DISCUSSION MEETING
ACTIVE MATTER AND BEYOND
ORGANIZERS: Jean-François Joanny (Collège de France), Vijaykumar Krishnamurthy (ICTS, India), Cristina Marchetti (University of California, Santa Barbara, USA), Gautam Menon (Ashoka University, India and IMSc Chennai, India), Shraddha Mishra (Indian Institute of Technology (BHU), Varanasi, India), Madan Rao (NCBS, India) and Prerna Sharma (IISc, India)
DATE & TIME: 06 November 2023 to 10 November 2023
VENUE: Ramanujan Lecture Hall, ICTS Bengaluru
Active matter is a novel class of driven nonequilibrium systems wherein a many-body system with an energy throughput consumes and dissipates energy at the level of the individual units. This field has grown in prominence in the last couple of decades with immense applicability in diverse areas such as granular and glassy systems, control theory, and biological systems. Many biologically crucial processes, such as the dynamics in the cellular cytoskeleton, the collective motion of cells, the progression of cancer, and the large-scale migratory behavior of bird flocks, mammal herds, ants, and fish schools have been modeled within the active matter framework.
The meeting will feature research talks that will discuss recent progress in the field. Additionally, several pedagogical talks will provide a broad overview for young researchers in the country and help develop an appreciation for the significant new developments. The meeting will provide ample opportunities for young researchers to interact with the speakers along with poster sessions to enable stimulating discussions.
Prof. Sriram Ramaswamy will be delivering three Infosys-ICTS Chandrasekhar lectures as part of this meeting. Considering the profound and pioneering contributions of Prof. Sriram Ramaswamy in developing the field of active matter and nurturing the younger generations, we plan to have a special session felicitating him during this meeting.
Accommodation will be provided for outstation participants at our on campus guest house.
CONTACT US: amab@icts.res.in
PROGRAM LINK: https://www.icts.res.in/discussion-meeting/amab2023
Okay uh great I want to first thank the organizers for organizing this wonderful uh conference and for having me here uh it’s a great honor and privilege to to be able to talk here and I wanted to begin with of course congratulating uh Shri um for his ous career and his
Birthday and I didn’t have any personal photos of sham so here’s a painting I gifted him yesterday um so happy 66th birthday um and I wanted to uh I first met shiram as a graduate student and had uh it was a great opportunity to work with him uh on on several problems in
Active liquid crystals and defects uh none of which I will tell you about today uh but I want to go back to of course a paper that’s been referenced many many many times uh in this conference already on you know one of his Landmark works on looking at the
Impact and importance of hydrodynamics and and fluid flows in active suspensions and so there’s been a lot of focus on wet active fluids and I want to tell you a little bit about what uh in some work that we’ve been doing in asking what happens in the context of
Wet active solids um and so that’s going to be the content of my talk today today um so what do I mean by wet active solids and uh when I say A little I want to tell you a little bit about physics in of these systems but also uh
Contextualize this in a biological context and say what can we use and how can we use uh some of these ideas of acat physics in solid systems uh to understand some potentially um important features of physiology um so water of course is the largest component by volume uh of all of our cells
Um and often times we don’t think about the movement and dynamics of water within cells as being really uh relevant for its motility in morphology but um it does play a role and and one place where we know a lot about water movements driving motion is of course in Plants
You know they drive fast motions particularly uh through hydraulic movements of water through hydrated tissues and cells uh most one of the more famous ones being the SN mapping of the Venus flly trap in animals of course we have muscles to go around and do our things including motion and behavior um
And I want to suggest and ask and think about um what is the role of the water within muscle fibers and is there um is there a way to think about in a coast grain sense of muscle as a soft active and hydraulic engine uh and what are the
Consequen quences of thinking of muscle as essentially what’s in the title a wet active solid so it’s not just a collection of molecules but it’s a solid Matrix of actomyosin sitting inside a membrane uh and all of this is immersed in a fluid which is cytool and the
Combined dynamics of all of these things what are what does it uh how does it constrain physiological properties and mechanics and dynamics of muscle and for the details uh of the work uh there’s a preprint if you’re interested uh this is work that I did with al- mahavan when I
Was um still at Harvard until a few months ago and I’m currently at the University of Michigan um okay so uh I want to perhaps begin with a broad uh question uh and sort of taking a step back which is if we if you want to think about the range
And limits of motion of muscle driven movements um now let’s look around in the natural world what’s the spread of of the kinds of things that muscle driven movements uh can accomplish and one of the most uh remarkable uh spread of features is in the rates of uh uh of
Such movements so there are some extremely fast movements that are driven by muscle in us it’s the fastest movements are on the 10 htz time scales which are eye movements but uh in sound production in snakes and insects but also most remarkably in Flight particularly in insect flight you see
Extremely rapid movements almost on the ranges of you know milliseconds or hundreds of thousands of Hertz time scales of um muscle driven sort of uh Wing beats and in many of these examples particularly in small insects including mosquitoes and bees uh these movements are not regulated and dictated directly
By the neurons or by calcium that is cycling and in many of these cases uh the muscle is Contracting at at rates that are much faster than the neurons can control and so there is an natural question is that uh first of all there’s this WID spread of of U of rates of
Contraction can we make sense of it can we understand it what are the parameters that we should think about in terms of going from you know the slow to the Fast and the fastest um and if the neurons and the calcium cycling that is eventually Upstream of uh the
Controlling of of uh um muscular contraction if that’s not the primary rate limiting step then what are the bustle intrinsic uh rate limiting steps and what are the biophysical principles of that and for this um as I I’m sure all of us would appreciate uh perhaps we
Should go just beyond thinking about the molecular kinetics and is there a CO grain effective mesoscale description uh that integrates the uh the properties of uh the molecular all the way up to the the fiber properties and so this is the sort of large scale set of questions
That I want to try to at least start on uh trying to get an handle over and uh provide you with a construction of at least one model uh which tries to do some of this and and demonstrate some of the consequences for physiology particularly in the context of Rapid
Movements uh okay so um in a course uh at at at a CO grain level you know one of the things again that we all sort of intuitively know and also appreciate uh just in terms of how um biology of cells are um muscle like every other cell is
Extremely complicated and it’s extremely complex in terms of its organization it’s very hierarchical it’s very multiscale you have um filaments of actin and myosin which form essentially a very well-ordered crystalline lattice um and and those structures are essentially on the Micron scale but individual fibers of muscles which are
Multinucleated long slender fibers can be very large and some of them can even be millimeter or centimeter scale uh long so you have to span this wide range of scales um a lot of focus has been on the molecular ingredients of contractility but at a CO grained level
Oh essentially one conceptual picture is to note that muscle is a soft it has uh some elastic compliance it’s active of course it can the motors consume chemical fuel to generate contractile forces it’s highly anisotropic uh these slender fibers are very different uh in in along the axis
Versus across uh and of course the final point which is all of these polymeric this polymeric Matrix is immersed in cytool which is essentially largely water um and so this Coast grain picture is what I want you to have in mind and so essentially I want to think about the
Uh I want to think about a CO grain mesoscale description of muscle fibers as an active sponge that’s what I mean by a wet active solid um and so immediately this picture suggests a problem if I have to uh contract rapidly so if you want to contract a large fluid
Filled fiber uh rapidly you cannot do that everywhere at the same time you cannot do it globally what you can do is you can contract locally and as you contract locally you squeze squeeze fluid and redistribute it internally internal to the fiber but that is a process that takes time and so the
Hypothesis is that um in very very rapid uh contractions of uh muscle potentially Hydraulics that is redistributions of fluid internal to the fiber should potentially be rate limiting and we should account for it so the question is how do we do that um and uh what are the
Evidences for this so can we get uh can we we make sense of this uh with the existing experimental evidence um and so some of the consequences of such a close grain picture as I already said is that you cannot you cannot have contractions that are Global but you can do it
Locally so that means deformations must be spatially heterogeneous you must have gradients you of course have three-dimensional deformations it’s not just a uniaxial system and of course uh naturally we within this picture we expect there should be fluid flow and fluid redistribution within the fiber um and so what’s the quantitative evidence
For this of course no one’s really gone and measured fluid in Contracting muscle fibers and there’s uh even measuring specially heterogeneous trins is is possible and there’s some evidence for it but it’s quite hard uh and so the state-of-the-art measurements uh that we sort of reanalyze from a number of
Different uh uh papers in the existing literature uh some of which are put up over here so let me walk you through what’s being plotted so in a in a variety of different organisms in various different uh conditions in vitro X Vivo inv Vivo what not details are not
Important basically if you think about an individual fiber it’s like a cylindrical you know it’s like a cylinder uh there are two primary modes of uh deformation if you D axis symmetry one is changing the length the other is changing the radius those are the two strains so the radial strain the axial
Strain that’s what’s Ed on the two axis for all of these uh examples and what you are seeing is spontaneous oscillations of muscle fibers uh are are what are plotted as these curves so as the fiber is oscillating uh it generates both radial and axial strain So three-dimensionally Def threedimensional
Deformations um and and these are all local strains uh and as you oscillate you you Traverse this curve now the first thing to take away from all of these uh all of these experimental data is that none of these deformations preserve local volume they’re not isocoric
Isocoric would mean that you sit on this black line um but none of these deformations preserve local volume suggesting that uh you this this conceptual picture that I pointed out that you have local contractions which squeeze and redistribute flow within the fiber is potentially relevant and is
Happening um so that’s the first piece of uh sort of take away from here the second is a point that I’ll come back to at a at a later point in this talk which is that uh some of in some conditions not all these uh deformations Cycles
Enclose a non-zero area and so you have strained Cycles which are three-dimensional and they have a nonzero area as you oscillate that’s something that’ll be important at the end okay so the local volume in these deformations is not conserved suggesting that fluid flow internal to the cell
Should be important so can we now the task at hand is can we build a model that naturally captures this and explains this and and demonstrates some consequences of having such um hydraulic movements okay um and so the for the to do this the framework that we use is of
Po elasticity so we use a two a mixture a biphasic mixture like model of a solid Matrix which is essentially to describe the uh actin and and myosin polymer Network which has in last compliance and and the fluid part of it is just a neonian fluid the basic ingredients
Are are described over here so globally the whole system is in you know there’s no inertia you have force balance there’s an elastic stress for the solid part the the pressure is the only relevant uh stress for the fluid the flow of the fluid itself is given by
Daria’s law which which captures the relative movement of the fluid relative to the solid uh is driven by pressure gradients on large scales and of course globally the whole system is incompressible even though the solid and the fluid independently are compressible because a solid is porous um and so this
Is just a statement of mass conservation because you have no exchange of material with the external world and a key consequence of of such a sponge like description is that pressure in this material doesn’t equilibrate instantly even though inertia is negligible um and the Sound Speed is effectively infinite
Uh pressure in fact takes some finite amount of time and this is it it it diffuses and so there is a time scale which is given by the ratio of the viscosity to the elastic modulus but there is a geometric parameter which can be very large and this is the length
Scale over which fluid has to move relative to the pore size which is the size through which the what the fluid has to uh permeate and so this is the prolastic or permeation time scale which can be quite large particularly because of this geometric and structural
Parameter um and we want to include this physical feature into a model for muscle of course all of this is passive this is if you want meat uh but if you make it active then there’s a new part to the elastic to the uh a new stress in the
Solid Matrix which is an active stress but the origin of the active stress is of course now uh the you have to think about the molecular kinetics of the myosin binding and unbinding from actin so for that we go down uh scale and we do a simple model of uh binding kinetics
Of Motors that bind and unbind with given rates and when they bind they generate forces we generate the active stress the details I won’t go into but just to flash um we have a kinetic equation uh for the motor density a corresponding equation that we can derive for the force generated by the
Motors when they bind and all of this gets packaged into an anisotropic active stress which generates not just axial contractile forces but also radial contractile forces simply because of the binding geometry of the motor the motor binds at a given angle and can generate forces in both directions and so there’s
Two ingredients that are important that we include over here which is pieces of biophysical feedback uh both of which are well known from single molecule experiments one is that the binding rate of the motor onto actin decreases with a separation between the filaments that makes sense the probability of Bing goes
Down as you separate the filaments further away the second is that the unbinding rate uh depends on the load on the motor and so both of these are are very generic pieces of feedback which we include in and now we have a complete uh model which connects the molecular
Kinetics to the mechanics and hydraulics of at the fiber scale what are the consequences of this um what one of the consequences is if the activity is large enough then you obtain spontaneous oscillations which now in a cartoon form are exactly what I suggested in in a conceptual from the conceptual picture
Which is you have active hydraulic oscillation so if you have a spatial gradient of active stresses wherein you have more myosin on one side Less on the other you start Contracting in a espcially inhomogeneous fashion as you contract you squeeze and you cause flow you cause fluid to flow from one end to
The other this l process happens on a time scale which is on this permeation or prolastic time scale the feedback of the load dependence of the motor kinetics causes uh further accumulation of uh myosin in regions of distension in regions of tension causing contraction and this this feedback cycle coupling
Fluid flow to the recruitment uh of myosin sustains in a in a in an oscillatory manner um with two times scales one being a kinetic time scale which is the time scale it takes to build up active stresses and the other being the time scale it takes to
Redistribute fluid within the fiber and the r the product of the two or the geometric mean of the two is what dictates the oscillation frequency question yeah so to K is the is related to binding unbinding fine that that’s why you can somehow get a high frequency
Yes yes so it’s it’s unpackaged version of The Binding and unbinding rates I’m not giving you the actual Expressions um but it’s a combination it’s not just the binding kinetics that dictates the uh eventual contraction rates but is a combination of The Binding kinetics and the prolastic time scale right
Yeah uh you mean Theta here that’s a fixed number there’s no Dynamics for that yeah okay so here so that’s and and B because I said that generic contractions uh you know typical contractions generically induce uh fluid flow within the fiber so you shouldn’t
Be able to do better than such a um uh you shouldn’t be able to contract at a rate faster than such a frequency and so if you compare to existing data here’s a plot of the non-dimensional oscillation frequency for a variety of organisms of different muscle types and what is
Plotted on the x-axis is the ratio of these two time scales which you can think of as a dum colon number on the blue end the kinetics dominates and there the frequency saturates uh whereas in the red end where Hydraulics dominates you have this bound which is
Depends on the is exactly the same expression as before which is geometric mean and the important thing is that in examples where I said such as an insect flight where you have some of the fastest uh muscle driven movements they all seem to sit in a regime where Hydraulics does dominate
Suggesting that to understand the biophysical limitations on uh the rates of contractions of muscle in these very Ultra fast uh situations we have to think about the the fluid dynamics internal to the fiber okay and the second thing to point out is the range of this non-dimensional number across various different
Organisms across the tree of life so uh suggesting there may be something interesting evolutionarily to think about uh the structural and the mechanical properties of muscle fibers okay uh in the last five minutes I want to quickly tell you about not Dynamics but mechanics and so uh we can take the
Same description of now we have threedimensional deformations of this wet active solid like description for muscle um and we can just do linear response and ask what are the mechanical uh what is the mechanical response of such a material in the simplest setting we just at linear elasticity mechanics
Is Quantified by relation between a stress and a strain of course now tensorial if you have deformations in different directions in an energy conserving system this Matrix of moduli uh is symmetric if you exchange the first and the last two indices that’s what is uh that’s related to a
Well-known reciprocal relation Max bet reciprocity in mechanics of course muscle doesn’t conserve energy so when you break energy conservation you don’t have to satisfy this equality and that in recent years has been christened odd elasticity and perhaps not surprisingly muscle is also OD elastic uh and in the
Simplest if you take the simplest modes of deformation an isotropic uh stress and a sheer stress with the corresponding strain so an isotropic and a sheer component for a strain given this uh very anisotropic geometry of muscle fibers you have a matrix of moduli the Diagon ones are are well
Known that’s just a bulk modulus and and a sheer modulus or young modulus the off diagonal elements can be different and the difference between the off diagonal elements or the asymmetric part is Zeta and that is the odd elastic or odd visco elastic uh contribution the nice thing
Is we can obtain this Zeta as a function of molecular and structural parameters from the model um and and the other point to make over here is that it naturally appears just with an isotropy there no chirality in the system to get a elasticity you just need an an
Isotropic uh espcially an isotropic active solid and historical Point uh this sort of um is a non um symmetric elastic response or an odd response was in fact already noted in a paper by zalak in 95 and 96 where he points out the breakdown of the major CI symmetry
In the model for muscle although it wasn’t taken up further later um and so one of the major consequences of this non-reciprocal response is of course work and energy production oh that um oh sorry um before I get to the work production part um what is the
Origin of the OD elasticity is that even if you think at a single crossbridge level you can show that the mechanical response of a crossbridge is uh in an average sense non-reciprocal and the simple understanding is that because the binding or The Binding rate of the motor depends on the spacing between the
Filaments the axial contraction depends on the radial stretch why and the other uh and the radial Force doesn’t need to depend on the axial stretch in the same manner and so in general um the contractile Force generated along the long axis uh depends on the um stretch the separation between the filaments and
That is um uh already the non-reciprocal mechanical element at the microscopic scale called go grained up to the macro skill is what leads to the OD elastic response Zeta um consequence of the OD elasticity is that as I said if you have deformation Cycles um in two directions
And you come back you perform a cycle with non-zero area then you can produce work and the work is the product of the OD elastic modulus and the area you enclose in such a cycle um and of course we do see Cycles as I already showed you particularly in physiological relevant
Situations such as in flight and so a natural question is can we is this important and do muscles and do insects use all elasticity to generate power to fly that we don’t quite know yet because one point is the odd model is is not measured but can we estimate it and so
To estimate it what we do is um compare our model to uh existing measurements of rology of muscle fibers in 1D and um the details again I won’t go into but in 1D in terms of uniaxial deformations um we can fit for essentially uh this is as a
Function of frequency the inphase part uh and so you get a complex modelist you can fit for the inace stiffness which is like a Young’s modulus and the uh the outer face part like a viscous modulus and use the parameters from such a fit the lines are fits to the data the data
Are dots um you can use these parameters from the fit to estimate within the model what the autastic model is should be and that’s what’s shown in Blue uh first thing to not is that it’s nonzero and the second thing to note is that it’s largely negative um and a negative modulus uh
Times a negative signed area in such a work cycle is a positive amount of work production and in this convention work produced uh a is positive positive uh and so you know this is just suggestive that there may be some benefit and use of using all lastic particularly three-dimensional deformations of muscle
Fibers um to generate work in physiologically relevant settings um and so the main takeaway is that um that’s a new mode of producing work there is another mode of producing work which has been thought of and and studied a fair bit which is a negative viscosity but I
Won more think go into that further and so to conclude um basically uh what I you know just to summarize quickly is that a CO grained picture of thinking of muscle fibers as an soft wet active solid is potentially uh a useful and relevant uh picture if you want to think
About the range and limits of its uh performance both in terms of rates of contraction and also its uh Power Generation and work production and there’s many question in terms of of uh given that the ingredients the actomyosin and the fluid environment they’re all very generic to many many
Cells perhaps there’s a broader uh category of um other biological cells or tissues in which similar ideas May apply and very quickly I want to put a advertisement which is I’ve as I’ve just moved to the University of Michigan uh in the last two months ago um as a as a
New faculty as an incoming faculty member in physics and um so I’ve just started my group and we work on a variety of different problems in active matter control soft mechanics and biology um and so we we’re looking for uh graduate students to join so if you
Know or if you are a graduate student who’s interested uh or if you’re an student who’s interested to do um to work on some of these problems then please write to me um and so let me put back the summary slide and take questions thank you [Applause] kinetics versus Hydraulics regime that
So there seems to be some correlation at least from the pictures that you showed that the smaller sized organisms use Hydraulics and the bigger ones use kinetics is that something that you can say in general is so um yeah there is a trend in which um so the small organ smaller organisms
Do you they have a larger frequency of um operation now um it’s likely that Hydraulics is more uh is okay in in a smaller organism simply because uh the hydraulic time scales depends on the size of the fiber and in a smaller organism the fibers are smaller and in a
Larger organism fluid flow is just way too slow so you then then you you um change the micr structural features um sort of evolutionarily so that these organisms work in a regime where kinetics is okay and then you don’t have to you’re not limited and constrained by
U the fluid flow and but um the a good a test for this would be if we can manipulate uh you know within Cy drosophila change the the spacing between filaments and the poe size or the or change the fiber length and see if there is a change in the oscillation
Frequency we have not done that in but if anyone has ideas um then then that would be a test right for asking if there is actually um what is the scaling with size NE question maybe connections to cber law would be very interesting cber yes uh in terms of metabolic
Scaling I do not know how directly to connect to metabolic scaling because of course in all of this uh I I’ve assume that um there’s other other things that can constrain speed right you know metabolic requirements uh neural signaling whatnot um so we’ve assumed that oxygen for instance and and ATP
Fuel is available in plenty um and I yeah I don’t know if there’s I I don’t know a direct way to connect it to cless uh but if you have ideas I would be interested in hearing yeah globally yes yes at certain pressures of course you will open water channels and things like
That so so how how would that begin to I mean and and I mean it’s not conceivable that you will have these squeezing pressures that you have water channels opening up yes yeah so aquaporin and whatnot can open and then eventually regulate the uh water and um right and
That could be quite local as well so you will yes I mean but usually that uh because we were focusing on very rapid uh movements on the millisecond or second time scales uh those processes are much slower and U and that’s why we neglect that uh and so we assume that
The membrane is impermeable on the time scales um and of course so this is this is one limit and and if you allow for permeation across the the membrane which is what uh water channels will all to do then you you’ll be able to cross uh simply because now if you permeate the
Membrane sufficiently then um you just squeeze the water out and uh and then you you can you can just you you don’t you’re not limited by by having to redistribute fluid within a confined space um so yes um but at least within the regimes of the examples that we were
Thinking of um that doesn’t seem to be the constraining feature of course on very long time scales with exercise and stuff you do have um increase in volume and hydration of muscle cells okay okay so yeah that that would be interesting to uh I would be curious to
Know more about that but at least in in the muscle context we didn’t find but there could be interesting osmo regulatory aspects on fast time scales as well thank you the in the literature on muscle there is this old law which is called Hills law which relates to force to by
Which you pull to the velocity of pulling yes which is I think consistent with any of the molecular Motors including the one that you use is there a regime where this would be satisfied in your calculations or in which limit should I find that back I guess Hydraulics is completely
Yeah yeah if you if you throw away hydraulic so actually the the uh just the kinetic model will if you if you assume a steady um steady speed of motion then you will reproduce Hills it yes yes in fact the kinetic model is very related to models that you all have
Used before uh in to just model uh single filaments with Motors on there oh we’re very slow so we’re somewhere here um yeah yeah okay are there any other question okay if there’s no other question let’s [Applause] than