Biológiai hálózatok reakciókinetikai vizsgálata = Reaction kinetic analysis of biological networks

Az ifjúsági OTKA támogatás lehetőséget nyújtott ahhoz, hogy a biokémiai reakciókinetika módszereit használva több biológiai kérdésen is dolgozzak. A biológiai napi ritmus és a sejtosztódási ciklus biokémiai oszcillációinak kapcsoltságát vizsgáltam matematikai modellekkel. Megállapítottam, hogy kvantált sejtciklusidő eloszláshoz vezethet ha a két oszcillátor eltérő saját periódussal rendelkezik és a modell alapján azt a feltételezést tettük, hogy ez a kapcsoltság fontos szerepet játszhat az emlős sejtek homeosztázisát reguláló méretkontrolljában. Egy másik kapcsolódó munkában azt a meglapítást tettük, hogy a napi ritmus szabályozó reakcióhálózat kísérletesen megfigyelt tulajdonságainak pontos modellezéséhez elengedhetetlen egy pozitív visszacsatolási hurok jelenléte a rendszerben. Más biológiai kérdéseket vizsgáltam élesztők sejtciklusának szabályozásával kapcsolatban: a sarjadzó élesztő sejtciklusának kritikus lépéseinek szabályzó mechanizmusában fontos szerepet játszó előre és visszacsatolási hurkokat találtam a rendszer matematikai modelljeivel, valamint vizsgáltam ezen sejtciklus átmenetek érzékenységét, sztochasztikáját és dinamikáját. Más cikkekben a hasadó élesztő sejtosztódását és növekedésének regulálását és szignalizációs utak egyszerű modelleit is vizsgáltam. A modellezéssel kapott predikciók közül néhányat már kísérletesen igazoltak is, mások jelenleg állnak tesztelés alatt. | The OTKA youth grant allowed me to work on various biology-oriented projects with the tools of biochemical reaction kinetics. I investigated by mathematical modeling the coupling of the biochemical oscillators of the daily rhythm and the cell division cycle. I found that the cell cycle time could show quantized distributions in case the two oscillators run with dissimilar basal periods. Furthermore the model suggests that this coupling might have an important role in homeostasis regulatory size control of mammalian cells. In another related work we showed that the presence of a positive feedback loop in the network of circadian clock regulation is inevitable to properly model some experimental observations on the daily rhythm. Additionally I investigated other biological questions related to the cell cycle regulation of yeast cells: with mathematical modeling of the network of the regulation in budding yeast I identified important feed-forward and feedback loops that control the critical cell cycle transitions, furthermore I investigated the sensitivity, stochasticity and dynamics of these transitions. In other articles I investigated the regulation of cell division and cell growth in fission yeast cells as well as studied simplified models of signaling pathways. Some of the predictions of the models have been already experimentally verified, some are still under experimental tests

Growth Rate as a Direct Regulator of the Start Network to Set Cell Size

Cells are able to adjust their growth and size to external inputs to comply with specific fates and developmental programs. Molecular pathways controlling growth also have an enormous impact in cell size, and bacteria, yeast, or epithelial cells modify their size as a function of growth rate. This universal feature suggests that growth (mass) and proliferation (cell number) rates are subject to general coordinating mechanisms. However, the underlying molecular connections are still a matter of debate. Here we review the current ideas on growth and cell size control, and focus on the possible mechanisms that could link the biosynthetic machinery to the Start network in budding yeast. In particular, we discuss the role of molecular chaperones in a competition framework to explain cell size control by growth at the individual cell level

Response dynamics of phosphorelays suggest their potential utility in cell signalling

Phosphorelays are extended two-component signalling systems found in diverse bacteria, lower eukaryotes and plants. Only few of these systems are characterized, and we still lack a full understanding of their signalling abilities. Here, we aim to achieve a global understanding of phosphorelay signalling and its dynamical properties. We develop a generic model, allowing us to systematically analyse response dynamics under different assumptions. Using this model, we find that the steady-state concentration of phosphorylated protein at the final layer of a phosphorelay is a linearly increasing, but eventually saturating function of the input. In contrast, the intermediate layers can display ultrasensitivity. We find that such ultrasensitivity is a direct result of the phosphorelay biochemistry; shuttling of a single phosphate group from the first to the last layer. The response dynamics of the phosphorelay results in tolerance of cross-talk, especially when it occurs as cross-deactivation. Further, it leads to a high signal-to-noise ratio for the final layer. We find that a relay length of four, which is most commonly observed, acts as a saturating point for these dynamic properties. These findings suggest that phosphorelays could act as a mechanism to reduce noise and effects of cross-talk on the final layer of the relay and enforce its input–response relation to be linear. In addition, our analysis suggests that middle layers of phosphorelays could embed thresholds. We discuss the consequence of these findings in relation to why cells might use phosphorelays along with enzymatic kinase cascades

Noise Reduction in Complex Biological Switches

Cells operate in noisy molecular environments via complex regulatory networks. It is possible to understand how molecular counts are related to noise in specific networks, but it is not generally clear how noise relates to network complexity, because different levels of complexity also imply different overall number of molecules. For a fixed function, does increased network complexity reduce noise, beyond the mere increase of overall molecular counts? If so, complexity could provide an advantage counteracting the costs involved in maintaining larger networks. For that purpose, we investigate how noise affects multistable systems, where a small amount of noise could lead to very different outcomes; thus we turn to biochemical switches. Our method for comparing networks of different structure and complexity is to place them in conditions where they produce exactly the same deterministic function. We are then in a good position to compare their noise characteristics relatively to their identical deterministic traces. We show that more complex networks are better at coping with both intrinsic and extrinsic noise. Intrinsic noise tends to decrease with complexity, and extrinsic noise tends to have less impact. Our findings suggest a new role for increased complexity in biological networks, at parity of function

Time scale and dimension analysis of a budding yeast cell cycle model

BACKGROUND: The progress through the eukaryotic cell division cycle is driven by an underlying molecular regulatory network. Cell cycle progression can be considered as a series of irreversible transitions from one steady state to another in the correct order. Although this view has been put forward some time ago, it has not been quantitatively proven yet. Bifurcation analysis of a model for the budding yeast cell cycle has identified only two different steady states (one for G1 and one for mitosis) using cell mass as a bifurcation parameter. By analyzing the same model, using different methods of dynamical systems theory, we provide evidence for transitions among several different steady states during the budding yeast cell cycle. RESULTS: By calculating the eigenvalues of the Jacobian of kinetic differential equations we have determined the stability of the cell cycle trajectories of the Chen model. Based on the sign of the real part of the eigenvalues, the cell cycle can be divided into excitation and relaxation periods. During an excitation period, the cell cycle control system leaves a formerly stable steady state and, accordingly, excitation periods can be associated with irreversible cell cycle transitions like START, entry into mitosis and exit from mitosis. During relaxation periods, the control system asymptotically approaches the new steady state. We also show that the dynamical dimension of the Chen's model fluctuates by increasing during excitation periods followed by decrease during relaxation periods. In each relaxation period the dynamical dimension of the model drops to one, indicating a period where kinetic processes are in steady state and all concentration changes are driven by the increase of cytoplasmic growth. CONCLUSION: We apply two numerical methods, which have not been used to analyze biological control systems. These methods are more sensitive than the bifurcation analysis used before because they identify those transitions between steady states that are not controlled by a bifurcation parameter (e.g. cell mass). Therefore by applying these tools for a cell cycle control model, we provide a deeper understanding of the dynamical transitions in the underlying molecular network

Cell cycle regulation by feed-forward loops coupling transcription and phosphorylation

The eukaryotic cell cycle requires precise temporal coordination of the activities of hundreds of ‘executor' proteins (EPs) involved in cell growth and division. Cyclin-dependent protein kinases (Cdks) play central roles in regulating the production, activation, inactivation and destruction of these EPs. From genome-scale data sets of budding yeast, we identify 126 EPs that are regulated by Cdk1 both through direct phosphorylation of the EP and through phosphorylation of the transcription factors that control expression of the EP, so that each of these EPs is regulated by a feed-forward loop (FFL) from Cdk1. By mathematical modelling, we show that such FFLs can activate EPs at different phases of the cell cycle depending of the effective signs (+ or −) of the regulatory steps of the FFL. We provide several case studies of EPs that are controlled by FFLs exactly as our models predict. The signal-transduction properties of FFLs allow one (or a few) Cdk signal(s) to drive a host of cell cycle responses in correct temporal sequence

Evolution of Opposing Regulatory Interactions Underlies the Emergence of Eukaryotic Cell Cycle Checkpoints

In eukaryotes the entry into mitosis is initiated by activation of cyclin-dependent kinases (CDKs), which in turn activate a large number of protein kinases to induce all mitotic processes. The general view is that kinases are active in mitosis and phosphatases turn them off in interphase. Kinases activate each other by cross- and self-phosphorylation, while phosphatases remove these phosphate groups to inactivate kinases. Crucial exceptions to this general rule are the interphase kinase Wee1 and the mitotic phosphatase Cdc25. Together they directly control CDK in an opposite way of the general rule of mitotic phosphorylation and interphase dephosphorylation. Here we investigate why this opposite system emerged and got fixed in almost all eukaryotes. Our results show that this reversed action of a kinase-phosphatase pair, Wee1 and Cdc25, on CDK is particularly suited to establish a stable G2 phase and to add checkpoints to the cell cycle. We show that all these regulators appeared together in LECA (Last Eukaryote Common Ancestor) and co-evolved in eukaryotes, suggesting that this twist in kinase-phosphatase regulation was a crucial step happening at the emergence of eukaryotes

Information cascades and the collapse of cooperation

In various types of structured communities newcomers choose their interaction partners by selecting a role-model and copying their social networks. Participants in these networks may be cooperators who contribute to the prosperity of the community, or cheaters who do not and simply exploit the cooperators. For newcomers it is beneficial to interact with cooperators but detrimental to interact with cheaters. However, cheaters and cooperators usually cannot be identified unambiguously and newcomers’ decisions are often based on a combination of private and public information. We use evolutionary game theory and dynamical networks to demonstrate how the specificity and sensitivity of those decisions can dramatically affect the resilience of cooperation in the community. We show that promiscuous decisions (high sensitivity, low specificity) are advantageous for cooperation when the strength of competition is weak; however, if competition is strong then the best decisions for cooperation are risk-adverse (low sensitivity, high specificity). Opportune decisions based on private and public information can still support cooperation but suffer of the presence of information cascades that damage cooperation, especially in the case of strong competition. Our research sheds light on the way the interplay of specificity and sensitivity in individual decision-making affects the resilience of cooperation in dynamical structured communities

Interpretation of morphogen gradients by a synthetic bistable circuit.

During development, cells gain positional information through the interpretation of dynamic morphogen gradients. A proposed mechanism for interpreting opposing morphogen gradients is mutual inhibition of downstream transcription factors, but isolating the role of this specific motif within a natural network remains a challenge. Here, we engineer a synthetic morphogen-induced mutual inhibition circuit in E. coli populations and show that mutual inhibition alone is sufficient to produce stable domains of gene expression in response to dynamic morphogen gradients, provided the spatial average of the morphogens falls within the region of bistability at the single cell level. When we add sender devices, the resulting patterning circuit produces theoretically predicted self-organised gene expression domains in response to a single gradient. We develop computational models of our synthetic circuits parameterised to timecourse fluorescence data, providing both a theoretical and experimental framework for engineering morphogen-induced spatial patterning in cell populations