arXiv subjects

Aleksandra M. Walczak

Publications and source records attributed to Aleksandra M. Walczak.

At least 73 records · Page 4Linked to original sources

arXiv2016

Precision of readout at the hunchback gene: analyzing short transcription time traces in living fly embryos

The simultaneous expression of the hunchback gene in the numerous nuclei of the developing fly embryo gives us a unique opportunity to study how transcription is regulated in living organisms. A recently developed MS2-MCP technique for imaging nascent messenger RNA in living Drosophila embryos allows us to quantify the dynamics of the developmental transcription process. The initial measurement of the morphogens by the hunchback promoter takes place during very short cell cycles, not only giving each nucleus little time for a precise readout, but also resulting in short time traces of transcription. Additionally, the relationship between the measured signal and the promoter state depends on the molecular design of the reporting probe. We develop an analysis approach based on tailor made autocorrelation functions that overcomes the short trace problems and quantifies the dynamics of transcription initiation. Based on live imaging data, we identify signatures of bursty transcription initiation from the hunchback promoter. We show that the precision of the expression of the hunchback gene to measure its position along the anterior-posterior axis is low both at the boundary and in the anterior even at cycle 13, suggesting additional post-transcriptional averaging mechanisms to provide the precision observed in fixed embryos.

q-bio.MN↗

arXiv2016

Measuring the sequence-affinity landscape of antibodies with massively parallel titration curves

Despite the central role that antibodies play in the adaptive immune system and in biotechnology, much remains unknown about the quantitative relationship between an antibody's amino acid sequence and its antigen binding affinity. Here we describe a new experimental approach, called Tite-Seq, that is capable of measuring binding titration curves and corresponding affinities for thousands of variant antibodies in parallel. The measurement of titration curves eliminates the confounding effects of antibody expression and stability that arise in standard deep mutational scanning assays. We demonstrate Tite-Seq on the CDR1H and CDR3H regions of a well-studied scFv antibody. Our data shed light on the structural basis for antigen binding affinity and suggests a role for secondary CDR loops in establishing antibody stability. Tite-Seq fills a large gap in the ability to measure critical aspects of the adaptive immune system, and can be readily used for studying sequence-affinity landscapes in other protein systems.

q-bio.QM↗

arXiv2016

Mouse T cell repertoires as statistical ensembles: overall characterization and age dependence

The ability of the adaptive immune system to respond to arbitrary pathogens stems from the broad diversity of immune cell surface receptors (TCRs). This diversity originates in a stochastic DNA editing process (VDJ recombination) that acts each time a new immune cell is created from a stem cell. By analyzing T cell sequence repertoires taken from the blood and thymus of mice of different ages, we quantify the significant changes in this process that occur in development from embryo to young adult. We find a rapid increase with age in the number of random insertions in the VDJ recombination process, leading to a dramatic increase in diversity. Since the blood accumulates thymic output over time, blood repertoires are mixtures of different statistical recombination processes and, by unraveling the mixture statistics, we can obtain a clear picture of the time evolution of the early immune system. Sequence repertoire analysis also allows us to detect the effect of selection on the output of the VDJ recombination process. The effects we find are nearly identical between thymus and blood, suggesting that they mainly reflect selection for proper folding of the TCR receptor protein.

q-bio.GN↗

arXiv2016

A model for the integration of conflicting exogenous and endogenous signals by dendritic cells

Cells of the immune system are confronted with opposing pro- and anti-inflammatory signals. Dendritic cells (DC) integrate these cues to make informed decisions whether to initiate an immune response. Confronted with exogenous microbial stimuli, DC endogenously produce both anti- (IL-10) and pro-inflammatory (TNF$α$) cues whose joint integration controls the cell's final decision. We combine experimental measurements with theoretical modeling to quantitatively describe the integration mode of these opposing signals. We propose a two step integration model that modulates the effect of the two types of signals: an initial bottleneck integrates both signals (IL-10 and TNF$α$), the output of which is later modulated by the anti-inflammatory signal. We show that the anti-inflammatory IL-10 signaling is long ranged, as opposed to the short-ranged pro-inflammatory TNF$α$ signaling. The model suggests that the population averaging and modulation of the pro-inflammatory response by the anti-inflammatory signal is a safety guard against excessive immune responses.

q-bio.MN↗

arXiv2016

Local equilibrium in bird flocks

The correlated motion of flocks is an instance of global order emerging from local interactions. An essential difference with analogous ferromagnetic systems is that flocks are active: animals move relative to each other, dynamically rearranging their interaction network. The effect of this off-equilibrium element is well studied theoretically, but its impact on actual biological groups deserves more experimental attention. Here, we introduce a novel dynamical inference technique, based on the principle of maximum entropy, which accodomates network rearrangements and overcomes the problem of slow experimental sampling rates. We use this method to infer the strength and range of alignment forces from data of starling flocks. We find that local bird alignment happens on a much faster timescale than neighbour rearrangement. Accordingly, equilibrium inference, which assumes a fixed interaction network, gives results consistent with dynamical inference. We conclude that bird orientations are in a state of local quasi-equilibrium over the interaction length scale, providing firm ground for the applicability of statistical physics in certain active systems.

q-bio.PE↗

arXiv2016

Rényi entropy, abundance distribution and the equivalence of ensembles

Distributions of abundances or frequencies play an important role in many fields of science, from biology to sociology, as does the Rényi entropy, which measures the diversity of a statistical ensemble. We derive a mathematical relation between the abundance distribution and the Rényi entropy, by analogy with the equivalence of ensembles in thermodynamics. The abundance distribution is mapped onto the density of states, and the Rényi entropy to the free energy. The two quantities are related in the thermodynamic limit by a Legendre transform, by virtue of the equivalence between the micro-canonical and canonical ensembles. In this limit, we show how the Rényi entropy can be constructed geometrically from rank-frequency plots. This mapping predicts that non-concave regions of the rank-frequency curve should result in kinks in the Rényi entropy as a function of its order. We illustrate our results on simple examples, and emphasize the limitations of the equivalence of ensembles when a thermodynamic limit is not well defined. Our results help choose reliable diversity measures based on the experimental accuracy of the abundance distributions in particular frequency ranges.

q-bio.PE↗

arXiv2016

Persisting fetal clonotypes influence the structure and overlap of adult human T cell receptor repertoires

The diversity of T-cell receptors recognizing foreign pathogens is generated through a highly stochastic recombination process, making the independent production of the same sequence rare. Yet unrelated individuals do share receptors, which together constitute a "public" repertoire of abundant clonotypes. The TCR repertoire is initially formed prenatally, when the enzyme inserting random nucleotides is downregulated, producing a limited diversity subset. By statistically analyzing deep sequencing T-cell repertoire data from twins, unrelated individuals of various ages, and cord blood, we show that T-cell clones generated before birth persist and maintain high abundances in adult organisms for decades, slowly decaying with age. Our results suggest that large, low-diversity public clones are created during pregnancy, and survive over long periods, providing the basis of the public repertoire.

q-bio.PE↗

arXiv2015

Diversity of immune strategies explained by adaptation to pathogen statistics

Biological organisms have evolved a wide range of immune mechanisms to defend themselves against pathogens. Beyond molecular details, these mechanisms differ in how protection is acquired, processed and passed on to subsequent generations -- differences that may be essential to long-term survival. Here, we introduce a mathematical framework to compare the long-term adaptation of populations as a function of the pathogen dynamics that they experience and of the immune strategy that they adopt. We find that the two key determinants of an optimal immune strategy are the frequency and the characteristic timescale of the pathogens. Depending on these two parameters, our framework identifies distinct modes of immunity, including adaptive, innate, bet-hedging and CRISPR-like immunities, which recapitulate the diversity of natural immune systems.

q-bio.PE↗

arXiv2015

repgenHMM: a dynamic programming tool to infer the rules of immune receptor generation from sequence data

The diversity of the immune repertoire is initially generated by random rearrangements of the receptor gene during early T and B cell development. Rearrangement scenarios are composed of random events -- choices of gene templates, base pair deletions and insertions -- described by probability distributions. Not all scenarios are equally likely, and the same receptor sequence may be obtained in several different ways. Quantifying the distribution of these rearrangements is an essential baseline for studying the immune system diversity. Inferring the properties of the distributions from receptor sequences is a computationally hard problem, requiring enumerating every possible scenario for every sampled receptor sequence. We present a Hidden Markov model, which accounts for all plausible scenarios that can generate the receptor sequences. We developed and implemented a method based on the Baum-Welch algorithm that can efficiently infer the parameters for the different events of the rearrangement process. We tested our software tool on sequence data for both the alpha and beta chains of the T cell receptor. To test the validity of our algorithm, we also generated synthetic sequences produced by a known model, and confirmed that its parameters could be accurately inferred back from the sequences. The inferred model can be used to generate synthetic sequences, to calculate the probability of generation of any receptor sequence, as well as the theoretical diversity of the repertoire. We estimate this diversity to be $\approx 10^{23}$ for human T cells. The model gives a baseline to investigate the selection and dynamics of immune repertoires.

q-bio.GN↗

arXiv2015

Habitat Fluctuations Drive Species Covariation in the Human Microbiota

Two species with similar resource requirements respond in a characteristic way to variations in their habitat -- their abundances rise and fall in concert. We use this idea to learn how bacterial populations in the microbiota respond to habitat conditions that vary from person-to-person across the human population. Our mathematical framework shows that habitat fluctuations are sufficient for explaining intra-bodysite correlations in relative species abundances from the Human Microbiome Project. We explicitly show that the relative abundances of phylogenetically related species are positively correlated and can be predicted from taxonomic relationships. We identify a small set of functional pathways related to metabolism and maintenance of the cell wall that form the basis of a common resource sharing niche space of the human microbiota.

q-bio.PE↗

arXiv2015

Noise expands the response range of the Bacillus subtilis competence circuit

Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus subtilis, which exhibits much larger noise in the duration of its competence events than a synthetically constructed analog that performs the same function. Here, using stochastic modeling and fluorescence microscopy, we show that this larger noise allows cells to exit terminal phenotypic states, which expands the range of stress levels to which cells are responsive and leads to phenotypic heterogeneity at the population level. This is an important example of how noise confers a functional benefit in a genetic decision-making circuit.

q-bio.MN↗

arXiv2015

Extending the dynamic range of transcription factor action by translational regulation

A crucial step in the regulation of gene expression is binding of transcription factor (TF) proteins to regulatory sites along the DNA. But transcription factors act at nanomolar concentrations, and noise due to random arrival of these molecules at their binding sites can severely limit the precision of regulation. Recent work on the optimization of information flow through regulatory networks indicates that the lower end of the dynamic range of concentrations is simply inaccessible, overwhelmed by the impact of this noise. Motivated by the behavior of homeodomain proteins, such as the maternal morphogen Bicoid in the fruit fly embryo, we suggest a scheme in which transcription factors also act as indirect translational regulators, binding to the mRNA of other transcription factors. Intuitively, each mRNA molecule acts as an independent sensor of the TF concentration, and averaging over these multiple sensors reduces the noise. We analyze information flow through this new scheme and identify conditions under which it outperforms direct transcriptional regulation. Our results suggest that the dual role of homeodomain proteins is not just a historical accident, but a solution to a crucial physics problem in the regulation of gene expression.

q-bio.MN↗

arXiv2015

Tiling solutions for optimal biological sensing

Biological systems, from cells to organisms, must respond to the ever changing environment in order to survive and function. This is not a simple task given the often random nature of the signals they receive, as well as the intrinsically stochastic, many body and often self-organized nature of the processes that control their sensing and response and limited resources. Despite a wide range of scales and functions that can be observed in the living world, some common principles that govern the behavior of biological systems emerge. Here I review two examples of very different biological problems: information transmission in gene regulatory networks and diversity of adaptive immune receptor repertoires that protect us from pathogens. I discuss the trade-offs that physical laws impose on these systems and show that the optimal designs of both immune repertoires and gene regulatory networks display similar discrete tiling structures. These solutions rely on locally non-overlapping placements of the responding elements (genes and receptors) that, overall, cover space nearly uniformly.

q-bio.QM↗

arXiv2015

Fluctuating fitness shapes the clone size distribution of immune repertoires

The adaptive immune system relies on the diversity of receptors expressed on the surface of B and T-cells to protect the organism from a vast amount of pathogenic threats. The proliferation and degradation dynamics of different cell types (B cells, T cells, naive, memory) is governed by a variety of antigenic and environmental signals, yet the observed clone sizes follow a universal power law distribution. Guided by this reproducibility we propose effective models of somatic evolution where cell fate depends on an effective fitness. This fitness is determined by growth factors acting either on clones of cells with the same receptor responding to specific antigens, or directly on single cells with no regards for clones. We identify fluctuations in the fitness acting specifically on clones as the essential ingredient leading to the observed distributions. Combining our models with experiments we characterize the scale of fluctuations in antigenic environments and we provide tools to identify the relevant growth signals in different tissues and organisms. Our results generalize to any evolving population in a fluctuating environment.

q-bio.PE↗

arXiv2015

Trade-offs in delayed information transmission in biochemical networks

In order to transmit biochemical signals, biological regulatory systems dissipate energy with concomitant entropy production. Additionally, signaling often takes place in challenging environmental conditions. In a simple model regulatory circuit given by an input and a delayed output, we explore the trade-offs between information transmission and the system's energetic efficiency. We determine the maximally informative network, given a fixed amount of entropy production and delayed response, exploring both the case with and without feedback. We find that feedback allows the circuit to overcome energy constraints and transmit close to the maximum available information even in the dissipationless limit. Negative feedback loops, characteristic of shock responses, are optimal at high dissipation. Close to equilibrium positive feedback loops, known for their stability, become more informative. Asking how the signaling network should be constructed to best function in the worst possible environment, rather than an optimally tuned one or in steady state, we discover that at large dissipation the same universal motif is optimal in all of these conditions.

q-bio.MN↗

arXiv2015

Inferring processes underlying B-cell repertoire diversity

We quantify the VDJ recombination and somatic hypermutation processes in human B-cells using probabilistic inference methods on high-throughput DNA sequence repertoires of human B-cell receptor heavy chains. Our analysis captures the statistical properties of the naive repertoire, first after its initial generation via VDJ recombination and then after selection for functionality. We also infer statistical properties of the somatic hypermutation machinery (exclusive of subsequent effects of selection). Our main results are the following: the B-cell repertoire is substantially more diverse than T-cell repertoires, due to longer junctional insertions; sequences that pass initial selection are distinguished by having a higher probability of being generated in a VDJ recombination event; somatic hypermutations have a non-uniform distribution along the V gene that is well explained by an independent site model for the sequence context around the hypermutation site.

q-bio.PE↗

arXiv2015

Flocking and turning: a new model for self-organized collective motion

Birds in a flock move in a correlated way, resulting in large polarization of velocities. A good understanding of this collective behavior exists for linear motion of the flock. Yet observing actual birds, the center of mass of the group often turns giving rise to more complicated dynamics, still keeping strong polarization of the flock. Here we propose novel dynamical equations for the collective motion of polarized animal groups that account for correlated turning including solely social forces. We exploit rotational symmetries and conservation laws of the problem to formulate a theory in terms of generalized coordinates of motion for the velocity directions akin to a Hamiltonian formulation for rotations. We explicitly derive the correspondence between this formulation and the dynamics of the individual velocities, thus obtaining a new model of collective motion. In the appropriate overdamped limit we recover the well-known Vicsek model, which dissipates rotational information and does not allow for polarized turns. Although the new model has its most vivid success in describing turning groups, its dynamics is intrinsically different from previous ones in a wide dynamical regime, while reducing to the hydrodynamic description of Toner and Tu at very large length-scales. The derived framework is therefore general and it may describe the collective motion of any strongly polarized active matter system.

cond-mat.stat-mech↗

arXiv2014

Capturing coevolutionary signals in repeat proteins

The analysis of correlations of amino acid occurrences in globular proteins has led to the development of statistical tools that can identify native contacts -- portions of the chains that come to close distance in folded structural ensembles. Here we introduce a statistical coupling analysis for repeat proteins -- natural systems for which the identification of domains remains challenging. We show that the inherent translational symmetry of repeat protein sequences introduces a strong bias in the pair correlations at precisely the length scale of the repeat-unit. Equalizing for this bias reveals true co-evolutionary signals from which local native-contacts can be identified. Importantly, parameter values obtained for all other interactions are not significantly affected by the equalization. We quantify the robustness of the procedure and assign confidence levels to the interactions, identifying the minimum number of sequences needed to extract evolutionary information in several repeat protein families. The overall procedure can be used to reconstruct the interactions at long distances, identifying the characteristics of the strongest couplings in each family, and can be applied to any system that appears translationally symmetric.

q-bio.BM↗