Prediction of stability changes upon mutation in an icosahedral capsid

Identifying the contributions to thermodynamic stability of capsids is of fundamental and practical importance. Here we use simulation to assess how mutations affect the stability of lumazine synthase from the hyperthermophile Aquifex aeolicus, a T = 1 icosahedral capsid; in the simulations the icosahedral symmetry of the capsid is preserved by simulating a single pentamer and imposing crystal symmetry, in effect simulating an infinite cubic lattice of icosahedral capsids. The stability is assessed by estimating the free energy of association using an empirical method previously proposed to identify biological units in crystal structures. We investigate the effect on capsid formation of seven mutations, for which it has been experimentally assessed whether they disrupt capsid formation or not. With one exception, our approach predicts the effect of the mutations on the capsid stability. The method allows the identification of interaction networks, which drive capsid assembly, and highlights the plasticity of the interfaces between subunits in the capsid

All-Atom Multiscale Computational Modeling Of Viral Dynamics

Thesis (Ph.D.) - Indiana University, Chemistry, 2009Viruses are composed of millions of atoms functioning on supra-nanometer length scales over timescales of milliseconds or greater. In contrast, individual atoms interact on scales of angstroms and femtoseconds. Thus they display dual microscopic/macroscopic characteristics involving processes that span across widely-separated time and length scales. To address this challenge, we introduced automatically generated collective modes and order parameters to capture viral large-scale low-frequency coherent motions. With an all-atom multiscale analysis (AMA) of the Liouville equation, a stochastic (Fokker-Planck or Smoluchowski) equation and equivalent Langevin equations are derived for the order parameters. They are shown to evolve on timescales much larger than the 10^(-14)-second timescale of fast atomistic vibrations and collisions. This justifies a novel multiscale Molecular Dynamics/Order Parameter eXtrapolation (MD/OPX) approach, which propagates viral atomistic and nanoscale dynamics simultaneously by solving the Langevin equations of order parameters implicitly without the need to construct thermal-average forces and friction/diffusion coefficients. In MD/OPX, a set of short replica MD runs with random atomic velocity initializations estimate the ensemble average rate of change in order parameters, extrapolation of which is then used to project the system over long time. The approach was implemented by using NAMD as the MD platform. Application of MD/OPX to cowpea chlorotic mottle virus (CCMV) capsid revealed that its swollen state undergoes significant energy-driven shrinkage in vacuum during 200ns simulation, while for the native state as solvated in a host medium at pH 7.0 and ionic strength I=0.2M, the N-terminal arms of capsid proteins are shown to be highly dynamic and their fast fluctuations trigger global expansion of the capsid. Viral structural transitions associated with both processes are symmetry-breaking involving local initiation and front propagation. MD/OPX accelerates MD for long-time simulation of viruses, as well as other large bionanosystems. By using universal inter-atomic force fields, it is generally applicable to all dynamical nanostructures and avoids the need of parameter recalibration with each new application. With our AMA method and MD/OPX, viral dynamics are predicted from laws of molecular physics via rigorous statistical mechanics

An integrated bioinformatics and computational biophysics approach to enterovirus surveillance and research

This PhD thesis examines the integration of complex computational methodologies with the surveillance and research of a genus of viruses implicated in a wide variety of clinical conditions, ranging from asymptomatic infection to death. These viruses, known as the enteroviruses, are some of the most studied viruses in history and as a result are represented by a vast body of literature. The fact that enterovirus research and surveillance rests upon such an extensive foundation of published material, makes enteroviruses a perfect candidate for the experimental application of modern computational methods, or in-silico experimentation. The hypothesis that computational power currently available can be utilised for multiple stages of virus study incorporating identification, epidemiology and atomic structure prediction forms the basis of this thesis. Fundamental to the understanding of virus behaviour is the determination of molecular structure and function, a fact which applies not only to viruses, but to biological entities in general. Extensive work was performed during the course of this thesis in adapting classical molecular dynamics techniques to the large scale simulation of a prototype poliovirus, using millions of simulated atoms. The successful application of these techniques has resulted in microsecond-timescale, atomistic simulations of complete virus particles. These simulations represent the first published instance of the simulation of a biologically complete pathogenic microorganism, incorporating the encoding genetic information. This thesis also examines the use of bioinformatics methods in the development and application of an advanced quantitative multiplex real-time reverse-transcription polymerase chain reaction (qRT-PCR) methodology, for the primary screening of samples from patients suffering acute flaccid paralysis (AFP), which is one of the most debilitating presentations of enterovirus infection. The application of this novel qRT-PCR method reduces the initial screening time of samples derived from a symptomatic patient from 4-5 days using virus culture, to four hours using the novel qRT-PCR. This novel qRT-PCR method can be rapidly scaled-up in response to an outbreak situation. The ability to screen large numbers of samples during an outbreak situation is important and is hampered when using virus culture methods exclusively. In Australia and the Western Pacific region over the last decade, the rate at which non-polio enteroviruses in cases of AFP have been identified, is on average 18%. With the introduction of PCR screening methods, a number of non-cultivable enteroviruses were identified, along with newly described and a previously undescribed enterovirus. Little is known about these newly described and novel enteroviruses. This thesis aimed to investigate the identification of viruses that may represent a significant public health threat and to then use their genetic sequence information to recreate major virus structural components in-silico. This reconstruction process was achieved by exploiting advances in comparative protein modelling and molecular dynamics simulation methods. In order to apply these methods to the reconstruction of previously undescribed viruses for which no structural data exist, validation of different comparative protein modelling techniques was required. The predictive in-silico methods generated reliable atomic coordinates, representing structures suitable for the reconstruction of virus capsid models for further study

Structural Studies of Non-Enveloped Viruses Associated with Human Diseases

Non-enveloped viruses encompass many human pathogens which are responsible for a broad range of diseases that have very significant impacts on human health. By studying the structures of such viruses, insights can be gained into aspects of their lifecycle, including receptor attachment, genome uncoating and capsid assembly. This information can then serve as a structural platform for the design of targeted antivirals and vaccines. This thesis aimed to use cryo-electron microscopy (cryo-EM) to structurally characterise the structures, and receptor binding, of two important human pathogens, BK polyomavirus (BKV) and Coxsackievirus A24v (CV-A24v). BKV causes polyomavirus-associated nephropathy and haemorrhagic cystitis in immunosuppressed patients. These are diseases for which we currently have limited treatment options. Initially, a modest resolution structure (~7 Å) of BKV is used to investigate the organisation of the viral genome and minor capsid proteins. Subsequently, high-resolution structures of BKV alone (3.8 Å) and in complex with the receptor fragment of GT1b ganglioside (3.4 Å) and heparin (3.6 Å) were determined. Collectively, these structures provide insights into capsid assembly, rationalise how GT1b enhances infection over smaller gangliosides studied previously and provide the first structural clues for glycosaminoglycan binding to BKV. CV-A24v is responsible for large outbreaks of acute haemorrhagic conjunctivitis (AHC), a painful, contagious eye disease. Here, ICAM-1 is identified as an essential receptor for CV-A24v and the high-resolution cryo-EM structure (3.9 Å) of the virus–ICAM-1 complex is presented, which reveals the critical ICAM-1–binding residues within the capsid. These data could help identify a possible conserved mode of receptor engagement among ICAM-1–binding enteroviruses. In addition, structures of the uncoating intermediates of CV-A24v are presented which describe the molecular basis of capsid expansion. Furthermore, the molecular details of a branched pocket factor binding site in CV-A24v are described which is unique amongst currently structurally characterised human enteroviruses

Stochastic Dynamics of Bionanosystems: Multiscale Analysis and Specialized Ensembles

An approach for simulating bionanosystems, such as viruses and ribosomes, is presented. This calibration-free approach is based on an all-atom description for bionanosystems, a universal interatomic force field, and a multiscale perspective. The supramillion-atom nature of these bionanosystems prohibits the use of a direct molecular dynamics approach for phenomena like viral structural transitions or self-assembly that develop over milliseconds or longer. A key element of these multiscale systems is the cross-talk between, and consequent strong coupling of, processes over many scales in space and time. We elucidate the role of interscale cross-talk and overcome bionanosystem simulation difficulties with automated construction of order parameters (OPs) describing supra-nanometer scale structural features, construction of OP dependent ensembles describing the statistical properties of atomistic variables that ultimately contribute to the entropies driving the dynamics of the OPs, and the derivation of a rigorous equation for the stochastic dynamics of the OPs. Since the atomic scale features of the system are treated statistically, several ensembles are constructed that reflect various experimental conditions. The theory provides a basis for a practical, quantitative bionanosystem modeling approach that preserves the cross-talk between the atomic and nanoscale features. A method for integrating information from nanotechnical experimental data in the derivation of equations of stochastic OP dynamics is also introduced.Comment: 24 page

Self-assembling nanoscale systems

Self-assembly is ubiquitous in different areas of science, for example in crystals and viruses, and also plays crucial roles in nanotechnology. Many commonalities link these self-assembling systems, in spite of their complexity and different length and time scales. In this thesis, we take an interdisciplinary perspective to gain new insights into self-assembly, exploring ways of modelling self-assembling systems that are relevant across these different fields. A challenge in nanotechnology is to develop self-assembling systems capable of generating a desired outcome. An example is graphene nanoribbons, which are a novel type of semiconductor material with great potential in the nanotech industry. In this context, it is unclear which strategies are best for controlling the output of a self-assembly process, either by manipulation of the thermodynamic environment of the assembling system, or other methods of directing self-assembly. We use quantitative modelling of the kinetics of self-assembly as a tool to predict experimental results in self-assembling systems that are too complex for detailed experimental investigation. Self-assembly of viral protein shells is an example from biology. Viruses have evolved niche methods of assembly that are both robust and highly efficient, as the virus mutation rates are very high, especially in RNA viruses. The viruses discussed in this thesis have an added layer of complexity; it is thought that sequence-specific interactions between viral genomes and the protein building blocks of the viral capsids have a strong impact on the assembly process. We have developed here novel analysis techniques for the modelling of this co-assembly scenario. We use these mechanistic insights to develop new theoretical tools to analyse structural data, providing unprecedented insights into the asymmetric organization of the packaged genome

Computer-aided approaches in drug design: the exigent way forward: dynamic perspectives into the mechanistic activities of small molecule inhibitors toward antiviral, antitubercular and anticancer therapeutic interventions.

Doctoral Degree. University of KwaZulu-Natal, Durban.The crucial role of CADD in the drug design process is now indisputable and has proven over the years that it can accelerate the discovery potential drug candidates while reducing the associated cost. Using knowledge and information about biological target or knowledge about a ligand with proven bioactivity, CADD, and its techniques can influence various drug discovery pipeline stages. The ability CADD approaches to elucidate drug-target interactions at the atomistic level allows for investigations of the mechanism of drugs' actions, revealing atomistic insights that influence drug design and improvement. CADD approaches also seek to augment traditional in vitro and in vivo experimental techniques and not replace them since CADD approaches can also allow modeling complex biological processes that hitherto seemed impossible to explore using experimental methods. According to the World Health Organization (WHO), featuring prominently in the top ten causes of death are cancer, lower respiratory tract infection, tuberculosis (TB), and viral infections such as HIV/AIDS. Collectively, these diseases are of global health concerns, considering a large number of associated deaths yearly. Over the years, several therapeutic interventions have been employed to treat, manage, or cure these diseases, including chemotherapy, surgery, and radiotherapy. Of these options, small molecule inhibitors have constituted an integral component in chemotherapy, thereby undoubtedly playing an essential role in patient management. Although significant success has been achieved using existing therapeutic approaches, the emergence of drug resistance and the challenges of associated adverse side effects has prompted the need for the drug design processes against these diseases to remain innovative, including combining existing drugs and establishing improved therapeutic options that could overcome resistance while maintaining minimal side effects to patients. Therefore, an exploration of drug target interactions towards unraveling mechanisms of actions as performed in the reports in this thesis are relevant since the molecular mechanism provided could form the basis for the design and identification of new therapeutic agents, improvement of the therapeutic activity of existing drugs, and also aid in the development of novel therapeutic strategies against these diseases of global health concern. Therefore the studies in this thesis employed CADD approaches to investigates molecular mechanisms of actions of novel therapeutic strategies directed towards some crucial therapeutics implicated in viral infections, tuberculosis, and cancer. Therapeutic targets studied included; SARS-CoV-2 RNA dependent RNA polymerase (SARS-CoV-2 RdRp), Human Rhinovirus B14 (HRV-B14) and human N-myristoyltransferases in viral infections, Dihydrofolate reductase (DHFR) and Flavin-dependent thymidylate synthase (FDTS) in TB, human variants of TCRCD1d, and Protein Tyrosine Phosphatase Receptor Zeta (PTPRZ) in cancer. The studies in this thesis is divided into three domains and begins with a thorough review of the concept of druggability and drug-likeness since the crux of the subsequent reports revolved around therapeutic targets and their inhibitions by small molecule inhibitors. This review highlights the principles of druggability and drug-likeness while detailing the recent advancements in drug discovery. The review concludes by presenting the different computational, highlighting their reliability for predictive analysis. In the first domain of the research, we sought to unravel the inhibitory mechanism of some small molecule inhibitors against some therapeutic targets in viral infections by explicitly focusing on the therapeutic targets; SARS-CoV-2 RdRp, HRV-B14, and N-myristoyltransferase. Therapeutic targeting of SARS-CoV-2 RdRp has been extensively explored as a viable approach in the treatment of COVID-19. By examining the binding mechanism of Remdesivir, which hitherto was unclear, this study sought to unravel the structural and conformational implications on SARS-CoV-2 RdRp and subsequently identify crucial pharmacophoric moieties of Remdesivir required for its inhibitory potency. Computational analysis showed that the modulatory activity of Remdesivir is characterized by an extensive array of high-affinity and consistent molecular interactions with specific active site residues that anchor Remdemsivir within the binding pocket for efficient binding. Results also showed that Remdesivir binding induces minimal individual amino acid perturbations, subtly interferes with deviations of C-α atoms, and restricts the systematic transition of SARS-CoV-2 RdRp from the “buried” hydrophobic region to the “surface exposed” hydrophilic region. Based on observed high-affinity interactions with SARS-CoV-2 RdRp, a pharmacophore model was generated, which showcased the crucial functional moieties of Remdesivir. The pharmacophore was subsequently employed for virtual screening to identify potential inhibitors of SARS-CoV-2 RdRp. The structural insights and the optimized pharmacophoric model provided would augment the design of improved analogs of Remdesivir that could expand treatment options for COVID-19. The next study sought to explore the therapeutic targeting of human rhinoviruses (HRV) amidst challenges associated with the existence of a wide variety of HRV serotypes. By employing advanced computational techniques, the molecular mechanism of inhibition of a novel benzothiophene derivative that reportedly binds HRV-B14 was investigated. An analysis of the residue-residue interaction profile revealed of HRV upon the benzothiophene derivative binding revealed a distortion of the hitherto compacted and extensively networked HRV structure. This was evidenced by the fewer inter-residue hydrogen bonds, reduced van der Waals interactions, and increased residue flexibility. However, a decrease in the north-south wall's flexibility around the canyon region also suggested that the benzothiophene derivative's binding impedes the “breathing motion” of HRV-B14; hence its inhibition. The next study in the first domain of the research investigated the structural and molecular mechanisms of action associated with the dual inhibitory activity of IMP-1088. This novel compound reportedly inhibits human N-myristoyltransferase subtypes 1 and 2 towards common cold therapy. This is because it has emerged that the pharmacological inhibition of Nmyristoyltransferase is an efficient non-cytotoxic strategy to completely thwart the replication process of rhinovirus toward common cold treatment. Using augmentative computational and nanosecond-based analyses, findings of the study revealed that the steady and consistent interactions of IMP-1088 with specific residues; Tyr296, Phe190, Tyr420, Leu453, Gln496, Val181, Leu474, Glu182, and Asn246, shared within the binding pockets of both HNMT subtypes, in addition to peculiar structural changes account for its dual inhibitory potency. Findings thus unveiled atomistic and structural perspectives that could form the basis for designing novel dualacting inhibitors of N-myristoyltransferase towards common cold therapy. In the second domain of the research, the mechanism of action of some small molecule inhibitors against DHFR, FDTS, and Mtb ATP synthase in treating tuberculosis is extensively investigated and reportedly subsequently. To begin with, the dual therapeutic targeting of crucial enzymes in the folate biosynthetic pathway was explored towards developing novel treatment methods for TB. Therefore, the study investigated the molecular mechanisms and structural dynamics associated with dual inhibitory activity of PAS-M against both DHFR and FDTS, which hitherto was unclear. MD simulations revealed that PAS-M binding towards DHFR and FDTS is characterized by a recurrence of strong conventional hydrogen bond interactions between a peculiar site residue the 2-aminov decahydropteridin-4-ol group of PAS-M. Structural dynamics of the bound complexes of both enzymes revealed that, upon binding, PAS-M is anchored at the entrance of hydrophobic pockets by a strong hydrogen bond interaction while the rest of the structure gains access to deeper hydrophobic residues to engage in favorable interactions. Further analysis of atomistic changes of both enzymes showed increased C-α atom deviations and an increase C-α atoms radius of gyration consistent with structural disorientations. These conformational changes possibly interfered with the enzymes' biological functions and hence their inhibition as experimentally reported. Additionally, in this domain, the therapeutic targeting of the ATP machinery of Mtb by Bedaquiline (BDQ) was explored towards unravelling the structures and atomistic perspectives that account for the ability of BDQ to selectively inhibits mycobacterial F1Fo-ATP synthase via its rotor c-ring. BDQ is shown to form strong interaction with Glu65B and Asp32B and, consequently, block these residues' role in proton binding and ion. BDQ binding was also revealed to impede the rotatory motion of the rotor c-ring by inducing a compact conformation on the ring with its bulky structure. Complementary binding of two molecules of BDQ to the rotor c-ring, proving that increasing the number of BDQ molecule enhances inhibitory potency. The last study in this research domain investigated the impact of triple mutations (L59V, E61D, and I66M) on the binding of BDQ to Mtb F1F0 ATP-synthase. The study showed that the mutations significantly impacted the binding affinity of BDQ, evidenced by a decrease in the estimated binding free energy (ΔG). Likewise, the structural integrity and conformational architecture of F1F0 ATP-synthase was distorted due to the mutation, which could have interfered with the binding of BDQ. The third domain of the research in this thesis investigated some small molecule inhibitors' inhibitory mechanism against some therapeutic targets in cancer, specifically PTPRZ and hTCRvi CD1d. Studies in the third domain of the research in the thesis began with the investigation of the investigation of the inhibitory mechanism of NAZ2329, an allosteric inhibitor of PTPRZ, by specifical investigating its binding effect on the atomic flexibility of the WPD-loop. Having been established as crucial determinant of the catalytic activity of PTPRZ an implicated protein in glioblastoma cells, its successfully therapeutic modulation could present a viable treatment option in glioblastoma. Structural insights from an MD simulation revealed that NAZ2329 binding induces an open conformation of the WPD-loop which subsequently prevents the participation of the catalytic aspartate of PTPRZ from participating in catalysis hence inhibiting the activity of PTPRZ. A pharmacophore was also created based of high energy contributing residues which highlighted essential moieties of NAZ2329 and could be used in screening compound libraries for potential inhibitors of PTPRZ. A second study in this domain sought to explore how structural modification could improve a therapeutic agent's potency from an atomistic perspective. This study was based on an earlier report in which the incorporation of a hydrocinnamoyl ester on C6’’ and C4-OH truncation of the sphingoid base of KRN7000 generated a novel compound AH10-7 high therapeutic potency and selectivity in human TCR-CD1d and subsequently results in the activation of invariant natural killer T cells (iNKT). The hydrocinnamoyl ester moiety was shown to engage in high-affinity interactions, possibly accounting for the selectivity and higher potency of AH10-7. Molecular and structural perspectives provided could aid in the design of novel α-GalCer derivatives for cancer immunotherapeutics. Chapter 3 provides theoretical insights into the various molecular modeling tools and techniques employed to investigate the various conformational changes, structural conformations, and the associated mechanism of inhibitions of the studied inhibitors towards viral, tuberculosis, and cancer therapy. Chapter 4 provided sufficient details on druggability and drug-likeness principles and their recent advancements in the drug discovery field. The study also presents the different computational tools and their reliability of predictive analysis in the drug discovery domain. It thus provides a comprehensive guide for computational-oriented drug discovery research. Chapter 5 provides an understanding of the binding mechanism of Remdesivir, providing structural and conformational implications on SARS-CoV-2 RdRp upon its binding and identifying its crucial pharmacophoric moieties. Chapter 6 explains the mechanism of inhibition of a novel benzothiophene derivative, revealing its distortion of the native extensively networked and compact residue profile. Chapter 7 unravels molecular and structural bases behind this dual inhibitory potential of the novel inhibitor IMP-1088 toward common cold therapy using augmentative computational and cheminformatics methods. The study also highlights the pharmacological propensities of IMP- 1088. Chapter 8 unravels the molecular mechanisms and structural dynamics of the dual inhibitory activity of PAS-M towards DHFR and FDTS. Chapter 9 reports the structural dynamics and atomistic perspectives that account for the reported ability of BDQ to halt the ion shuttling ability of mycobacterial c-ring. Chapter 10 presents the structural dynamics and conformational changes that occur on Mtb F1F0 ATP-synthase binding as a result of the triple mutations using molecular dynamics simulations, free energy binding, and residue interaction network (RIN) analyses. Chapter 11 explored the impact of NAZ2329, a recently identified allosteric inhibitor of Protein Tyrosine Phosphatase Receptor Zeta (PTPRZ), on the atomic flexibility of the WPD-loop, an essential loop in the inhibition of PTPRZ. The study also presents the drug-likeness of NAZ2329 using in silico techniques and its general inhibitory mechanism. Chapter 12 provides atomistic insights into the structural dynamics and selective mechanisms of AH10-7 for human TCR-CD1d towards activating iNKT cells. The studies in this thesis collectively present a thorough and comprehensive in silico perspective that characterizes the pharmacological inhibition of some known therapeutic targets in viral infections, tuberculosis, and cancer. The augmentative integration of computational methods to provide structural insights could help design highly selective inhibitors of these therapeutic targets. Therefore, the findings presented are fundamental to the design and development of next generation lead compounds with improved therapeutic activities and minimal toxicities

Electron cryo-microscopy studies of bacteriophage phi8 and archaeal virus SH1

Symmetry is a key principle in viral structures, especially the protein capsid shells. However, symmetry mismatches are very common, and often correlate with dynamic functionality of biological significance. The three-dimensional structures of two isometric viruses, bacteriophage phi8 and the archaeal virus SH1 were reconstructed using electron cryo-microscopy. Two image reconstruction methods were used: the classical icosahedral method yielded high resolution models for the symmetrical parts of the structures, and a novel asymmetric in-situ reconstruction method allowed us to resolve the symmetry mismatches at the vertices of the viruses. Evidence was found that the hexameric packaging enzyme at the vertices of phi8 does not rotate relative to the capsid. The large two-fold symmetric spikes of SH1 were found not to be responsible for infectivity. Both virus structures provided insight into the evolution of viruses. Comparison of the phi8 polymerase complex capsid with those of phi6 and other dsRNA viruses suggests that the quaternary structure in dsRNA bacteriophages differs from other dsRNA viruses. SH1 is unusual because there are two major types of capsomers building up the capsid, both of which seem to be composed mainly of single beta-barrels perpendicular to the capsid surface. This indicates that the beta-barrel may be ancestral to the double beta-barrel fold.Virukset koostuvat yksinkertaisimmillaan perimäaineksesta (DNA tai RNA) ja sitä suojaavasta proteiinikuoresta. Proteiinikuoren rakenne on usein symmetrinen: monta kopiota samaa proteiinia nivoutuu yhteen säännölliseen muodostelmaan. Symmetria on yleensä joko helikaalinen (kierreportaat), jolloin virus on sauvamainen, tai ikosahedraalinen (5- ja 6-kulmioista ommeltu jalkapallo), jolloin syntyy pallomaisia viruksia. On kuitenkin tavallista, että jotkin viruksen toiminnan kannalta tärkeät rakenteet eivät noudata symmetriaa. Jalkapallossa esimerkiksi on vain yksi venttiilin paikka, eli yksi nahkapalasista poikkeaa muista. Viruksen tapauksessa taas vastaavalla tavalla muista poikkeavassa paikassa saattaa olla perimäaineksen pakkaamiseen tarvittava koneisto. Tässä työssä on tutkittu kahden pallomaisen viruksen, phi8:n ja SH1 kolmiulotteisia (3D) rakenteita. phi8 sairastuttaa erästä bakteeria, joka puolestaan sairastuttaa tiettyjä palkokasveja. SH1 sairastuttaa arkkieliöitä (bakteerien tapaisia yksisoluisia eliöitä), joita löytyy vaaleanpunaisista suolajärvistä Australiasta. Rakenteet määritettiin elektronimikroskooppikuvista laskennallisin keinoin. Perusajatus on, että kun kaksiulotteisissa mikroskooppikuvissa virus näkyy monesta eri suunnasta, nämä kuvat yhdistämällä saadaan selville viruksen 3D rakenne. Virukset erottuvat heikosti mikroskooppikuvissa, joten myös laskettu 3D rakenne on epäselvä. Sitä voidaan kuitenkin selkeyttää käyttäen hyväksi symmetriaa. Tällöin oletetaan, että virus on täysin symmetrinen, mistä seuraa, että laskettu 3D rakenne näyttää virheellisesti ne osat, jotka eivät seuraa symmetriaa. Esimerkiksi jalkapallon venttiilin paikka saattaisi ilmaantua 12 eri paikkaan tai kadota kokonaan näkyvistä. Tässä työssä jatkokehitettiin menetelmää, jonka avulla voidaan saada oikea kuva ventiilinpaikoista. Menetelmää sovellettiin molempiin tutkittuihin viruksiin. Virusten rakenteet kertovat niiden sukulaisuussuhteista, joten rakennetutkimus on myös sukututkimusta. Vain yhden phi8:n lähisukulaisen rakenne tunnettiin aiemmin, joten määritetty rakenne mahdollisti perheen sisäisen vertailun. SH1:n perheestä puolestaan ei ollut mitään tietoa, eikä sen rakennekaan nyt paljastanut varmuudella sen olevan sukua tunnetuille viruksille. On tosin mahdollista, että eräs yleinen viruskuoriproteiinityyppi on kehittynyt SH1:n tapaisen viruksen kuoresta

Problems at the Nexus of Geometry and Soft Matter: Rings, Ribbons and Shells

There has been an increasing appreciation of the role in which elasticity plays in soft matter. The understanding of many shapes and conformations of complex systems during equilibrium or non-equilibrium processes, ranging from the macroscopic to the microscopic, can be explained to a large extend by the theory of elasticity. We are motivated by older studies on how topology and shape couple in different novel systems and in this thesis, we present novel systems and tools for gaining fundamental insights into the wonderful world of geometry and soft matter. We first look at how defects, topology and geometry come together in the physics of thin membranes. Topological constraint plays a fundamental role on the morphology of crumpling membranes of genus zero and suggest how different fundamental shapes, such as platonic solids, can arise through a crumpling process. We present a way of classifying disclinations using a generalized “Casper-Klug” coordination number. We show that there exist symmetry breaking during the crumpling process, which can be described using Landau theory and that thin membranes preserve the memory of their defects. Next we consider the problem of the shapes of Bacillus spores and show how one can understand the folding patterns seen in bacterial coats by looking at the simplified problem of two concentric rings connected via springs. We show that when the two rings loses contact, rucks spontaneous formed leading to the complex folding patterns. We also develop a simple system of an extensible elastic on a spring support to study bifurcation in system that has adhesion. We explain the bifurcation diagram and show how it differs from the classical results. Lastly, we investigate the statistical mechanics of the Sadowsky ribbon in a similar spirit to the famous Kratky-Porod model. We present a detail theoretical and numerical calculations of the Sadowsky ribbon under the effect of external force and torsion. This model may be able to explain new and novel biopolymers ranging from actin, microtubules to rod-like viruses that lies outside the scope of WLC model. This concludes the thesis.Physic