Theory and Computation of Biological Processes and Complex Materials

The Spakowitz lab is engaged in projects that address fundamental chemical and physical processes that underlie a range of key biological mysteries and cutting-edge materials applications. Current research in our lab focuses on three main research themes: DNA Biophysics, Protein Self Assembly, and Charge Transport in Conjugated Polymers. These broad research areas offer complementary perspectives on chemical and physical processes, and we leverage this complementarity throughout our research. Our approach draws from a diverse range of theoretical and computational methods, including analytical theory of semiflexible polymers, polymer field theory, continuum elastic mechanics, Brownian dynamics simulation, equilibrium and dynamic Monte Carlo simulations, and analytical theory and numerical simulations of reaction-diffusion phenomena. A common thread in our work is the need to capture phenomena over many length and time scales, and our flexibility in research methodologies allows us to address these problems at an unprecedented level of precision.

Academic Appointments

Honors & Awards

  • Terman Fellow, Stanford University (2006-2009)
  • CAREER Award, NSF (2009)

Professional Education

  • PhD, California Institute of Technology (2004)

Current Research and Scholarly Interests

Theory and computation of biological processes and complex materials

2015-16 Courses

Stanford Advisees

  • Postdoctoral Faculty Sponsor
    Jie Lu

All Publications

  • Percolation, Tie-Molecules, and the Microstructural Determinants of Charge Transport in Semicrystalline Conjugated Polymers ACS MACRO LETTERS Mollinger, S. A., Krajina, B. A., Noriega, R., Salleo, A., Spakowitz, A. J. 2015; 4 (7): 708-712
  • Thermodynamic model of heterochromatin formation through epigenetic regulation JOURNAL OF PHYSICS-CONDENSED MATTER Mulligan, P. J., Koslover, E. F., Spakowitz, A. J. 2015; 27 (6)


    Gene regulation in eukaryotes requires the segregation of silenced genomic regions into densely packed heterochromatin, leaving the active genes in euchromatin regions more accessible. We introduce a model that connects the presence of epigenetically inherited histone marks, methylation at histone 3 lysine-9, to the physical compaction of chromatin fibers via the binding of heterochromatin protein 1 (HP1). Our model demonstrates some of the key physical features that are necessary to explain experimental observations. In particular, we demonstrate that strong cooperative interactions among the HP1 proteins are necessary to see the phase segregation of heterochromatin and euchromatin regions. We also explore how the cell can use the concentration of HP1 to control condensation and under what circumstances there is a threshold of methylation over which the fibers will compact. Finally, we consider how different potential in vivo fiber structures as well as the flexibility of the histone 3 tail can affect the bridging of HP1. Many of the observations that we make about the HP1 system are guided by general thermodynamics principles and thus could play a role in other DNA organizational processes such as the binding of linker histones.

    View details for DOI 10.1088/0953-8984/27/6/064109

    View details for Web of Science ID 000348501300010

    View details for PubMedID 25563699

  • Physical Modeling of Chromosome Segregation in Escherichia coli Reveals Impact of Force and DNA Relaxation BIOPHYSICAL JOURNAL Lampo, T. J., Kuwada, N. J., Wiggins, P. A., Spakowitz, A. J. 2015; 108 (1): 146-153


    The physical mechanism by which Escherichia coli segregates copies of its chromosome for partitioning into daughter cells is unknown, partly due to the difficulty in interpreting the complex dynamic behavior during segregation. Analysis of previous chromosome segregation measurements in E. coli demonstrates that the origin of replication exhibits processive motion with a mean displacement that scales as t(0.32). In this work, we develop a model for segregation of chromosomal DNA as a Rouse polymer in a viscoelastic medium with a force applied to a single monomer. Our model demonstrates that the observed power-law scaling of the mean displacement and the behavior of the velocity autocorrelation function is captured by accounting for the relaxation of the polymer chain and the viscoelastic environment. We show that the ratio of the mean displacement to the variance of the displacement during segregation events is a critical metric that eliminates the compounding effects of polymer and medium dynamics and provides the segregation force. We calculate the force of oriC segregation in E. coli to be ∼0.49 pN.

    View details for DOI 10.1016/j.bpj.2014.10.074

    View details for Web of Science ID 000347468900020

    View details for PubMedID 25564861

  • Membrane indentation triggers clathrin lattice reorganization and fluidization SOFT MATTER Cordella, N., Lampo, T. J., Melosh, N., Spakowitz, A. J. 2015; 11 (3): 439-448

    View details for DOI 10.1039/c4sm01650e

    View details for Web of Science ID 000346911600002

  • Modulation of DNA loop lifetimes by the free energy of loop formation PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Chen, Y., Johnson, S., Mulligan, P., Spakowitz, A. J., Phillips, R. 2014; 111 (49): 17396-17401


    Storage and retrieval of the genetic information in cells is a dynamic process that requires the DNA to undergo dramatic structural rearrangements. DNA looping is a prominent example of such a structural rearrangement that is essential for transcriptional regulation in both prokaryotes and eukaryotes, and the speed of such regulations affects the fitness of individuals. Here, we examine the in vitro looping dynamics of the classic Lac repressor gene-regulatory motif. We show that both loop association and loop dissociation at the DNA-repressor junctions depend on the elastic deformation of the DNA and protein, and that both looping and unlooping rates approximately scale with the looping J factor, which reflects the system's deformation free energy. We explain this observation by transition state theory and model the DNA-protein complex as an effective worm-like chain with twist. We introduce a finite protein-DNA binding interaction length, in competition with the characteristic DNA deformation length scale, as the physical origin of the previously unidentified loop dissociation dynamics observed here, and discuss the robustness of this behavior to perturbations in several polymer parameters.

    View details for DOI 10.1073/pnas.1415685111

    View details for Web of Science ID 000345921500025

  • Multiscale dynamics of semiflexible polymers from a universal coarse-graining procedure PHYSICAL REVIEW E Koslover, E. F., Spakowitz, A. J. 2014; 90 (1)
  • Membrane Fluctuations Destabilize Clathrin Protein Lattice Order BIOPHYSICAL JOURNAL Cordella, N., Lampo, T. J., Mehraeen, S., Spakowitz, A. J. 2014; 106 (7): 1476-1488


    We develop a theoretical model of a clathrin protein lattice on a flexible cell membrane. The clathrin subunit is modeled as a three-legged pinwheel with elastic deformation modes and intersubunit binding interactions. The pinwheels are constrained to lie on the surface of an elastic sheet that opposes bending deformation and is subjected to tension. Through Monte Carlo simulations, we predict the equilibrium phase behavior of clathrin lattices at various levels of tension. High membrane tensions, which correspond to suppressed membrane fluctuations, tend to stabilize large, flat crystalline structures similar to plaques that have been observed in vivo on cell membranes that are adhered to rigid surfaces. Low tensions, on the other hand, give rise to disordered, defect-ridden lattices that behave in a fluidlike manner. The principles of two-dimensional melting theory are applied to our model system to further clarify how high tensions can stabilize crystalline order on flexible membranes. These results demonstrate the importance of environmental physical cues in dictating the collective behavior of self-assembled protein structures.

    View details for DOI 10.1016/j.bpj.2013.11.4505

    View details for Web of Science ID 000333754300007

    View details for PubMedID 24703309

  • Rheology and simulation of 2-dimensional clathrin protein network assembly SOFT MATTER VanDersarl, J. J., Mehraeen, S., Schoen, A. P., Heilshorn, S. C., Spakowitz, A. J., Melosh, N. A. 2014; 10 (33): 6219-6227


    Clathrin is a three-legged protein complex that assembles into lattice structures on the cell membrane and transforms into fullerene-like cages during endocytosis. This dynamic structural flexibility makes clathrin an attractive building block for guided assembly. The assembly dynamics and the mechanical properties of clathrin protein lattices are studied using rheological measurements and theoretical modelling in an effort to better understand two dynamic processes: protein adsorption to the interface and assembly into a network. We find that percolation models for protein network formation are insufficient to describe clathrin network formation, but with Monte Carlo simulations we can describe the dynamics of network formation very well. Insights from this work can be used to design new bio-inspired nano-assembly systems.

    View details for DOI 10.1039/c4sm00025k

    View details for Web of Science ID 000340438600010

  • Chain conformations dictate multiscale charge transport phenomena in disordered semiconducting polymers PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Noriega, R., Salleo, A., Spakowitz, A. J. 2013; 110 (41): 16315-16320


    Existing models for the electronic properties of conjugated polymers do not capture the spatial arrangement of the disordered macromolecular chains over which charge transport occurs. Here, we present an analytical and computational description in which the morphology of individual polymer chains is dictated by well-known statistical models and the electronic coupling between units is determined using Marcus theory. The multiscale transport of charges in these materials (high mobility at short length scales, low mobility at long length scales) is naturally described with our framework. Additionally, the dependence of mobility with electric field and temperature is explained in terms of conformational variability and spatial correlation. Our model offers a predictive approach to connecting processing conditions with transport behavior.

    View details for DOI 10.1073/pnas.1307158110

    View details for Web of Science ID 000325395600023

  • Caulobacter chromosome in vivo configuration matches model predictions for a supercoiled polymer in a cell-like confinement PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Hong, S., Toro, E., Mortensen, K. I., de la Rosa, M. A., Doniach, S., Shapiro, L., Spakowitz, A. J., McAdams, H. H. 2013; 110 (5): 1674-1679


    We measured the distance between fluorescent-labeled DNA loci of various interloci contour lengths in Caulobacter crescentus swarmer cells to determine the in vivo configuration of the chromosome. For DNA segments less than about 300 kb, the mean interloci distances, , scale as n(0.22), where n is the contour length, and cell-to-cell distribution of the interloci distance r is a universal function of r/n(0.22) with broad cell-to-cell variability. For DNA segments greater than about 300 kb, the mean interloci distances scale as n, in agreement with previous observations. The 0.22 value of the scaling exponent for short DNA segments is consistent with theoretical predictions for a branched DNA polymer structure. Predictions from Brownian dynamics simulations of the packing of supercoiled DNA polymers in an elongated cell-like confinement are also consistent with a branched DNA structure, and simulated interloci distance distributions predict that confinement leads to "freezing" of the supercoiled configuration. Lateral positions of labeled loci at comparable positions along the length of the cell are strongly correlated when the longitudinal locus positions differ by <0.16 μm. We conclude that the chromosome structure is supercoiled locally and elongated at large length scales and that substantial cell-to-cell variability in the interloci distances indicates that in vivo crowding prevents the chromosome from reaching an equilibrium arrangement. We suggest that the force causing rapid transport of loci remote from the parS centromere to the distal cell pole may arise from the release at the polar region of potential energy within the supercoiled DNA.

    View details for DOI 10.1073/pnas.1220824110

    View details for Web of Science ID 000314558100027

    View details for PubMedID 23319648

  • Theoretical and Computational Modeling of Target-Site Search Kinetics In Vitro and In Vivo BIOPHYSICAL JOURNAL Koslover, E. F., Diaz de la Rosa, M. A., Spakowitz, A. J. 2011; 101 (4): 856-865


    Access to genetically encoded data depends on the dynamics of DNA-binding proteins searching for specific target sites in the genome. This search process is thought to occur by facilitated diffusion-a combination of three-dimensional diffusion and one-dimensional sliding. Although facilitated diffusion is capable of significantly speeding up the search in vitro, the importance of this mechanism in vivo remains unclear. We use numeric simulations and analytical theory to model the target-search dynamics of DNA-binding proteins under a wide range of conditions. Our models reproduce experimental measurements of search-rate enhancement within bulk in vitro experiments, as well as the target search time for transcription factors measured in vivo. We find that facilitated diffusion can accelerate the search process only for a limited range of parameters and only under dilute DNA conditions. We address the role of DNA configuration and confinement, demonstrating that facilitated diffusion does not speed up the search on coiled versus straight DNA. Furthermore, we show that, under in vivo conditions, the search process becomes effectively diffusive and is independent of DNA configuration. We believe our results cast in a new light the role of facilitated diffusion in DNA targeting kinetics within the cell.

    View details for DOI 10.1016/j.bpj.2011.06.066

    View details for Web of Science ID 000294103600015

    View details for PubMedID 21843476

  • Tension-dependent structural deformation alters single-molecule transition kinetics PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Sudhanshu, B., Mihardja, S., Koslover, E. F., Mehraeen, S., Bustamante, C., Spakowitz, A. J. 2011; 108 (5): 1885-1890


    We analyze the response of a single nucleosome to tension, which serves as a prototypical biophysical measurement where tension-dependent deformation alters transition kinetics. We develop a statistical-mechanics model of a nucleosome as a wormlike chain bound to a spool, incorporating fluctuations in the number of bases bound, the spool orientation, and the conformations of the unbound polymer segments. With the resulting free-energy surface, we perform dynamic simulations that permit a direct comparison with experiments. This simple approach demonstrates that the experimentally observed structural states at nonzero tension are a consequence of the tension and that these tension-induced states cease to exist at zero tension. The transitions between states exhibit substantial deformation of the unbound polymer segments. The associated deformation energy increases with tension; thus, the application of tension alters the kinetics due to tension-induced deformation of the transition states. This mechanism would arise in any system where the tether molecule is deformed in the transition state under the influence of tension.

    View details for DOI 10.1073/pnas.1010047108

    View details for Web of Science ID 000286804700028

    View details for PubMedID 21245354

  • Bacterial Chromosomal Loci Move Subdiffusively through a Viscoelastic Cytoplasm PHYSICAL REVIEW LETTERS Weber, S. C., Spakowitz, A. J., Theriot, J. A. 2010; 104 (23)


    Tracking of fluorescently labeled chromosomal loci in live bacterial cells reveals a robust scaling of the mean square displacement (MSD) as ?(0.39). We propose that the observed motion arises from relaxation of the Rouse modes of the DNA polymer within the viscoelastic environment of the cytoplasm. The time-averaged and ensemble-averaged MSD of chromosomal loci exhibit ergodicity, and the velocity autocorrelation function is negative at short time lags. These observations are most consistent with fractional Langevin motion and rule out a continuous time random walk model as an explanation for anomalous motion in vivo.

    View details for DOI 10.1103/PhysRevLett.104.238102

    View details for Web of Science ID 000278493500016

    View details for PubMedID 20867274

  • Twist- and Tension-Mediated Elastic Coupling between DNA-Binding Proteins PHYSICAL REVIEW LETTERS Koslover, E. F., Spakowitz, A. J. 2009; 102 (17)


    We study the effective interaction between DNA-binding proteins that arises from elastic stresses in the DNA when tension is applied. Using the wormlike chain model, we calculate the free energy cost of introducing multiple nearby bends in the DNA. We find that the bend deformation energy promotes aggregation to straighten the linker DNA, while twist resistance of the linker leads to damped oscillations in the coupling free energy between two proteins. We calculate the mean first encounter time for proteins sliding along DNA, indicating, in some cases, an optimal applied tension for protein assembly. Our results highlight the need to consider DNA twist even when no torsion is applied and the DNA ends are free to rotate. The variable-range oscillatory coupling between DNA-binding proteins may provide a versatile mechanism for tension-mediated gene regulation.

    View details for DOI 10.1103/PhysRevLett.102.178102

    View details for Web of Science ID 000265948300074

    View details for PubMedID 19518837

  • An in vitro assay for entry into cilia reveals unique properties of the soluble diffusion barrier JOURNAL OF CELL BIOLOGY Breslow, D. K., Koslover, E. F., Seydel, F., Spakowitz, A. J., Nachury, M. V. 2013; 203 (1): 129-147


    Specific proteins are concentrated within primary cilia, whereas others remain excluded. To understand the mechanistic basis of entry into cilia, we developed an in vitro assay using cells in which the plasma membrane was permeabilized, but the ciliary membrane was left intact. Using a diffusion-to-capture system and quantitative analysis, we find that proteins >9 nm in diameter (∼100 kD) are restricted from entering cilia, and we confirm these findings in vivo. Interference with the nuclear pore complex (NPC) or the actin cytoskeleton in permeabilized cells demonstrated that the ciliary diffusion barrier is mechanistically distinct from those of the NPC or the axon initial segment. Moreover, applying a mass transport model to this system revealed diffusion coefficients for soluble and membrane proteins within cilia that are compatible with rapid exploration of the ciliary space in the absence of active transport. Our results indicate that large proteins require active transport for entry into cilia but not necessarily for movement inside cilia.

    View details for DOI 10.1083/jcb.201212024

    View details for Web of Science ID 000325742200013

    View details for PubMedID 24100294

  • Systematic Coarse-Graining of Microscale Polymer Models as Effective Elastic Chains MACROMOLECULES Koslover, E. F., Spakowitz, A. J. 2013; 46 (5): 2003-2014

    View details for DOI 10.1021/ma302056v

    View details for Web of Science ID 000316168600034

  • Coarse grain model of nanostructured alkaline exchange membranes: Phase behavior and transport property predictions Mao, S., He, S., Coletta, E., Toney, M., Frank, C., W., Spakowitz, A., J. 2013
  • Theoretical study of nanostructured alkaline exchange membrane transport property Mao, S., Spakowitz, A., J., Coletta, E., He, S., Toney, M., Frank, C., W. 2013
  • Theoretical study of nanostructured alkaline exchange membrane phase behavior and transport property Mao, S., Spakowitz, A., J., Coletta, E., He, S., Frank, C., W., Toney, M. 2013
  • Theoretical model for HP1-Induced heterochromatin formation Mulligan, P., J., Koslover, E., F., Spakowitz, A., J. 2013
  • Systematic coarse-graining of the wormlike chain model for dynamic simulations Koslover, E., F., Spakowitz, A., J. 2013
  • Semiflexible polymer model for charge mobility in liquid crystalline organic semiconductors Mollinger, S., Noriega, R., Salleo, A., Spakowitz, A., J. 2013
  • Self-assembled protein structures are altered by underlying fluctuations Cordella, N., Lampo, T., Heilshorn, S., C., Spakowitz, A., J. 2013
  • Membrane Fluctuations Destrabilize Clathrin Protein Lattice Order Biophysical Journal Cordella, N., Lampo, T., J., Mehraeen, S., Spakowitz, A., J. 2013
  • Physical modeling of chromosome segregation in E. Coli reveals impact of force and DNA relaxation Lampo, T., Kuwada, N., Wiggins, P., Spakowitz, A., J. 2013
  • Effect of conformation in charge transport for semiflexible polymers Noriega, R., Salleo, A., Spakowitz, A., J. 2013
  • An amphiphilic polysulfone-graft-poly(ethylene) glycol random copolymer for alkaline exchange membrane fuel cells He, S., Mao, S., Spakowitz, A., J., Frank, C., W. 2013
  • Dynamic remodelling of disordered protein aggregates is an alternative pathway to achieve robust self-assembly of nanostructures SOFT MATTER Schoen, A. P., Cordella, N., Mehraeen, S., Arunagirinathan, M. A., Spakowitz, A. J., Heilshorn, S. C. 2013; 9 (38): 9137-9145

    View details for DOI 10.1039/c3sm50830g

    View details for Web of Science ID 000324423700012

  • Discretizing elastic chains for coarse-grained polymer models SOFT MATTER Koslover, E. F., Spakowitz, A. J. 2013; 9 (29): 7016-7027

    View details for DOI 10.1039/c3sm50311a

    View details for Web of Science ID 000321273000046

  • Single molecule imaging reveals a major role for diffusion in the exploration of ciliary space by signaling receptors. eLife Ye, F., Breslow, D. K., Koslover, E. F., Spakowitz, A. J., Nelson, W. J., Nachury, M. V. 2013; 2


    The dynamic organization of signaling cascades inside primary cilia is key to signal propagation. Yet little is known about the dynamics of ciliary membrane proteins besides a possible role for motor-driven Intraflagellar Transport (IFT). To characterize these dynamics, we imaged single molecules of Somatostatin Receptor 3 (SSTR3, a GPCR) and Smoothened (Smo, a Hedgehog signal transducer) in the ciliary membrane. While IFT trains moved processively from one end of the cilium to the other, single SSTR3 and Smo underwent mostly diffusive behavior interspersed with short periods of directional movements. Statistical subtraction of instant velocities revealed that SSTR3 and Smo spent less than a third of their time undergoing active transport. Finally, SSTR3 and IFT movements could be uncoupled by perturbing either membrane protein diffusion or active transport. Thus ciliary membrane proteins move predominantly by diffusion, and attachment to IFT trains is transient and stochastic rather than processive or spatially determined. DOI:

    View details for DOI 10.7554/eLife.00654

    View details for PubMedID 23930224

  • Intrinsic fluctuations lead to broad range of transduced forces in tethered-bead single-molecule experiments PHYSICAL REVIEW E Mehraeen, S., Spakowitz, A. J. 2012; 86 (2)


    We build a theoretical platform for predicting the behavior of tethered-bead single-molecule experiments, accounting for bead translational and rotational fluctuations, the specific type of experimental setup, and the detailed application of tension to the tether molecule. Within this framework, the external force applied to the bead is distinguished from the instantaneous force transduced to the tether molecule, resulting in a distinction between the observable response of the bead and the underlying force fluctuations felt by the tether that directly affect the biomolecular processes being studied. Our theoretical model indicates that the spread of the distribution of tether forces increases with applied external force, resulting in substantial deviations between the external and tether forces. We find that the impact of rotational and translational fluctuations of the bead motion is larger in magnetic tweezers than optical tweezers. However, this distinction diminishes at large external forces, and our asymptotic expressions offer a simple route for experimental analyses. Overall, our theory demonstrates that fluctuations in the tether molecule due to bead rotation and translation lead to a broad range of tether forces.

    View details for DOI 10.1103/PhysRevE.86.021902

    View details for Web of Science ID 000307278000001

    View details for PubMedID 23005780

  • Force fluctuations impact kinetics of biomolecular systems PHYSICAL REVIEW E Koslover, E. F., Spakowitz, A. J. 2012; 86 (1)


    A wide array of biological processes occur at rates that vary significantly with force. Instantaneous molecular forces fluctuate due to thermal noise and active processes, leading to concomitant fluctuations in biomolecular rate constants. We demonstrate that such fluctuations have a dramatic effect on the transition kinetics of force-dependent processes. As an illustrative, biologically relevant example, we model the pausing of eukaryotic RNA polymerase as it transcribes nucleosomal DNA. Incorporating force fluctuations in the model yields qualitatively different predictions for the pausing time scales when compared to behavior under the average force alone. We use our model to illustrate the broad range of behaviors that can arise in biomolecular processes that are susceptible to force fluctuations. The fluctuation time scale, which varies significantly for in vivo biomolecular processes, yields very different results for overall rates and dramatically alters the force regime of relevance to the transition. Our results emphasize the importance of transient high-force behavior for determining kinetics in the fluctuating environment of a living cell.

    View details for DOI 10.1103/PhysRevE.86.011906

    View details for Web of Science ID 000306331400005

    View details for PubMedID 23005451

  • Analytical Tools To Distinguish the Effects of Localization Error, Confinement, and Medium Elasticity on the Velocity Autocorrelation Function BIOPHYSICAL JOURNAL Weber, S. C., Thompson, M. A., Moerner, W. E., Spakowitz, A. J., Theriot, J. A. 2012; 102 (11): 2443-2450


    Single particle tracking is a powerful technique for investigating the dynamic behavior of biological molecules. However, many of the analytical tools are prone to generate results that can lead to mistaken interpretations of the underlying transport process. Here, we explore the effects of localization error and confinement on the velocity autocorrelation function, C?. We show that calculation of C? across a range of discretizations can distinguish the effects of localization error, confinement, and medium elasticity. Thus, under certain regimes, C? can be used as a diagnostic tool to identify the underlying mechanism of anomalous diffusion. Finally, we apply our analysis to experimental data sets of chromosomal loci and RNA-protein particles in Escherichia coli.

    View details for DOI 10.1016/j.bpj.2012.03.062

    View details for Web of Science ID 000305003100006

    View details for PubMedID 22713559

  • Nonthermal ATP-dependent fluctuations contribute to the in vivo motion of chromosomal loci PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Weber, S. C., Spakowitz, A. J., Theriot, J. A. 2012; 109 (19): 7338-7343


    Chromosomal loci jiggle in place between segregation events in prokaryotic cells and during interphase in eukaryotic nuclei. This motion seems random and is often attributed to brownian motion. However, we show here that locus dynamics in live bacteria and yeast are sensitive to metabolic activity. When ATP synthesis is inhibited, the apparent diffusion coefficient decreases, whereas the subdiffusive scaling exponent remains constant. Furthermore, the magnitude of locus motion increases more steeply with temperature in untreated cells than in ATP-depleted cells. This "superthermal" response suggests that untreated cells have an additional source of molecular agitation, beyond thermal motion, that increases sharply with temperature. Such ATP-dependent fluctuations are likely mechanical, because the heat dissipated from metabolic processes is insufficient to account for the difference in locus motion between untreated and ATP-depleted cells. Our data indicate that ATP-dependent enzymatic activity, in addition to thermal fluctuations, contributes to the molecular agitation driving random (sub)diffusive motion in the living cell.

    View details for DOI 10.1073/pnas.1119505109

    View details for Web of Science ID 000304090600048

    View details for PubMedID 22517744

  • Membrane fluctuations alter the fluidity of clathrin protein lattices Spakowitz, A., J., Cordella, N., Mehraeen, S. 2012
  • Viral Packaging of Nucleic Acids Polymer Science: A Comprehensive Reference Spakowitz, A., J., Muthukumar, M. edited by Möller, M., Matyjaszewski, K. Elsevier Academic Press, San Diego, CA.. 2012: 231-245
  • Self-Assembly of Clathrin Protein 3D Structures Arunagirinathan, M., A., Gibbons, B., J., Schoen, A., P., Spakowitz, A., J., Heilshorn, S., C. 2012
  • Force Fluctuations Impact Genome Processing Kinetics Spakowitz, A., J., Koslover, E. 2012
  • Bridging Length Scales: Hierarchical Coarse-Graining of Elastic Biopolymer Models Koslover, E., F., Spakowitz, A., J. 2012
  • Stability of Heterochromatin Condensation Due to Cooperative Binding Mulligan, P., J., Koslover, E., F., Spakowitz, A., J. 2012
  • Force Fluctuations Play a Key Role in Biomolecular Kinetics Koslover, E., F., Spakowtiz, A., J. 2012
  • Selective dispersion of high purity semiconducting single-walled carbon nanotubes with regioregular poly(3-alkylthiophene)s NATURE COMMUNICATIONS Lee, H. W., Yoon, Y., Park, S., Oh, J. H., Hong, S., Liyanage, L. S., Wang, H., Morishita, S., Patil, N., Park, Y. J., Park, J. J., Spakowitz, A., Galli, G., Gygi, F., Wong, P. H., Tok, J. B., Kim, J. M., Bao, Z. 2011; 2


    Conjugated polymers, such as polyfluorene and poly(phenylene vinylene), have been used to selectively disperse semiconducting single-walled carbon nanotubes (sc-SWNTs), but these polymers have limited applications in transistors and solar cells. Regioregular poly(3-alkylthiophene)s (rr-P3ATs) are the most widely used materials for organic electronics and have been observed to wrap around SWNTs. However, no sorting of sc-SWNTs has been achieved before. Here we report the application of rr-P3ATs to sort sc-SWNTs. Through rational selection of polymers, solvent and temperature, we achieved highly selective dispersion of sc-SWNTs. Our approach enables direct film preparation after a simple centrifugation step. Using the sorted sc-SWNTs, we fabricate high-performance SWNT network transistors with observed charge-carrier mobility as high as 12?cm(2)?V(-1)?s(-1) and on/off ratio of >10(6). Our method offers a facile and a scalable route for separating sc-SWNTs and fabrication of electronic devices.

    View details for DOI 10.1038/ncomms1545

    View details for Web of Science ID 000297686500028

    View details for PubMedID 22086341

  • A Boltzmann-weighted hopping model of charge transport in organic semicrystalline films JOURNAL OF APPLIED PHYSICS Kwiatkowski, J. J., Jimison, L. H., Salleo, A., Spakowitz, A. J. 2011; 109 (11)

    View details for DOI 10.1063/1.3594686

    View details for Web of Science ID 000292214700082

  • Heterochromatin Protein 1: An Epigenetic Mechanism for Chromatin Condensation Mulligan, P., J., Koslover, E., F., Spakowitz, A., J. 2011
  • Impact of Defect Creation and Motion On the Large-Scale Reorganization Dynamics of Self-Assembled Clathrin Lattices Mehraeen, S., Cordella, N., Spakowitz, A., J. 2011
  • Force Fluctuations Dictate Kinetics of Biomolecular Systems Spakowitz, A., J. 2011
  • Theoretical Modeling of the Packaging and Accessibility of DNA Koslover, E., F., Mulligan, P., J., Díaz de la Rosa, M., A., Spakowitz, A., J. 2011
  • Force Fluctuations Dictate Kinetics of Biomolecular Systems Koslover, E., F., Spakowitz, A., J. 2011
  • Impact of defect creation and motion on the thermodynamics and large-scale reorganization of self-assembled clathrin lattices SOFT MATTER Mehraeen, S., Cordella, N., Yoo, J. S., Spakowitz, A. J. 2011; 7 (19): 8789-8799

    View details for DOI 10.1039/c1sm05053b

    View details for Web of Science ID 000295085700015

  • Local Geometry and Elasticity in Compact Chromatin Structure BIOPHYSICAL JOURNAL Koslover, E. F., Fuller, C. J., Straight, A. F., Spakowitz, A. J. 2010; 99 (12): 3941-3950


    The hierarchical packaging of DNA into chromatin within a eukaryotic nucleus plays a pivotal role in both the accessibility of genomic information and the dynamics of replication. Our work addresses the role of nanoscale physical and geometric properties in determining the structure of chromatin at the mesoscale level. We study the packaging of DNA in chromatin fibers by optimization of regular helical morphologies, considering the elasticity of the linker DNA as well as steric packing of the nucleosomes and linkers. Our model predicts a broad range of preferred helix structures for a fixed linker length of DNA; changing the linker length alters the predicted ensemble. Specifically, we find that the twist registry of the nucleosomes, as set by the internucleosome repeat length, determines the preferred angle between the nucleosomes and the fiber axis. For moderate to long linker lengths, we find a number of energetically comparable configurations with different nucleosome-nucleosome interaction patterns, indicating a potential role for kinetic trapping in chromatin fiber formation. Our results highlight the key role played by DNA elasticity and local geometry in regulating the hierarchical packaging of the genome.

    View details for DOI 10.1016/j.bpj.2010.10.024

    View details for Web of Science ID 000285438900017

    View details for PubMedID 21156136

  • Subdiffusive motion of a polymer composed of subdiffusive monomers PHYSICAL REVIEW E Weber, S. C., Theriot, J. A., Spakowitz, A. J. 2010; 82 (1)


    We use Brownian dynamics simulations and analytical theory to investigate the physical principles underlying subdiffusive motion of a polymer. Specifically, we examine the consequences of confinement, self-interaction, viscoelasticity, and random waiting on monomer motion, as these physical phenomena may be relevant to the behavior of biological macromolecules in vivo. We find that neither confinement nor self-interaction alter the fundamental Rouse mode relaxations of a polymer. However, viscoelasticity, modeled by fractional Langevin motion, and random waiting, modeled with a continuous time random walk, lead to significant and distinct deviations from the classic polymer-dynamics model. Our results provide diagnostic tools--the monomer mean square displacement scaling and the velocity autocorrelation function--that can be applied to experimental data to determine the underlying mechanism for subdiffusive motion of a polymer.

    View details for DOI 10.1103/PhysRevE.82.011913

    View details for Web of Science ID 000280067800007

    View details for PubMedID 20866654

  • Dynamic Strategies for Target-Site Search by DNA-Binding Proteins BIOPHYSICAL JOURNAL de la Rosa, M. A., Koslover, E. F., Mulligan, P. J., Spakowitz, A. J. 2010; 98 (12): 2943-2953


    Gene regulatory proteins find their target sites on DNA remarkably quickly; the experimental binding rate for lac repressor is orders-of-magnitude higher than predicted by free diffusion alone. It has been proposed that nonspecific binding aids the search by allowing proteins to slide and hop along DNA. We develop a reaction-diffusion theory of protein translocation that accounts for transport both on and off the strand and incorporates the physical conformation of DNA. For linear DNA modeled as a wormlike chain, the distribution of hops available to a protein exhibits long, power-law tails that make the long-time displacement along the strand superdiffusive. Our analysis predicts effective superdiffusion coefficients for given nonspecific binding and unbinding rate parameters. Translocation rate exhibits a maximum at intermediate values of the binding rate constant, while search efficiency is optimized at larger binding rate constant values. Thus, our theory predicts a region of values of the nonspecific binding and unbinding rate parameters that balance the protein translocation rate and the efficiency of the search. Published data for several proteins falls within this predicted region of parameter values.

    View details for DOI 10.1016/j.bpj.2010.02.055

    View details for Web of Science ID 000278913500023

    View details for PubMedID 20550907

  • Modeling Targeted Binding of Nanoparticles to Cell Surfaces Cordella, N., Mehraeen, S., Spakowitz, A., J. 2010
  • Theoretical Modeling of the Weaving of Clathrin Into Nanoscale Baskets Mehraeen, S., Cordella, N., Yoo, J., S., Spakowitz, Andrew, J. 2010
  • Theoretical Model of HP1-Induced Heterochromatin Formation Mulligan, P., J., Koslover, E., F., Spakowitz, Andrew, J. 2010
  • Target site search strategy of DNA-binding proteins Díaz de la Rosa, M., A., Koslover, E., F., Mulligan, P., J., Spakowitz, A., J. 2010
  • Role of DNA fluctuations and conformations in RNP polymerase translocation and bulge formation in a single nucleosome Sudhanshu, B., Koslover, E., F., Mihardja, S., Spakowitz, A., J. 2010
  • Role of DNA Elasticity and Nucleosome Geometry in Hierarchical Packaging of Chromatin Koslover, E., F., Fuller, C., Straight, A., F., Spakowitz, A., J. 2010
  • A Predictive Theoretical Model For Clathrin Self-Assembly Mehraeen, S., Cordella, N., Spakowitz, A., J. 2010
  • Chromosomal loci move subdiffusively through a viscoelastic cytoplasm Physical Review Letters Weber, S., Spakowitz, A., J., Theriot, J. 2010; 104: 238102
  • Translocation Dynamics of DNA-Binding Proteins Díaz de la Rosa, M., A., Koslover, E., F., Mulligan, P., J., Spakowitz, A., J. 2010
  • Modeling Effects of Nanoparticle Size and Ligand Display On Targeted Cell-Surface Binding Cordella, N., Mehraeen, S., Yoo, J., S., Spakowitz, Andrew, J. 2010
  • Chromosomal Loci Move Subdiffusively through a Viscoelastic Cytoplasm Spakowitz, A., J., Weber, S., Theriot, J. 2010
  • The Impact of Biological Fluctuations On Transport Processes within Live Bacterial Cells Spakowitz, A., J., Weber, S., Theriot, J. 2010
  • Mathematical Modeling of Charge Transport in Conjugated-Polymer Materials Spakowitz, A., J. 2010
  • Twist and Tension-Mediated Elastic Coupling between DNA-Bending Proteins Koslover, E., F., Spakowitz, A., J. 2009
  • Target Site Search Strategy Of Gene Regulatory Proteins Díaz de la Rosa, M., A., Spakowitz, A., J. 2009
  • Theoretical model for the self-assembly of clathrin into targeted nanoscale assemblies Mehraeen, S., Schoen, A., Hwang, S., Y., Heilshorn, S., C., Spakowitz, A., J. 2009
  • Target site search strategy of gene regulatory proteins Spakowitz, A., J. 2009
  • End-to-end distribution for a wormlike chain in arbitrary dimensions PHYSICAL REVIEW E Mehraeen, S., Sudhanshu, B., Koslover, E. F., Spakowitz, A. J. 2008; 77 (6)


    We construct an efficient methodology for calculating wormlike chain statistics in arbitrary D dimensions over all chain rigidities, from fully rigid to completely flexible. The structure of our exact analytical solution for the end-to-end distribution function for a wormlike chain in arbitrary D dimensions in Fourier-Laplace space (i.e., Fourier-transformed end position and Laplace-transformed chain length) adopts the form of an infinite continued fraction, which is advantageous for its compact structure and stability for numerical implementation. We then proceed to present a step-by-step methodology for performing the Fourier-Laplace inversion in order to make full use of our results in general applications. Asymptotic methods for evaluating the Laplace inversion (power-law expansion and Rayleigh-Schrödinger perturbation theory) are employed in order to improve the accuracy of the numerical inversions of the end-to-end distribution function in real space. We adapt our results to the evaluation of the single-chain structure factor, rendering simple, closed-form expressions that facilitate comparison with scattering experiments. Using our techniques, the accuracy of the end-to-end distribution function is enhanced up to the limit of the machine precision. We demonstrate the utility of our methodology with realizations of the chain statistics, giving a general methodology that can be applied to a wide range of biophysical problems.

    View details for DOI 10.1103/PhysRevE.77.061803

    View details for Web of Science ID 000257287500091

    View details for PubMedID 18643291

  • Optical measurement of mechanical forces inside short DNA loops BIOPHYSICAL JOURNAL Shroff, H., Sivak, D., Siegel, J. J., McEvoy, A. L., Siu, M., Spakowitz, A., Geissler, P. L., Liphardt, J. 2008; 94 (6): 2179-2186


    Knowledge of the mechanical properties of double-stranded DNA (dsDNA) is essential to understand the role of dsDNA looping in gene regulation and the mechanochemistry of molecular machines that operate on dsDNA. Here, we use a newly developed tool, force sensors with optical readout, to measure the forces inside short, strained loops composed of both dsDNA and single-stranded DNA. By varying the length of the loops and their proportion of dsDNA, it was possible to vary their internal forces from 1 pN to >20 pN. Surprisingly, internal loop forces changed erratically as the amount of dsDNA was increased for a given loop length, with the effect most notable in the smallest loop (57 nucleotides). Monte Carlo simulations based on the helical wormlike chain model accurately predict internal forces when more than half of the loop is dsDNA but fail otherwise. Mismatches engineered into the double-stranded regions increased flexibility, suggesting that Watson-Crick basepaired dsDNA can withstand high compressive forces without recourse to multibase melts. Fluorescence correlation spectroscopy further excluded transient melting (microsecond to millisecond duration) as a mechanism for relief of compressive forces in the tested dsDNAs. DNA loops with integrated force sensors may allow the comprehensive mapping of the elasticity of short dsDNAs as a function of both sequence and salt.

    View details for DOI 10.1529/biophysj.107.114413

    View details for Web of Science ID 000253676200022

    View details for PubMedID 18065484

  • Three-dimensional architecture of the bacteriophage phi 29 packaged genome and elucidation of its packaging process VIROLOGY Comolli, L. R., Spakowitz, A. J., Siegerist, C. E., Jardine, P. J., Grimes, S., Anderson, D. L., Bustamante, C., Downing, K. H. 2008; 371 (2): 267-277


    The goal of the work reported here is to understand the precise molecular mechanism of the process of DNA packaging in dsDNA bacteriophages. Cryo-EM was used to directly visualize the architecture of the DNA inside the capsid and thus to measure fundamental physical parameters such as inter-strand distances, local curvatures, and the degree of order. We obtained cryo-EM images of bacteriophage that had packaged defined fragments of the genome as well as particles that had partially completed the packaging process. The resulting comparison of structures observed at intermediate and final stages shows that there is no unique, deterministic DNA packaging pathway. Monte Carlo simulations of the packaging process provide insights on the forces involved and the resultant structures.

    View details for DOI 10.1016/j.virol.2007.07.035

    View details for Web of Science ID 000253060200007

    View details for PubMedID 18001811

  • Unraveling the Dynamics of Supercoiled DNA with Theoretical Modeling Díaz de la Rosa, M., A., Spakowitz, A., J. 2008
  • Structural Fluctuations In the Nucleosome Core Particle Sudhanshu, B., Spakowitz, A., J. 2008
  • Chemical Physics Of DNA Packaging In A Nucleosome Core Particle Sudhanshu, B., Spakowitz, A., J. 2008
  • Direct optical measurement of stresses inside circularized DNA loops Siegel, J., Shroff, H., Sivak, D., McEvoy, A., Spakowitz, A., Geissler, P., Liphardt, J. CELL PRESS. 2007: 350A-350A
  • Target-Site Search Strategies of DNA-Binding Proteins Díaz de la Rosa, M., A., Spakowitz, A., J. 2007
  • Theory of Translational and Rotational Fluctuations in Tethered-Bead Single-Molecule Experiments Mehraeen, S., Spakowitz, A., J. 2007
  • Target Site Search Strategy Of Gene Regulatory Proteins Díaz de la Rosa, M., A., Spakowitz, A., J. 2007
  • Chemical Physics Of DNA Packaging In A Nucleosome Core Particle Sudhanshu, B., Spakowitz, A., J. 2007
  • Wrapping Transitions for a Single Nucleosome Under Tension Sudhanshu, B., Spakowitz, A., J. 2007
  • High flexibility of DNA on short length scales probed by atomic force microscopy NATURE NANOTECHNOLOGY Wiggins, P. A., Van der Heijden, T., Moreno-Herrero, F., Spakowitz, A., Phillips, R., Widom, J., Dekker, C., Nelson, P. C. 2006; 1 (2): 137-141


    The mechanics of DNA bending on intermediate length scales (5-100 nm) plays a key role in many cellular processes, and is also important in the fabrication of artificial DNA structures, but previous experimental studies of DNA mechanics have focused on longer length scales than these. We use high-resolution atomic force microscopy on individual DNA molecules to obtain a direct measurement of the bending energy function appropriate for scales down to 5 nm. Our measurements imply that the elastic energy of highly bent DNA conformations is lower than predicted by classical elasticity models such as the worm-like chain (WLC) model. For example, we found that on short length scales, spontaneous large-angle bends are many times more prevalent than predicted by the WLC model. We test our data and model with an interlocking set of consistency checks. Our analysis also shows how our model is compatible with previous experiments, which have sometimes been viewed as confirming the WLC.

    View details for DOI 10.1038/nnano.2006.63

    View details for Web of Science ID 000243902600017

    View details for PubMedID 18654166

  • Effect of force on mononucleosomal dynamics PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Mihardja, S., Spakowitz, A. J., Zhang, Y., Bustamante, C. 2006; 103 (43): 15871-15876


    Using single-molecule optical-trapping techniques, we examined the force-induced dynamic behavior of a single nucleosome core particle. Our experiments using the DNA construct containing the 601 nucleosome-positioning sequence revealed that the nucleosome unravels in at least two major stages. The first stage, which we attributed to the unraveling of the first DNA wrap around the histone octamer, could be mechanically induced in a reversible manner, and when kept at constant force within a critical force range, exhibited two-state hopping behavior. From the hopping data, we determined the force-dependent equilibrium constant and rates for opening/closing of the outer wrap. Our investigation of the second unraveling event at various loading rates, which we attributed to the inner DNA wrap, revealed that this unraveling event cannot be described as a simple two-state process. We also looked at the behavior of the mononucleosome in a high-salt buffer, which revealed that the outer DNA wrap is more sensitive to changes in the ionic environment than the inner DNA wrap. These findings are needed to understand the energetics of nucleosome remodeling.

    View details for DOI 10.1073/pnas.0607526103

    View details for Web of Science ID 000241568500027

    View details for PubMedID 17043216

  • Wormlike chain statistics with twist and fixed ends EUROPHYSICS LETTERS Spakowitz, A. J. 2006; 73 (5): 684-690
  • DNA Structure within a Virus Particle Spakowitz, A., J., Comolli, L., Siegerist, C., E., Grimes, S., Jardine, P., Downing, K., H. 2006
  • Coupled Translational and Rotational Fluctuations of Tethered Beads Spakowitz, A., J., Bustamante, C. 2006
  • Wrapping Transitions in a Single Nucleosome Under Tension Spakowitz, A., J., Mihardja, S., Bustamante, C. 2006
  • Biocompatible force sensor with optical readout and dimensions of 6 nm(3) NANO LETTERS Shroff, H., Reinhard, B. M., Siu, M., Agarwal, H., Spakowitz, A., Liphardt, J. 2005; 5 (7): 1509-1514


    We have developed a nanoscopic force sensor with optical readout. The sensor consists of a single-stranded DNA oligomer flanked by two dyes. The DNA acts as a nonlinear spring: when the spring is stretched, the distance between the two dyes increases, resulting in reduced Förster resonance energy transfer. The sensor was calibrated between 0 and 20 pN using a combined magnetic tweezers/single-molecule fluorescence microscope. We show that it is possible to tune the sensor's force response by varying the interdye spacing and that the FRET efficiency of the sensors decreases with increasing force. We demonstrate the usefulness of these sensors by using them to measure the forces internal to a single polymer molecule, a small DNA loop. Partial conversion of the single-stranded DNA loop to a double-stranded form results in the accumulation of strain: a force of approximately 6 pN was measured in the loop upon hybridization. The sensors should allow measurement of forces internal to various materials, including programmable DNA self-assemblies, polymer meshes, and DNA-based machines.

    View details for DOI 10.1021/nl050875h

    View details for Web of Science ID 000230571300058

    View details for PubMedID 16178266

  • DNA packaging in bacteriophage: Is twist important? Biophysical Journal Spakowitz, A., J., Wang, Z., G. 2005; 88: 3912
  • Semiflexible chain statistics with fixed end orientations Spakowitz, A., J. 2005
  • Topological considerations in nucleic acid hybridization kinetics Nucleic Acids Research Bois, J., S., Venkataraman, S., Choi, H., M. T., Spakowitz, A., J., Wang, Z., G., Pierce, N., A. 2005; 33 (13): 4090
  • End-to-end distance vector distribution with fixed end orientations for the wormlike chain model Phys. Rev. E Spakowitz, A., J., Wang, Z., G. 2005; 72: 41802
  • Exact results for a semiflexible polymer chain in an aligning field Macromolecules Spakowitz, A., J., Wang, Z., G. 2004; 37: 5814
  • Semiflexible polymer solutions: I. phase behavior and single-chain statistics Journal of Chemical Physics Spakowitz, A., J., Wang, Z., G. 2003; 119: 13113
  • A semiflexible polymer confined to a spherical surface Physical Review Letters Spakowitz, A., J., Wang, Z., G. 2003; 91: 166102
  • Towards an Understanding of the Physical Manipulation of DNA Spakowitz, A., J., Wang, Z., G. 2003
  • Twist Effect in DNA Packaging Spakowitz, A., J., Wang, Z., G. 2003
  • Shape dynamics of elastic filaments due to internal strain Spakowitz, A., J., Wang, Z., G. 2002
  • Free expansion of elastic filaments Physical Review E Spakowitz, A., J., Wang, Z., G. 2001; 64: 61802