Student Poster Abstracts

Exploring the energy landscape of C. elegans neural activities

Recent advances in experimental techniques and application of the maximum entropy principle have allowed us to build models for joint probability distribution of activity in groups of up to 50 neurons in Caenorhabditis elegans, a nematode with 302 neurons. These models, which are equivalent to the Boltzmann distribution for a family of Potts glasses, successfully predict the static observables of the network. The energy landscape defined by these models exhibits curious signatures of collective behavior, including a large number of energy minima, as in models for memory, and a clustering of energy barriers that is reminiscent of the dynamical transitions in disordered systems. While these models describe the distribution of network states at a single time, the observed neural dynamics are not consistent with a simple Brownian-like motion on the energy landscape. In particular, the real dynamics exhibit much longer correlation times than predicted from the heights of energy barriers alone. We will show progress towards understanding how the nematode actually explores the energy landscape of its neural network.

Diverse communities behave like typical random ecosystems

With a brief letter to Nature in 1972, Robert May triggered a worldwide research program in theoretical ecology and complex systems that continues to this day. Building on powerful mathematical results about large random matrices, he argued that systems with sufficiently large numbers of interacting components are generically unstable. In the ecological context, May’s thesis directly contradicted the longstanding ecological intuition that diversity promotes stability. In economics and finance, May’s work helped to consolidate growing concerns about the fragility of an increasingly interconnected global marketplace. In this Letter, we draw on recent theoretical progress in random matrix theory and statistical physics to fundamentally extend and reinterpret May’s theorem. We confirm that a wide range of ecological models become unstable at the point predicted by May, even when the models do not strictly follow his assumptions. Surprisingly, increasing the interaction strength or diversity beyond the May threshold results in a reorganization of the ecosystem–through extinction of a fixed fraction of species–into a new stable state whose properties are well described by purely random interactions. This self-organized state remains stable for arbitrarily large ecosystem and suggests a new interpretation of May’s original conclusions: when interacting complex systems with many components become sufficiently large, they will generically undergo a transition to a “typical” self-organized, stable state.

Alternative stable states in a model of microbial community limited by multiple essential nutrients

Microbial communities routinely have several alternative stable states observed for the same environmental parameters. Transitions between such alternative stable states could be sudden and irreversible making external manipulation of these systems more complicated. Can we predict which specific perturbations may induce such regime shifts and which ones would have only a transient effect? To study this topic we introduce a model of a microbial ecosystem colonized by a large number of specialist species. Growth of each of the species can be limited by essential nutrients of two types, e.g. carbon and nitrogen, each represented in the environment by multiple metabolites. We demonstrate that our model has an exponentially large number of potential stable states realized for different environmental parameters. Using game theoretical methods adapted from the stable marriage problem we predict all of these states based only on ranked lists of competitive abilities of species for each of the nutrients. We show that for every set of nutrient influxes, several mutually uninvadable stable states are generally feasible and we distinguish them based upon their dynamic stability. We further explore an intricate network of discontinuous transitions (regime shifts) between these alternative states both in the course of community assembly, or upon changes of nutrient influxes.

Microbial population in fluctuating environments, how the size influences the strategy

The survival of organisms in randomly fluctuating environments not only depends on their ability to grow in different nutrients conditions but also depends on the time needed to adapt to the new habitat. Recent work has shown that, like many other physiological quantities, the adaptation time fluctuates in a stochastic manner across single cells and that the underlying distribution can dramatically change across genotypes. To understand how natural selection may have acted in order to shape such distribution we develop a mathematical theory on how the reproductive success of iso-genic populations depends on their lag time distribution and initial population size. Our model suggests that in general large populations favor the so-called “bet-hedging” strategy where, by phenotype randomization, subsets of the total population are adapted to different environment types. In this scenario the first responding organisms will dominate the offspring structure and, in analogy with the theory of aging, we show why natural selection is insensitive to slow responding cells suggesting that persister like phenotype may very generally be expected to occur in microbial population. These results strictly depend on the characteristic population size and we show how a sensing mechanism, where by sensing the environment and switching to the right phenotype, becomes a more efficient strategy when the colony size becomes relatively small.

Mechanics of behavior: Comprehensive search behavior encoded in cytoskeletal dynamics of single cell Lacrymaria olor

E.M. Flaum^1,2, S.M. Coyle², B.M. Benson^1,3, D. Krishnamurthy^1,4, M. Prakash^1,5,6

¹Bioengineering, Stanford University, ²Graduate Program in Biophysics, Stanford University, ³Applied Physics, Stanford University, ⁴Mechanical Engineering, Stanford University, ⁵Faculty Scholar, Howard Hughes Medical Institute, ⁶Investigator, Chan Zuckerberg BioHub

Complex animal behavior arises from interplay between actuators (muscles), sensors (proprioception, vision) and control (neuronal circuits). Surprisingly, single eukaryotic cells such as protists are also capable of complex real-time animal like behavior, such as escape or hunting with actuation, sensing and control embedded in a single cell. How a complex algorithm such as search behavior might be encoded in intrinsic dynamics of a single cell remains unknown. Here we elucidate the mechanics of search behavior in a predatory ciliate Lacrymaria olor. Remarkably L.olor has the ability to extend and contract its “neck” seven body lengths in a second, while it efficiently searches the space around it for prey on the order of minutes. Our recent work establishes that L. olor’s comprehensive search strategy while hunting is encoded in the coupling of antagonistic active systems: subcellular structures that use surface cilia and cortical cytoskeletal contractility (Coyle et al, 2018). Here we reveal the underlying geometrical features of the cellular cytoskeleton that enables rapid extension and contraction. These large morphological changes in cell shape are bounded by several membrane and cell volume constraints that together program the dynamics of this active filament. By performing force spectroscopy and controlled membrane tension experiments in live cells, we reveal the role of this dynamic force landscape and how it shapes the search phase space. Our work combines theoretical active filament models with experimental data to  unravel how active mechanics leads to emergent behavior in single cells. 

Screening of topological defects in 2D crystals: the role of dislocations and curvature.

Two-dimensional crystallization on curved surfaces is the subject of ongoing research across different length scales. The hexagonal lattice is the most efficient 2D close packing structure for particles with isotropic interactions. Such crystals are therefore commonly found in various physical systems, where they adopt different shapes. While flat space can be perfectly tiled with an hexagonal lattice, crystals on closed surfaces, like the sphere, are topologically constrained to accommodate at least some defects, even at zero temperature and regardless of their size. These point defects are called disclinations and they are sources of great mechanical stress. The stress induced locally can be partially relieved by the intrinsic curvature of the crystal but, interestingly, also by the spontaneous formation of additional defect lines, referred to as dislocations scars. In this poster, we investigate curvature and dislocation scars as screening mechanisms of disclination stress. We find that their interplay can greatly influence the crystal shape and size-dependent properties. In the context of our continuum model for elasticity of closed crystals, we discuss the behaviour of the crystal energy with the scar density and crystal size. Our model leads to a defined expression of the elastic energy of any closed crystal, as a function of its size.

Stochastic architectures in the retina

A significant amount of work has been done on the surprising level of developmental precision in biology. However, development is not precise in many cases – especially among larger organisms, it seems that instead of attempting to recreate a very precise pattern, the aim of development is to fall within some class of architectures which are similar in some functional sense, but highly variable at the cell-to-cell level. There are many examples of this, including the dramatically different numbers of neurons found in different brain areas among humans. Another example is the retina, where the placement of photoreceptors is nearly crystalline for some organisms, such as flies, but is much closer to randomly placed for others, such as humans. We investigate this, and attempt to understand the regimes where a perfectly precise solution is required, and where a more stochastic solution is sufficient.

Statistical Physics Modelling and Information Processing in the Adaptive Immune System

Adaptive immunity in vertebrates develops during the life-time of an organism by processes of mutation and selection, common to Darwinian evolution. Pathogens adopt different molecular strategies to overcome the immune challenge. For chronic infections, the battle against the immune system lasts for years within a patient, e.g., 10-15 years for HIV. During this time, the symptoms are minor, but viral and immune cell populations undergo rapid sequence turnover to overcome the challenge imposed by the other, forming a co-evolutionary arms race. Recently, sequencing an entire antibody repertoire has become feasible, opening a new path for quantitative understanding of this system. Statistical inference on such data together with mechanistic and phenomenological modelling have taught us a great deal about the space of the immune interaction that can distinguish between self-molecules (proteins of the host) and non-self infecting pathogens. However, we still lack a statistical understanding of how predictable an immune response may be against evolving pathogens, and thus, how controllable it is by external interventions (e.g. vaccination or drugs). The objective of my research is to use statistical learning methods combined with machine learning approaches to develop predictive models of immune repertoire response.

Stochastic Yield Catastrophes and Robustness in Self-Assembly

A guiding principle in self-assembly is that, for high production yield, nucleation of structures must be significantly slower than their growth. However, details of the mechanism that impedes nucleation are broadly considered irrelevant. In this work, we analyze self-assembly into finite-sized target structures employing mathematical modeling. We investigate two key scenarios to delay nucleation: (i) by introducing a slow activation step for the assembling constituents and, (ii) by decreasing the dimerization rate. These scenarios have widely different characteristics. While the dimerization scenario exhibits robust behavior, the activation scenario is highly sensitive to demographic fluctuations. These demographic fluctuations ultimately disfavor growth compared to nucleation and can suppress yield completely. The occurrence of this stochastic yield catastrophe does not depend on model details but is generic as soon as number fluctuations between constituents are taken into account. On a broader perspective, our results reveal that stochasticity is an important limiting factor for self-assembly and that the specific implementation of the nucleation process plays a significant role in determining the yield.

Accelerating adaptation via dynamic population structure

Population structure can reduce clonal interference among beneficial mutations and also slows the spread of beneficial mutations. Thus, with a smooth fitness landscape, a well-mixed population is expected to be a better choice in achieving the fastest adaption. Indeed, this relative adaption speed has  been  used  to  probe  for  the  presence  of  local  fitness peaks in microbial evolution experiments.

We would like to investigate the allele fixation in such circumstance. Here, based on practical manipulations in evolutionary experiments, we consider occasional events, including recombination and mutation, among the structured population in a smooth fitness landscape. 

Our simulations show that the structured population with both periodic migration and recombination could have advantage over a well-mixed population. This result challenges the previous assumption, and also provides new clues in designing the evolutionary experiments to maximize the rate of phenotypic change.

Simplified Protein Contact Networks

Proteins perform many functions in living cells and their three-dimensional structures play a key role for this. Solved protein tertiary structures can be converted into protein contact networks for further analysis and structural comparison. Sathyapriya et al. have shown that three-dimensional protein structures can be reconstructed from partial contact networks with a large fraction of edges missing, implying that much simpler networks could capture the necessary structural information [1]. I will describe a new method of defining, constructing and comparing simplified protein contact networks and show that, despite having a much smaller number of edges than full protein contact networks, these simplified networks provide important information about the three-dimensional structure of a protein. In future, I plan to use these simplified networks to study the configuration space occupied by solved protein tertiary structures.

[1] Sathyapriya, R., Duarte, J. M., Stehr, H., Filippis, I. & Lappe, M. PLoS Computational Biology 5, e1000584 (2009)

Run-and-tumble particles: an exact solution for two particles in 1d

Within the scientific community, a recent surge of interest has occurred in the area of active matter. This is because active particles, which consume energy to perform motion, are inherently out-of-equilibrium objects. Consequently, they often exhibit behaviour which is strikingly different from their passive counterparts. 

Run-and-tumble particles, which serve as a model for Escherichia coli bacteria, form an interesting subset of the field of active matter. 

Field-theoretic methods have often been used to investigate systems of run-and-tumble particles, but while some progress has been made from a microscopic point of view, such treatments have hitherto been less common. In 2016, Slowman, Blythe, and Evans made progress on the microscopic front when they published an exact solution to a two-particle run-and-tumble model in one dimension. This poster aims to give an overview of their work.

Balancing speed and accuracy in a proofreading scheme

DNA duplication, transcription or RNA transcription are highly accurate biological processes. However, simple thermodynamics considerations are not enough to explain the low error rates actually observed in these mechanisms. John Hopfield (Natl. Acad. Sci. U.S.A. 71 (10): 4135–9, 1974) and Jacques Ninio (Biochimie. 57 (5): 587–95, 1975) were the first to model a kinetic proofreading system as a solution to this apparent paradox. Continuing in their direction, our research is focusing on a more general model allowing us to explore different selectivity mechanisms. Particularly we aim to show how the accuracy of the system can be tuned by energy consumption. Preliminary results suggest that selectivity and speed in a process cannot be maximized at the same time. Comparison with real biological systems would allow us to observe which strategy nature chose to favor.

The Role of Drug Kinetics on the Evolution of Resistance

Emergence of drug resistance due to treatment non-adherence is a problem especially in chronic prolonged viral infections like the Human Immunodeficiency virus (HIV) and Hepatitis B (HBV) and C (HCV) viruses. Long acting drugs are being developed as one way to address this problem. Though this promises to be useful in the context of treatment adherence, we do not yet know how this would affect resistance. With this in mind, we analyze the effect of dosing intervals on the establishment of resistance due to mutants existing prior to treatment and those that are produced during treatment in the presence of time-dependent drug profiles. We find that there exists a initial time-frame after treatment initiation that has the most influence on the establishment probability. Depending upon the nature of the drug kinetics during this time, increasing the dosing interval might be better or worse for the establishment of resistance. Our results suggest that drug kinetics affect selection and competition in the system in a complicated manner and need to be factored in while designing new treatment strategies.

Understanding and modeling hidden dynamics in Drosophila aging

The process of aging affects multiple aspects of animal behavior, from behavioral outputs to the physiological mechanisms that control them. It remains unclear, however, the extent to which this is a result of the gradual failure of individual components or the explicit execution of physiological alterations in gene expression and neural circuitry. We analyze behavioral data of aging male and female fruit flies (D. melanogaster) and investigate the sexual dimorphism that emerges from measuring the total repertoire of behaviors as a function of age, long time-scale dynamics in behavioral transitions, and coarse-grained hierarchical structures that underlie these dynamics. These coarse-grained structures provide information about predictability as a function of age, the structure of the behavioral dynamics, and how these behaviors are affected by the aging process. In addition, we establish a model that is capable of reproducing the long time scale dynamics and other underlying mechanisms of the data.

Criticality, Neuronal Avalanches and Collective Oscillations

Helena Christina P. de A. Bastos¹, Mauro Copelli^*1
1Physics Department - Universidade Federal da Pernambuco

In the last decade, several studies have attempted to model brain criticality, the conjecture according to which the brain as a dynamical system would operate near a second-order phase transition. Since the distribution of the sizes of neuronal avalanches in vitro was shown to be a power law P(s) \sim s^-\tau, with \tau \simeq 1:5 [1], the coincidence with the result for mean-eld directed percolation (MF-DP) led many to believe that a critical brain would be near the transition between an absorbing and an active state. The abundance of models which went along this direction, however, failed to reproduce long-range time correlations (LRTCs), another signature of criticality which was observed experimentally [2]. Addressing these issues, our group recently revisited the CROS (“CRitical OScillations”) model, in which the interplay of excitation and inhibition eventually leads to a transition with the onset of alpha-band oscillations [3] where they observed both power-law distributions and LRTCs. The model was shown to display continuously varying exponents for avalanche size and duration within a transition region [4]. The exponents were linearly related with a nontrivial slope that coincides with the experimental results also described by our group [5]. The model still lacks some essential features that are present in the experimental data. For instance, we found that the scaling relation connecting the exponents of avalanche size and duration is satised at an intermediate (critical) value of spiking rate variability both for anesthetized and non-anesthetized animals, but not for the model. At the critical point, the exponents observed experimentally do not agree with the MF-DP universality class [5], thus inviting new models to explain the data. Our poster intends to revisit the methods and results of [5] and [4].

Keywords: Criticality, CROS model, DFA, neuronal avalanches

References

[1] Beggs JM, Plenz D. Neuronal Avalanches in Neocortical Circuits. Journal of Neuroscience. 2003;23(35):11167-11177. doi:10.1523/jneurosci.23-35-11167.2003.

[2] Ribeiro et al. Spike Avalanches Exhibit Universal Dynamics Across All Major Behaviors. PLOS ONE. 2010;5(11):e14129. doi: 10.1371/journal.pone.0014129.

[3] Poil et al. Critical-state dynamics of avalanches and oscillations jointly emerge from balances excitation/inibition in neural networks. Journal of Neuroscience. 2012;32(29):9817-23. doi:10.1523/jneurosci.5990-11.2012.

[4] Dalla Porta L, Copelli M. Modeling Neuronal Avalanches and long-range temporal correlations at the emergency of collective oscillations: continuously varying exponents mimic M/EEG results. bioRxiv. 2018. doi:10.1101/423921

[5] Fontenele et al. Criticality between cortical states. bioRxiv. 2018. doi:10.1101/454934

Olfactory navigation by hunting octopuses: how to take decisions using a broken signal

Biological systems are surrounded by fluids and evolved spectacular adaptations to decode the sparse information brought by turbulence. My research project focuses on octopuses hunting in the ocean: they localize their prey using turbulent odor, water movement and pressure. I model octopuses and their environment using statistical fluid dynamics and decision theory. In my simulations a turbulent scalar (odor) evolves in water from a localized source (prey). Odor is an intermittent quantity that spreads from the source disgregating in fluctuating puffs.

The shape of these intermittent puffs changes as they are deformed by the turbulent airflow far from the source. Detections occur within a conical volume which is the typical shape of the plume. I am currently developing algorithms to understand how can a octopus interpret this fluctuating signal to find its prey. Does it need a spatial or temporal memory for successful inference? I will show that simple inferences can be accomplished simply by averaging over the body of the octopus. However, to extract reliable information for more complex tasks, the dynamic features of this broken signal must be used.

Statistical response in immune repertoires

Immune system is a collection of cells and molecules in an organism whose primary function is the defense against the so-called antigens[1]. It can be subdivided into two main subsystems, the innate system and the adaptive system. A distinction between them is related to specicity. In that sense, the innate immune response is not specialized for specic pathogens and does not need a long start-up phase, whereas the adaptative immune response is very specic relying on a diverse repertoire of receptors which have the ability to change its clone composition via the formation of memory repertoires of B and T cells after pathogen encounters.

Considering the interaction of the immune system with the target population (e.g., bacteria, viruses or tumor cells) as a dynamic process can lead to the development of new mathematical models to study the dynamics of both immune responses at the molecular, cellular and tissue scales. In this light, we propose the mathematical tools modelling the dynamics of the adaptive immune repertoires as a Bayesian system for learning the pathogenic environment[2]. Finally, some example of new approaches that will be explored for the upcoming years will be introduced[3].

[1] S. G. Rudnev. Mathematical models in immunology. Mathematical Models of Life Support Systems, 2.

[2] Andreas Mayer, Vijay Balasubramanian, Aleksandra M. Walczak, and Thierry Mora. How a well-adapting immune system remembers. arXiv e-prints, page arXiv:1806.05753, Jun 2018.

[3] Raluca Eftimie, Joseph J. Gillard, and Doreen A. Cantrell. Mathematical models for immunology: Current state of the art and future research directions. Bulletin of Mathematical Biology, 78(10):2091{2134, Oct 2016.

Dividing active droplets: A model for protocells

Rabea Seyboldt¹, David Zwicker¹², Christoph A. Weber¹², Anthony A. Hyman³, Frank Jülicher¹

¹Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany

²School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA

³Max Planck Institute of Molecular Cell Biology and Genetics, 01307 Dresden, Germany

seyboldt@pks.mpg.de

Macromolecular aggregation and phase separation into droplets has been proposed as a mechanism to organize chemical reactions that could have been a key precursors at the origins of the first living cells. However, it remains unclear how early protocells could have proliferated and divided. Deformed droplets usually relax towards a spherical shape and do not easily divide. Our theoretical study shows that in the presence of chemical reactions that produce droplet material, a chemically active droplet may undergo a shape instability and subsequently divide into two daughter droplets, which may then grow and divide again. We also find that when considering the effects of hydrodynamics which tend to stabilize spherical droplets, the shape instability can still occur for sufficiently small droplets. Our work suggests that chemically active droplets that divide and propagate could serve as a model for prebiotic protocells.

Nonlinear Poisson effect in critical mechanical networks

Fibrous networks of stiff athermal biopolymers such as collagen, a major structural component of the extracellular matrix, have been shown to exhibit anomalously large apparent Poisson ratios, i.e. significant transverse contraction under small applied longitudinal extension. Here we show that this effect can be understood in the context of a macroscopic mechanical phase transition from a bending-dominated regime to a stretching-dominated regime at a critical applied extension controlled by the network connectivity. We measure this effect using a variety of 2D and 3D model network structures and propose a phase diagram governing the transition as a function of connectivity and strain.

A new role for sparse expansions in neural networks

Multiple sensory pathways in the brain rely on sparsely active populations of neurons downstream from the input stimuli. The biological reason for the occurrence of expanded structure in the brain is unclear, but may be because expansion can increase the expressive power of a neural network. Here we consider whether expanding the hidden layer of a network can lead to improved learning even when this is not a factor.

To study this setting we use a teacher-student framework where a perceptron teacher network generates labels which are corrupted with small amounts of noise. We then train a student network that is structurally matched to the teacher and can achieve optimal accuracy if given the teacher’s synaptic weights. In this setting, adding hidden units with random connectivity to the input does not improve the capacity of the student network to match the teacher. Moreover, adding such units will increase the expressive capacity of the network leading to a risk of over-fitting the noise.

However, we show that by making the hidden units sparsely active, their addition can substantially improve learning in the student. We also demonstrate that ablation of the expanded layer after training the student enhances this effect, and provide theoretical justification as to why. This finding has implications for the design of artificial neural networks and for the understanding 

Single Molecule Studies of a Novel Mechanism of Bacterial Transcription Initiation

In bacteria, gene transcription begins with the binding of an RNA polymerase (RNAP) core enzyme to the initiation factor σ, which allows it to recognize promoter sequences on the DNA and initiate RNA synthesis. In the canonical transcription cycle, upon reaching the termination sequence and releasing the transcript, RNAP detaches from the DNA and is free to restart the process. However, previous work in our lab has shown that following termination, bacterial RNAP frequently remains bound to the DNA template, and sometimes exhibits one-dimensional sliding over thousands of basepairs. Moreover, in the presence of free σ factor molecules in solution, the sliding, DNA-bound polymerase is often observed to restart transcription. This mechanism of transcription initiation might have implications for the transcriptional coupling of nearby genes.

In this work, I present single-molecule fluorescence-microscopy experiments we are doing to further characterize this novel mechanism of transcription initiation in vitro, and to evaluate its role in the coupling and coordination of gene expression.  

Collective sensing by cell populations with feedback and communication

Cells sense their environment with remarkable precision, and recent experiments have shown that this precision can be enhanced by cell-cell communication. However, most theoretical investigations of this effect have assumed linear sensing and communication, whereas it is well known that cells use nonlinear feedback to internally amplify sensed signals. Here, using a minimal stochastic model we investigate the interplay of feedback and communication in determining sensory precision. We find that feedback can induce a critical transition and long-range correlations among cells. We investigate the associated sensing tradeoff: on the one hand, we expect long-range order to enhance communication; on the other hand, fluctuations become large at the critical point, so order may come at the cost of precision.