Alessio Del Fabbro

COMPUTATIONAL CHALLENGES OF TUMOR SPHEROID MODELING

The speed and the versatility of todays computers open up new opportunities to simulate complex biological systems. Here we review a computational approach recently proposed by us to model large tumor cell populations and spheroids, and we put forward general considerations that apply to any fine-grained numerical model of tumors. We discuss ways to bypass computational limitations and discuss our incremental approach, where each step is validated by experimental observations on a quantitative basis. We present a few results on the growth of tumor cells in closed and open environments and of tumor spheroids. This study suggests new ways to explore the initial growth phase of solid tumors and to optimize antitumor treatments.

Thresholds, long delays and stability from generalized allosteric effect in protein networks

Post-transductional modifications tune the functions of proteins and regulate the collective dynamics of biochemical networks that determine how cells respond to environmental signals. For example, protein phosphorylation and nitrosylation are well known to play a pivotal role in the intracellular transduction of activation and death signals. A protein can have multiple sites where chemical groups can reversibly attach in processes such as phosphorylation or nitrosylation. A microscopic description of these processes must take into account the intrinsic probabilistic nature of the underlying reactions. We apply combinatorial considerations to standard enzyme kinetics and in this way we extend to the dynamic regime a simplified version of the traditional models on the allosteric regulation of protein functions. We link a generic modification chain to a downstream Michaelis–Menten enzymatic reaction and we demonstrate numerically that this accounts both for thresholds and long time delays in the conversion of the substrate by the enzyme. The proposed mechanism is stable and robust and the higher the number of modification sites, the greater the stability. We show that a high number of modification sites converts a fast reaction into a slow process, and the slowing down depends on the number of sites and may span many orders of magnitude; in this way multisite modification of proteins stands out as a general mechanism that allows the transfer of information from the very short time scales of enzyme reactions (milliseconds) to the long time scale of cell response (hours).

Modular model of TNFα cytotoxicity

MOTIVATION Tumour Necrosis Factor alpha (TNF) initiates a complex series of biochemical events in the cell upon binding to its type R1 receptor (TNF-R1). Recent experimental work has unravelled the molecular regulation of the signalling complexes that lead either to cell survival or death. Survival signals are activated by direct binding of TNF to TNF-R1 at the cell membrane whereas apoptotic signals by endocytosed TNF/TNF-R1 complexes. Here we describe a reduced, effective model with few free parameters, where we group some intricate mechanisms into effective modules, that successfully describes this complex set of actions. We study the parameter space to show that the model is structurally stable and robust over a broad range of parameter values. RESULTS We use state-of-the-art Bayesian methods (a Sequential Monte Carlo sampler) to perform inference of plausible values of the model parameters from experimental data. As a result, we obtain a robust model that can provide a solid basis for further modelling of TNF signalling. The model is also suitable for inclusion in multi-scale simulation programs that are presently under development to study the behaviour of large tumour cell populations. AVAILABILITY We provide supplementary material that includes all mathematical details and all algorithms (Matlab code) and models (SBML descriptions). CONTACT edoardo.milotti@ts.infn.it

Optimal generation of entanglement under local control

We study the optimal generation of entanglement between two qubits subject to local unitary control. With the only assumptions of linear control and unitary dynamics, by means of a numerical protocol based on the variational approach (Pontryagins Minimum Principle), we evaluate the optimal control strategy leading to the maximal achievable entanglement in an arbitrary interaction time, taking into account the energy cost associated to the controls. In our model we can arbitrarily choose the relative weight between a large entanglement and a small energy cost.

Dynamics of intracellular Ca2+ oscillations in the presence of multisite Ca2+-binding proteins

We study the dynamics of intracellular calcium oscillations in the presence of proteins that bind calcium on multiple sites and that are generally believed to act as passive calcium buffers in cells. These multisite calcium-binding proteins set a sharp threshold for calcium oscillations, and calcium oscillations stop at high concentrations of calcium-binding proteins. However even in these adverse conditions, internal noise, which shows up spontaneously in cells in the process of calcium wave formation, can lead to self-oscillations. This produces oscillatory behaviors strikingly similar to those observed in real cells. In addition, for given intracellular concentrations of both calcium and calcium-binding proteins the regularity of these oscillations changes and reaches a maximum as a function of the noise variance, and we find that the overall system dynamics displays coherence resonance. Thus it turns out that the calcium-binding proteins can have an important and non-trivial regularizing role.