Bryan C. Daniels

Discontinuities at the DNA supercoiling transition.

While slowly turning the ends of a single molecule of DNA at constant applied force, a discontinuity was recently observed at the supercoiling transition when a small plectoneme is suddenly formed. This can be understood as an abrupt transition into a state in which stretched and plectonemic DNA coexist. We argue that there should be discontinuities in both the extension and the torque at the transition and provide experimental evidence for both. To predict the sizes of these discontinuities and how they change with the overall length of DNA, we organize a phenomenological theory for the coexisting plectonemic state in terms of four parameters. We also test supercoiling theories, including our own elastic rod simulation, finding discrepancies with experiment that can be understood in terms of the four coexisting state parameters.

Automated adaptive inference of phenomenological dynamical models

Dynamics of complex systems is often driven by large and intricate networks of microscopic interactions, whose sheer size obfuscates understanding. With limited experimental data, many parameters of such dynamics are unknown, and thus detailed, mechanistic models risk overfitting and making faulty predictions. At the other extreme, simple ad hoc models often miss defining features of the underlying systems. Here we develop an approach that instead constructs phenomenological, coarse-grained models of network dynamics that automatically adapt their complexity to the available data. Such adaptive models produce accurate predictions even when microscopic details are unknown. The approach is computationally tractable, even for a relatively large number of dynamical variables. Using simulated data, it correctly infers the phase space structure for planetary motion, avoids overfitting in a biological signalling system and produces accurate predictions for yeast glycolysis with tens of data points and over half of the interacting species unobserved.

Control of finite critical behaviour in a small-scale social system

Many adaptive systems sit near a tipping or critical point. For systems near a critical point small changes to component behaviour can induce large-scale changes in aggregate structure and function. Criticality can be adaptive when the environment is changing, but entails reduced robustness through sensitivity. This tradeoff can be resolved when criticality can be tuned. We address the control of finite measures of criticality using data on fight sizes from an animal society model system (Macaca nemestrina, n=48). We find that a heterogeneous, socially organized system, like homogeneous, spatial systems (flocks and schools), sits near a critical point; the contributions individuals make to collective phenomena can be quantified; there is heterogeneity in these contributions; and distance from the critical point (DFC) can be controlled through biologically plausible mechanisms exploiting heterogeneity. We propose two alternative hypotheses for why a system decreases the distance from the critical point.

Efficient Inference of Parsimonious Phenomenological Models of Cellular Dynamics Using S-Systems and Alternating Regression

The nonlinearity of dynamics in systems biology makes it hard to infer them from experimental data. Simple linear models are computationally efficient, but cannot incorporate these important nonlinearities. An adaptive method based on the S-system formalism, which is a sensible representation of nonlinear mass-action kinetics typically found in cellular dynamics, maintains the efficiency of linear regression. We combine this approach with adaptive model selection to obtain efficient and parsimonious representations of cellular dynamics. The approach is tested by inferring the dynamics of yeast glycolysis from simulated data. With little computing time, it produces dynamical models with high predictive power and with structural complexity adapted to the difficulty of the inference problem.

Sparse code of conflict in a primate society

Animals living in groups collectively produce social structure. In this context individuals make strategic decisions about when to cooperate and compete. This requires that individuals can perceive patterns in collective dynamics, but how this pattern extraction occurs is unclear. Our goal is to identify a model that extracts meaningful social patterns from a behavioral time series while remaining cognitively parsimonious by making the fewest demands on memory. Using fine-grained conflict data from macaques, we show that sparse coding, an important principle of neural compression, is an effective method for compressing collective behavior. The sparse code is shown to be efficient, predictive, and socially meaningful. In our monkey society, the sparse code of conflict is composed of related individuals, the policers, and the alpha female. Our results suggest that sparse coding is a natural technique for pattern extraction when cognitive constraints and small sample sizes limit the complexity of inferential models. Our approach highlights the need for cognitive experiments addressing how individuals perceive collective features of social organization.

Dual Coding Theory Explains Biphasic Collective Computation in Neural Decision-Making

A central question in cognitive neuroscience is how unitary, coherent decisions at the whole organism level can arise from the distributed behavior of a large population of neurons with only partially overlapping information. We address this issue by studying neural spiking behavior recorded from a multielectrode array with 169 channels during a visual motion direction discrimination task. It is well known that in this task there are two distinct phases in neural spiking behavior. Here we show Phase I is a distributed or incompressible phase in which uncertainty about the decision is substantially reduced by pooling information from many cells. Phase II is a redundant or compressible phase in which numerous single cells contain all the information present at the population level in Phase I, such that the firing behavior of a single cell is enough to predict the subjects decision. Using an empirically grounded dynamical modeling framework, we show that in Phase I large cell populations with low redundancy produce a slow timescale of information aggregation through critical slowing down near a symmetry-breaking transition. Our model indicates that increasing collective amplification in Phase II leads naturally to a faster timescale of information pooling and consensus formation. Based on our results and others in the literature, we propose that a general feature of collective computation is a “coding duality” in which there are accumulation and consensus formation processes distinguished by different timescales.

Nucleation at the DNA supercoiling transition

Twisting DNA under a constant applied force reveals a thermally activated transition into a state with a supercoiled structure known as a plectoneme. Using transition-state theory, we predict the rate of this plectoneme nucleation to be of order 10(4) Hz. We reconcile this with experiments that have measured hopping rates of order 10 Hz by noting that the viscous drag on the bead used to manipulate the DNA limits the measured rate. We find that the intrinsic bending caused by disorder in the base-pair sequence is important for understanding the free-energy barrier that governs the transition. Both analytic and numerical methods are used in the calculations. We provide extensive details on the numerical methods for simulating the elastic rod model with and without disorder.

Collective memory in primate conflict implied by temporal scaling collapse

In biological systems, prolonged conflict is costly, whereas contained conflict permits strategic innovation and refinement. Causes of variation in conflict size and duration are not well understood. We use a well-studied primate society model system to study how conflicts grow. We find conflict duration is a ‘first to fight’ growth process that scales superlinearly, with the number of possible pairwise interactions. This is in contrast with a ‘first to fail’ process that characterizes peaceful durations. Rescaling conflict distributions reveals a universal curve, showing that the typical time scale of correlated interactions exceeds nearly all individual fights. This temporal correlation implies collective memory across pairwise interactions beyond those assumed in standard models of contagion growth or iterated evolutionary games. By accounting for memory, we make quantitative predictions for interventions that mitigate or enhance the spread of conflict. Managing conflict involves balancing the efficient use of limited resources with an intervention strategy that allows for conflict while keeping it contained and controlled.

Absence of Kondo lattice coherence effects in Ce0.6La0.4Pb3: A magnetic-field study

The specific heat of polycrystalline Ce0.6La0.4Pb3 has been measured in magnetic fields ranging from 0to14T. After subtraction of a lattice contribution, the specific heat between 1K and 10K is well described by the S=12 single-impurity Kondo model with just one adjustable parameter: the zero-field Kondo temperature. In particular, the variation in the temperature and the height of the peak in C vs T is captured with good accuracy. This fit suggests that lattice coherence effects play no significant role in the magnetic-field response of this concentrated Kondo system.

Automated, predictive, and interpretable inference of C. elegans escape dynamics.

The roundworm C. elegans exhibits robust escape behavior in response to rapidly rising temperature. The behavior lasts for a few seconds, shows history dependence, involves both sensory and motor systems, and is too complicated to model mechanistically using currently available knowledge. Instead we model the process phenomenologically, and we use the Sir Isaac dynamical inference platform to infer the model in a fully automated fashion directly from experimental data. The inferred model requires incorporation of an unobserved dynamical variable, and is biologically interpretable. The model makes accurate predictions about the dynamics of the worm behavior, and it can be used to characterize the functional logic of the dynamical system underlying the escape response. This work illustrates the power of modern artificial intelligence to aid in discovery of accurate and interpretable models of complex natural systems.