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Stochastic Biophysics of Cellular Radiosensitivity: From Molecular Noise and Repair Kinetics to Evolutionary Demographics

Radiation-induced DNA double-strand breaks (DSBs) drive cellular mortality, mutagenesis, and severe evolutionary bottlenecks. While classical phenomenological models, such as the Linear-Quadratic (LQ) framework, reliably predict macroscopic population survival, they obscure the intrinsic single-cell stochasticity that governs critical rare events like tumor recurrence or the emergence of radioresistant persisters. To bridge this divide, we develop a mathematically exact stochastic differential equation (SDE) framework that models continuous DSB induction and repair as a Feller square-root process. By deriving exact closed-form expressions for the foci moments, we establish a highly efficient Maximum Likelihood Estimation (MLE) pipeline that circumvents computationally exhaustive Monte Carlo simulations, allowing the direct extraction of deterministic repair velocities and intrinsic molecular noise from empirical single-cell $\gamma$-H2AX data. Integrating this kinetic model with a cumulative damage hazard via the Feynman-Kac formalism, our framework seamlessly recovers the classic macroscopic LQ survival topology from microscopic first principles. Furthermore, systematic sensitivity analysis uncovers a fundamental evolutionary duality: while initial physical damage operates additively, ultimate cellular fate is driven by a nonlinear survival response governed by the trade-off between the damage hazard rate and intrinsic molecular noise strength. Crucially, we demonstrate that this molecular noise inherently enhances population survival. Governed by Jensen's inequality, stochastic variance acts as a non-genetic bet-hedging mechanism that buffers the population by favoring cells with transiently low damage loads. Ultimately, this exact stochastic framework bridges microscopic biophysics and macroscopic demographics, offering deep mechanistic insights into the evolutionary roots of radioresistance.

biophysics

Scaling properties of evolutionary paths in a biophysical model of protein adaptation

The enormous size and complexity of genotypic sequence space frequently requires consideration of coarse-grained sequences in empirical models. We develop scaling relations to quantify the effect of this coarse-graining on properties of fitness landscapes and evolutionary paths. We first consider evolution on a simple Mount Fuji fitness landscape, focusing on how the length and predictability of evolutionary paths scale with the coarse-grained sequence length and number of alleles. We obtain simple scaling relations for both the weak- and strong-selection limits, with a non-trivial crossover regime at intermediate selection strengths. We apply these results to evolution on a biophysical fitness landscape designed to describe how proteins evolve new binding interactions while maintaining their folding stability. We combine numerical calculations for coarse-grained protein sequences with the scaling relations to obtain quantitative properties of the model for realistic binding interfaces and a full amino acid alphabet.

Evolutionary Biology

The basis of sharp spike onset in standard biophysical models

In most vertebrate neurons, spikes initiate in the axonal initial segment. When recorded in the soma, they have a surprisingly sharp onset, as if sodium (Na) channels opened abruptly. On the basis of multicompartmental models, this phenomenon has been previously attributed to the progressive sharpening of spikes as they backpropagate from the initiation site to the soma. Here we show in the same models that the biophysical basis of the phenomenon is not backpropagation but critical resistive coupling between the soma and the initial segment. Accordingly, spike initiation results from the interplay between Na current and axial resistive current flowing from axonal initiation site to soma, rather than between local Na and potassium transmembrane currents at the initiation site. The sharp onset of somatic spikes is therefore not an artifact of recording spikes at the incorrect location, but rather the signature that spike initiation does not follow the standard account.

Neuroscience

Biophysically motivated regulatory network inference: progress and prospects

Via a confluence of genomic technology and computational developments the possibility of network inference methods that automatically learn large comprehensive models of cellular regulation is closer than ever. This perspective will focus on enumerating the elements of computational strategies that, when coupled to appropriate experimental designs, can lead to accurate large-scale models of chromatin-state and transcriptional regulatory structure and dynamics. We highlight four research questions that require further investigation in order to make progress in network inference: using overall constraints on network structure like sparsity, use of informative priors and data integration to constrain individual model parameters, estimation of latent regulatory factor activity under varying cell conditions, and new methods for learning and modeling regulatory factor interactions. We conclude that methods combining advances in these four categories of required effort with new genomic technologies will result in biophysically motivated dynamic genome-wide regulatory network models for several of the best studied organisms and cell types.

Bioinformatics

Tuning the course of evolution on the biophysical fitness landscape of an RNA virus

Predicting viral evolution remains a major challenge with profound implications for public health. Viral evolutionary pathways are determined by the fitness landscape, which maps viral genotype to fitness. However, a quantitative description of the landscape and the evolutionary forces on it remain elusive. Here, we apply a biophysical fitness model based on capsid folding stability and antibody binding affinity to predict the evolutionary pathway of norovirus escaping a neutralizing antibody. The model is validated by experimental evolution in bulk culture and in a drop-based microfluidics device, the \"Evolution Chip\", which propagates millions of independent viral sub-populations. We demonstrate that along the axis of binding affinity, selection for escape variants and drift due to random mutations have the same direction. However, along folding stability, selection and drift are opposing forces whose balance is tuned by viral population size. Our results demonstrate that predictable epistatic tradeoffs shape viral evolution.

evolutionary biology

Understanding inhibitor resistance in Mps1 kinase through novel biophysical assays and structures

Monopolar spindle 1 (Mps1/TTK) is a protein kinase essential in mitotic checkpoint signalling, preventing anaphase until all chromosomes are properly attached to spindle microtubules. Mps1 has emerged as a potential target for cancer therapy, and a variety of compounds have been developed to inhibit its kinase activity. Mutations in the catalytic domain of Mps1 that give rise to inhibitor resistance, but retain catalytic activity and do not display cross-resistance to other Mps1 inhibitors, have been described. Here we characterize the interactions of two such mutants, Mps1 C604Y and C604W, which raise resistance to two closely related compounds, NMS-P715 and its derivative Cpd-5, but not to the well-characterised Mps1 inhibitor, reversine. We show that estimates of the IC50 (employing a novel specific and efficient assay that utilizes a fluorescently labelled substrate) and of the binding affinity (KD) indicate that in both mutants, Cpd-5 should be better tolerated than the closely related NMS-P715. To gain further insight, we determined the crystal structure of the Mps1 kinase mutants bound to Cpd-5 and NMS-P715, and compare the binding modes of Cpd-5, NMS-P715 and reversine. The difference in steric hindrance between Tyr/Trp604 and the trifluoromethoxy moiety of NMS-P715, the methoxy moiety of Cpd-5, and complete absence of such a group in reversine, account for differences we observe in vitro. Our analysis enforces the notion that inhibitors targeting Mps1 drug-resistant mutations can emerge as a feasible intervention strategy based on existing scaffolds, if the clinical need arises.\n\nSummary statementThe inhibition of specific Mps1 kinase inhibitors towards the wild-type protein and inhibitor-resistant mutants is explained by a novel specific activity assay, biophysical characterisation, and X-ray structures.\n\nAbbreviations

biochemistry

Beyond The Linear Genome: Comprehensive Determination Of The Endogenous Circular Elements In C. elegans And Human Genomes Via An Unbiased Genomic-Biophysical Method

Investigations aimed at defining the 3-D configuration of eukaryotic chromosomes have consistently encountered an endogenous population of chromosome-derived circular genomic DNA, referred to as extrachromosomal circular DNA (eccDNA). While the production, distribution, and activities of eccDNAs remain understudied, eccDNA formation from specific regions of the linear genome has profound consequences on the regulatory and coding capabilities for these regions. High-throughput sequencing has only recently made extensive genomic mapping of eccDNA sequences possible and had yet to be applied using a rigorous approach that distinguishes ascertainment bias from true enrichment. Here, we define eccDNA distribution, utilizing a set of unbiased topology-dependent approaches for enrichment and characterization. We use parallel biophysical, enzymatic, and informatic approaches to obtain a comprehensive profiling of eccDNA in C. elegans and in three human cell types, where eccDNAs were previously uncharacterized. We also provide quantitative analysis of the eccDNA loci at both unique and repetitive regions. Our studies converge on and support a consistent picture in which endogenous genomic DNA circles are present in normal physiological DNA metabolism, and in which the circles come from both coding and noncoding genomic regions. Prominent among the coding regions generating DNA circles are several genes known to produce a diversity of protein isoforms, with mucin proteins and titin as specific examples.

genomics

Organoid And Tissue Patterning Through Phase Separation: Use Of A Vertex Model To Relate Dynamics Of Patterning To Underlying Biophysical Parameters

AO_SCPLOWBSTRACTC_SCPLOWExactly a century ago, DArcy Thompson set an agenda for understanding tissue development in terms of underlying biophysical, mathematically-tractable mechanisms. One such mechanism, discovered by Steinberg in the 1960s, is adhesion-mediated sorting of cell mixtures into homotypic groups. Interest in this phase separation mechanism has recently surged, partly because of its use to create synthetic biological patterning mechanisms and partly because it has been found to drive events critical to the formation of organoids from stem cells, making the process relevant to biotechnology as well as to basic development. Here, we construct quantitative model of patterning by phase separation, informed by laboratory data, and use it to explore the relationship between degree of adhesive difference and speed, type and extent of resultant patterning. Our results can be used three ways; to predict the outcome of mix-ing cells with known properties, to estimate the properties required to make some designed organoid system, or to estimate underlying cellular properties from observed behaviour.

developmental biology

Producing Hfq/Sm Proteins and sRNAs for Structural and Biophysical Studies of Ribonucleoprotein Assembly

Hfq is a bacterial RNA-binding protein that plays key roles in the post-transcriptional regulation of gene expression. Like other Sm proteins, Hfq assembles into toroidal discs that bind RNAs with varying affinities and degrees of sequence specificity. By simultaneously binding to a regulatory small RNA (sRNA) and an mRNA target, Hfq hexamers facilitate productive RNA[···]RNA interactions; the generic nature of this chaperone-like functionality makes Hfq a hub in many sRNA-based regulatory networks. That Hfq is crucial in diverse cellular pathways--including stress response, quorum sensing and biofilm formation-- has motivated genetic and RNAomic studies of its function and physiology (in vivo), as well as biochemical and structural analyses of Hfq[···]RNA interactions (in vitro). Indeed, crystallographic and bio-physical studies first established Hfq as a member of the phylogenetically-conserved Sm superfamily. Crystallography and other biophysical methodologies enable the RNA-binding properties of Hfq to be elucidated in atomic detail, but such approaches have stringent sample requirements, viz.: reconstituting and characterizing an Hfq*RNA complex requires ample quantities of well-behaved (sufficient purity, homogeneity) specimens of Hfq and RNA (sRNA, mRNA fragments, short oligoribonucleotides, or even single nucleotides). The production of such materials is covered in this Chapter, with a particular focus on recombinant Hfq proteins for crystallization experiments.\n\nAbbreviations\n\nJournal formatMethods in Molecular Biology (Springer Protocols series); this volume is entitled \"Bacterial Regulatory RNA: Methods and Protocols\"; an author guide is linked at http://www.springer.com/series/7651

biochemistry

Inferring the selection window in antimicrobial resistance using deep mutational scanning data and biophysics-based fitness models

Mutant-selection window (MSW) hypothesis in antimicrobial resistance implies a range for antimicrobial concentration that promotes selection of single-step resistant mutants. Since the inception and experimental verification, MSW has been at the forefront of strategies to minimize development of antimicrobial resistance (AR). Setting the upper and lower limits of MSW requires an understanding of the dependence of selection coefficient of arising mutations to antimicrobial concentration. In this work, we employed a biophysics-based and experimentally calibrated fitness model to estimate MSW in the case of Ampicillin and Cefotaxime resistance in E.coli TEM-1 beta lactamase. In line with experimental observations, we show that selection is active at very low levels of antimicrobials. Furthermore, we elucidate the dependence of MSW to catalytic efficiency of mutants, fraction of mutants in the population and discuss the role of population genetic parameters such as population size and mutation rate. Altogether, our analysis and formalism provide a predictive model of MSW with direct implications in the design of dosage strategies.

evolutionary biology

Biophysical models reveal the relative importance of transporter proteins and impermeant anions in chloride homeostasis

Fast synaptic inhibition in the nervous system depends on the transmembrane flux of Cl- ions based on the neuronal Cl- driving force. Established theories regarding the determinants of Cl- driving force have recently been questioned. Here we present biophysical models of Cl- homeostasis using the pump-leak model. Using numerical and novel analytic solutions, we demonstrate that the Na+/K+-ATPase, ion conductances, impermeant anions, electrodiffusion, water fluxes and cation-chloride cotransporters (CCCs) play roles in setting the Cl- driving force. Our models, together with experimental validation, show that while impermeant anions can contribute to setting [Cl-]i in neurons, they have a negligible effect on the driving force for Cl- locally and cell-wide. In contrast, we demonstrate that CCCs are well-suited for modulating Cl- driving force and hence inhibitory signalling in neurons. Our findings reconcile recent experimental findings and provide a framework for understanding the interplay of different chloride regulatory processes in neurons.

neuroscience

A biophysical dynamic module for the polarisation of auxin efflux carriers PIN-FORMED (PIN)

Intracellular polarisation of auxin efflux carriers is crucial for understanding how auxin gradients form in plants. The polarisation dynamics of auxin efflux carriers PIN-FORMED (PIN) depends on both biomechanical forces as well as chemical, molecular and genetic factors. Biomechanical forces have shown to affect the localisation of PIN transporters to the plasma membrane. We proposed a biophysical module of PIN polarisation that integrates biomechanical, molecular, and cellular processes as well as their non-linear interactions. The module was implemented as a discrete Boolean model and then approximated to a continuous dynamic system, in order to explore the relative contribution of the factors mediating PIN polarisation at the scale of single cell. Our models recovered qualitative behaviours that have been experimentally observed and enabled us to postulate that, in the context of PIN polarisation, the effects of the mechanical forces can predominate over the activity of molecular factors such as the GTPase ROP6 and the CRIB-motif CRIB-motif RIC1.

plant biology

Biophysically Realistic Neuron Models for Simulation of Cortical Stimulation

1.ObjectiveWe implemented computational models of human and rat cortical neurons for simulating the neural response to cortical stimulation with electromagnetic fields.\n\nApproachWe adapted model neurons from the library of Blue Brain models to reflect biophysical and geometric properties of both adult rat and human cortical neurons and coupled the model neurons to exogenous electric fields (E-fields). The models included 3D reconstructed axonal and dendritic arbors, experimentally-validated electrophysiological behaviors, and multiple, morphological variants within cell types. Using these models, we characterized the single-cell responses to intracortical microstimulation (ICMS) and uniform E-field with dc as well as pulsed currents.\n\nMain resultsThe strength-duration and current-distance characteristics of the model neurons to ICMS agreed with published experimental results, as did the subthreshold polarization of cell bodies and axon terminals by uniform dc E-fields. For all forms of stimulation, the lowest threshold elements were terminals of the axon collaterals, and the dependence of threshold and polarization on spatial and temporal stimulation parameters was strongly affected by morphological features of the axonal arbor, including myelination, diameter, and branching.\n\nSignificanceThese results provide key insights into the mechanisms of cortical stimulation. The presented models can be used to study various cortical stimulation modalities while incorporating detailed spatial and temporal features of the applied E-field.

bioengineering

Biophysical Principles of Lineage Factor PU.1 Binding Revealed by NextPBMs

Determining the biophysical principles that shape transcription factor (TF) binding in a cell-specific manner is key to quantitative models of gene expression. High-throughput (HT) in vitro methods measuring protein-DNA binding are invaluable for relating TF binding affinity to genome-wide binding; however, the impact of cell-specific post-translational modifications (PTMs) and cofactors are not routinely assessed. To address these limitations, we describe a new HT approach, called nextPBMs (nuclear extract protein-binding microarrays), to characterize TF binding that accounts for PTMs and endogenous cofactors. We use nextPBMs to examine the DNA binding of the lineage factor PU.1/Spi1 and IRF8 in human monocytes. We identify two binding modes for PU.1 in monocytes - autonomous binding unaffected by PTMs and cooperative binding with IRF8, and identify a single cooperative mode for IRF8. We characterize the DNA binding of PU.1:IRF8 complexes, and show how nextPBMs can be used to discover cell-specific cofactors and characterize TF cooperativity at single-nucleotide resolution. We show that chromatin state and cofactors both influence the affinity requirements for PU.1 binding sites. Furthermore, we find that the influences of cooperative (IRF8) and collaborative (C/EBP) cofactors on PU.1-binding-site affinity are independent and additive.

molecular biology

Biophysical basis of disruption in alpha rhythm in Alzheimer’s disease

Alpha is one of the most prominent rhythms (7.5-12.5 Hz) detected in electroencephalography (EEG) during wakeful relaxation with closed eyes. In response to elevated ambient acetylcholine levels, a subclass of thalamic pacemaker cells generate alpha. This rhythm is intrinsic to the cell and is robustly orchestrated by an interplay of hyperpolarization activated cyclic nucleotide gated channels(HCN) and calcium-ion channels. It has been shown that decreased expression of HCN channels is correlated to Alzheimer's Diseased (AD). In early stages of AD, alpha is known to be down-regulated and lowered in coherence. We use this well characterized and quantified rhythm to understand the changes in ion channel properties that lead to disruption of alpha as seen in AD in a biophysically detailed network model of the thalamo-cortical circuit that generates the alpha-rhythm. Our computational model allows us to explore the causal links between alpha rhythms, HCN channels and amyloid-beta aggregation. The most commonly used drugs(acetylcholinesterase inhibitors) in AD increase the duration and level of acetylcholine and provide temporary symptomatic relief in some cases. Our simulations show how increasing acetylcholine can provide rescue for a small range of aberrant HCN expression. We hypothesize that reduced alpha rhythm frequency and coherence is a result of down-regulated HCN expression, rather then compromised cholinergic modulation(as is currently thought). The model predicts that lowering of the alpha-rhythm can modify the network activity in the thalamo-cortical circuit and lead to an increase in the inhibitory drive to the thalamus.

neuroscience

Biophysical underpinning of astroglial physiology probed with realistic cell models

Electrically non-excitable astroglia take up neurotransmitters, buffer extracellular K+ and generate Ca2+ signals that release molecular regulators of neural circuitry. The underlying machinery remains enigmatic, mainly because the nanoscopic, sponge-like astrocyte morphology has been difficult to access experimentally or explore theoretically. Here, we have systematically evaluated the multi-scale morphology of protoplasmic astroglia to construct a realistic multi-compartmental cell model that can be biophysically interrogated in NEURON computational environment. This approach has been implemented as an astrocyte-model builder ASTRO. As a proof of concept, we explored a hippocampal astrocyte reconstructed in silico against a battery of physiological and imaging experiments. This exploration has unveiled some basic features of astroglial physiology inaccessible empirically, such as the characteristic length of membrane voltage propagation, membrane effects of local glutamate transport, spatiotemporal dynamics of intracellular K+ redistribution, key Ca2+ buffering properties, and some basic relationships between free Ca2+ dynamics and experimental readout of fluorescent Ca2+ indicators.

neuroscience

Biophysical model of axonal stimulation in epiretinal visual prostheses

Visual prostheses aim to restore vision to people blinded from degenerative photoreceptor diseases by electrically stimulating surviving neurons in the retina. However, a major challenge with epiretinal prostheses is that they may accidentally activate passing axon fibers, causing severe perceptual distortions. To investigate the effect of axonal stimulation on the retinal response, we developed a computational model of a small population of morphologically and biophysically detailed retinal ganglion cells, and simulated their response to epiretinal electrical stimulation. We found that activation thresholds of ganglion cell somas and axons varied systematically with both stimulus pulse duration and electrode-retina distance. These findings have important implications for the improvement of stimulus encoding methods for epiretinal prostheses.

neuroscience

A Biophysical Platform for Electromechanical Stimulation of Engineered Cardiac Tissues

Human engineered cardiac tissues (ECTs) provide an in vitro model for studying human cardiac physiology and drug responses, but their performance remains limited by culture systems that do not fully reproduce the heart's electrical and mechanical environment. Electrical stimulation (ES) and mechanical stimulation (MS) have each been used to improve ECT function. Their combination, referred to as electromechanical stimulation (ES+MS), can provide further benefits. However, ES+MS depends not only on the presence of both cues but also on how they are coordinated in time. Here, we developed an incubator-compatible biophysical platform that delivers ES and MS independently or in combination, with programmable control over timing, amplitude, frequency, duration, and waveform. Calibration and dynamic characterization demonstrated tissue-relevant strain delivery, rapid and repeatable motion, and minimal attenuation and timing lag at the designated frequency of 1.5 Hz. We then compared four 6 h conditioning regimens: unstimulated control, ES alone, unsynchronized ES+MS, and synchronized ES+MS. We hypothesized that the synchronized ES+MS group, in which electrical excitation was aligned with peak externally applied strain, would produce the greatest increase in contractile force. Consistent with this hypothesis, synchronized ES+MS increased normalized twitch force by approximately 44% on average, whereas the other groups showed no comparable improvement. Twitch-timing metrics did not exhibit coordinated enhancement after 6 h, suggesting that the force increase reflects an adaptive biomechanical response rather than broad tissue maturation. These findings identify ES-MS timing as an important design parameter for ECT conditioning.

bioengineering