Publications

2024

1. 

   DNA replication timing reveals genome-wide features of transcription and fragility

   Francisco Berkemeier, Peter Richard Cook, and Michael A Boemo

   bioRxiv, 2024

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   DNA replication in humans requires precise regulation to ensure accurate genome duplication and maintain genome integrity. A key indicator of this regulation is replication timing, which reflects the interplay between origin firing and fork dynamics. We present a high-resolution (1-kilobase) mathematical model that maps firing rate distributions to replication timing profiles across various cell lines, validated using Repli-seq data. The model effectively captures genome-wide replication patterns while identifying local discrepancies. Notably, regions where the model and data diverge often overlap with fragile sites and long genes, highlighting the influence of genomic architecture on replication dynamics. Conversely, regions of high concordance are associated with open chromatin and active promoters, where elevated firing rates facilitate timely fork progression and reduce replication stress. By establishing these correlations, our model provides a valuable framework for exploring the structural interplay between replication timing, transcription, and chromatin organisation, offering new insights into mechanisms underlying replication stress and its implications for genome stability and disease.

   @article{berkemeier2024dna,
     title = {DNA replication timing reveals genome-wide features of transcription and fragility},
     author = {Berkemeier, Francisco and Cook, Peter Richard and Boemo, Michael A},
     journal = {bioRxiv},
     pages = {2024--11},
     year = {2024},
     publisher = {Cold Spring Harbor Laboratory},
     url = {https://www.biorxiv.org/content/10.1101/2024.11.25.625090v2},
   }

2. 

   Regulation of replication timing in Saccharomyces cerevisiae

   Rosie Berners-Lee, Eamonn Gilmore, Francisco Berkemeier, and Michael A Boemo

   bioRxiv, 2024

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   In order to maintain genomic integrity, DNA replication must be highly coordinated. Disruptions in this process can cause replication stress which is aberrant in many pathologies including cancer. Despite this, little is known about the mechanisms governing the temporal regulation of DNA replication initiation, thought to be related to the limited copy number of firing factors. Here, we present a high (1-kilobase) resolution stochastic model of Saccharomyces cerevisiae whole-genome replication in which origins compete to associate with limited firing factors. After developing an algorithm to fit this model to replication timing data, we validated the model by reproducing experimental inter-origin distances, origin efficiencies, and replication fork directionality. This suggests the model accurately simulates the aspects of DNA replication most important for determining its dynamics. We also use the model to predict measures of DNA replication dynamics which are yet to be determined experimentally and investigate the potential impacts of variations in firing factor concentrations on DNA replication.

   @article{berners2024regulation,
     title = {Regulation of replication timing in Saccharomyces cerevisiae},
     author = {Berners-Lee, Rosie and Gilmore, Eamonn and Berkemeier, Francisco and Boemo, Michael A},
     journal = {bioRxiv},
     pages = {2024--10},
     year = {2024},
     publisher = {Cold Spring Harbor Laboratory},
     url = {https://www.biorxiv.org/content/10.1101/2024.10.11.617780v1.abstract},
   }

2023

1. 

   Coupling dynamics of 2D Notch-Delta signalling

   Francisco Berkemeier, and Karen M Page

   Mathematical Biosciences, 2023

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   Understanding pattern formation driven by cell-cell interactions has been a significant theme in cellular biology for many years. In particular, due to their implications within many biological contexts, lateral-inhibition mechanisms present in the Notch-Delta signalling pathway led to an extensive discussion between biologists and mathematicians. Deterministic and stochastic models have been developed as a consequence of this discussion, some of which address long-range signalling by considering cell protrusions reaching non-neighbouring cells. The dynamics of such signalling systems reveal intricate properties of the coupling terms involved in these models. In this work, we investigate the advantages and drawbacks of a single-parameter long-range signalling model across diverse scenarios. By employing linear and multi-scale analyses, we discover that pattern selection is not only partially explained but also depends on nonlinear effects that extend beyond the scope of these analytical techniques.

   @article{berkemeier2023coupling,
     title = {Coupling dynamics of 2D Notch-Delta signalling},
     author = {Berkemeier, Francisco and Page, Karen M},
     journal = {Mathematical Biosciences},
     volume = {360},
     pages = {109012},
     year = {2023},
     publisher = {Elsevier},
     url = {https://www.sciencedirect.com/science/article/pii/S0025556423000536},
   }

2. 

   Unifying evolutionary dynamics: a set theory exploration of symmetry and interaction

   Francisco Berkemeier, and Karen M Page

   bioRxiv, 2023

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   Within the expansive landscape of evolutionary dynamics, symmetry features embedded in well-established models significantly influence the interpretation of individual interaction patterns. Such symmetries are determined through interaction kernel functions, which serve as mathematical models for characterizing the complexity of interactions between individuals, each with distinct phenotypes. By incorporating analytical tools from logic and set theory, we aim to provide a deeper understanding of these functions, relevant to mechanisms of evolution. We prove that the kernels introduced in Champagnat et al.’s unifying framework exist provided birth and death rates are symmetric with respect to non-focal traits. The kernels may nevertheless be highly challenging to construct, thereby indicating a complex underlying mathematical infrastructure within unified evolutionary dynamics. We show how interaction kernels for asymmetric frameworks arising in evolutionary graph theory can be derived by incorporating individuals’ graph labels into their phenotypes. These insights invite new avenues for research, providing a fresh understanding of the interactions between individuals in broader biological contexts.

   @article{berkemeier2023unifying,
     title = {Unifying evolutionary dynamics: a set theory exploration of symmetry and interaction},
     author = {Berkemeier, Francisco and Page, Karen M},
     journal = {bioRxiv},
     pages = {2023--09},
     year = {2023},
     publisher = {Cold Spring Harbor Laboratory},
     url = {https://www.biorxiv.org/content/10.1101/2023.09.27.559729v1.abstract},
   }

2022

1. 

   Cell-cell interactions in epithelial patterning: Notch-Delta signalling and evolutionary dynamics

   Francisco Pinto Berkemeier

   UCL (University College London). PhD Thesis , 2022

   Abs Bib WEB PDF

   Understanding pattern formation driven by cell-cell interactions has been a significant theme in cellular biology for many years. In particular, due to its implications on many biological contexts, lateral-inhibition mechanisms present in the Notch-Delta signalling pathway led to an extensive discussion between biologists and mathematicians. Deterministic and stochastic models have been developed as a consequence of this discussion, some of which address long-range signalling by considering cell protrusions reaching non-neighbouring cells. The dynamics of such signalling systems reveal intricate properties of the coupling terms involved in these models. In the broader context of evolutionary dynamics, signalling and patterning contribute to the definition of phenotypes of individuals within an interacting population, whose mathematical description has been unified under various conceptual frameworks. In this thesis, we examine the benefits and limitations of new and existing models of cell signalling and differentiation in a variety of contexts, including applications in general and well-studied patterning tissues in Drosophila melanogaster. Using linear and weakly nonlinear stability analyses, we find that pattern selection relies on nonlinear effects that are not covered by such analytical methods. The direct application of such models on the Drosophila wing disc development and patterning of sensory organ precursor cells further shows the patterning reliance on long-range signalling dynamics and the tissue’s mechanical properties. We also develop a theoretical framework to understand the restrictions of abstract models of evolutionary dynamics and interacting species, including a Notch-Delta application. Using a set theory argument, we find that symmetry with respect to non-focal traits is an intrinsic requirement in well-established evolutionary models.

   @phdthesis{berkemeier2022cell,
     title = {Cell-cell interactions in epithelial patterning: Notch-Delta signalling and evolutionary dynamics},
     author = {Berkemeier, Francisco Pinto},
     year = {2022},
     school = {UCL (University College London)},
     url = {https://discovery.ucl.ac.uk/id/eprint/10158781/},
   }

2019

1. 

   A Priori Regularity of Parabolic Partial Differential Equations

   Francisco Berkemeier, and Diogo A Gomes

   In New Trends in Analysis and Geometry, 2019

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   We consider parabolic partial differential equations and develop methods that provide a priori estimates for solutions with singular initial data. These estimates are obtained by understanding the time decay of norms of solutions. First, we derive regularity results for the Fokker-Planck equation by estimating the decay of Lebesgue norms. These estimates depend on integral bounds for the advection and diffusion. Then, we apply similar methods to the heat equation. Finally, we conclude by extending our techniques to the porous media equation. The sharpness of our results is confirmed by examining known solutions of these equations. Our main contribution is the use of functional inequalities to establish the decay of norms through nonlinear differential inequalities. These are then combined with ODE methods to deduce estimates for the norms of solutions and their derivatives.

   @incollection{berkemeier2019priori,
     title = {A Priori Regularity of Parabolic Partial Differential Equations},
     author = {Berkemeier, Francisco and Gomes, Diogo A},
     booktitle = {New Trends in Analysis and Geometry},
     year = {2019},
     publisher = {Cambridge Scholars Publishing},
     url = {https://books.google.co.uk/books?hl=en&lr=&id=Q2DNDwAAQBAJ&oi=fnd&pg=PA17&ots=VyUnv-8m1J&sig=pf5WCG7Ch1QEKW0YUXSeYq6g5T0&redir_esc=y#v=onepage&q&f=false},
   }