# Dr Andrea Rocco

## Academic and research departments

School of Mathematics and Physics, Department of Microbial Sciences.## About

### Biography

Andrea Rocco graduated in Physics at the University of Pisa (Italy) in 1994, discussing a thesis in quantum field theory. In 1998 he obtained his PhD in Physics from the University of North Texas (USA), where he focused on the role of stochastic processes in classical and quantum mechanical systems.

Between 1998 and 2007 Andrea held postdoctoral positions at the University of Barcelona (Spain), the University of Rome "La Sapienza" (Italy), CWI (The Netherlands), and the University of Oxford (UK). During this period of time, his research spanned several areas, from the general fields of statistical mechanics and pattern formation to the modelling of biological systems. In 2007 he obtained a Lectureship in Applied Mathematics at the University of Bath (UK), where he taught mathematical biology modules at both MSc and undergraduate levels.

In 2009 Andrea joined the University of Surrey (UK), where he is now Associate Professor (Reader) in Physics and Mathematical Biology, with a shared appointment between the Department of Microbial Sciences and the Department of Physics.

## Research

### Research interests

My current research activity covers several topics in the broad fields of theoretical physics and biological physics.

In theoretical physics my current focus is on fundamental problems in quantum mechanics. It concerns the theory of open quantum systems, and addresses questions regarding the emergence of decoherence, the quantum-classical transition, and the resulting thermodynamics in the classical limit.

In biological physics my interest is in off-equilibrium stochastic dynamics and critical phenomena in living systems, and in particular in noise-induced transitions in gene networks and non-ergodic behaviours. My bio-inspired research does not focus on building high complexity models of biological systems, but rather on uncovering general and fundamental properties of living matter.

This research relies on a strong and very active research group, counting over the years on a number of postdoctoral fellows and PhD students. It is funded by the John Templeton Foundation, the UK Biotechnology and Biological Sciences Research Council (BBSRC), The Leverhulme Trust, and the University of Surrey, which I gratefully acknowledge.

I am always happy to consider **applications for PhD positions**. Interested candidates are welcome to enquire by email to discuss suitable topics. Given the theoretical aspects involved, a solid mathematical or theoretical physics background is required in all projects. I don't have **openings at the postdoctoral level** at the moment, but a number of grant applications are currently under evaluation, and openings may appear in the close future.

### Research projects

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)].

## Supervision

### Postgraduate research supervision

#### Current Group Members

**Postdoctoral level**

**Thomas Guff**: Open Quantum Systems, Quantum Thermodynamics, Irreversibility

**PhD students**

**Marc-Thomas Russo:**Emergence of macroscopic irreversibility in open classical and quantum systems (Supervisors: A. Rocco, J. Al-Khalili)**Matthew Freed:**Non-Markovian open quantum systems (Supervisors: J. Al-Khalili, A. Rocco)**Joe Bryant:**Evaluation and design of auto-regulatory feedback models for RNA-binding proteins (Supervisors: A. Gerber, A. Rocco)**Monica Hill:**Mathematical modelling of herpes simplex virus transmission in 2- and 3- dimensions (Supervisors: G. Elliott, A. Rocco)

**Internships**

**Chintalpati Umashankar Shastry:**Renormalization Group approach to open quantum systems

#### Past Group Members

**Postdoctoral level**

**Raneem Aizouk**: Dynamical models of stem cell differentiation**Saeed Farjami**: Dynamical models of stem cell differentiation**Gerardo Aquino**: Stochastic fluctuations in cell differentiation**Finn Gubay**: Stochastic fluctuations in cell differentiation**Hossein Nili**: Mathematical modelling of biofilm formation and treatment in the upper respiratory tract.

**PhD students**

**Michael Clarke-Whittet**: Noise and quantum decoherence in cellular systems (Supervisors: A. Gerber, A. Rocco - completed 2023)**Sonal Dahale**: Transcriptomic data-driven metabolic modelling of nematodes for biocontrol of agricoltural, domestic, and veterinary pests (Supervisors: C. Avignone-Rossa, A. Rocco - completed 2023).**Lester Buxton**: The role of noise in quantum decoherence (Supervisors: A. Rocco, J. Al-Khalili - completed 2022)**Sapphire Lally**: Coherence Dynamics in non-Markovian Quantum Brownian Motion (Supervisors: J. Al-Khalili, A. Rocco - completed 2022)**Nick Werren**: Memory effects in open quantum systems, (Supervisors: A. Rocco, J. Al-Khalili - completed 2020)**Jake Reeves**: A computational study of the role of nuclear receptor interactions in steatosis (Supervisors: C. Avignone-Rossa, A. Rocco - completed 2020)**Winifred Nyinoh**: Molecular investigation of drug synergy in*mycobacteria,*(Supervisors: J. McFadden, A. Rocco - completed 2018).

**MSc students**

**Ethan Wyke**, MSc in Physics: Quantum tunnelling through a stochastically fluctuating barrier (Supervisors: A. Rocco, J. Al-Khalili - completed 2017)**Noah Mesfin**, MSc in Systems Biology: A model for the expression dynamics of the nicotinic acid degradation pathway in pseudomonas putida KT2440 (Supervisors: J. Jimenez, A. Rocco - completed 2014).

## Teaching

**Topics in Theoretical Physics (Level M - Module Lead, ***Module Descriptor***)**

This module introduces important topics and techniques in theoretical physics with a wide range of applications. Topics covered include functions of complex variable, calculus of variations, and Integral transforms. Both the mathematical techniques and their applications are covered at a level appropriate for Masters level students coming to the end of their degree and who should be able to pull many different ideas in theoretical physics together.

**Introduction to Mathematical Biology (Level 3 - Module Lead, ***Module Descriptor***)**

This module aims at providing students with the problem-solving skills required to construct and solve simple mathematical models of molecular networks. Dynamical modelling, in terms of ordinary differential equations, is introduced, using gene regulatory networks as case studies (regulatory cascades, feedback loops, logic gates). The students are provided with the general techniques to analyse such models, and compute the solution numerically with the aid of dedicated software. Derivation of qualitative features, relating to steady states analysis, multistability, and oscillatory behaviours, is also discussed.

## Publications

G Aquino and **A. Rocco**, *Noise-induced transitions in gene circuits: A perturbative approach for slow noise*, Phys. Rev. E **107**, 044401 (2023).

**A. Rocco**, *On macroscopic irreversibility*, in Paolo Grigolini and 50 Years of Statistical Physics, Eds. B.J. West & S. Bianco, Cambridge Scholars Publishing (2023).

T. Subkhankulova, K. Camargo Sosa, L.A. Uroshlev, M. Nikaido, N. Shriever, A.S. Kasianov, X. Yang, F.S.L.M. Rodrigues, T.J. Carney, G. Bavister, H. Schwetlick, J.H.P. Dawes, **A. Rocco**, V.J. Makeev, R.N. Kelsh, *Zebrafish pigment cells develop directly from persistent highly multipotent progenitors*. *Nat Commun* **14**, 1258 (2023).

M. Clarke‐Whittet, **A. Rocco**, A.P. Gerber, *Parameterising Translational Feedback Models of Autoregulatory RNA‐Binding Proteins in Saccharomyces cerevisiae**, *Microorganisms* ***10**, 340 (2022).

S. Lally, N. Werren, J. Al-Khalili, and **A. Rocco**, *Master equation for non-Markovian quantum Brownian motion: The emergence of lateral coherences*, Phys. Rev. A **105**, 012209 (2022).

R.N. Kelsh, K. Camargo Sosa, S. Farjami, M. Makeev, J.H.P. Dawes, and **A. Rocco,** *Cyclical fate restriction: A new view of neural crest cell fate specification*, Development **148**, dev176057 (2021).

S. Farjami, K. Camargo Sosa, J.H.P. Dawes, R.N. Kelsh and **A. Rocco, ***Novel generic models for differentiating stem cells reveal oscillatory mechanisms**, *J. R. Soc. Interface **18**, 20210442 (2021)

G. Aquino and **A. Rocco**, *Bimodality in gene expression without feedback: From Gaussian white noise to log-normal coloured noise*, Math. Biosci. Eng. **17** (6), 6993 (2020)

S.M. Hingley-Wilson, N. Ma, Y. Hu, R. Casey, A. Bramming, R.J. Curry, H.L. Tang, H. Wu, R.E. Butler, W.R. Jacobs, **A. Rocco***, J. McFadden*,* **Loss of phenotypic inheritance associated with ydcI mutation leads to increased frequency of small, slow persisters in Escherichia coli*, PNAS **117** (8), 4152 (2020) [ * equal senior authorship]

K. Petratou, T. Subkhankulova, J.A. Lister, **A. Rocco**, H. Schwetlick, R.N. Kelsh, *A systems biology approach uncovers the core gene regulatory network governing iridophore fate choice from the neural crest**, *PLoS genetics **14** (10), e1007402 (2018)

L. Vibert, G. Aquino, I. Gehring, T. Subkankulova, T.F. Schilling, **A. Rocco**, R.N. Kelsh,* **An ongoing role for Wnt signaling in differentiating melanocytes in vivo**, *Pigment cell & melanoma research **30** (2), 219 (2017)

Y. Hu, S. Wang, N. Ma, S.M. Hingley-Wilson, **A. Rocco**, J. McFadden, H. Tang,* **Trajectory energy minimization for cell growth tracking and genealogy analysis**,* Royal Society Open Science **4** (5), UNSP 170207 (2017)

A.A. Mannan, Y. Toya, K. Shimizu, J. McFadden, A.M. Kierzek*, **A. Rocco*,*** **Integrating kinetic model of E. coli with genome scale metabolic fluxes overcomes its open system problem and reveals bistability in central metabolism,* PloS one **10** (10), e0139507 (2015) [ * equal senior authorship]

**A. Rocco***, A. Kierzek, J. McFadden,* **Slow protein fluctuations explain the emergence of growth phenotypes and persistence in clonal bacterial populations**,* PloS one **8 **(1), e54272 (2013) [ * corresponding author]

**A. Rocco**, A. Kierzek, J. McFadden,* **Stochastic Effects in Metabolic Networks**, *in Encyclopedia of Systems Biology, Eds. W. Dubitzky, O. Wolkenhauer, K.-H. Cho, H. Yokota, 1991, Springer (2013)

**A. Rocco**, A. Kierzek, J. McFadden,* **Stochastic gene expression in bacterial pathogens: A mechanism for persistence?* In Systems Biology of Tuberculosis, Eds. J. McFadden, D.J.V. Beste, A.M. Kierzek, 157, Springer (2013)

E.R. Greenhill, **A. Rocco**, L. Vibert, M. Nikaido, R.N. Kelsh,* An iterative genetic and dynamical modelling approach identifies novel features of the gene regulatory network underlying melanocyte development**,* PLoS genetics **7** (9), e1002265 (2011) [see also modelling supplementary material]

E. Greenhill, **A. Rocco**, M. Nikaido, R.N. Kelsh,* Melanocytes, modeling and maths-do we really understand differentiation?* Pigment Cell & Melanoma Research **5** (22), 21 (2009)

L. Vibert, **A. Rocco**, M. Nikkaido, E.R. Greenhill, R.N. Kelsh,* Testing in vivo the genetic regulatory network underlying melanocyte differentiation,* Mechanisms of Development **126**, S316 (2009)

**A. Rocco**,* Stochastic control of metabolic pathways,* Phys. Biol. **6**, 016002 (2009)

G. Lunter, **A. Rocco**, N. Mimouni, A. Heger, A. Caldeira, J. Hein,* Uncertainty in Homology Inferences: Assessing and Improving Genomic Sequence Alignment**,* Genome Res. **18**, 298 (2008) [see also commentary paper]

U. Ebert, C. Montijn, T.M.P. Briels, W. Hundsdorfer, B. Meulenbroek, **A. Rocco**, E.M. van Veldhuizen,* The multiscale nature of streamers**,* Plasma Sources Sci. Technol. **15**, S118 (2006)

B. Meulenbroek, **A. Rocco**, U. Ebert, *Streamer branching rationalized by conformal mapping techniques**, *Phys Rev. E **69**, 067402 (2004)

B. Coluzzi, A. Crisanti, E. Marinari, F. Ritort, **A. Rocco**,* A New Method to Compute the Configurational Entropy in Spin Glasses,* Eur. Phys. J. B **32**, 495 (2003)

**A. Rocco**, U. Ebert and W. Hundsdorfer,* Branching of Negative Streamers in free flight**,* Phys. Rev. E **66**, 035102 (2002)

A. Crisanti, F. Ritort, **A. Rocco**, and M. Sellitto,* Is the Stillinger and Weber decomposition relevant for coarsening models?* J. Phys.: Condens. Matter **14**, 1523 (2002)

**A. Rocco**, L. Ramírez-Piscina, J. Casademunt,* Kinematic reduction of reaction-diffusion fronts with multiplicative noise: Derivation of stochastic sharp-interface equations**,* Phys. Rev. E **65**, 056116 (2002)

A. Torcini, A. Vulpiani, **A. Rocco,*** Front propagation in chaotic and noisy reaction diffusion systems: A discrete-time map approach,* Eur. Phys. J. B **25**, 333 (2002)

**A. Rocco**, J. Casademunt, U. Ebert, and W. van Saarloos,* Diffusion coefficient of propagating fronts with multiplicative noise**,* Phys. Rev. E **65**, 012102 (2002)

G. Tripathy, **A. Rocco**, J. Casademunt, and W. van Saarloos,* Universality class of fluctuating pulled fronts**,* Phys. Rev. Lett. **86**, 5215 (2001)

A. Crisanti, F. Ritort, **A. Rocco**, and M. Sellitto,* Inherent Structures and non-equilibrium dynamics of 1D constrained kinetic models: A comparison study,* J. Chem. Phys. **113**, 10615 (2000)

F.X. Magdaleno, **A. Rocco**, J. Casademunt,* Interface dynamics in Hele-Shaw flows with centrifugal forces: Preventing cusp singularities with rotation**,* Phys. Rev. E **62**, R5887 (2000)

**A. Rocco**, U. Ebert, and W. van Saarloos,* Subdiffusive fluctuations of "pulled" fronts with multiplicative noise**,* Phys. Rev. E **62**, R13 (2000)

P. Grigolini, **A. Rocco** and B.J. West, *Fractional Calculus as a Macroscopic Manifestation of Randomness**,* Phys. Rev. E **59** 2603 (1999)

**A. Rocco** and B.J. West, *Fractional Calculus and the Evolution of Fractal Phenomena**,* Physica A **265**, 535 (1999)

**A. Rocco** and P. Grigolini, *The Markov approximation revisited: Inconsistency of the standard quantum Brownian motion model**,* Phys. Lett. A **252**, 115 (1999)

P. Allegrini, P. Grigolini, **A. Rocco,*** Slow motion as a thermal gradient effect,* Phys. Lett. A **233**, 309 (1997)