Studies on genetic and epigenetic regulation of gene expression dynamics

The information required to build an organism is contained in its genome and the first biochemical process that activates the genetic information stored in DNA is transcription. Cell type specific gene expression shapes cellular functional diversity and dysregulation of transcription is a central tenet of human disease. Therefore, understanding transcriptional regulation is central to understanding biology in health and disease. Transcription is a dynamic process, occurring in discrete bursts of activity that can be characterized by two kinetic parameters; burst frequency describing how often genes burst and burst size describing how many transcripts are generated in each burst. Genes are under strict regulatory control by distinct sequences in the genome as well as epigenetic modifications. To properly study how genetic and epigenetic factors affect transcription, it needs to be treated as the dynamic cellular process it is. In this thesis, I present the development of methods that allow identification of newly induced gene expression over short timescales, as well as inference of kinetic parameters describing how frequently genes burst and how many transcripts each burst give rise to. The work is presented through four papers: In paper I, I describe the development of a novel method for profiling newly transcribed RNA molecules. We use this method to show that therapeutic compounds affecting different epigenetic enzymes elicit distinct, compound specific responses mediated by different sets of transcription factors already after one hour of treatment that can only be detected when measuring newly transcribed RNA. The goal of paper II is to determine how genetic variation shapes transcriptional bursting. To this end, we infer transcriptome-wide burst kinetics parameters from genetically distinct donors and find variation that selectively affects burst sizes and frequencies. Paper III describes a method for inferring transcriptional kinetics transcriptome-wide using single-cell RNA-sequencing. We use this method to describe how the regulation of transcriptional bursting is encoded in the genome. Our findings show that gene specific burst sizes are dependent on core promoter architecture and that enhancers affect burst frequencies. Furthermore, cell type specific differential gene expression is regulated by cell type specific burst frequencies. Lastly, Paper IV shows how transcription shapes cell types. We collect data on cellular morphologies, electrophysiological characteristics, and measure gene expression in the same neurons collected from the mouse motor cortex. Our findings show that cells belonging to the same, distinct transcriptomic families have distinct and non-overlapping morpho-electric characteristics. Within families, there is continuous and correlated variation in all modalities, challenging the notion of cell types as discrete entities

Relations between diagonalization, proof systems, and complexity gaps

AbstractIn this paper we study diagonal processes over time bounded computations of one-tape Turing machines by diagonalizing only over those machines for which there exist formal proofs that they operate in the given time bound. This replaces the traditional “clock” in resource bounded diagonalization by formal proofs about running times and establishes close relations between properties of proof systems and existence of sharp time bounds for one-tape Turing machine complexity classes. These diagonalization methods also show that the Gap Theorem for resource bounded computations can hold only for those complexity classes which differ from the corresponding provable complexity classes. Furthermore, we show that there exist recursive time bounds T(n) such that the class of languages for which we can formally prove the existence of Turing machines which accept them in time T(n) differs from the class of languages accepted by Turing machines for which we can prove formally that they run in time T(n). We also investigate the corresponding problems for tape bound computations and discuss the difference time and tapebounded computations

Credimus

We believe that economic design and computational complexity---while already important to each other---should become even more important to each other with each passing year. But for that to happen, experts in on the one hand such areas as social choice, economics, and political science and on the other hand computational complexity will have to better understand each other's worldviews. This article, written by two complexity theorists who also work in computational social choice theory, focuses on one direction of that process by presenting a brief overview of how most computational complexity theorists view the world. Although our immediate motivation is to make the lens through which complexity theorists see the world be better understood by those in the social sciences, we also feel that even within computer science it is very important for nontheoreticians to understand how theoreticians think, just as it is equally important within computer science for theoreticians to understand how nontheoreticians think

On the Structure of Solutions of Computable Real Functions

The relationship between the structure of a domain and the complexity of computing over that domain is a fundamental question of computer science. This paper studies how the structure of the real numbers constrains the behavior of computable real functions. In particular, we uncover a close correlation between the structure of the zero set of a computable real function, and the complexity of the zeros. We show that computable real functions with hard solutions perforce have many solutions. Furthermore, as the complexity of solutions increases, the number of solutions increases. We prove that computable real functions with nonrecursive, nonarithmetical, or random zeros have solution sets that are, respectively, infinite,“˜ uncountable, or of positive measure. In addition, we show that the computational complexity of the zero set of a computable real function is limited by its topological complexity. These results suggest an emerging paradigm-the inability of machines to name complex strings can serve as the basis of powerful proof techniques in computational complexity theory

Completeness Results for Parameterized Space Classes

The parameterized complexity of a problem is considered "settled" once it has been shown to lie in FPT or to be complete for a class in the W-hierarchy or a similar parameterized hierarchy. Several natural parameterized problems have, however, resisted such a classification. At least in some cases, the reason is that upper and lower bounds for their parameterized space complexity have recently been obtained that rule out completeness results for parameterized time classes. In this paper, we make progress in this direction by proving that the associative generability problem and the longest common subsequence problem are complete for parameterized space classes. These classes are defined in terms of different forms of bounded nondeterminism and in terms of simultaneous time--space bounds. As a technical tool we introduce a "union operation" that translates between problems complete for classical complexity classes and for W-classes.Comment: IPEC 201

Unification and Logarithmic Space

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof theory and more specifically linear logic and Geometry of Interaction. We show how unification can be used to build a model of computation by means of specific subalgebras associated to finite permutations groups. We then prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space. We also show that the construction can naturally represent pointer machines, an intuitive way of understanding logarithmic space computing

Computing with and without arbitrary large numbers

In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some problems. However, this has only been shown so far for specific problems. We provide a characterization of the power of such extra inputs for general problems. To do so, we first correct a classical result by Simon and Szegedy (1992) as well as one by Simon (1981). In the former we show mistakes in the proof and correct these by an entirely new construction, with no great change to the results. In the latter, the original proof direction stands with only minor modifications, but the new results are far stronger than those of Simon (1981). In both cases, the new constructions provide the theoretical tools required to characterize the power of arbitrary large numbers.Comment: 12 pages (main text) + 30 pages (appendices), 1 figure. Extended abstract. The full paper was presented at TAMC 2013. (Reference given is for the paper version, as it appears in the proceedings.

On Measuring Non-Recursive Trade-Offs

We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general. We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences in the decidability status of basic decision problems on the other. We develop a qualitative classification of non-recursive trade-offs in order to obtain a better understanding of this very fundamental behaviour of descriptional systems