publications

2024

1. Exploring the benefits of DNA-target search with antenna

   Lucas Hedström ,  and  Ludvig Lizana

   arXiv.2311.11727, 2024

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   The most common gene regulation mechanism is when a protein binds to a regulatory sequence to change RNA transcription. However, these sequences are short relative to the genome length, so finding them poses a challenging search problem. This paper presents two mathematical frameworks capturing different aspects of this problem. First, we study the interplay between diffusional flux through a target where the searching proteins get sequestered on DNA far from the target because of non-specific interactions. From this model, we derive a simple formula for the optimal protein-DNA unbinding rate, maximizing the particle flux. Second, we study how the flux flows through a target on a single antenna with variable length. Here, we identify a non-trivial logarithmic correction to the linear behavior relative to the target size proposed by Smoluchowski’s flux formula.

2. The scales, mechanisms, and dynamics of the genome architecture

   Ludvig Lizana ,  and  Yuri B. Schwartz

   Science Advances, 2024

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   Even when split into several chromosomes, DNA molecules that make up our genome are too long to fit into the cell nuclei unless massively folded. Such folding must accommodate the need for timely access to selected parts of the genome by transcription factors, RNA polymerases, and DNA replication machinery. Here we review our current understanding of the genome folding inside the interphase nuclei. We consider the resulting genome architecture at three scales and summarize the insights gained from recent experimental observations and diverse computational models.

3. Enhancer-Insulator Pairing Reveals Heterogeneous Dynamics in Long-Distance 3D Gene Regulation

   Lucas Hedström ,  Ralf Metzler ,  and  Ludvig Lizana

   PRX life, 2024

   arXiv

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   Cells regulate fates and complex body plans using spatiotemporal signaling cascades that al- ter gene expression. Enhancers, short DNA sequences (50-150 base pairs), help coordinate these cascades by attracting regulatory proteins to enhance the transcription of distal genes by bind- ing to promoters. In humans, there are hundreds of thousands of enhancers dispersed across the genome, which poses a challenging coordination task to prevent unintended gene activation. To mit- igate this problem, the genome contains additional DNA elements, insulators, that block enhancer- promoter interactions. However, there is an open problem with how the insulation works, especially as enhancer-insulator pairs may be separated by millions of base pairs. Based on recent empirical data from Hi-C experiments, this paper proposes a new mechanism that challenges the common paradigm that rests on specific insulator-insulator interactions. Instead, this paper introduces a stochastic looping model where enhancers bind weakly to surrounding chromatin. After calibrating the model to experimental data, we use simulations to study the broad distribution of hitting times between an enhancer and a promter when there are blocking insulators. In some cases, there is a large difference between average and most probable hitting times, making it difficult to assign a typical time scale, hinting at highly defocused regulation times. We also map our computational model onto a resetting problem that allows us to derive several analytical results. Besides offering new insights into enhancer-insulator interactions, our paper advances the understanding of gene regulatory networks and causal connections between genome folding and gene activation.

4. Identifying stable communities in Hi-C using multifractal network modularity

   Lucas Hedström ,  Antón Carcedo Martínez ,  and  Ludvig Lizana

   arXiv:2405.05425, 2024

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   Chromosome capture techniques like Hi-C have expanded our understanding of mammalian genome 3D architecture and how it influences gene activity. To analyze Hi-C data sets, researchers increasingly treat them as DNA-contact networks and use standard community detection techniques to identify mesoscale 3D communities. However, there are considerable challenges in finding significant communities because the Hi-C networks have cross-scale interactions and are almost fully connected. This paper presents a pipeline to distill 3D communities that remain intact under experimental noise. To this end, we bootstrap an ensemble of Hi-C datasets representing noisy data and extract 3D communities that we compare with the unperturbed dataset. Notably, we extract the communities by maximizing local modularity (using the Generalized Louvain method), which considers the multifractal spectrum recently discovered in Hi-C maps. Our pipeline finds that stable communities (under noise) typically have above-average internal contact frequencies and tend to be enriched in active chromatin marks. We also find they fold into more nested cross-scale hierarchies than less stable ones. Apart from presenting how to systematically extract robust communities in Hi-C data, our paper offers new ways to generate null models that take advantage of the network’s multifractal properties. We anticipate this has a broad applicability to several network applications.

5. Target search on networks-within-networks with applications to protein-DNA interactions

   Lucas Hedström ,  Seong-Gyu Yang ,  and  Ludvig Lizana

   arXiv preprint arXiv:2411.02660, 2024

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   We present a novel framework for understanding node target search in systems organized as hierarchical networks-within-networks. Our work generalizes traditional search models on complex networks, where the mean-first passage time is typically inversely proportional to the node degree. However, real-world search processes often span multiple network layers, such as moving from an external environment into a local network, and then navigating several internal states. This multilayered complexity appears in scenarios such as international travel networks, tracking email spammers, and the dynamics of protein-DNA interactions in cells. Our theory addresses these complex systems by modeling them as a three-layer multiplex network: an external source layer, an intermediate spatial layer, and an internal state layer. We derive general closed-form solutions for the steady-state flux through a target node, which serves as a proxy for inverse mean-first passage time. Our results reveal a universal relationship between search efficiency and network-specific parameters. This work extends the current understanding of multiplex networks by focusing on systems with hierarchically connected layers. Our findings have broad implications for fields ranging from epidemiology to cellular biology and provide a more comprehensive understanding of search dynamics in complex, multilayered environments.

2023

1. Polycomb proteins translate histone methylation to chromatin folding

   Ludvig Lizana ,  Negar Nahali ,  and  Yuri B Schwartz

   Journal of Biological Chemistry, 2023

   bioRxiv

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   Epigenetic repression often involves covalent histone modifications. Yet, how the presence of a histone mark translates into changes in chromatin structure that ultimately benefits the repression is largely unclear. Polycomb group proteins comprise a family of evolutionarily conserved epigenetic repressors. They act as multi-subunit complexes one of which tri-methylates histone H3 at Lysine 27 (H3K27). Here we describe a novel Monte Carlo–Molecular Dynamics simulation framework, which we employed to discover that stochastic interaction of Polycomb Repressive Complex 1 (PRC1) with tri-methylated H3K27 is sufficient to fold the methylated chromatin. Unexpectedly, such chromatin folding leads to spatial clustering of the DNA elements bound by PRC1. Our results provide further insight into mechanisms of epigenetic repression and the process of chromatin folding in response to histone methylation.

2. Mapping the semi-nested community structure of 3D chromosome contact networks

   Dolores Bernenko ,  Sang Hoon Lee ,  Per Stenberg , and 1 more author

   PLOS Computational Biology, 2023

   bioRxiv

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   Mammalian DNA folds into 3D structures that facilitate and regulate genetic processes such as transcription, DNA repair, and epigenetics. Several insights derive from chromosome capture methods, such as Hi-C, which allow researchers to construct contact maps depicting 3D interactions among all DNA segment pairs. These maps show a complex cross-scale organization spanning megabase-pair compartments to short-ranged DNA loops. To better understand the organizing principles, several groups analyzed Hi-C data assuming a Russian-doll-like nested hierarchy where DNA regions of similar sizes merge into larger and larger structures. Apart from being a simple and appealing description, this model explains, e.g., the omnipresent chequerboard pattern seen in Hi-C maps, known as A/B compartments, and foreshadows the co-localization of some functionally similar DNA regions. However, while successful, this model is incompatible with the two competing mechanisms that seem to shape a significant part of the chromosomes’ 3D organization: loop extrusion and phase separation. This paper aims to map out the chromosome’s actual folding hierarchy from empirical data. To this end, we take advantage of Hi-C experiments and treat the measured DNA-DNA interactions as a weighted network. From such a network, we extract 3D communities using the generalized Louvain algorithm. This algorithm has a resolution parameter that allows us to scan seamlessly through the community size spectrum, from A/B compartments to topologically associated domains (TADs). By constructing a hierarchical tree connecting these communities, we find that chromosomes are more complex than a perfect hierarchy. Analyzing how communities nest relative to a simple folding model, we found that chromosomes exhibit a significant portion of nested and non-nested community pairs alongside considerable randomness. In addition, by examining nesting and chromatin types, we discovered that nested parts are often associated with active chromatin. These results highlight that cross-scale relationships will be essential components in models aiming to reach a deep understanding of the causal mechanisms of chromosome folding.

3. Modelling chromosome-wide target search

   Lucas Hedström ,  and  Ludvig Lizana

   New Journal of Physics, 2023

   arXiv

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   The most common gene regulation mechanism is when a transcription factor (TF) protein binds to a regulatory sequence to increase or decrease RNA transcription. However, TFs face two main challenges when searching for these sequences. First, the sequences are vanishingly short relative to the genome length. Second, there are many nearly identical sequences scattered across the genome, causing proteins to suspend the search. But as pointed out in a computational study of LacI regulation in Escherichia coli, such almost-targets may lower search times if considering DNA looping. In this paper, we explore if this also occurs over chromosome-wide distances. To this end, we developed a cross-scale computational framework that combines established facilitated-diffusion models for basepair-level search and a network model capturing chromosome-wide leaps. To make our model realistic, we used Hi-C data sets as a proxy for 3D proximity between long-ranged DNA segments and binding profiles for more than 100 TFs. Using our cross-scale model, we found that median search times to individual targets critically depend on a network metric combining node strength (sum of link weights) and local dissociation rates. Also, by randomizing these rates, we found that some actual 3D target configurations stand out as considerably faster or slower than their random counterparts. This finding hints that chromosomes’ 3D structure funnels essential TFs to relevant DNA regions.

4. Mapping robust multiscale communities in chromosome contact networks

   Anton Holmgren ,  Dolores Bernenko ,  and  Ludvig Lizana

   Scientific Reports, 2023

   arXiv

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   To better understand DNA’s 3D folding in cell nuclei, researchers developed chromosome capture methods such as Hi-C that measure the contact frequencies between all DNA segment pairs across the genome. As Hi-C data sets often are massive, it is common to use bioinformatics methods to group DNA segments into 3D regions with correlated contact patterns, such as Topologically associated domains and A/B compartments. Recently, another research direction emerged that treats the Hi-C data as a network of 3D contacts. In this representation, one can use community detection algorithms from complex network theory that group nodes into tightly connected mesoscale communities. However, because Hi-C networks are so densely connected, several node partitions may represent feasible solutions to the community detection problem but are indistinguishable unless including other data. Because this limitation is a fundamental property of the network, this problem persists regardless of the community-finding or data-clustering method. To help remedy this problem, we developed a method that charts the solution landscape of network partitions in Hi-C data from human cells. Our approach allows us to scan seamlessly through the scales of the network and determine regimes where we can expect reliable community structures. We find that some scales are more robust than others and that strong clusters may differ significantly. Our work highlights that finding a robust community structure hinges on thoughtful algorithm design or method cross-evaluation.

5. Exploring 3D community inconsistency in human chromosome contact networks

   Dolores Bernenko ,  Sang Hoon Lee ,  and  Ludvig Lizana

   Journal of Physics: Complexity, 2023

   arXiv

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   Researchers have developed chromosome capture methods such as Hi-C to better understand DNA’s 3D folding in nuclei. The Hi-C method captures contact frequencies between DNA segment pairs across the genome. When analyzing Hi-C data sets, it is common to group these pairs using standard bioinformatics methods (e.g. PCA). Other approaches handle Hi-C data as weighted networks, where connected node pairs represent DNA segments in 3D proximity. In this representation, one can leverage community detection techniques developed in complex network theory to group nodes into mesoscale communities containing nodes with similar connection patterns. While there are several successful attempts to analyze Hi-C data in this way, it is common to report and study the most typical community structure. But in reality, there are often several valid candidates. Therefore, depending on algorithm design, different community detection methods focusing on slightly different connectivity features may have differing views on the ideal node groupings. In fact, even the same community detection method may yield different results if using a stochastic algorithm. This ambiguity is fundamental to community detection and shared by most complex networks whenever interactions span all scales in the network. This is known as community inconsistency. This paper explores this inconsistency of 3D communities in Hi-C data for all human chromosomes. We base our analysis on two inconsistency metrics, one local and one global, and quantify the network scales where the community separation is most variable. For example, we find that TADs are less reliable than A/B compartments and that nodes with highly variable node-community memberships are associated with open chromatin. Overall, our study provides a helpful framework for data-driven researchers and increases awareness of some inherent challenges when clustering Hi-C data into 3D communities.

6. Forecasting histone methylation by Polycomb complexes with minute-scale precision

   Moa J. Lundkvist ,  Ludvig Lizana ,  and  Yuri B. Schwartz

   Science Advances, 2023

   bioRxiv

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   Animals use the Polycomb system to epigenetically repress developmental genes. The repression requires trimethylation of lysine 27 of histone H3 (H3K27me3) by Polycomb Repressive Complex 2 (PRC2), but the dynamics of this process is poorly understood. To bridge the gap, we developed a computational model that forecasts H3K27 methylation in Drosophila with high temporal resolution and spatial accuracy of contemporary experimental techniques. Using this model, we show that pools of methylated H3K27 in dividing cells are defined by the effective concentration of PRC2 and the replication frequency. We find that the allosteric stimulation by preexisting H3K27me3 makes PRC2 better in methylating developmental genes as opposed to indiscriminate methylation throughout the genome. Applied to Drosophila development, our model argues that, in this organism, the intergenerationally inherited H3K27me3 does not “survive” rapid cycles of embryonic chromatin replication and is unlikely to transmit the memory of epigenetic repression to the offspring. Our model is adaptable to other organisms, including mice and humans. Computational forecasts of histone methylation shed light on the intergenerational inheritance of epigenetic repression.

2022

1. Fractal and knot-free chromosomes facilitate nucleoplasmic transport

   Yeonghoon Kim ,  Ludvig Lizana ,  and  Jae-Hyung Jeon

   Physical Review Letters, 2022

   arXiv

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   Chromosomes in the nucleus assemble into hierarchies of 3D domains that, during interphase, share essential features with a knot-free condensed polymer known as the fractal globule (FG). The FG-like chromosome likely affects macromolecular transport, yet its characteristics remain poorly understood. Using computer simulations and scaling analysis, we show that the 3D folding and macromolecular size of the chromosomes determine their transport characteristics. Large-scale subdiffusion occurs at a critical particle size where the network of accessible volumes is critically connected. Condensed chromosomes have connectivity networks akin to simple Bernoulli bond percolation clusters, regardless of the polymer models. However, even if the network structures are similar, the tracer’s walk dimension varies. It turns out that the walk dimension depends on the network topology of the accessible volume and dynamic heterogeneity of the tracer’s hopping rate. We find that the FG structure has a smaller walk dimension than other random geometries, suggesting that the FG-like chromosome structure accelerates macromolecular diffusion and target-search.

2021

1. Modeling protein target search in human chromosomes

   Markus Nyberg ,  Tobias Ambjörnsson ,  Per Stenberg , and 1 more author

   Physical Review Research, 2021

   arXiv

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   Several processes in the cell, such as gene regulation, start when key proteins recognize and bind to short DNA sequences. However, as these sequences can be hundreds of million times shorter than the genome, they are hard to find by simple diffusion: diffusion-limited association rates may underestimate in vitro measurements up to several orders of magnitude. Moreover, the rates increase if the DNA is coiled rather than straight. Here we model how this works in vivo in mammalian cells. We use chromatin-chromatin contact data from Hi-C experiments to map the protein target-search onto a network problem. The nodes represent DNA segments and the weight of the links are proportional to measured contact probabilities. We then put forward a diffusion-reaction equation for the density of searching protein that allows us to calculate the association rates across the genome analytically. For segments where the rates are high, we find that they are enriched with active gene starts and have high RNA expression levels. This paper suggests that the DNA’s 3D conformation is important for protein search times in vivo and offers a method to interpret protein-binding profiles in eukaryotes that cannot be explained by the DNA sequence itself.

2019

1. Mapping the spectrum of 3D communities in human chromosome conformation capture data

   Sang Hoon Lee ,  Yeonghoon Kim ,  Sungmin Lee , and 4 more authors

   Scientific reports, 2019
2. Genomic 3D compartments emerge from unfolding mitotic chromosomes

   Rajendra Kumar ,  Ludvig Lizana ,  and  Per Stenberg

   Chromosoma, 2019
3. Highly interacting regions of the human genome are enriched with enhancers and bound by DNA repair proteins

   Haitham Sobhy ,  Rajendra Kumar ,  Jacob Lewerentz , and 2 more authors

   Scientific reports, 2019
4. First-passage statistics under stochastic resetting in bounded domains

   Xavier Durang ,  Sungmin Lee ,  Ludvig Lizana , and 1 more author

   Journal of Physics A: Mathematical and Theoretical, 2019

2018

1. Zero-crossing statistics for non-Markovian time series

   Markus Nyberg ,  Ludvig Lizana ,  and  Tobias Ambjörnsson

   Physical Review E, 2018
2. Persistence of non-Markovian Gaussian stationary processes in discrete time

   Markus Nyberg ,  and  Ludvig Lizana

   Physical Review E, 2018

2017

1. Smoluchowski rate for diffusion-controlled reactions of molecules with antenna

   Oleg A Vasilyev ,  Ludvig Lizana ,  and  Gleb Oshanin

   Journal of Physics A: Mathematical and Theoretical, 2017
2. Genome contact map explorer: a platform for the comparison, interactive visualization and analysis of genome contact maps

   Rajendra Kumar ,  Haitham Sobhy ,  Per Stenberg , and 1 more author

   Nucleic acids research, 2017

2016

1. A simple method to calculate first-passage time densities with arbitrary initial conditions

   Markus Nyberg ,  Tobias Ambjörnsson ,  and  Ludvig Lizana

   New Journal of Physics, 2016
2. Tracer particles in two-dimensional elastic networks diffuse logarithmically slow

   Ludvig Lizana ,  Tobias Ambjörnsson ,  and  Michael A Lomholt

   Journal of Physics A: Mathematical and Theoretical, 2016

2015

1. Many-body effects on tracer particle diffusion with applications for single-protein dynamics on DNA

   Sebastian Ahlberg ,  Tobias Ambjörnsson ,  and  Ludvig Lizana

   New Journal of Physics, 2015

2014

1. Single-file diffusion with non-thermal initial conditions

   Ludvig Lizana ,  Michael A Lomholt ,  and  Tobias Ambjörnsson

   Physica A: Statistical Mechanics and its Applications, 2014
2. Exact expressions for the mobility and electrophoretic mobility of a weakly charged sphere in a simple electrolyte

   Ludvig Lizana ,  and  Alexander Y Grosberg

   Europhysics Letters, 2014
3. Dynamics of interacting information waves in networks

   Atieh Mirshahvalad ,  Alcides Viamontes Esquivel ,  Ludvig Lizana , and 1 more author

   Physical Review E, 2014
4. Non-Markovian effects in the first-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems

   Robin Forsling ,  Lloyd P Sanders ,  Tobias Ambjörnsson , and 1 more author

   The Journal of Chemical Physics, 2014
5. Severe slowing-down and universality of the dynamics in disordered interacting many-body systems: ageing and ultraslow diffusion

   Lloyd P Sanders ,  Michael A Lomholt ,  Ludvig Lizana , and 3 more authors

   New Journal of Physics, 2014
6. Ageing single file motion

   Ralf Metzler ,  Lloyd Sanders ,  Michael Andersen Lomholt , and 3 more authors

   The European Physical Journal Special Topics, 2014
7. First-passage dynamics of obstructed tracer particle diffusion in one-dimensional systems

   Robin Forsling ,  Lloyd Sanders ,  Tobias Ambjörnsson , and 1 more author

   arXiv preprint arXiv:1401.2933, 2014

2013

1. Quality control system response to stochastic growth of amyloid fibrils

   Simone Pigolotti ,  Ludvig Lizana ,  Daniel Otzen , and 1 more author

   FEBS letters, 2013
2. Effects of city-size heterogeneity on epidemic spreading in a metapopulation: a reaction-diffusion approach

   Halvor Lund ,  Ludvig Lizana ,  and  Ingve Simonsen

   Journal of statistical physics, 2013
3. Microscopic origin of the logarithmic time evolution of aging processes in complex systems

   Michael A Lomholt ,  Ludvig Lizana ,  Ralf Metzler , and 1 more author

   Physical review letters, 2013

2011

1. Dissimilar bouncy walkers

   Michael A Lomholt ,  Ludvig Lizana ,  and  Tobias Ambjörnsson

   The Journal of chemical physics, 2011
2. Modeling the spatial dynamics of culture spreading in the presence of cultural strongholds

   Ludvig Lizana ,  Namiko Mitarai ,  Kim Sneppen , and 1 more author

   Physical Review E, 2011
3. Structural correlations in bacterial metabolic networks

   Sebastian Bernhardsson ,  Philip Gerlee ,  and  Ludvig Lizana

   BMC evolutionary biology, 2011

2010

1. Structural correlations in bacterial metabolic networks

   P Gerlee ,  S Bernhardsson ,  L Lizana , and 1 more author

   In FEBS JOURNAL , 2010