How cells know where to go? Signal Detection and Processing at the Microorganism Level Herbert Levine UCSD – Center for Theoretical Biological Physics (NSF) Outline: Experiments on chemotactic response in Dictyostelium Signal versus noise in gradient sensing Nonlinear amplification via signal transduction Cell motility mechanics *Work also supported by NIGMS P01 * Collaboration between 2 bio labs, 1 exp phys lab, and a theory group

Cells know where to go Wild-type leukocyte response to fin wound Matthias et al (2006) Cells can bias their motility machinery based on detecting signals; Much of the time, these signals are diffusing chemicals, but cells can also use mechanical cues Applications to immune response, wound healing, cancer metastasis

Close-up view of chemotaxis Dictybase Website Cell moves about one cell diameter per minute Decision-making maintains flexibility (limited hysteresis) We work on chemotaxis in a model organism, the Dictyostelium amoeba simplified signaling availability of genetics tools ease of experiments chemotaxis is crucial for survival

Questions for theory Can one predict macroscopic measures of cell motility given the space-time course of an applied signal and (possibly) the cell history –Cell speed, directional persistence, chemotactic index –Not just averages, but also distributions –Not just wild-type, but also mutant strains We will tackle this problem in stages –Sensing of the signal –Making the chemotactic decision –Driving the cell ’ s acto-myosin motor

Mutual Information Sensing is done roughly 50K receptors, each with a binding constant of 30nM. How much information do we get about a parameter which affects our noisy measurement? Given the on and off rates for the receptors (measured in single molecule measurements), we can calculate the mutual information contained in one measurement snapshot result in bits for small gradients

Microfluidics Revolutionizing measurements Soft lithography Stable gradients Controlled geometries Rapid switching Brings experiments to where they can be compared more quantitatively to theory From A. Groisman lab; Skoge et al (2010)

Cell migration in a gradient cAMP gradient flow rate 640  m/s 1h real time = 8 sec movie From Song et al

Compare to experiment We can directly compare this number to the information about the gradient indicated by the actual cell motion C.I. =  Movement up gradient 5% gradient C.I. = ±  no gradient Fuller, Chen et al, PNAS (2010)

In shallow gradients the E + I mutual information is limited by the external mutual information (receptor occupancy). E + I mutual information decrees at higher concentrations due to an increase in internal noise. We also analyzed the instantaneous angle of the cells in the devices. Result: The cell operates at the sensor noise limit for small gradients and concentrations; eventually limited by other noise and/or processing losses Distribution allows calculation of the cell ’ s output information

Cell Decision Model Can we go beyond this phenomenological approach to discuss actual gradient sensing process We will focus on a gradient sensing approach, which tries to explain how external signals can get amplified to the level of decisions

Subcellular polarity markers; front vs back Receptors Occupancy PI 3 K PTEN RAC Myosin Starting with the work of Parent and Devreotes, response can be tracked by subcellular markers Uniform receptor Lipid modifications F-actin at the front Myosin at the rear These allow for the measurement of the kinetics of the gradient sensing step

Focus on RAS Ras is activated by a GEF; inactivated by a GAP Note: Can attach fluorescent marker to RBD; can be used to track decision

Cell in a microfluidic device with chemoattractant gradient, variable vertical height. Most of the cell in focal plane: no bleaching issues Visualize Ras*, an upstream signaling component Monica Skoge, Loomis lab Ras activations correlates with cell motility (Hecht et al)

Detailed measure of correlation From Hecht et al PLoS Comp. Bio (2011) Measure is the cosine of angle between patch and protrusion Done both in under agar expts and in microfluidic chamber

Models of Gradient sensing Gradient sensing is hard because it cannot be done by local circuits in the cell Models must postulate an inhibitory mechanism (either direct or via depletion; direct can involve either chemical or mechanical coupling) Models make quantitative predictions that can be used to rule them out or allow them to survive

Model classification First, gradient determines allowed protrusion direction (needs comparison mechanism, based on global inhibitor) Pseudopods are formed independently of previous ones Pseudopods occur independently of gradient direction, often by splitting mechanism Gradient biases lifetimes (needs comparison mechanism, based on global inhibitor) Sensing and pseudopod dynamics are strongly coupled; both feedforward and feedback is needed Strong gradient? Weak gradient? “Instructive” Reality? “Selective” X

LEGI Local activation and global inhibition explains adaptation to global stimulus versus steady gradient response Membrane-bound activator Diffusing inhibitor We will assume that RAS is the effector molecule Ras* Parent+Devreotes; Iglesias +Levchenko Ph-domain

LEGI as applied to RAS activation Since A and I are both proportional to S in steady-state, uniform S results in a transient activation of E but eventual perfect adaptation. With a non-uniform S, I gives average value and A remains local - pattern in the effector E

LEGI Local activation and global inhibition explains adaptation to global stimulus versus steady gradient response Membrane-bound activator Diffusing inhibitor We will assume that RAS is the effector molecule Ras* Parent+Devreotes; Iglesias +Levchenko Ph-domain

Perfect Adaptation Only two simple ways to obtain perfect adaptation in signaling; integral feedback (B) versus incoherent feed-forward (A) Integral feedback relevant for E. Coli chemotaxis; here, other strategy is used Can be directly investigated using microfluidic device (~ 1 sec switching time) and fluorescent marker with Ras binding domain K. Takeda, Firtel lab

Adaptation kinetics Takeda et al, Science Sign., (2012) X

Amplifying by Ultrasensitivity Assume that the K ’ s are very small and the baseline rates are balanced Loomis, Levine, Rappel (2009) Janetopoulos et al 2004

“ Phase-field ” simulation of Reaction-diffusion equations Use Monte Carlo calculation to obtain noise signal at the receptor level Use this receptor noise signal as input in a 2d calculation of the internal signalng pathways Mathematical methods can be used to calculate effect of receptor noise on internal pathways

Snapshots With physiological surface diffusion (for lipids), mean concentration of 1nM with K d =30nM, N=70K 2% 5% 10%

Mutual Information after processing Preliminary results Model captures high concentration saturation Possible need for new mechanism at low C Can be compared to other gradient sensing models Background c = 5nm

Back to the gradient problem In the presence of a gradient, activated Ras becomes localized to the front but in a stochastic, patchy fashion –May be due to feedback from the actin cytoskeleton –Models which couple “ compass ” systems (LEGI) to excitable ( “ actin ” ) dynamics (see Hecht et al, PRL (2010); Xiong et al PNAS (2010) As we have seen, these patches are very highly correlated with sites of actin polymerization and membrane protrusion –Models for Ras patches can be used to create simple models of cell morphodynamics

Actin-Myosin dynamics

Back to the gradient problem In the presence of a gradient, activated Ras becomes localized to the front but in a stochastic, patchy fashion –May be due to feedback from the actin cytoskeleton –Models which couple “ compass ” systems (LEGI) to excitable ( “ actin ” ) dynamics (see Hecht et al, PRL (2010); Xiong et al PNAS (2010) As we have seen, these patches are very highly correlated with sites of actin polymerization and membrane protrusion –Models for Ras patches can be used to create simple models of cell morphodynamics

Pseudopod distributions We can then choose patches completely at random from this distribution We then embed this in simple motility model

Fun and Games Note: Mechanical model contains just nodes connected by springs, together with an overall area constraint and patch forcing

Left-right temporal ordering? Even in a random pseudopod simulation, there is automatically left- right bias for chemotaxing cells Alternative - Otsugi (2010)

A word about applications Amoeboid motion is one of the ways that tumor cells can spread This capability limits current approaches to metastatic disease We have begun studying the interplay of noise with more complex 3d geometries for amoeboid motion Friedl and Wolf, 2003 (Hecht et al PloS One (2011))

Summary Chemotactic response requires a sophisticated biophysics approach –Models are necessarily spatially-extended –Noise is not negligible –Cell geometry is complex and changeable We have used a variety of methods to look initially at the signaling and more recently at the mechanics Eventually, we will understand how it really works!