As a theoretical physicist, my research focus has primarily been within the general fields of statistical mechanics, nonlinear dynamics, and pattern formation. In recent years, I have made a transition towards the study of biological systems, for which I adopt a variety of theoretical methodologies borrowed from physics and mathematics, such as dynamical systems theory and the theory of stochastic processes.
My current research focuses in particular on noise propagation across molecular networks, critical phenomena in living systems, stochastic dynamics in cell differentiation, and noise effects in open quantum systems. In general, my research questions regard understanding the noise-induced transitions in gene networks, stochastic off-equilibrium dynamics and non-ergodic behaviours, and the balance between biological variability and individual robustness. In my group, the emphasis is not on building high complexity models, but rather on uncovering general and fundamental mechanisms. The ultimate goal is to construct a theoretical framework in which fluctuations can be understood in general terms, and their role in shaping the organism dynamics elucidated.
I am always happy to consider applications for PhD positions in my group (see below for further details on my research). 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.
Stochastic effects in subcellular networks
Molecular networks, such as gene regulatory networks or metabolic 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. In particular, extrinsic noise can have highly non-trivial and counterintuitive effects, which may lead to noise-induced transitions [Rocco et al, in “Systems Biology of Tuberculosis”, Springer (2013)]. 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. I am now interested in the principles underpinning noise propagation across different layers of regulation in gene networks.
Dynamics of cell differentiation
A major problem in developmental biology is to explain the emergence of different cell types from multipotent stem cells. In collaboration with Robert Kelsh (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)]. We are now interested in assessing the role played by noise, both intrinsic and extrinsic, in the dynamics of the differentiation process. This project is currently funded by BBSRC. More details in our dedicated website, Systems Biology of Stem Cell Differentiation.
Ergodicity breaking in isogenic bacterial populations
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 static heterogeneities in the population, which distinguish individual cells from each other. In collaboration with Johnjoe McFadden (Univesity of Surrey), we have recently investigated the possibility that such static heterogeneities are in fact produced by the stochastic bursting activity of gene expression, supplemented with specific mechanisms capable of slowing down fluctuations. To explain this mechanism in general terms, we have introduced in the context of bacterial growth the concept of 'ergodicity breaking', borrowed from statistical mechanics and dynamical systems theory. This has also led us to a novel explanation of the phenomenon of so-called bacterial persistence, or drug tolerance [Rocco et al, PLoS ONE (2013)]. The proposed mechanism is currently under experimental validation.
Memory and noise in Open Quantum Systems
In my group we are also investigating the effect that stochastic fluctuations may have on the reduced dynamics of a quantum system. Fluctuations in the environment of the system, as well as intrinsic fluctuations, may break the time-scale separation between system of interest and thermal bath, which is at the basis of the derivation of Markovian (memory-less) reduced quantum-mechanical descriptions. When memory is present, the resulting quantum master equations for the reduced density operator are not expected to satisfy the celebrated Lindblad form, and can show non-trivial dynamics. In particular we are interested in analyzing the effect of correlated noise on the continuum measurement process exerted by the environment on the system of interest, and in turn on its decoherence times. We also aim to investigate the possible relevance of these processes in a biological context.
In the past, I have been involved in the study of branching of gas discharges (so-called streamers), and in 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 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 contributed to identifying 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 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)].
A role for Wnt signaling in melanocyte specification from neural crest is conserved across vertebrates, but possible ongoing roles in melanocyte differentiation have received little attention. Using a systems biology approach to investigate the gene regulatory network underlying stable melanocyte differentiation in zebrafish highlighted a requirement for a positive feedback loop involving the melanocyte master regulator Mitfa. Here we test the hypothesis that Wnt signaling contributes to that positive feedback. We show firstly that Wnt signaling remains active in differentiating melanocytes and secondly that enhanced Wnt signaling drives elevated transcription of mitfa. We show that chemical activation of the Wnt signaling pathway at early stages of melanocyte development enhances melanocyte specification as expected, but importantly that at later (differentiation) stages it results in altered melanocyte morphology, although melanisation is not obviously affected. Downregulation of Wnt signaling also results in altered melanocyte morphology and organisation. We conclude that Wnt signaling plays a role in regulating ongoing aspects of melanocyte differentiation in zebrafish.
One of the most challenging problems in microbiology is to understand how a small fraction of microbes that resists killing by antibiotics can emerge in a population of genetically identical cells, the phenomenon known as persistence or drug tolerance. Its characteristic signature is the biphasic kill curve, whereby microbes exposed to a bactericidal agent are initially killed very rapidly but then much more slowly. Here we relate this problem to the more general problem of understanding the emergence of distinct growth phenotypes in clonal populations. We address the problem mathematically by adopting the framework of the phenomenon of so-called weak ergodicity breaking, well known in dynamical physical systems, which we extend to the biological context. We show analytically and by direct stochastic simulations that distinct growth phenotypes can emerge as a consequence of slow-down of stochastic fluctuations in the expression of a gene controlling growth rate. In the regime of fast gene transcription, the system is ergodic, the growth rate distribution is unimodal, and accounts for one phenotype only. In contrast, at slow transcription and fast translation, weakly non-ergodic components emerge, the population distribution of growth rates becomes bimodal, and two distinct growth phenotypes are identified. When coupled to the well-established growth rate dependence of antibiotic killing, this model describes the observed fast and slow killing phases, and reproduces much of the phenomenology of bacterial persistence. The model has major implications for efforts to develop control strategies for persistent infections.
The mechanisms generating stably differentiated cell-types from multipotent precursors are key to understanding normal development and have implications for treatment of cancer and the therapeutic use of stem cells. Pigment cells are a major derivative of neural crest stem cells and a key model cell-type for our understanding of the genetics of cell differentiation. Several factors driving melanocyte fate specification have been identified, including the transcription factor and master regulator of melanocyte development, Mitf, and Wnt signalling and the multipotency and fate specification factor, Sox10, which drive mitf expression. While these factors together drive multipotent neural crest cells to become specified melanoblasts, the mechanisms stabilising melanocyte differentiation remain unclear. Furthermore, there is controversy over whether Sox10 has an ongoing role in melanocyte differentiation. Here we use zebrafish to explore in vivo the gene regulatory network (GRN) underlying melanocyte specification and differentiation. We use an iterative process of mathematical modelling and experimental observation to explore methodically the core melanocyte GRN we have defined. We show that Sox10 is not required for ongoing differentiation and expression is downregulated in differentiating cells, in response to Mitfa and Hdac1. Unexpectedly, we find that Sox10 represses Mitf-dependent expression of melanocyte differentiation genes. Our systems biology approach allowed us to predict two novel features of the melanocyte GRN, which we then validate experimentally. Specifically, we show that maintenance of mitfa expression is Mitfa-dependent, and identify Sox9b as providing an Mitfa-independent input to melanocyte differentiation. Our data supports our previous suggestion that Sox10 only functions transiently in regulation of mitfa and cannot be responsible for long-term maintenance of mitfa expression; indeed, Sox10 is likely to slow melanocyte differentiation in the zebrafish embryo. More generally, this novel approach to understanding melanocyte differentiation provides a basis for systematic modelling of differentiation in this and other cell-types.
Sequence alignment underpins all of comparative genomics, yet it remains an incompletely solved problem. In particular, the statistical uncertainty within inferred alignments is often disregarded, while parametric or phylogenetic inferences are considered meaningless without confidence estimates. Here, we report on a theoretical and simulation study of pairwise alignments of genomic DNA at human–mouse divergence. We find that >15% of aligned bases are incorrect in existing whole-genome alignments, and we identify three types of alignment error, each leading to systematic biases in all algorithms considered. Careful modeling of the evolutionary process improves alignment quality; however, these improvements are modest compared with the remaining alignment errors, even with exact knowledge of the evolutionary model, emphasizing the need for statistical approaches to account for uncertainty. We develop a new algorithm, Marginalized Posterior Decoding (MPD), which explicitly accounts for uncertainties, is less biased and more accurate than other algorithms we consider, and reduces the proportion of misaligned bases by a third compared with the best existing algorithm. To our knowledge, this is the first nonheuristic algorithm for DNA sequence alignment to show robust improvements over the classic Needleman–Wunsch algorithm. Despite this, considerable uncertainty remains even in the improved alignments. We conclude that a probabilistic treatment is essential, both to improve alignment quality and to quantify the remaining uncertainty. This is becoming increasingly relevant with the growing appreciation of the importance of noncoding DNA, whose study relies heavily on alignments. Alignment errors are inevitable, and should be considered when drawing conclusions from alignments. Software and alignments to assist researchers in doing this are provided at http://genserv.anat.ox.ac.uk/grape/.
Spontaneous branching of discharge channels is frequently observed, but not well understood. We recently proposed a new branching mechanism based on simulations of a simple continuous discharge model in high fields. We here present analytical results for such streamers in the Lozansky-Firsov limit where they can be modeled as moving equipotential ionization fronts. This model can be analyzed by conformal mapping techniques which allow the reduction of the dynamical problem to finite sets of nonlinear ordinary differential equations. Our solutions illustrate that branching is generic for the intricate head dynamics of streamers in the Lozansky-Firsov limit.
We have recently shown that a negative streamer in a sufficiently high homogeneous field can branch spontaneously due to a Laplacian instability, rather than approach a stationary mode of propagation with fixed radius. In our previous simulations, the streamer started from a wide initial ionization seed on the cathode. We here demonstrate, in improved simulations, that a streamer emerging from a single electron branches in the same way. In fact, though the evolving streamer is much more narrow, it branches after an even shorter propagation distance.
We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.
It has recently been proposed that fluctuating “pulled” fronts propagating into an unstable state should not be in the standard Kardar-Parisi-Zhang (KPZ) universality class for rough interface growth. We introduce an effective field equation for this class of problems, and show on the basis of it that noisy pulled fronts in d 1 1 bulk dimensions should be in the universality class of the d 1 1 1 1 D KPZ equation rather than of the d 1 1 D KPZ equation. Our scenario ties together a number of heretofore unexplained observations in the literature, and is supported by previous numerical results.
We study the propagation of a “pulled” front with multiplicative noise that is created by a local perturbation of an unstable state. Unlike a front propagating into a metastable state, where a separation of time scales for sufficiently large t creates a diffusive wandering of the front position about its mean, we predict that for so-called pulled fronts, the fluctuations are subdiffusive with root mean square wandering Δ(t)∼t1/4, not t1/2. The subdiffusive behavior is confirmed by numerical simulations: For t<~600, these yield an effective exponent slightly larger than 1/4.
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