Conservation Laws in Cellular Automata

Conservation laws in physics are numerical invariants of the dynamics of a system. In cellular automata (CA), a similar concept has already been defined and studied. To each local pattern of cell states a real value is associated, interpreted as the “energy” (or “mass”, or . . . ) of that pattern.The overall “energy” of a configuration is simply the sum of the energy of the local patterns appearing on different positions in the configuration. We have a conservation law for that energy, if the total energy of each configuration remains constant during the evolution of the CA. For a given conservation law, it is desirable to find microscopic explanations for the dynamics of the conserved energy in terms of flows of energy from one region toward another. Often, it happens that the energy values are from non-negative integers, and are interpreted as the number of “particles” distributed on a configuration. In such cases, it is conjectured that one can always provide a microscopic explanation for the conservation laws by prescribing rules for the local movement of the particles. The onedimensional case has already been solved by Fuk´s and Pivato. We extend this to two-dimensional cellular automata with radius-0,5 neighborhood on the square lattice. We then consider conservation laws in which the energy values are chosen from a commutative group or semigroup. In this case, the class of all conservation laws for a CA form a partially ordered hierarchy. We study the structure of this hierarchy and prove some basic facts about it. Although the local properties of this hierarchy (at least in the group-valued case) are tractable, its global properties turn out to be algorithmically inaccessible. In particular, we prove that it is undecidable whether this hierarchy is trivial (i.e., if the CA has any non-trivial conservation law at all) or unbounded. We point out some interconnections between the structure of this hierarchy and the dynamical properties of the CA. We show that positively expansive CA do not have non-trivial conservation laws. We also investigate a curious relationship between conservation laws and invariant Gibbs measures in reversible and surjective CA. Gibbs measures are known to coincide with the equilibrium states of a lattice system defined in terms of a Hamiltonian. For reversible cellular automata, each conserved quantity may play the role of a Hamiltonian, and provides a Gibbs measure (or a set of Gibbs measures, in case of phase multiplicity) that is invariant. Conversely, every invariant Gibbs measure provides a conservation law for the CA. For surjective CA, the former statement also follows (in a slightly different form) from the variational characterization of the Gibbs measures. For one-dimensional surjective CA, we show that each invariant Gibbs measure provides a conservation law. We also prove that surjective CA almost surely preserve the average information content per cell with respect to any probability measure.

The Integrin Tail: A Tale of Cell Motility and Division

Integrin transmembrane receptor functions are regulated by adaptor molecules binding to their alpha and beta subunit intracellular domains, or tails, thus affecting integrin traffic and adhesion during e.g. cell motility. Interestingly, many cellular proteins function in both cell motility and cell division, thus raising the possibility that integrins might be involved in regulating the cell cycle. A thorough understanding of cell division is essential in cell biology and in human malignancies. It is well established that failures to complete cell cycle can give rise to genetically unstable cells with tumorigenic properties. Transformed cells promote the disruption of intercellular adhesions such as tight junctions, and this correlates with the onset of cell motility, invasion and unfavorable prognosis in cancer. In this study, we analyzed integrin regulation, mediated by adaptor binding to the  subunit tail, during cell motility and cell division. We revealed a novel molecular mechanism by which Rab21, through association with the integrin alpha subunits, drives integrin endosomal traffic during mitotic phases. In addition, we found indications for this finding in vivo, as <i>RAB21i> gene deletions were mapped in ovarian and prostate cancer samples. Importantly, the multinucleated phenotype of cultured ovarian cancer cells could be reverted by Rab21 overexpression. In this thesis work, we also show how the tight junction protein ZO-1 unexpectedly interacts with the 5 integrin cytoplasmic domain in the lamellipodia to promote cell motility and at the cleavage furrow to support separation of the daughter cells. The alpha5-ZO-1 complex formation was dependent on PKC which regulates ZO-1 phosphorylation and its subcellular localization. In addition, by an <i>in situi> detection method, we showed that a subset of metastatic human lung cancers expressed the alpha5beta-ZO-1 complex. Taken together, we were able to identify new molecular pathways that regulate integrin functions in an alpha tail-mediated fashion. These findings firmly suggest that genetic alterations in integrin traffic may lead to progression of tumorigenesis as a result of failed cell division. Also, the interplay of integrins and ZO-1 in forming spatially regulated adhesive structures broadens our view of crosstalk between pathways and distinct adhesive structures that can be involved in cancer cell biology.

Viral and cellular modulation of virus-induced apoptosis in experimental infection models

The aim of this study was to investigate herpes simplex virus type 1 (HSV-1)- and measles virus (MV)-induced cell death. HSV-1 with deletion in genes encoding infected cell protein (ICP)4 and protein kinase Us3 (d120) induced apoptosis and cathepsin activation in epithelial (HEp-2) and monocytic (U937) cells. Inhibition of cathepsin activity decreased the amount of d120-induced apoptosis indicating that d120-induced apoptosis could be cathepsin-mediated. Also, HSV-1 infection increased caspase activation suggesting that d120-induced apoptosis is probably caspase-mediated. Cystatin treatment decreased the activity of cathepsins and the replication of HSV-1 indicating that cathepsins contribute to HSV-1 infection. Interestingly, d120 induced also necroptosis in monocytic cells. This is the first report on necroptosis in HSV-1- infected cells. MV induced apoptosis in uninfected bystander T lymphocytes, probably via interaction of MV-infected monocytes with uninfected lymphocytes. The expression of death receptor Fas was clearly increased on the surface of lymphocytes. The number of apoptotic cells and the activation of cathepsins and caspases were increased in MVinfected U937 cells suggesting that MV-induced apoptosis could be cathepsin- and caspase-mediated. Cystatin treatment inhibited cathepsin activities but not MV-induced apoptosis. Besides HSV-1-induced apoptosis, innate immune responses were studied in HSV-1-infection. HSV-1 viruses with either ICP4 and Us3, or Us3 deletion only, increased the expression of Toll-like receptor (TLR)3 and stimulated its downstream pathways leading to increased expression of type I interferon gene and to functional interferons. These findings suggest that besides controlling apoptosis, HSV-1 ICP4 and Us3 genes are involved in the control of TLR3 response in infected cell.

The Dual Role of HIF Hydroxylase PHD3 in Cancer Cell Survival

Most advanced tumours face periods of reduced oxygen availability i.e. hypoxia. During these periods tumour cells undergo adaptive changes enabling their survival under adverse conditions. In cancer hypoxia-induced cellular changes cause tumour progression, hinder cancer treatment and are indicative of poor prognosis. Within cells the main regulator of hypoxic responses is the hypoxia-inducible factor (HIF). HIF governs the expression of over a hundred hypoxia-inducible genes that regulate a number of cellular functions such as angiogenesis, glucose metabolism and cell migration. Therefore the activity of HIF must be tightly governed. HIF is regulated by a family of prolyl hydroxylase enzymes, PHDs, which mark HIF for destruction in normoxia. Under hypoxic conditions PHDs lose much of their enzymatic activity as they need molecular oxygen as a cofactor. Out of the three PHDs (PHD1, 2 and 3) PHD2 has been considered to be the main HIF-1 regulator in normoxic conditions. PHD3 on the other hand shows the most robust induction in response to oxygen deprivation and it has been implied as the main HIF-1 regulator under prolonged hypoxia. SQSTM1/p62 (p62) is an adaptor protein that functions through its binding motifs to bring together proteins in order to regulate signal transduction. In non-stressed situations p62 levels are kept low but its expression has been reported to be upregulated in many cancers. It has a definitive role as an autophagy receptor and as such it serves a key function in cancer cell survival decisions. In my thesis work I evaluated the significance of PHD3 in cancer cell and tumour biology. My results revealed that PHD3 has a dual role in cancer cell fate. First, I demonstrated that PHD3 forms subcellular protein aggregates in oxygenated carcinoma cells and that this aggregation promotes apoptosis induction in a subset of cancer cells. In these aggregates an adaptor protein SQSTM1/p62 interacts with PHD3 and in so doing regulates PHD3 expression. SQSTM1/p62 expression is needed to keep PHD3 levels low in normoxic conditions. Its levels rapidly decrease in response to hypoxia allowing PHD3 protein levels to be upregulated and the protein to be diffusely expressed throughout the cell. The interaction between PHD3 and SQSTM1/p62 limits the ability of PHD3 to function on its hydroxylation target protein HIF-1alpha. Second, the results indicate that when PHD3 is upregulated under hypoxia it protects cancer cells by allowing cell cycle to proceed from G1 to S-phase. My data demonstrates that PHD3 may either cause cell death or protect the cells depending on its expression pattern and the oxygen availability of tumours.

Cellular responses to stress and kinase signaling activation : apoptosis and differentiation

Stressignaler avkänns många gånger av membranbundna proteiner som översätter signalerna till kemisk modifiering av molekyler, ofta proteinkinaser Dessa kinaser överför de avkodade budskapen till specifika transkriptionsfaktorer genom en kaskad av sekventiella fosforyleringshändelser, transkriptionsfaktorerna aktiverar i sin tur de gener som behövs för att reagera på stressen. En av de mest kända måltavlorna för stressignaler är transkriptionsfaktor AP-1 familjemedlemen c-Jun. I denna studie har jag identifierat den nukleolära proteinet AATF som en ny regulator av c-Jun-medierad transkriptionsaktivitet. Jag visar att stresstimuli inducerar omlokalisering av AATF vilket i sin tur leder till aktivering av c-Jun. Den AATF-medierad ökningen av c-Jun-aktiviteten leder till en betydande ökning av programmerad celldöd. Parallellt har jag vidarekarakteriserat Cdk5/p35 signaleringskomplexet som tidigare har identifierats i vårt laboratorium som en viktig faktor för myoblastdifferentiering. Jag identifierade den atypiska PKCξ som en uppströms regulator av Cdk5/p35-komplexet och visar att klyvning och aktivering av Cdk5 regulatorn p35 är av fysiologisk betydelse för differentieringsprocessen och beroende av PKCξ aktivitet. Jag visar att vid induktion av differentiering fosforylerar PKCξ p35 vilket leder till calpain-medierad klyvning av p35 och därmed ökning av Cdk5-aktiviteten. Denna avhandling ökar förståelsen för de regulatoriska mekanismer som styr c-Jun-transkriptionsaktiviteten och c-Jun beroende apoptos genom att identifiera AATF som en viktig faktor. Dessutom ger detta arbete nya insikter om funktionen av Cdk5/p35-komplexet under myoblastdifferentiering och identifierar PKCξ som en uppströms regulator av Cdk5 aktivitet och myoblast differentiering.

Novel Cellular Luminescence Probes for Immunological and Toxicological Assessments

Escherichia coli K-12 (pEGFPluxABCDEAmp) (E. coli-lux), constitutively emitting bioluminescence (BL), was constructed and its BL emitting properties tested in different growth and killing conditions. The BL emission directly correlated with the number of viable E. coli-lux cells, and when subjected to the antimicrobial agent, the diminishment of the BL signal was linked directly to the number of killed bacterial cells. The method provided a very convenient application, especially when compared to conventional plate counting assays. This novel real-time based method was utilized in both immunological and toxicological assessments. The parameters such as the activation phase, the lytic phase and the capacity of the killing of the serum complement system were specified not only in humans but also in other species. E. coli-lux was also successfully used to study the antimicrobial activities of insect haemolymph. The mechanisms of neutrophil activity, like that of a myeloperoxidase (MPO)-H2O2-halide system, were studied using the E. coli-lux approach. The fundamental role of MPO was challenged, since during the actual killing in described circumstances in phagolysosome the MPO system was inactivated and chlorination halted. The toxicological test system, assessing indoor air total toxicity, particularly suitable for suspected mold damages, was designed based on the E. coli-lux method. Susceptibility to the vast number of various toxins, both pure chemicals and dust samples from the buildings and extracts from molds, were investigated. The E. coli-lux application was found to possess high sensitivity and specificity attributes. Alongside the analysis system, the sampling kit for indoor dust was engineered based on the swipe stick and the container. The combination of practical specimen collector and convenient analysis system provided accurate toxic data from the dust sample within hours. Neutrophils are good indicators of the pathophysiological state of the individual, and they can be utilized as a toxicological probe due to their ability to emit chemiluminescence (CL). Neutrophils can either be used as probe cells, directly exposed to the agent studied, or they can act as indicators of the whole biological system exposed to the agent. Human neutrophils were exposed to the same toxins as tested with the E. coli-lux system and measured as luminol amplified CL emission. The influence of the toxins on the individuals was investigated by exposing rats with moniliniformin, the mycotoxin commonly present in Finnish grains. The activity of the rat neutrophils was found to decrease significantly during the 28 days of exposure.