Gonc̆arov polynomials and parking functions

AbstractLet u be a sequence of non-decreasing positive integers. A u-parking function of length n is a sequence (x1,x2,…,xn) whose order statistics (the sequence (x(1),x(2),…,x(n)) obtained by rearranging the original sequence in non-decreasing order) satisfy x(i)⩽ui. The Gonc̆arov polynomials gn(x;a0,a1,…,an−1) are polynomials defined by the biorthogonality relation:ε(ai)Dign(x;a0,a1,…,an−1)=n!δin,where ε(a) is evaluation at a and D is the differentiation operator. In this paper we show that Gonc̆arov polynomials form a natural basis of polynomials for working with u-parking functions. For example, the number of u-parking functions of length n is (−1)ngn(0;u1,u2,…,un). Various properties of Gonc̆arov polynomials are discussed. In particular, Gonc̆arov polynomials satisfy a linear recursion obtained by expanding xn as a linear combination of Gonc̆arov polynomials, which leads to a decomposition of an arbitrary sequence of positive integers into two subsequences: a “maximum” u-parking function and a subsequence consisting of terms of higher values. Many counting results for parking functions can be derived from this decomposition. We give, as examples, formulas for sum enumerators, and a linear recursion and Appell relation for factorial moments of sums of u-parking functions

Structural features and domain movements controlling substrate binding and cofactor specificity in class II HMG-CoA reductase

The key mevalonate pathway enzyme 3-hydroxy-3-methylglutaryl coenzyme A (HMG-CoA) reductase (HMGR) uses the cofactor NAD(P)H to reduce HMG-CoA to mevalonate in the production of countless metabolites and natural products. Although inhibition of HMGR by statin drugs is well-understood, several mechanistic details of HMGR catalysis remain unresolved, and the structural basis for the wide range of cofactor specificity for either NADH or NADPH among HMGRs from different organisms is also unknown. Here, we present crystal structures of HMGR from Streptococcus pneumoniae (SpHMGR) alongside kinetic data of the enzyme’s cofactor preferences. Our structure of SpHMGR bound with its kinetically preferred NADPH cofactor suggests how NADPH-specific binding and recognition are achieved. In addition, our structure of HMG-CoA-bound SpHMGR reveals large, previously unknown conformational domain movements that may control HMGR substrate binding and enable cofactor exchange without intermediate release during the catalytic cycle. Taken together, this work provides critical new insights into both the HMGR reaction mechanism and the structural basis of cofactor specificity

Structural features and domain movements controlling substrate binding and cofactor specificity in class II HMG-CoA reductase

The key mevalonate pathway enzyme 3-hydroxy-3-methylglutaryl coenzyme A (HMG-CoA) reductase (HMGR) uses the cofactor NAD(P)H to reduce HMG-CoA to mevalonate in the production of countless metabolites and natural products. Although inhibition of HMGR by statin drugs is well-understood, several mechanistic details of HMGR catalysis remain unresolved, and the structural basis for the wide range of cofactor specificity for either NADH or NADPH among HMGRs from different organisms is also unknown. Here, we present crystal structures of HMGR from Streptococcus pneumoniae (SpHMGR) alongside kinetic data of the enzyme’s cofactor preferences. Our structure of SpHMGR bound with its kinetically preferred NADPH cofactor suggests how NADPH-specific binding and recognition are achieved. In addition, our structure of HMG-CoA-bound SpHMGR reveals large, previously unknown conformational domain movements that may control HMGR substrate binding and enable cofactor exchange without intermediate release during the catalytic cycle. Taken together, this work provides critical new insights into both the HMGR reaction mechanism and the structural basis of cofactor specificity

Propositional complexity in normal Cantonese-speakers

"A dissertation submitted in partial fulfilment of the requirements for the Bachelor of Science (Speech and Hearing Sciences), The University of Hong Kong, April 29, 1996."Also available in print.Thesis (B.Sc)--University of Hong Kong, 1996published_or_final_versionSpeech and Hearing SciencesBachelorBachelor of Science in Speech and Hearing Science

Structural studies of metalloenzyme complexes in acetogenic carbon fixation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Chemistry, 2011.Vita. Cataloged from PDF version of thesis.Includes bibliographical references.Acetogenic bacteria use the Wood-Ljungdahl carbon fixation pathway to produce cellular carbon from CO₂. This process requires several metalloenzymes that employ transition metals such as iron, nickel, and cobalt towards the production of acetyl-CoA, the final product. In one stage of the pathway, the cobalt-containing B₁₂ cofactor harbored by the corrinoid iron-sulfur protein (CFeSP) transfers a methyl group from methyltetrahydrofolate (CH₃-H₄folate), which is bound by a methyltransferase enzyme (MeTr), to a nickel-containing metallocluster called the A-cluster of the downstream enzyme, acetyl-CoA synthase (ACS). Such B12-dependent methyl transfer reactions require the construction of large, multimodular enzyme complexes whose threedimensional assemblies are, at present, largely uncharacterized. X-ray crystallography was used to solve the structure of a CFeSP/MeTr complex, the first crystal structure of a B12-dependent methyltransferase to depict all protein domains required for B12 binding, activation, protection, and catalysis. This structure, along with in crystallo activity data, illustrates how conformational movements, which can occur within protein crystals, enable the B12 cofactor to alternate between a sequestered conformation for cofactor protection and an active conformation for catalysis. Small-angle X-ray scattering (SAXS) experiments were also conducted to explore the quaternary composition of the complex in solution and revealed that multiple CFeSP/MeTr complexes can be formed. In another reaction of the Wood-Ljungdahl carbon fixation pathway, a nickel and iron containing metallocluster called the C-cluster of carbon monoxide dehydrogenase (CODH) reduces a second molecule of CO₂ to CO, an intermediate that is channeled to the ACS A-cluster. Although the structure of the C-cluster was first described a decade ago, its catalytic mechanism remained unresolved. To provide mechanistic insight into the chemistry employed at the C-cluster, crystal structures were determined with substrate and inhibitor molecules bound to the C-cluster of the CODH/ACS complex. These structures capture states of the C-cluster at key steps in the reaction and contribute to a consensus model for C-cluster chemistry. With structural descriptions for both CFeSP/MeTr and CODH/ACS complexes, this work has illuminated the molecular details for metalloenzyme complex assembly and catalysis in the acetogenic Wood-Ljungdahl carbon fixation pathway.by Yan Kung.Ph.D

Christian discipleship today: A study of the ethics of the Kingdom in the theologies of Stanley Hauerwas and Jon Sobrino

The purpose of this thesis is twofold. First, it seeks to contend and illustrate the hermeneutical role of discipleship in theological reflection. Secondly, it seeks to examine and analyze the meaning of discipleship in terms of the ethical, missiological and theological dimensions. These are carried out through the study of the ethics of the Kingdom in the theologies of Stanley Hauerwas and Jon Sobrino. Chapter one of this thesis is concerned about the agent of the Kingdom in terms of spirituality and ecclesiology. For Hauerwas, Christian spirituality is primarily about the imitation of Christ in terms of character, vision and virtue, with particular emphasis on the Sermon on the Mount, while for Sobrino, Christian spirituality is principally about following the historical Jesus in terms of liberation, with particular reference to the jubilee proclamation. This basic difference in orientation unavoidably results in their different understanding of the church. Chapter two of this thesis discusses the theological use of model. In short, model refers to the means helping us to understand a subject, but it is not the subject itself. Although both Hauerwas and Sobrino do not particularly refer to the notion of model, Hauerwas' use of narrative and Sobrino's use of justice are examples of the use of the notion of model. Chapter three of this thesis examines the practice of the Kingdom. It asserts the primacy of praxis in theological reflection, provided that praxis is not understood as equivalent to pragmatism. Hauerwas' pacifism reveals his understanding of praxis in the context of the cultural-linguistic tradition. That is to say, Christian pacifism is solely built on its Christological foundation and primarily addressed to the Christian community. Its strength is not to reduce the religious identity of a community to the general religious dimension of common human experience, but its weakness tends not to emphasize the need to explicate the public dimension of its religious identity. Sobrino's evangelization illustrates his understanding of praxis in the context of the Marxist tradition. In this tradition, evangelization is primarily understood as the transformation of the sinful world. Its strength gives practice a very strong societal orientation, and provides a hermeneutical privilege, criterion and standpoint, by which one can test the interpretation of the Christian tradition. Its weakness is overshadowed by its socio-political relevance. Nevertheless, Hauerwas' and Sobrino's accounts help us to realize that the distinctiveness of the Christian identity and its social relevance are inter-related. Ignoring either of them distorts the Christian convictions. The final chapter of this thesis attempts to summarize and reflect the result of the preceding studies about discipleship in terms of the ethical, missiological and theological dimensions. The ethical dimension of discipleship is concerned about a messianic lifestyle. It is a life of conversion, worshipping, following Jesus, being an alternative community and leading a life which brings transvaluation. The missiological dimension of discipleship relates to the promises of Jesus to be present in the apostolate, the sacrament and fellowship of Christians, in the "least of the bretliren", and in his parousia. Finally, the theological dimension of discipleship emphasizes that theology is primarily a practical theology in terms of the centrality of praxis and a theology of, for, and by, the people. (Abstract shortened by ProQuest.)