intravitreal injection, resulted in sequence specific mRNA knockdown in the retina with no obvious signs of toxicity, as judged by ophthalmic examination.

An improved understanding of the early behavioral indicators of lumbosacral disease in working dogs may allow earlier interventions and help reduce premature retirement because of disability. However, recognition of early behavioral indicators can be challenging in stoic, high-drive working dogs because they often mask clinical signs. The purpose of this feasibility study was to develop a technique for visualizing canine skeletal movements during working tasks and to describe veterinary clinical specialist opinions on the utility of the visualization technique. Three detection-trained police dogs with a recent history of working task deficits and suspected lumbosacral disease were recruited for the study. Conventional and motion capture video recordings were acquired as dogs performed walking and search high working tasks. Whole-body computed tomography (CT) scans were acquired using clinical multislice CT scanners. Image data from motion capture recordings and whole-body CT scans were analyzed and merged. Three-dimensional (3D) computer animation video clips of skeletal movements were created for each dog and each task, using multiple viewing angle perspectives. Interactive meetings with veterinary clinical specialist reviewers were used to refine point placements for the final renderings. Veterinary clinical specialists reviewed final 3D animation movie clips and recorded their opinions on the utility for the visualization technique. Veterinary clinical specialists reported that the computer animations helped them recognize behavioral characteristics that they had not initially noticed in physical examinations. Potential applications for this visualization technique include creating educational training aids for veterinary students, owners, and handlers; assisting veterinarians in planning rehabilitative treatments; and assisting researchers in developing computer models for biomechanical analyses. Future controlled prospective studies are needed in a large number of normal and affected working dogs to improve accuracy of the visualization technique and test the effect of the technique on observer performance.

Let $a(\lambda)$ and $b(\lambda)$ be two polynomials with coefficients in complex numbers and let $f_{\lamb$ be a one-parameter family of polynomials indexed by all complex numbers $\lambda$. We study whether there exist infinitely many complex numbers $\lambda$ such that both $a(\lambda)$ and $b(\lambda)$ are preperiodic for $f_{\lambda}$.

Let K be a number field, let f(x) in K(x) be a rational function of degree d> 1, and let z in K be a wandering point such that f^n(z) is nonzero for all n > 0. We prove that if the abc-conjecture holds for K, then for all but finitely many positive integers n, there is a prime p of K such that p | f^n(z) and p does not divide f^m(z) for all positive integers m < n. We prove the same result unconditionally for function fields of characteristic 0 when f is not isotrivial., 15 pages

Following work of Bugeaud, Corvaja, and Zannier for integers, Ailon and Rudnick prove that for any multiplicatively independent polynomials, $a, b \in {\mathbb C}[x]$, there is a polynomial $h$ such that for all $n$, we have \[ \gcd(a^n - 1, b^n - 1) \mid h\] We prove a compositional analog of this theorem, namely that if $f, g \in {\mathbb C}[x]$ are nonconstant compositionally independent polynomials and $c(x) \in {\mathbb C}[x]$, then there are at most finitely many $\lambda$ with the property that there is an $n$ such that $(x - \lambda)$ divides $\gcd(f^{\circ n}(x) - c(x), g^{\circ n}(x) - c(x))$., Comment: 22 pages

LetKbe a number field or a function field of characteristic 0, letφ∈K(z) with deg(φ) ⩾ 2, and letα∈ ℙ1(K). LetSbe a finite set of places ofKcontaining all the archimedean ones and the primes whereφhas bad reduction. After excluding all the natural counterexamples, we define a subsetA(φ,α) of ℤ⩾0× ℤ>0and show that for all but finitely many (m,n) ∈A(φ,α) there is a prime 𝔭 ∉Ssuch that ord𝔭(φm+n(α)−φm(α)) = 1 andαhas portrait (m,n) under the action ofφmodulo 𝔭. This latter condition implies ord𝔭(φu+v(α)−φu(α)) ⩽ 0 for (u,v) ∈ ℤ⩾0× ℤ>0satisfyingu

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Next generation NNRTIs are sought which possess both broad spectrum antiviral activity against key mutant strains and a high genetic barrier to the selection of new mutant viral strains. Pyridones were evaluated as an acyclic conformational constraint to replace the aryl ether core of MK-4965 (1) and the more rigid indazole constraint of MK-6186 (2). The resulting pyridone compounds are potent inhibitors of HIV RT and have antiviral activity in cell culture that is superior to other next generation NNRTI's.

La conjecture de Mordell-Lang decrit l'intersection d'un sous-groupe de type fini avec une variete fermee d'une variete semi-abelienne. De facon equivalente, cette conjecture decrit l'intersection des sous-varietes fermees avec l'ensemble des images de l'origine sous un semigroupe de translations de type fini. Nous etudions la question analogue dans laquelle les translations sont remplacees par les endomorphismes d'un groupe algebrique (et l'origine est remplacee par un autre point). Nous montrons qui la conclusion de la conjecture de Mordell-Lang reste vraie dans cette situation si, ou bien, (1) la variete semi-abelienne est simple, ou, (2) la variete semi-abelienne est A 2 , ou A est une variete semi-abeliennne de dimension 1, ou (3) la sous-variete est une sous-variete semi-abeliennne de dimension 1, ou enfin, (4) la matrice jacobienne a l'origine de chaque endomorphisme est diagonalisable. Nous donnons aussi des exemples qui montrent que la conclusion est fausse si nous affaiblissons n'importe laquelle de ces hypotheses.

We prove a special case of a dynamical analogue of the classical Mordell- Lang conjecture. Specifically, let phi be a rational function with no periodic critical points other than those that are to ...

Let K be a number field with algebraic closure K-bar, let S be a finite set of places of K containing the archimedean places, and let f be a Chebyshev polynomial. We prove that if a in K-bar is not preperiodic, then there are only finitely many preperiodic points b in K-bar which are S-integral with respect to a., Comment: 12 pages

We prove a dynamical version of the Bogomolov conjecture in the special case of lines in affine space A^m under the action of a map (f_1,...,f_m) where each f_i is a polynomial in Q-bar[X] of the same degree., 6 pages; more explanation of the cited results on Julia sets has been added and a few typos have been corrected

Using a combination of traditional Medicinal Chemistry/SAR analysis, crystallography, and molecular modeling, we have designed and synthesized a series of novel, highly potent NNRTIs that possess broad antiviral activity against a number of key clinical mutations.

We prove that the local height of a point on a Drinfeld module can be computed by averaging the logarithm of the distance to that point over the torsion points of the module. This gives rise to a Drinfeld module analog of a weak version of Siegel's integral points theorem over number fields and to an analog of a theorem of Schinzel's regarding the order of a point modulo certain primes.

Using an alternative notion of good reduction, an analog of the Shafarevich theorem for elliptic curves is proved for morphisms of the projective line over number fields., Comment: 11 pages

We prove a Siegel type statement for finitely generated \(\phi\)-submodules of \(\mathbb{G}_a\) under the action of a Drinfeld module \(\phi\). This provides a positive answer to a question we asked in a previous paper. We also prove an analog for Drinfeld modules of a theorem of Silverman for nonconstant rational maps of \(\mathbb{P}^1\) over a number field.

Let $X$ be a Noetherian space, let $\Phi:X\longrightarrow X$ be a continuous function, let $Y\subseteq X$ be a closed set, and let $x\in X$. We show that the set $S:=\{n\in\mathbb{N}\colon \Phi^n(x)\in Y\}$ is a union of at most finitely many arithmetic progressions along with a set of Banach density zero. In particular, we obtain that given any quasi-projective variety $X$, any rational map $\Phi:X\longrightarrow X$, any subvariety $Y\subseteq X$, and any point $x\in X$ whose orbit under $\Phi$ is in the domain of definition for $\Phi$, the set $S$ is a finite union of arithmetic progressions together with a set of Banach density zero. This answers a question posed by Laurent Denis [7]. We prove a similar result for the backward orbit of a point and provide some quantitative bounds.

Pyrimidino-thiazolyl carbonitriles were prepared that are potent VEGFR-2 (KDR) kinase inhibitors. The modification of lead structures resulted in 3m which exhibited the best overall profile in KDR inhibitory activity, iv/po pharmacokinetics, and reduced hERG affinity.

The abc-conjecture is applied to various questions involving the number of distinct fields , as we vary over integers n.

There are many opportunities to use macromolecules, such as peptides and oligonucleotides, for intracellular applications. Despite this, general methods for delivering these molecules to the cytosol in a safe and efficient manner are not available. Efforts to develop a variety of intracellular drug delivery systems such as viral vectors, lipoplexes, nanoparticles, and amphiphilic peptides have been made, but various challenges such as delivery efficiency, toxicity, and controllability remain. A central challenge is the ability to selectively perturb, not destroy, the membrane to facilitate cargo introduction. Herein, we describe our efforts to design and characterize peptides that form pores inside membranes at acidic pH, so-called pH-switchable pore formation (PSPF) peptides, as a potential means for facilitating cargo translocation through membranes. Consistent with pore formation, these peptides exhibit low-pH-triggered selective release of ATP and miRNA, but not hemoglobin, from red blood cells. Consistent with these observations, biophysical studies (tryptophan fluorescence, circular dichroism, size-exclusion chromatography, analytical ultracentrifugation, and attenuated total reflectance Fourier transformed infrared spectroscopy) show that decreased pH destabilizes the PSPF peptides in aqueous systems while promoting their membrane insertion. Together, these results suggest that reduced pH drives insertion of PSPF peptides into membranes, leading to target-specific escape through a proposed pore formation mechanism.

Let $c_1, c_2, c_3$ be distinct complex numbers, and let $d\ge 3$ be an integer. We show that the set of all pairs $(a,b)\in \mathbb{C}\times \mathbb{C}$ such that each $c_i$ is preperiodic for the action of the polynomial $x^d+ax+b$ is not Zariski dense in the affine plane.

Let K be a number field, let f: P_1 --> P_1 be a nonconstant rational map of degree greater than 1, let S be a finite set of places of K, and suppose that u, w in P_1(K) are not preperiodic under f. We prove that the set of (m,n) in N^2 such that f^m(u) is S-integral relative to f^n(w) is finite and effectively computable. This may be thought of as a two-parameter analog of a result of Silverman on integral points in orbits of rational maps. This issue can be translated in terms of integral points on an open subset of P_1^2; then one can apply a modern version of the method of Runge, after increasing the number of components at infinity by iterating the rational map. Alternatively, an ineffective result comes from a well-known theorem of Vojta., 17 pages; minor revisions made