Dr Andrea Rocco

When a quantum system is coupled to its environment, so-called open quantum system (OQS), it undergoes a very rapid decoherence process which is associated to the quantum-classical transition, one of the most fascinating and still poorly understood phenomena in fundamental physics.

Solving the dynamics of OQSs is challenging. It usually relies on a series of techniques based on Feynman path integrals, which aim to derive a quantum master equation for the reduced density matrix of the system. In my group we study different types of environments, and their effects on the reduced dynamics obtained. Recent results show that when we consider non-Markovian dynamics, occurring when there is no time-scale separation between environment and system, the decoherence process is substantially modified, with the emergence of what we call 'lateral coherences'  [Lally et al., Phys. Rev A (2022)]. We are now considering dissipative and fluctuating environments, and the implications of these on the decoherence process and the resulting thermodynamics in the classical limit.

This research line may open the way to the formulation of possible control mechanisms in all those quantum technologies application in which harnessing quantum effects is desirable.

Molecular networks, such as gene regulatory networks, are affected by stochastic fluctuations.

Fluctuations due to low copy numbers of proteins, or to gene expression bursts, define so-called 'intrinsic' noise, while fluctuations originating in the environment are usually referred to as 'extrinsic' noise. This part of my research concerns the study of both intrinsic and extrinsic noise, and of their interplay, by using Langevin and Fokker-Planck approaches. In particular, extrinsic noise can have highly non-trivial and counterintuitive effects, which may lead to noise-induced transitions [Rocco et al., Springer (2013)], well known in a variety of physical and chemical systems. Consideration of these effects has led me to introduce the concept of stochastic control in metabolic networks [Rocco, Phys. Biol. (2009)], where noise itself is proven to be able to act as a control mechanism that tunes metabolic concentrations and fluxes.

In my group we are now developing a novel dynamical framework which describes bounded, non-gaussian, and nonlinear noise in the case of slow extrinsic fluctuations in gene expression [Aquino & Rocco, Math. Biosci. Eng. (2020)].

Stochastic fluctuations are at the base of much of the variability that we see in biology. Different phenotypes are well known to arise in populations of genetically identical cells in the same environment. It is an intriguing conjecture that this variability is under positive selection. Yet, what precisely its origin is remains an unanswered question.

The requirement that distinct phenotypes be observable over typical experimental times suggests that they result from (quasi) static heterogeneities in the population. In collaboration with colleagues at the University of Surrey, we have investigated theoretically the possibility that such static heterogeneities are produced by stochastic bursting of gene expression, supplemented with specific mechanisms capable of slowing down fluctuations. This mechanism can be explained in general terms by the concept of 'weak ergodicity breaking', familiar in statistical mechanics to describe slowly relaxing systems. This has also led to a novel explanation of the phenomenon of so-called bacterial persistence or phenotypic drug tolerance [Rocco et al., PLoS ONE (2013)], the phenomenon by which an isogenic population of bacterial cells shows different levels of sensitivity to antibiotic treatment.

Recent results confirm that the origin of this phenomenon is stochastic [Hu et al., R. Soc. Open Sci. (2017); Hingley-Wilson et al., PNAS (2020)], and highlight possible ways of targeting phenotypic drug tolerance. Work is in progress to model theoretically the population structure seen in the experiments.

A major problem in developmental biology is to explain the emergence of different cell types from multipotent stem cells.

The problem is exquisitely suitable for the mathematical framework of Dynamical Systems Theory, which naturally leads to description and understanding of cellular decision making processes in terms of bifurcation analysis. In collaboration with experimentalists at the University of Bath, we have constructed the first core gene regulatory network describing stable differentiation of melanocytes in zebrafish [Greenhill et al., PLoS Genetics (2011)]. By using a combination of mathematical analysis and simulations, we could predict mathematically and validate experimentally several new features of this network. More recently we have refined that core network, to include an analysis of the role played by Wnt signaling in melanocyte differentiation [Vibert et al., Pigment Cell & Melanoma Research (2017)], and extended it to other neural crest derived pigment cells [Petratou et al., PLoS Genetics (2018)].

Currently we are investigating the relevance of cyclic dynamics in the differentiation process [Farjami et al., J. Royal Soc. Interface (2021); Kelsh et al., Development (2021)].

My research activity in the past has covered a number of different areas in theoretical physics, here briefly summarized.

In low-temperature plasma physics, I have studied branching phenomena in gas discharges (so-called streamers), and I have contributed to the development of the related description in terms of conformal mapping techniques [see for instance Ebert et al., Plasma Sources Sci. Technol. (2006) for a review].

I have also studied the effect of extrinsic noise on the propagation of reaction-diffusion fronts. In the case of the so-called Fisher Equation (FKPP), I have contributed to identify the anomalous sub-diffusive behaviour characterizing the front position [Rocco et al., Phys. Rev. E (2000)], and to generalize it through the definition of a new roughness universality class for travelling waves in 2 bulk dimensions [Tripathy et al., Phys. Rev. Lett. (2001)].

In the context of off-equilibrium statistical mechanics, I have also addressed fundamental issues on complexity reduction in models for glasses [Crisanti et al., J. Chem. Phys. (2000)].

During my PhD, I developed fractional calculus techniques to study fractal phenomena in both space and time [Rocco & West, Physica (1999); Grigolini et al., Phys. Rev. E (1999)]. I have also addressed the study of Open Quantum Systems in terms of constrained path integrals [Rocco & Grigolini, Phys. Lett. A (1999)].