Computational methodology for enhanced sensitivity analysis of gene regulatory networks

Biološko računalništvo je zasnovano na procesnih platformah, ki izhajajo iz bioloških preklopnih struktur z zmožnostjo procesiranja informacij. Te strukture večinoma temeljijo na gensko regulatornih omrežjih (GRO). Njihova dinamika spominja na delovanje računalniških preklopnih gradnikov. Uporaba bioloških preklopnih struktur je trenutno še v povojih, saj je njihova učinkovitost neprimerno manjša od silicijevih ekvivalentov. Kljub temu njihove aplikacije že posegajo v farmakaloška, medicinska in industrijska področja. Natančno načrtovanje na podlagi matematičnega in računalniškega modeliranja je ključnega pomena za razvoj in implementacijo tovrstnih aplikacij. GRO lahko opišemo s sistemom kemijskih reakcij. Njihovo dinamiko definiramo na molekularnem nivoju z množico kemijskih zvrsti in njihovih medsebojnih interakcij. Za generiranje časovne evolucije vsake kemijske zvrsti lahko uporabljamo stohastični simulacijski algoritem (SSA). V njem posamično reakcijo simuliramo na osnovi Monte Carlo eksperimenta. Glavna slabost te metode je računska kompleksnost, ki se poveča linearno s številom reakcij, ki jih je potrebno upoštevati v simulaciji. V primeru prevelikega števila reakcij postane stohastični simulacijski algoritem neobvladljiv. Tovrstne primere najdemo pri nekaterih GRO, ki vsebujejo več neekoperativnih DNA vezavnih mest transkripcijskih faktorjev in ki so pogosta pri sodobnih bioloških procesnih strukturah. Dodaten problem se pojavi, ko želimo vse reakcije sistema simulirati v enem samem časovnem okvirju. V GRO se nekatere reakcije izvedejo tudi za več redov velikosti hitreje od drugih. Pri GRO, ki vsebujejo več nekooperativnih DNA vezavnih mest transkripcijskih faktorjev, se pojavi ravno taka okoliščina. Vezava transkripcijskih faktorjev poteka mnogo hitreje kot reakcije genske ekspresije, zato je pogosto potrebno to razliko ustrezno obravnavati. Poleg tega je število vseh reakcij vezave in disociacije eksponentno odvisno od števila vezavnih mest. V disertaciji smo razvili dinamični večnivojski stohastični simulacijski algoritem (DMSSA), ki občutno zmanjša časovno kompleksnost stohastičnega simulacijskega algoritma pri tovrstnih GRO. DMSSA je zmožen reakcije vezave izvajati neodvisno od reakcij, ki zadevajo gensko ekspresijo. Izvedba reakcij vezave poteka znotraj vgnezdenega SSA. Prednost takega pristopa je v ločenju množice reakcij sistema na dve neodvisni podmnožici, in sicer na množico hitrih in množico počasnih reakcij. Počasne reakcije potekajo v časovni skali, ki sovpada z redom velikosti hitrosti reakcij v genski ekspresiji, kot sta reakciji transkripcije in translacije. Te reakcije DMSSA izvede manj pogosto. Hitre reakcije, kot sta reakciji vezave in disociacije tranksripcijskih faktorjev na/iz DNA vezavna mesta, se po drugi strani izvajajo bolj pogosto. V pričujoči disertaciji pokažemo, da se natančnost DMSSA ujema s SSA. Uporabo DMSSA pokažemo na dveh modelih s področja sistemske in sintezne biologije. V disertaciji se dodatno osredotočimo na pomen ocenitve občutljivosti večnivojskih stohastičnih modelov GRO, ki vsebujejo več nekooperativnih DNA vezavnih mest. Z analizo občutljivosti lahko sortiramo vhodne parametre na osnovi največjega vpliva na izhode modela. Analiza občutljivosti stohastičnih modelov predstavlja računski izziv zaradi računske kompleksnosti algoritmov, ki se uporabljajo za pridobitev odzivov samih modelov. V disertaciji predlagamo uporabo spremenjene Morrisove metode na osnovi alternativnih elementarnih učinkov, s katerimi lahko ocenimo občutljivost parametrov modela neodvisno od njegove večnivojske razsežnosti. Za pohitritev simulacij stohastičnih modelov smo v sklopu disertacije razvili orodje ParMSSA, ki vsebuje simulator za paralelno izvajanje stohastičnih simulacij z algoritmom DMSSA. Orodje ParMSSA je zmožno paralelno izvajati več instanc DMSSA algoritma z različnimi vhodnimi parametri za potrebe analize občutljivosti s spremenjeno Morrisovo metodo. Rezultate pridobljene na podlagi občutljivostne analize z orodjem ParMSSA je možno neposredno uporabljati za ocenjevanje robustnosti stohastičnih večnivojskih modelov GRO, ki vsebujejo večkratna nekooperativna DNA vezavna mesta trankripcijskih faktorjev. Uporabo razvitih algoritmov skupaj z orodjem smo demonstrirali na dveh vzorčnih primerih, tj. na analizi mehanizma preklopa v virusu Epstein-Barr in na analizi sintetičnega represilatorja z več vezavnimi mesti za transkripcijske faktorje. Na slednjem smo pokazali, da povečevanje števila vezavnih mest za transkripcijske faktorje povečuje robustnost sistema in s tem oscilatornega delovanja.Biological computing is held towards a new era of processing platforms based on the bio-logical computer structures that are at the heart of biological systems with information processing capabilities. These bio-logical computer structures are mostly based on gene regulatory networks, mainly because their dynamics reminds the computer logic structures functioning. The use of these bio-structures is still in its early days since they are for the time being far less effective than their silicon counterparts. However, their use can be already exploited for a wide range of applications, covering pharmacological, medical and industrial. In order to develop such applications, a precise design that is based on computational modelling is vital in the process of their implementation. Gene regulatory networks can be described as a chemical reacting systems. The dynamics of such systems is defined at the molecular level with a set of interacting reactions. The stochastic simulation algorithm can be used to generate the time evolution trajectories of each chemical species by firing each reaction according to a Monte-Carlo experiment. The main shortcoming of this approach is its computational complexity, which increases linearly with the total number of reactions that have to be simulated. When the number of reactions becomes too high, the stochastic simulation algorithm turns out to be impracticable. This is the case of certain gene regulatory networks, which can be either found in nature or can be artificially constructed. An additional problem lies in the fact that reactions in such networks can often occur at different time scales, which can differ by many orders of magnitude. Such scenario occurs when gene regulatory networks contain multiple cis-regulatory binding sites, on which different transcription factors are able to bind non-cooperatively. The transcription factors binding occurs much faster than the average reactions in the gene expression, therefore, this time-scale gap needs to be accounted into the simulation. Moreover, the transcription control can be affected by specific dispositions of the bound transcription factors, which is only possible to simulate, if all the reactions that can produce the same dispositions are defined. The number of such reactions increases exponentially with the number of binding sites. In order to decrease the time complexity of the stochastic simulation algorithm for such gene regulatory networks, an alternative algorithm called the dynamic multi-scale stochastic algorithm (DMSSA) is proposed, in which the reactions involved in the transcription regulation can be simulated independently, by performing the stochastic simulation algorithm in a nested fashion. This is conditioned by the property of the set of reactions, describing the gene regulatory network, being divided into two subsets, i.e. a set of "fast" reactions, which occur frequently in a short time scale, and a set of "slow" reactions, which occur less frequently in longer time scales. This thesis demonstrates the equivalence between this approach and the standard stochastic simulation algorithm and shows its capabilities on two gene regulatory models, that are commonly used as examples in systems and synthetic biology. The thesis focuses on how to identify the most important input parameters of multi-scale models, that affect the system the most. This is a common practice during the design of bio-logical structures and can be achieved with the sensitivity analysis. It may be difficult to carry out such analysis for complex reaction networks exhibiting different time scales. In order to cope with this issue, an alternative computation of the elementary effects in the Morris screening method is proposed, which is able to sort all the model parameters, independently on their structural or time scale definitions, in order of importance, i.e. which parameter carries the largest influence on the response of the model. To ease the use of the simulation algorithm and to perform the sensitivity analysis, the thesis presents ParMSSA, an OpenCL based engine for performing parallel stochastic simulations on multi-core architectures. ParMSSA aims to accelerate the simulations, performed with our approach. ParMSSA is capable to run concurrently multiple instances of DMSSA, which are usually needed for reducing the noisy results of stochastic simulations. ParMSSA provides also a framework for performing the Morris screening experiment on reaction networks, which allows users to carry out the sensitivity analysis of observed systems. The simulation results provided by the ParMSSA can be easily interpreted and can be used to assess the robustness of the bio-logical computer structures. The proposed algorithms and the proposed simulation engine were applied on two case studies, i.e. on the Epstein-Barr virus genetic switch and on the synthetic repressilator with multiple transcription factor binding sites. The results of the sensitivity analysis of the repressilator revealed that larger numbers of binding sites increase the robustness of the system and thus the robustness of the oscillatory behaviour