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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.

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.

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 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.

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 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

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.

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 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.

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.

We have prepared a series of potent, dual inhibitors of the prenyl transferases farnesyl protein transferase (FPTase) and geranyl-geranyl protein transferase I (GGPTase). The compounds were shown to possess potent activity against both enzymes in cell culture. Mechanistic analysis has shown that the compounds are CAAX competitive for FPTase inhibition but geranyl-geranyl pyrophosphate (GGPP) competitive for GGPTase inhibiton.

This paper deals with generalizations of Hilbert's irreducibility theorem. The classical Hilbert irreducibility theorem states that for any cover f of the projective line defined over a number field k, there exist infinitely many k-rational points on the projective line such that the fiber of f over P is irreducible over k. In this paper, we consider similar statements about algebraic points of higher degree on curves of any genus. We prove that Hilbert's irreducibility theorem admits a natural generalization to rational points on an elliptic curve and thus, via a theorem of Abramovich and Harris, to points of degree 3 or less on any curve. We also present examples that show that this generalization does not hold for points of degree 4 or more. These examples come from an earlier geometric construction of Debarre and Fahlaoui; some additional necessary facts about this construction can be found in the appendix provided by Debarre. We exhibit a connection between these irreducibility questions and the sharpness of Vojta's inequality for algebraic points on curves. In particular, we show that Vojta's inequality is not sharp for the algebraic points arising in our examples.

Let OK be any domain with field of fractions K . Let F(x, y) ∈ OK [x, y] be a homogeneous polynomial of degree n, coprime to y, and assumed to have unit content (i.e., the coefficients of F generate the unit ideal in OK ). Assume that gcd(n, char(K )) = 1. Let h ∈ OK and assume that the polynomial hzn − F(x, y) is irreducible in K[x, y, z]. We denote by X F,h/K the nonsingular complete model of the projective plane curve CF,h/K defined by the equation hzn − F(x, y) = 0. We shall assume in this article that g(X F,h) ≥ 2. When K is a number field, Mordell’s Conjecture (now Faltings’ Theorem) implies that |X F,h(K )| < ∞. Caporaso, Harris, and Mazur ([CHM, 1.1]) have shown that if Lang’s conjecture for varieties of general type is true, then for any number field K , the size |X(K )| of the set of K -rational points of any curve X/K of genus g(X) ≥ 2 can be bounded by a constant depending only on g(X). Prior to the paper [CHM], Mazur and others had asked whether |X(K )| can be bounded by a constant depending only on g(X) and the Mordell-Weil rank of X/K over K (that is, the rank of the group J(K ) of K -rational points of the jacobian J/K of X/K ). These farreaching questions are totally open. As we shall recall in Sect. 1, the method of Chabauty-Coleman sometimes yields a bound for |X F,h(K )| depending only on g(X F,h) when it is known in advance that the Mordell-Weil rank of X F,h/K is small. Unfortunately, the Chabauty-Coleman method does not yield a bound for |X F,h(K )| independent of the coefficients of hzn − F(x, y) for all curves of the form X F,h . It does, however, produce such a nice bound for the number of primitive integral solutions of F(x, y) = h, as we now explain. Let K = Q and OK = Z. A classical Thue equation is an equation F(x, y) = h where F(x, 1) does not have repeated roots. Thue showed in 1909 that such an equation has finitely many solutions (x, y) ∈ Z2 if n ≥ 3.

This paper deals with upper bounds on arithmetic discriminants of algebraic points on curves over number fields. It is shown, via a result of Zhang, that the arithmetic discriminants of algebraic points that are not pullbacks of rational points on the projective line are smaller than the arithmetic discriminants of families of linearly equivalent algebraic points. It is also shown that bounds on the arithmetic discriminant yield information about how the fields of definition k(P) and k(f(P)) differ when P is an algebraic point on a curve C and f : C --C' is a nonconstant morphism of curves. In particular, it is demonstrated that k(P) 74 k(f(P)), with at most finitely many exceptions, whenever the degrees of P and f are sufficiently small, relative to the difference between the genera g(C) and g(C'). The paper concludes with a detailed analysis of the arithmetic discriminants of quadratic points on bi-elliptic curves of genus 2. Let C be a curve defined over a number field k, and let X be a regular model for C over the ring of integers R of k. In [V 3], Vojta proves that, for any c > 0, all points P E C(k) of bounded degree satisfy the inequality (0.0.1) hK(P) < da(P) + EhA(P) + 0(1), where A is any ample divisor on C, hA and hK are Weil heights associated with A and the canonical divisor K, respectively, and da(P) is the arithmetic discriminant of P. The arithmetic discriminant depends on the choice of a regular model X; it is defined as (Hp.(Wx/B+HP)) [k(P) : k] where Hp is the arithmetic curve on X corresponding to P and Wx/B is the sheaf of relative differentials of X over B = Spec R. The difference between arithmetic discriminants derived from different regular models is always bounded. Hence, (0.0.1) is not affected by one's choice of a regular model. The arithmetic discriminant is related to d(P), the normalized field discriminant of the field of definition of P, which is defined as d(P) '_ log IN|Dk(p)/k [k(P): ] One may obtain da(P) by adding to d(P) terms corresponding to singularities of Hp at finite places and v-adic distances between the conjugates of P at infinite places v (see [V 2, Section 3]). The precise nature of the relationship between Received by the editors November 30, 1999 and, in revised form, February 25, 2000. 2000 Mathematics Subject Classification. Primary 11G30, 11J25. ()2001 American Mathematical Society

Summary A method of data analysis is described in which the determination of exact probabilities associated with randomized mean differences between two independent samples may be programmed on a small computer. Application of the enumerative and probabilistic features of this method to specific randomization test analyses performed by other investigators revealed the presence of errors in several previously published reports.

Under suitable hypotheses, we prove a dynamical version of the Mordell–Lang conjecture for subvarieties of quasiprojective varieties X, endowed with the action of a morphism Φ:X→X. We also prove a version of the Mordell–Lang conjecture that holds for any endomorphism of a semiabelian variety. We use an analytic method based on the technique of Skolem, Mahler, and Lech, along with results of Herman and Yoccoz from nonarchimedean dynamics.

Some auditory discriminations cannot be acquired by the cat after large bilateral ablations of auditory cortex at maturity. However, if such ablations are sustained during infancy, these discriminations are readily learned. The function of the cortex in auditory discrimination depends on the age of the nervous system at the time of injury.